(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
active(U11(tt, V2)) → mark(U12(isNat(V2)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNat(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt, N)) → mark(N)
active(U51(tt, M, N)) → mark(U52(isNat(N), M, N))
active(U52(tt, M, N)) → mark(s(plus(N, M)))
active(U61(tt)) → mark(0)
active(U71(tt, M, N)) → mark(U72(isNat(N), M, N))
active(U72(tt, M, N)) → mark(plus(x(N, M), N))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNat(V1), V2))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNat(x(V1, V2))) → mark(U31(isNat(V1), V2))
active(plus(N, 0)) → mark(U41(isNat(N), N))
active(plus(N, s(M))) → mark(U51(isNat(M), M, N))
active(x(N, 0)) → mark(U61(isNat(N)))
active(x(N, s(M))) → mark(U71(isNat(M), M, N))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X)) → U12(active(X))
active(U21(X)) → U21(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X)) → U32(active(X))
active(U41(X1, X2)) → U41(active(X1), X2)
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(s(X)) → s(active(X))
active(plus(X1, X2)) → plus(active(X1), X2)
active(plus(X1, X2)) → plus(X1, active(X2))
active(U61(X)) → U61(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2, X3)) → U72(active(X1), X2, X3)
active(x(X1, X2)) → x(active(X1), X2)
active(x(X1, X2)) → x(X1, active(X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X)) → mark(U12(X))
U21(mark(X)) → mark(U21(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X)) → mark(U32(X))
U41(mark(X1), X2) → mark(U41(X1, X2))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
s(mark(X)) → mark(s(X))
plus(mark(X1), X2) → mark(plus(X1, X2))
plus(X1, mark(X2)) → mark(plus(X1, X2))
U61(mark(X)) → mark(U61(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2, X3) → mark(U72(X1, X2, X3))
x(mark(X1), X2) → mark(x(X1, X2))
x(X1, mark(X2)) → mark(x(X1, X2))
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X)) → U12(proper(X))
proper(isNat(X)) → isNat(proper(X))
proper(U21(X)) → U21(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X)) → U32(proper(X))
proper(U41(X1, X2)) → U41(proper(X1), proper(X2))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(s(X)) → s(proper(X))
proper(plus(X1, X2)) → plus(proper(X1), proper(X2))
proper(U61(X)) → U61(proper(X))
proper(0) → ok(0)
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2, X3)) → U72(proper(X1), proper(X2), proper(X3))
proper(x(X1, X2)) → x(proper(X1), proper(X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X)) → ok(U12(X))
isNat(ok(X)) → ok(isNat(X))
U21(ok(X)) → ok(U21(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X)) → ok(U32(X))
U41(ok(X1), ok(X2)) → ok(U41(X1, X2))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
s(ok(X)) → ok(s(X))
plus(ok(X1), ok(X2)) → ok(plus(X1, X2))
U61(ok(X)) → ok(U61(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2), ok(X3)) → ok(U72(X1, X2, X3))
x(ok(X1), ok(X2)) → ok(x(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
Rewrite Strategy: INNERMOST
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted Cpx (relative) TRS to CDT
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
isNat(ok(z0)) → ok(isNat(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(U11(tt, z0)) → c(U12'(isNat(z0)), ISNAT(z0))
ACTIVE(U12(tt)) → c1
ACTIVE(U21(tt)) → c2
ACTIVE(U31(tt, z0)) → c3(U32'(isNat(z0)), ISNAT(z0))
ACTIVE(U32(tt)) → c4
ACTIVE(U41(tt, z0)) → c5
ACTIVE(U51(tt, z0, z1)) → c6(U52'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c7(S(plus(z1, z0)), PLUS(z1, z0))
ACTIVE(U61(tt)) → c8
ACTIVE(U71(tt, z0, z1)) → c9(U72'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c10(PLUS(x(z1, z0), z1), X(z1, z0))
ACTIVE(isNat(0)) → c11
ACTIVE(isNat(plus(z0, z1))) → c12(U11'(isNat(z0), z1), ISNAT(z0))
ACTIVE(isNat(s(z0))) → c13(U21'(isNat(z0)), ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c14(U31'(isNat(z0), z1), ISNAT(z0))
ACTIVE(plus(z0, 0)) → c15(U41'(isNat(z0), z0), ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(U51'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(x(z0, 0)) → c17(U61'(isNat(z0)), ISNAT(z0))
ACTIVE(x(z0, s(z1))) → c18(U71'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(tt) → c66
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(0) → c78
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
S tuples:
ACTIVE(U11(tt, z0)) → c(U12'(isNat(z0)), ISNAT(z0))
ACTIVE(U12(tt)) → c1
ACTIVE(U21(tt)) → c2
ACTIVE(U31(tt, z0)) → c3(U32'(isNat(z0)), ISNAT(z0))
ACTIVE(U32(tt)) → c4
ACTIVE(U41(tt, z0)) → c5
ACTIVE(U51(tt, z0, z1)) → c6(U52'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c7(S(plus(z1, z0)), PLUS(z1, z0))
ACTIVE(U61(tt)) → c8
ACTIVE(U71(tt, z0, z1)) → c9(U72'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c10(PLUS(x(z1, z0), z1), X(z1, z0))
ACTIVE(isNat(0)) → c11
ACTIVE(isNat(plus(z0, z1))) → c12(U11'(isNat(z0), z1), ISNAT(z0))
ACTIVE(isNat(s(z0))) → c13(U21'(isNat(z0)), ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c14(U31'(isNat(z0), z1), ISNAT(z0))
ACTIVE(plus(z0, 0)) → c15(U41'(isNat(z0), z0), ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(U51'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(x(z0, 0)) → c17(U61'(isNat(z0)), ISNAT(z0))
ACTIVE(x(z0, s(z1))) → c18(U71'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(tt) → c66
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(0) → c78
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:
active, U11, U12, U21, U31, U32, U41, U51, U52, s, plus, U61, U71, U72, x, proper, isNat, top
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84
(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 8 trailing nodes:
ACTIVE(isNat(0)) → c11
ACTIVE(U12(tt)) → c1
ACTIVE(U41(tt, z0)) → c5
PROPER(tt) → c66
ACTIVE(U21(tt)) → c2
ACTIVE(U32(tt)) → c4
PROPER(0) → c78
ACTIVE(U61(tt)) → c8
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
isNat(ok(z0)) → ok(isNat(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(U11(tt, z0)) → c(U12'(isNat(z0)), ISNAT(z0))
ACTIVE(U31(tt, z0)) → c3(U32'(isNat(z0)), ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c6(U52'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c7(S(plus(z1, z0)), PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c9(U72'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c10(PLUS(x(z1, z0), z1), X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c12(U11'(isNat(z0), z1), ISNAT(z0))
ACTIVE(isNat(s(z0))) → c13(U21'(isNat(z0)), ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c14(U31'(isNat(z0), z1), ISNAT(z0))
ACTIVE(plus(z0, 0)) → c15(U41'(isNat(z0), z0), ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(U51'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(x(z0, 0)) → c17(U61'(isNat(z0)), ISNAT(z0))
ACTIVE(x(z0, s(z1))) → c18(U71'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
S tuples:
ACTIVE(U11(tt, z0)) → c(U12'(isNat(z0)), ISNAT(z0))
ACTIVE(U31(tt, z0)) → c3(U32'(isNat(z0)), ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c6(U52'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c7(S(plus(z1, z0)), PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c9(U72'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c10(PLUS(x(z1, z0), z1), X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c12(U11'(isNat(z0), z1), ISNAT(z0))
ACTIVE(isNat(s(z0))) → c13(U21'(isNat(z0)), ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c14(U31'(isNat(z0), z1), ISNAT(z0))
ACTIVE(plus(z0, 0)) → c15(U41'(isNat(z0), z0), ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(U51'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(x(z0, 0)) → c17(U61'(isNat(z0)), ISNAT(z0))
ACTIVE(x(z0, s(z1))) → c18(U71'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:
active, U11, U12, U21, U31, U32, U41, U51, U52, s, plus, U61, U71, U72, x, proper, isNat, top
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c, c3, c6, c7, c9, c10, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84
(5) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(6) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
isNat(ok(z0)) → ok(isNat(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(U11(tt, z0)) → c(U12'(isNat(z0)), ISNAT(z0))
ACTIVE(U31(tt, z0)) → c3(U32'(isNat(z0)), ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c6(U52'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c7(S(plus(z1, z0)), PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c9(U72'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c10(PLUS(x(z1, z0), z1), X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c12(U11'(isNat(z0), z1), ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c14(U31'(isNat(z0), z1), ISNAT(z0))
ACTIVE(plus(z0, 0)) → c15(U41'(isNat(z0), z0), ISNAT(z0))
ACTIVE(x(z0, 0)) → c17(U61'(isNat(z0)), ISNAT(z0))
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
S tuples:
ACTIVE(U11(tt, z0)) → c(U12'(isNat(z0)), ISNAT(z0))
ACTIVE(U31(tt, z0)) → c3(U32'(isNat(z0)), ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c6(U52'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c7(S(plus(z1, z0)), PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c9(U72'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c10(PLUS(x(z1, z0), z1), X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c12(U11'(isNat(z0), z1), ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c14(U31'(isNat(z0), z1), ISNAT(z0))
ACTIVE(plus(z0, 0)) → c15(U41'(isNat(z0), z0), ISNAT(z0))
ACTIVE(x(z0, 0)) → c17(U61'(isNat(z0)), ISNAT(z0))
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
K tuples:none
Defined Rule Symbols:
active, U11, U12, U21, U31, U32, U41, U51, U52, s, plus, U61, U71, U72, x, proper, isNat, top
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c, c3, c6, c7, c9, c10, c12, c14, c15, c17, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18
(7) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(8) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
isNat(ok(z0)) → ok(isNat(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
S tuples:
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
K tuples:none
Defined Rule Symbols:
active, U11, U12, U21, U31, U32, U41, U51, U52, s, plus, U61, U71, U72, x, proper, isNat, top
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1
(9) CdtUsableRulesProof (EQUIVALENT transformation)
The following rules are not usable and were removed:
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
(10) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
S tuples:
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1
(11) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U11(
z0,
z1)) →
c19(
U11'(
active(
z0),
z1),
ACTIVE(
z0)) by
ACTIVE(U11(U11(tt, z0), x1)) → c19(U11'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c19(U11'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c19(U11'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c19(U11'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
(12) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U11(tt, z0), x1)) → c19(U11'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c19(U11'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c19(U11'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c19(U11'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U11(tt, z0), x1)) → c19(U11'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c19(U11'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c19(U11'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c19(U11'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19
(13) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing tuple parts
(14) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U11(tt, z0), x1)) → c19(U11'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c19(U11'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c19(U11'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c19(U11'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
S tuples:
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U11(tt, z0), x1)) → c19(U11'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c19(U11'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c19(U11'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c19(U11'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19
(15) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(16) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c
(17) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U12(
z0)) →
c20(
U12'(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(U12(U11(tt, z0))) → c20(U12'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c20(U12'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c20(U12'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c20(U12'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
(18) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U11(tt, z0))) → c20(U12'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c20(U12'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c20(U12'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c20(U12'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U11(tt, z0))) → c20(U12'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c20(U12'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c20(U12'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c20(U12'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20
(19) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(20) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U11(tt, z0))) → c20(U12'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c20(U12'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c20(U12'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c20(U12'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
S tuples:
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U11(tt, z0))) → c20(U12'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c20(U12'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c20(U12'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c20(U12'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20
(21) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(22) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2
(23) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U21(
z0)) →
c21(
U21'(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(U21(U11(tt, z0))) → c21(U21'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c21(U21'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c21(U21'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c21(U21'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
(24) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U11(tt, z0))) → c21(U21'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c21(U21'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c21(U21'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c21(U21'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U11(tt, z0))) → c21(U21'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c21(U21'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c21(U21'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c21(U21'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21
(25) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 5 trailing tuple parts
(26) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U11(tt, z0))) → c21(U21'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c21(U21'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c21(U21'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c21(U21'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
S tuples:
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U11(tt, z0))) → c21(U21'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c21(U21'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c21(U21'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c21(U21'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21
(27) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(28) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3
(29) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U31(
z0,
z1)) →
c22(
U31'(
active(
z0),
z1),
ACTIVE(
z0)) by
ACTIVE(U31(U11(tt, z0), x1)) → c22(U31'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U31(U31(tt, z0), x1)) → c22(U31'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c22(U31'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c22(U31'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c22(U31'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
(30) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U11(tt, z0), x1)) → c22(U31'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U31(U31(tt, z0), x1)) → c22(U31'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c22(U31'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c22(U31'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c22(U31'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U11(tt, z0), x1)) → c22(U31'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U31(U31(tt, z0), x1)) → c22(U31'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c22(U31'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c22(U31'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c22(U31'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22
(31) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(32) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U11(tt, z0), x1)) → c22(U31'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c22(U31'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c22(U31'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c22(U31'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c22(U31'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
S tuples:
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U11(tt, z0), x1)) → c22(U31'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c22(U31'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c22(U31'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c22(U31'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c22(U31'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22
(33) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(34) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4
(35) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U32(
z0)) →
c23(
U32'(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(U32(U11(tt, z0))) → c23(U32'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U32(U31(tt, z0))) → c23(U32'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c23(U32'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c23(U32'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c23(U32'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
(36) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U11(tt, z0))) → c23(U32'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U32(U31(tt, z0))) → c23(U32'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c23(U32'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c23(U32'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c23(U32'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U11(tt, z0))) → c23(U32'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U32(U31(tt, z0))) → c23(U32'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c23(U32'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c23(U32'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c23(U32'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23
(37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 8 trailing tuple parts
(38) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U11(tt, z0))) → c23(U32'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c23(U32'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c23(U32'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c23(U32'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c23(U32'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
S tuples:
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U11(tt, z0))) → c23(U32'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c23(U32'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c23(U32'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c23(U32'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c23(U32'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23
(39) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(40) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5
(41) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U41(
z0,
z1)) →
c24(
U41'(
active(
z0),
z1),
ACTIVE(
z0)) by
ACTIVE(U41(U11(tt, z0), x1)) → c24(U41'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U41(U31(tt, z0), x1)) → c24(U41'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c24(U41'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c24(U41'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c24(U41'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
(42) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U11(tt, z0), x1)) → c24(U41'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U41(U31(tt, z0), x1)) → c24(U41'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c24(U41'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c24(U41'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c24(U41'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U11(tt, z0), x1)) → c24(U41'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U41(U31(tt, z0), x1)) → c24(U41'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c24(U41'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c24(U41'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c24(U41'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24
(43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 10 trailing tuple parts
(44) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U11(tt, z0), x1)) → c24(U41'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c24(U41'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c24(U41'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c24(U41'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c24(U41'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
S tuples:
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U11(tt, z0), x1)) → c24(U41'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c24(U41'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c24(U41'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c24(U41'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c24(U41'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24
(45) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(46) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6
(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U51(
z0,
z1,
z2)) →
c25(
U51'(
active(
z0),
z1,
z2),
ACTIVE(
z0)) by
ACTIVE(U51(U11(tt, z0), x1, x2)) → c25(U51'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U12(tt)))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U21(tt)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c25(U51'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U32(tt)))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2), ACTIVE(U41(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c25(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c25(U51'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(isNat(0)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c25(U51'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c25(U51'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c25(U51'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
(48) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c25(U51'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U12(tt)))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U21(tt)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c25(U51'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U32(tt)))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2), ACTIVE(U41(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c25(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c25(U51'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(isNat(0)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c25(U51'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c25(U51'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c25(U51'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c25(U51'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U12(tt)))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U21(tt)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c25(U51'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U32(tt)))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2), ACTIVE(U41(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c25(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c25(U51'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(isNat(0)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c25(U51'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c25(U51'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c25(U51'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25
(49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 5 trailing tuple parts
(50) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c25(U51'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c25(U51'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c25(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c25(U51'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c25(U51'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c25(U51'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c25(U51'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(