The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(1)).

(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

active(U101(tt, M, N)) → mark(U102(isNatKind(M), M, N))
active(U102(tt, M, N)) → mark(U103(isNat(N), M, N))
active(U103(tt, M, N)) → mark(U104(isNatKind(N), M, N))
active(U104(tt, M, N)) → mark(plus(x(N, M), N))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V1, V2)) → mark(U32(isNatKind(V1), V1, V2))
active(U32(tt, V1, V2)) → mark(U33(isNatKind(V2), V1, V2))
active(U33(tt, V1, V2)) → mark(U34(isNatKind(V2), V1, V2))
active(U34(tt, V1, V2)) → mark(U35(isNat(V1), V2))
active(U35(tt, V2)) → mark(U36(isNat(V2)))
active(U36(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatKind(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatKind(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, N)) → mark(U72(isNatKind(N), N))
active(U72(tt, N)) → mark(N)
active(U81(tt, M, N)) → mark(U82(isNatKind(M), M, N))
active(U82(tt, M, N)) → mark(U83(isNat(N), M, N))
active(U83(tt, M, N)) → mark(U84(isNatKind(N), M, N))
active(U84(tt, M, N)) → mark(s(plus(N, M)))
active(U91(tt, N)) → mark(U92(isNatKind(N)))
active(U92(tt)) → mark(0)
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNat(x(V1, V2))) → mark(U31(isNatKind(V1), V1, V2))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U41(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U51(isNatKind(V1)))
active(isNatKind(x(V1, V2))) → mark(U61(isNatKind(V1), V2))
active(plus(N, 0)) → mark(U71(isNat(N), N))
active(plus(N, s(M))) → mark(U81(isNat(M), M, N))
active(x(N, 0)) → mark(U91(isNat(N), N))
active(x(N, s(M))) → mark(U101(isNat(M), M, N))
mark(U101(X1, X2, X3)) → active(U101(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U102(X1, X2, X3)) → active(U102(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U103(X1, X2, X3)) → active(U103(mark(X1), X2, X3))
mark(isNat(X)) → active(isNat(X))
mark(U104(X1, X2, X3)) → active(U104(mark(X1), X2, X3))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(x(X1, X2)) → active(x(mark(X1), mark(X2)))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2, X3)) → active(U31(mark(X1), X2, X3))
mark(U32(X1, X2, X3)) → active(U32(mark(X1), X2, X3))
mark(U33(X1, X2, X3)) → active(U33(mark(X1), X2, X3))
mark(U34(X1, X2, X3)) → active(U34(mark(X1), X2, X3))
mark(U35(X1, X2)) → active(U35(mark(X1), X2))
mark(U36(X)) → active(U36(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(U51(X)) → active(U51(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2)) → active(U71(mark(X1), X2))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U81(X1, X2, X3)) → active(U81(mark(X1), X2, X3))
mark(U82(X1, X2, X3)) → active(U82(mark(X1), X2, X3))
mark(U83(X1, X2, X3)) → active(U83(mark(X1), X2, X3))
mark(U84(X1, X2, X3)) → active(U84(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(0) → active(0)
U101(mark(X1), X2, X3) → U101(X1, X2, X3)
U101(X1, mark(X2), X3) → U101(X1, X2, X3)
U101(X1, X2, mark(X3)) → U101(X1, X2, X3)
U101(active(X1), X2, X3) → U101(X1, X2, X3)
U101(X1, active(X2), X3) → U101(X1, X2, X3)
U101(X1, X2, active(X3)) → U101(X1, X2, X3)
U102(mark(X1), X2, X3) → U102(X1, X2, X3)
U102(X1, mark(X2), X3) → U102(X1, X2, X3)
U102(X1, X2, mark(X3)) → U102(X1, X2, X3)
U102(active(X1), X2, X3) → U102(X1, X2, X3)
U102(X1, active(X2), X3) → U102(X1, X2, X3)
U102(X1, X2, active(X3)) → U102(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U103(mark(X1), X2, X3) → U103(X1, X2, X3)
U103(X1, mark(X2), X3) → U103(X1, X2, X3)
U103(X1, X2, mark(X3)) → U103(X1, X2, X3)
U103(active(X1), X2, X3) → U103(X1, X2, X3)
U103(X1, active(X2), X3) → U103(X1, X2, X3)
U103(X1, X2, active(X3)) → U103(X1, X2, X3)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U104(mark(X1), X2, X3) → U104(X1, X2, X3)
U104(X1, mark(X2), X3) → U104(X1, X2, X3)
U104(X1, X2, mark(X3)) → U104(X1, X2, X3)
U104(active(X1), X2, X3) → U104(X1, X2, X3)
U104(X1, active(X2), X3) → U104(X1, X2, X3)
U104(X1, X2, active(X3)) → U104(X1, X2, X3)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
x(mark(X1), X2) → x(X1, X2)
x(X1, mark(X2)) → x(X1, X2)
x(active(X1), X2) → x(X1, X2)
x(X1, active(X2)) → x(X1, X2)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2, X3) → U31(X1, X2, X3)
U31(X1, mark(X2), X3) → U31(X1, X2, X3)
U31(X1, X2, mark(X3)) → U31(X1, X2, X3)
U31(active(X1), X2, X3) → U31(X1, X2, X3)
U31(X1, active(X2), X3) → U31(X1, X2, X3)
U31(X1, X2, active(X3)) → U31(X1, X2, X3)
U32(mark(X1), X2, X3) → U32(X1, X2, X3)
U32(X1, mark(X2), X3) → U32(X1, X2, X3)
U32(X1, X2, mark(X3)) → U32(X1, X2, X3)
U32(active(X1), X2, X3) → U32(X1, X2, X3)
U32(X1, active(X2), X3) → U32(X1, X2, X3)
U32(X1, X2, active(X3)) → U32(X1, X2, X3)
U33(mark(X1), X2, X3) → U33(X1, X2, X3)
U33(X1, mark(X2), X3) → U33(X1, X2, X3)
U33(X1, X2, mark(X3)) → U33(X1, X2, X3)
U33(active(X1), X2, X3) → U33(X1, X2, X3)
U33(X1, active(X2), X3) → U33(X1, X2, X3)
U33(X1, X2, active(X3)) → U33(X1, X2, X3)
U34(mark(X1), X2, X3) → U34(X1, X2, X3)
U34(X1, mark(X2), X3) → U34(X1, X2, X3)
U34(X1, X2, mark(X3)) → U34(X1, X2, X3)
U34(active(X1), X2, X3) → U34(X1, X2, X3)
U34(X1, active(X2), X3) → U34(X1, X2, X3)
U34(X1, X2, active(X3)) → U34(X1, X2, X3)
U35(mark(X1), X2) → U35(X1, X2)
U35(X1, mark(X2)) → U35(X1, X2)
U35(active(X1), X2) → U35(X1, X2)
U35(X1, active(X2)) → U35(X1, X2)
U36(mark(X)) → U36(X)
U36(active(X)) → U36(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
U51(mark(X)) → U51(X)
U51(active(X)) → U51(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X)) → U62(X)
U62(active(X)) → U62(X)
U71(mark(X1), X2) → U71(X1, X2)
U71(X1, mark(X2)) → U71(X1, X2)
U71(active(X1), X2) → U71(X1, X2)
U71(X1, active(X2)) → U71(X1, X2)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U81(mark(X1), X2, X3) → U81(X1, X2, X3)
U81(X1, mark(X2), X3) → U81(X1, X2, X3)
U81(X1, X2, mark(X3)) → U81(X1, X2, X3)
U81(active(X1), X2, X3) → U81(X1, X2, X3)
U81(X1, active(X2), X3) → U81(X1, X2, X3)
U81(X1, X2, active(X3)) → U81(X1, X2, X3)
U82(mark(X1), X2, X3) → U82(X1, X2, X3)
U82(X1, mark(X2), X3) → U82(X1, X2, X3)
U82(X1, X2, mark(X3)) → U82(X1, X2, X3)
U82(active(X1), X2, X3) → U82(X1, X2, X3)
U82(X1, active(X2), X3) → U82(X1, X2, X3)
U82(X1, X2, active(X3)) → U82(X1, X2, X3)
U83(mark(X1), X2, X3) → U83(X1, X2, X3)
U83(X1, mark(X2), X3) → U83(X1, X2, X3)
U83(X1, X2, mark(X3)) → U83(X1, X2, X3)
U83(active(X1), X2, X3) → U83(X1, X2, X3)
U83(X1, active(X2), X3) → U83(X1, X2, X3)
U83(X1, X2, active(X3)) → U83(X1, X2, X3)
U84(mark(X1), X2, X3) → U84(X1, X2, X3)
U84(X1, mark(X2), X3) → U84(X1, X2, X3)
U84(X1, X2, mark(X3)) → U84(X1, X2, X3)
U84(active(X1), X2, X3) → U84(X1, X2, X3)
U84(X1, active(X2), X3) → U84(X1, X2, X3)
U84(X1, X2, active(X3)) → U84(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

Rewrite Strategy: INNERMOST

(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)

Converted CpxTRS to CDT

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U101(tt, z0, z1)) → mark(U102(isNatKind(z0), z0, z1))
active(U102(tt, z0, z1)) → mark(U103(isNat(z1), z0, z1))
active(U103(tt, z0, z1)) → mark(U104(isNatKind(z1), z0, z1))
active(U104(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(U11(tt, z0, z1)) → mark(U12(isNatKind(z0), z0, z1))
active(U12(tt, z0, z1)) → mark(U13(isNatKind(z1), z0, z1))
active(U13(tt, z0, z1)) → mark(U14(isNatKind(z1), z0, z1))
active(U14(tt, z0, z1)) → mark(U15(isNat(z0), z1))
active(U15(tt, z0)) → mark(U16(isNat(z0)))
active(U16(tt)) → mark(tt)
active(U21(tt, z0)) → mark(U22(isNatKind(z0), z0))
active(U22(tt, z0)) → mark(U23(isNat(z0)))
active(U23(tt)) → mark(tt)
active(U31(tt, z0, z1)) → mark(U32(isNatKind(z0), z0, z1))
active(U32(tt, z0, z1)) → mark(U33(isNatKind(z1), z0, z1))
active(U33(tt, z0, z1)) → mark(U34(isNatKind(z1), z0, z1))
active(U34(tt, z0, z1)) → mark(U35(isNat(z0), z1))
active(U35(tt, z0)) → mark(U36(isNat(z0)))
active(U36(tt)) → mark(tt)
active(U41(tt, z0)) → mark(U42(isNatKind(z0)))
active(U42(tt)) → mark(tt)
active(U51(tt)) → mark(tt)
active(U61(tt, z0)) → mark(U62(isNatKind(z0)))
active(U62(tt)) → mark(tt)
active(U71(tt, z0)) → mark(U72(isNatKind(z0), z0))
active(U72(tt, z0)) → mark(z0)
active(U81(tt, z0, z1)) → mark(U82(isNatKind(z0), z0, z1))
active(U82(tt, z0, z1)) → mark(U83(isNat(z1), z0, z1))
active(U83(tt, z0, z1)) → mark(U84(isNatKind(z1), z0, z1))
active(U84(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U91(tt, z0)) → mark(U92(isNatKind(z0)))
active(U92(tt)) → mark(0)
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNatKind(z0), z0, z1))
active(isNat(s(z0))) → mark(U21(isNatKind(z0), z0))
active(isNat(x(z0, z1))) → mark(U31(isNatKind(z0), z0, z1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(z0, z1))) → mark(U41(isNatKind(z0), z1))
active(isNatKind(s(z0))) → mark(U51(isNatKind(z0)))
active(isNatKind(x(z0, z1))) → mark(U61(isNatKind(z0), z1))
active(plus(z0, 0)) → mark(U71(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U81(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U91(isNat(z0), z0))
active(x(z0, s(z1))) → mark(U101(isNat(z1), z1, z0))
mark(U101(z0, z1, z2)) → active(U101(mark(z0), z1, z2))
mark(tt) → active(tt)
mark(U102(z0, z1, z2)) → active(U102(mark(z0), z1, z2))
mark(isNatKind(z0)) → active(isNatKind(z0))
mark(U103(z0, z1, z2)) → active(U103(mark(z0), z1, z2))
mark(isNat(z0)) → active(isNat(z0))
mark(U104(z0, z1, z2)) → active(U104(mark(z0), z1, z2))
mark(plus(z0, z1)) → active(plus(mark(z0), mark(z1)))
mark(x(z0, z1)) → active(x(mark(z0), mark(z1)))
mark(U11(z0, z1, z2)) → active(U11(mark(z0), z1, z2))
mark(U12(z0, z1, z2)) → active(U12(mark(z0), z1, z2))
mark(U13(z0, z1, z2)) → active(U13(mark(z0), z1, z2))
mark(U14(z0, z1, z2)) → active(U14(mark(z0), z1, z2))
mark(U15(z0, z1)) → active(U15(mark(z0), z1))
mark(U16(z0)) → active(U16(mark(z0)))
mark(U21(z0, z1)) → active(U21(mark(z0), z1))
mark(U22(z0, z1)) → active(U22(mark(z0), z1))
mark(U23(z0)) → active(U23(mark(z0)))
mark(U31(z0, z1, z2)) → active(U31(mark(z0), z1, z2))
mark(U32(z0, z1, z2)) → active(U32(mark(z0), z1, z2))
mark(U33(z0, z1, z2)) → active(U33(mark(z0), z1, z2))
mark(U34(z0, z1, z2)) → active(U34(mark(z0), z1, z2))
mark(U35(z0, z1)) → active(U35(mark(z0), z1))
mark(U36(z0)) → active(U36(mark(z0)))
mark(U41(z0, z1)) → active(U41(mark(z0), z1))
mark(U42(z0)) → active(U42(mark(z0)))
mark(U51(z0)) → active(U51(mark(z0)))
mark(U61(z0, z1)) → active(U61(mark(z0), z1))
mark(U62(z0)) → active(U62(mark(z0)))
mark(U71(z0, z1)) → active(U71(mark(z0), z1))
mark(U72(z0, z1)) → active(U72(mark(z0), z1))
mark(U81(z0, z1, z2)) → active(U81(mark(z0), z1, z2))
mark(U82(z0, z1, z2)) → active(U82(mark(z0), z1, z2))
mark(U83(z0, z1, z2)) → active(U83(mark(z0), z1, z2))
mark(U84(z0, z1, z2)) → active(U84(mark(z0), z1, z2))
mark(s(z0)) → active(s(mark(z0)))
mark(U91(z0, z1)) → active(U91(mark(z0), z1))
mark(U92(z0)) → active(U92(mark(z0)))
mark(0) → active(0)
U101(mark(z0), z1, z2) → U101(z0, z1, z2)
U101(z0, mark(z1), z2) → U101(z0, z1, z2)
U101(z0, z1, mark(z2)) → U101(z0, z1, z2)
U101(active(z0), z1, z2) → U101(z0, z1, z2)
U101(z0, active(z1), z2) → U101(z0, z1, z2)
U101(z0, z1, active(z2)) → U101(z0, z1, z2)
U102(mark(z0), z1, z2) → U102(z0, z1, z2)
U102(z0, mark(z1), z2) → U102(z0, z1, z2)
U102(z0, z1, mark(z2)) → U102(z0, z1, z2)
U102(active(z0), z1, z2) → U102(z0, z1, z2)
U102(z0, active(z1), z2) → U102(z0, z1, z2)
U102(z0, z1, active(z2)) → U102(z0, z1, z2)
isNatKind(mark(z0)) → isNatKind(z0)
isNatKind(active(z0)) → isNatKind(z0)
U103(mark(z0), z1, z2) → U103(z0, z1, z2)
U103(z0, mark(z1), z2) → U103(z0, z1, z2)
U103(z0, z1, mark(z2)) → U103(z0, z1, z2)
U103(active(z0), z1, z2) → U103(z0, z1, z2)
U103(z0, active(z1), z2) → U103(z0, z1, z2)
U103(z0, z1, active(z2)) → U103(z0, z1, z2)
isNat(mark(z0)) → isNat(z0)
isNat(active(z0)) → isNat(z0)
U104(mark(z0), z1, z2) → U104(z0, z1, z2)
U104(z0, mark(z1), z2) → U104(z0, z1, z2)
U104(z0, z1, mark(z2)) → U104(z0, z1, z2)
U104(active(z0), z1, z2) → U104(z0, z1, z2)
U104(z0, active(z1), z2) → U104(z0, z1, z2)
U104(z0, z1, active(z2)) → U104(z0, z1, z2)
plus(mark(z0), z1) → plus(z0, z1)
plus(z0, mark(z1)) → plus(z0, z1)
plus(active(z0), z1) → plus(z0, z1)
plus(z0, active(z1)) → plus(z0, z1)
x(mark(z0), z1) → x(z0, z1)
x(z0, mark(z1)) → x(z0, z1)
x(active(z0), z1) → x(z0, z1)
x(z0, active(z1)) → x(z0, z1)
U11(mark(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, mark(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, mark(z2)) → U11(z0, z1, z2)
U11(active(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, active(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, active(z2)) → U11(z0, z1, z2)
U12(mark(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, mark(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, mark(z2)) → U12(z0, z1, z2)
U12(active(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, active(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, active(z2)) → U12(z0, z1, z2)
U13(mark(z0), z1, z2) → U13(z0, z1, z2)
U13(z0, mark(z1), z2) → U13(z0, z1, z2)
U13(z0, z1, mark(z2)) → U13(z0, z1, z2)
U13(active(z0), z1, z2) → U13(z0, z1, z2)
U13(z0, active(z1), z2) → U13(z0, z1, z2)
U13(z0, z1, active(z2)) → U13(z0, z1, z2)
U14(mark(z0), z1, z2) → U14(z0, z1, z2)
U14(z0, mark(z1), z2) → U14(z0, z1, z2)
U14(z0, z1, mark(z2)) → U14(z0, z1, z2)
U14(active(z0), z1, z2) → U14(z0, z1, z2)
U14(z0, active(z1), z2) → U14(z0, z1, z2)
U14(z0, z1, active(z2)) → U14(z0, z1, z2)
U15(mark(z0), z1) → U15(z0, z1)
U15(z0, mark(z1)) → U15(z0, z1)
U15(active(z0), z1) → U15(z0, z1)
U15(z0, active(z1)) → U15(z0, z1)
U16(mark(z0)) → U16(z0)
U16(active(z0)) → U16(z0)
U21(mark(z0), z1) → U21(z0, z1)
U21(z0, mark(z1)) → U21(z0, z1)
U21(active(z0), z1) → U21(z0, z1)
U21(z0, active(z1)) → U21(z0, z1)
U22(mark(z0), z1) → U22(z0, z1)
U22(z0, mark(z1)) → U22(z0, z1)
U22(active(z0), z1) → U22(z0, z1)
U22(z0, active(z1)) → U22(z0, z1)
U23(mark(z0)) → U23(z0)
U23(active(z0)) → U23(z0)
U31(mark(z0), z1, z2) → U31(z0, z1, z2)
U31(z0, mark(z1), z2) → U31(z0, z1, z2)
U31(z0, z1, mark(z2)) → U31(z0, z1, z2)
U31(active(z0), z1, z2) → U31(z0, z1, z2)
U31(z0, active(z1), z2) → U31(z0, z1, z2)
U31(z0, z1, active(z2)) → U31(z0, z1, z2)
U32(mark(z0), z1, z2) → U32(z0, z1, z2)
U32(z0, mark(z1), z2) → U32(z0, z1, z2)
U32(z0, z1, mark(z2)) → U32(z0, z1, z2)
U32(active(z0), z1, z2) → U32(z0, z1, z2)
U32(z0, active(z1), z2) → U32(z0, z1, z2)
U32(z0, z1, active(z2)) → U32(z0, z1, z2)
U33(mark(z0), z1, z2) → U33(z0, z1, z2)
U33(z0, mark(z1), z2) → U33(z0, z1, z2)
U33(z0, z1, mark(z2)) → U33(z0, z1, z2)
U33(active(z0), z1, z2) → U33(z0, z1, z2)
U33(z0, active(z1), z2) → U33(z0, z1, z2)
U33(z0, z1, active(z2)) → U33(z0, z1, z2)
U34(mark(z0), z1, z2) → U34(z0, z1, z2)
U34(z0, mark(z1), z2) → U34(z0, z1, z2)
U34(z0, z1, mark(z2)) → U34(z0, z1, z2)
U34(active(z0), z1, z2) → U34(z0, z1, z2)
U34(z0, active(z1), z2) → U34(z0, z1, z2)
U34(z0, z1, active(z2)) → U34(z0, z1, z2)
U35(mark(z0), z1) → U35(z0, z1)
U35(z0, mark(z1)) → U35(z0, z1)
U35(active(z0), z1) → U35(z0, z1)
U35(z0, active(z1)) → U35(z0, z1)
U36(mark(z0)) → U36(z0)
U36(active(z0)) → U36(z0)
U41(mark(z0), z1) → U41(z0, z1)
U41(z0, mark(z1)) → U41(z0, z1)
U41(active(z0), z1) → U41(z0, z1)
U41(z0, active(z1)) → U41(z0, z1)
U42(mark(z0)) → U42(z0)
U42(active(z0)) → U42(z0)
U51(mark(z0)) → U51(z0)
U51(active(z0)) → U51(z0)
U61(mark(z0), z1) → U61(z0, z1)
U61(z0, mark(z1)) → U61(z0, z1)
U61(active(z0), z1) → U61(z0, z1)
U61(z0, active(z1)) → U61(z0, z1)
U62(mark(z0)) → U62(z0)
U62(active(z0)) → U62(z0)
U71(mark(z0), z1) → U71(z0, z1)
U71(z0, mark(z1)) → U71(z0, z1)
U71(active(z0), z1) → U71(z0, z1)
U71(z0, active(z1)) → U71(z0, z1)
U72(mark(z0), z1) → U72(z0, z1)
U72(z0, mark(z1)) → U72(z0, z1)
U72(active(z0), z1) → U72(z0, z1)
U72(z0, active(z1)) → U72(z0, z1)
U81(mark(z0), z1, z2) → U81(z0, z1, z2)
U81(z0, mark(z1), z2) → U81(z0, z1, z2)
U81(z0, z1, mark(z2)) → U81(z0, z1, z2)
U81(active(z0), z1, z2) → U81(z0, z1, z2)
U81(z0, active(z1), z2) → U81(z0, z1, z2)
U81(z0, z1, active(z2)) → U81(z0, z1, z2)
U82(mark(z0), z1, z2) → U82(z0, z1, z2)
U82(z0, mark(z1), z2) → U82(z0, z1, z2)
U82(z0, z1, mark(z2)) → U82(z0, z1, z2)
U82(active(z0), z1, z2) → U82(z0, z1, z2)
U82(z0, active(z1), z2) → U82(z0, z1, z2)
U82(z0, z1, active(z2)) → U82(z0, z1, z2)
U83(mark(z0), z1, z2) → U83(z0, z1, z2)
U83(z0, mark(z1), z2) → U83(z0, z1, z2)
U83(z0, z1, mark(z2)) → U83(z0, z1, z2)
U83(active(z0), z1, z2) → U83(z0, z1, z2)
U83(z0, active(z1), z2) → U83(z0, z1, z2)
U83(z0, z1, active(z2)) → U83(z0, z1, z2)
U84(mark(z0), z1, z2) → U84(z0, z1, z2)
U84(z0, mark(z1), z2) → U84(z0, z1, z2)
U84(z0, z1, mark(z2)) → U84(z0, z1, z2)
U84(active(z0), z1, z2) → U84(z0, z1, z2)
U84(z0, active(z1), z2) → U84(z0, z1, z2)
U84(z0, z1, active(z2)) → U84(z0, z1, z2)
s(mark(z0)) → s(z0)
s(active(z0)) → s(z0)
U91(mark(z0), z1) → U91(z0, z1)
U91(z0, mark(z1)) → U91(z0, z1)
U91(active(z0), z1) → U91(z0, z1)
U91(z0, active(z1)) → U91(z0, z1)
U92(mark(z0)) → U92(z0)
U92(active(z0)) → U92(z0)

Tuples:

ACTIVE(U101(tt, z0, z1)) → c(MARK(U102(isNatKind(z0), z0, z1)), U102'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(U102(tt, z0, z1)) → c1(MARK(U103(isNat(z1), z0, z1)), U103'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U103(tt, z0, z1)) → c2(MARK(U104(isNatKind(z1), z0, z1)), U104'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U104(tt, z0, z1)) → c3(MARK(plus(x(z1, z0), z1)), PLUS(x(z1, z0), z1), X(z1, z0))
ACTIVE(U11(tt, z0, z1)) → c4(MARK(U12(isNatKind(z0), z0, z1)), U12'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(U12(tt, z0, z1)) → c5(MARK(U13(isNatKind(z1), z0, z1)), U13'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U13(tt, z0, z1)) → c6(MARK(U14(isNatKind(z1), z0, z1)), U14'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U14(tt, z0, z1)) → c7(MARK(U15(isNat(z0), z1)), U15'(isNat(z0), z1), ISNAT(z0))
ACTIVE(U15(tt, z0)) → c8(MARK(U16(isNat(z0))), U16'(isNat(z0)), ISNAT(z0))
ACTIVE(U16(tt)) → c9(MARK(tt))
ACTIVE(U21(tt, z0)) → c10(MARK(U22(isNatKind(z0), z0)), U22'(isNatKind(z0), z0), ISNATKIND(z0))
ACTIVE(U22(tt, z0)) → c11(MARK(U23(isNat(z0))), U23'(isNat(z0)), ISNAT(z0))
ACTIVE(U23(tt)) → c12(MARK(tt))
ACTIVE(U31(tt, z0, z1)) → c13(MARK(U32(isNatKind(z0), z0, z1)), U32'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(U32(tt, z0, z1)) → c14(MARK(U33(isNatKind(z1), z0, z1)), U33'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U33(tt, z0, z1)) → c15(MARK(U34(isNatKind(z1), z0, z1)), U34'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U34(tt, z0, z1)) → c16(MARK(U35(isNat(z0), z1)), U35'(isNat(z0), z1), ISNAT(z0))
ACTIVE(U35(tt, z0)) → c17(MARK(U36(isNat(z0))), U36'(isNat(z0)), ISNAT(z0))
ACTIVE(U36(tt)) → c18(MARK(tt))
ACTIVE(U41(tt, z0)) → c19(MARK(U42(isNatKind(z0))), U42'(isNatKind(z0)), ISNATKIND(z0))
ACTIVE(U42(tt)) → c20(MARK(tt))
ACTIVE(U51(tt)) → c21(MARK(tt))
ACTIVE(U61(tt, z0)) → c22(MARK(U62(isNatKind(z0))), U62'(isNatKind(z0)), ISNATKIND(z0))
ACTIVE(U62(tt)) → c23(MARK(tt))
ACTIVE(U71(tt, z0)) → c24(MARK(U72(isNatKind(z0), z0)), U72'(isNatKind(z0), z0), ISNATKIND(z0))
ACTIVE(U72(tt, z0)) → c25(MARK(z0))
ACTIVE(U81(tt, z0, z1)) → c26(MARK(U82(isNatKind(z0), z0, z1)), U82'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(U82(tt, z0, z1)) → c27(MARK(U83(isNat(z1), z0, z1)), U83'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U83(tt, z0, z1)) → c28(MARK(U84(isNatKind(z1), z0, z1)), U84'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U84(tt, z0, z1)) → c29(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0))
ACTIVE(U91(tt, z0)) → c30(MARK(U92(isNatKind(z0))), U92'(isNatKind(z0)), ISNATKIND(z0))
ACTIVE(U92(tt)) → c31(MARK(0))
ACTIVE(isNat(0)) → c32(MARK(tt))
ACTIVE(isNat(plus(z0, z1))) → c33(MARK(U11(isNatKind(z0), z0, z1)), U11'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(isNat(s(z0))) → c34(MARK(U21(isNatKind(z0), z0)), U21'(isNatKind(z0), z0), ISNATKIND(z0))
ACTIVE(isNat(x(z0, z1))) → c35(MARK(U31(isNatKind(z0), z0, z1)), U31'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(isNatKind(0)) → c36(MARK(tt))
ACTIVE(isNatKind(plus(z0, z1))) → c37(MARK(U41(isNatKind(z0), z1)), U41'(isNatKind(z0), z1), ISNATKIND(z0))
ACTIVE(isNatKind(s(z0))) → c38(MARK(U51(isNatKind(z0))), U51'(isNatKind(z0)), ISNATKIND(z0))
ACTIVE(isNatKind(x(z0, z1))) → c39(MARK(U61(isNatKind(z0), z1)), U61'(isNatKind(z0), z1), ISNATKIND(z0))
ACTIVE(plus(z0, 0)) → c40(MARK(U71(isNat(z0), z0)), U71'(isNat(z0), z0), ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c41(MARK(U81(isNat(z1), z1, z0)), U81'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(x(z0, 0)) → c42(MARK(U91(isNat(z0), z0)), U91'(isNat(z0), z0), ISNAT(z0))
ACTIVE(x(z0, s(z1))) → c43(MARK(U101(isNat(z1), z1, z0)), U101'(isNat(z1), z1, z0), ISNAT(z1))
MARK(U101(z0, z1, z2)) → c44(ACTIVE(U101(mark(z0), z1, z2)), U101'(mark(z0), z1, z2), MARK(z0))
MARK(tt) → c45(ACTIVE(tt))
MARK(U102(z0, z1, z2)) → c46(ACTIVE(U102(mark(z0), z1, z2)), U102'(mark(z0), z1, z2), MARK(z0))
MARK(isNatKind(z0)) → c47(ACTIVE(isNatKind(z0)), ISNATKIND(z0))
MARK(U103(z0, z1, z2)) → c48(ACTIVE(U103(mark(z0), z1, z2)), U103'(mark(z0), z1, z2), MARK(z0))
MARK(isNat(z0)) → c49(ACTIVE(isNat(z0)), ISNAT(z0))
MARK(U104(z0, z1, z2)) → c50(ACTIVE(U104(mark(z0), z1, z2)), U104'(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) → c51(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(x(z0, z1)) → c52(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U11(z0, z1, z2)) → c53(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) → c54(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0))
MARK(U13(z0, z1, z2)) → c55(ACTIVE(U13(mark(z0), z1, z2)), U13'(mark(z0), z1, z2), MARK(z0))
MARK(U14(z0, z1, z2)) → c56(ACTIVE(U14(mark(z0), z1, z2)), U14'(mark(z0), z1, z2), MARK(z0))
MARK(U15(z0, z1)) → c57(ACTIVE(U15(mark(z0), z1)), U15'(mark(z0), z1), MARK(z0))
MARK(U16(z0)) → c58(ACTIVE(U16(mark(z0))), U16'(mark(z0)), MARK(z0))
MARK(U21(z0, z1)) → c59(ACTIVE(U21(mark(z0), z1)), U21'(mark(z0), z1), MARK(z0))
MARK(U22(z0, z1)) → c60(ACTIVE(U22(mark(z0), z1)), U22'(mark(z0), z1), MARK(z0))
MARK(U23(z0)) → c61(ACTIVE(U23(mark(z0))), U23'(mark(z0)), MARK(z0))
MARK(U31(z0, z1, z2)) → c62(ACTIVE(U31(mark(z0), z1, z2)), U31'(mark(z0), z1, z2), MARK(z0))
MARK(U32(z0, z1, z2)) → c63(ACTIVE(U32(mark(z0), z1, z2)), U32'(mark(z0), z1, z2), MARK(z0))
MARK(U33(z0, z1, z2)) → c64(ACTIVE(U33(mark(z0), z1, z2)), U33'(mark(z0), z1, z2), MARK(z0))
MARK(U34(z0, z1, z2)) → c65(ACTIVE(U34(mark(z0), z1, z2)), U34'(mark(z0), z1, z2), MARK(z0))
MARK(U35(z0, z1)) → c66(ACTIVE(U35(mark(z0), z1)), U35'(mark(z0), z1), MARK(z0))
MARK(U36(z0)) → c67(ACTIVE(U36(mark(z0))), U36'(mark(z0)), MARK(z0))
MARK(U41(z0, z1)) → c68(ACTIVE(U41(mark(z0), z1)), U41'(mark(z0), z1), MARK(z0))
MARK(U42(z0)) → c69(ACTIVE(U42(mark(z0))), U42'(mark(z0)), MARK(z0))
MARK(U51(z0)) → c70(ACTIVE(U51(mark(z0))), U51'(mark(z0)), MARK(z0))
MARK(U61(z0, z1)) → c71(ACTIVE(U61(mark(z0), z1)), U61'(mark(z0), z1), MARK(z0))
MARK(U62(z0)) → c72(ACTIVE(U62(mark(z0))), U62'(mark(z0)), MARK(z0))
MARK(U71(z0, z1)) → c73(ACTIVE(U71(mark(z0), z1)), U71'(mark(z0), z1), MARK(z0))
MARK(U72(z0, z1)) → c74(ACTIVE(U72(mark(z0), z1)), U72'(mark(z0), z1), MARK(z0))
MARK(U81(z0, z1, z2)) → c75(ACTIVE(U81(mark(z0), z1, z2)), U81'(mark(z0), z1, z2), MARK(z0))
MARK(U82(z0, z1, z2)) → c76(ACTIVE(U82(mark(z0), z1, z2)), U82'(mark(z0), z1, z2), MARK(z0))
MARK(U83(z0, z1, z2)) → c77(ACTIVE(U83(mark(z0), z1, z2)), U83'(mark(z0), z1, z2), MARK(z0))
MARK(U84(z0, z1, z2)) → c78(ACTIVE(U84(mark(z0), z1, z2)), U84'(mark(z0), z1, z2), MARK(z0))
MARK(s(z0)) → c79(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0))
MARK(U91(z0, z1)) → c80(ACTIVE(U91(mark(z0), z1)), U91'(mark(z0), z1), MARK(z0))
MARK(U92(z0)) → c81(ACTIVE(U92(mark(z0))), U92'(mark(z0)), MARK(z0))
MARK(0) → c82(ACTIVE(0))
U101'(mark(z0), z1, z2) → c83(U101'(z0, z1, z2))
U101'(z0, mark(z1), z2) → c84(U101'(z0, z1, z2))
U101'(z0, z1, mark(z2)) → c85(U101'(z0, z1, z2))
U101'(active(z0), z1, z2) → c86(U101'(z0, z1, z2))
U101'(z0, active(z1), z2) → c87(U101'(z0, z1, z2))
U101'(z0, z1, active(z2)) → c88(U101'(z0, z1, z2))
U102'(mark(z0), z1, z2) → c89(U102'(z0, z1, z2))
U102'(z0, mark(z1), z2) → c90(U102'(z0, z1, z2))
U102'(z0, z1, mark(z2)) → c91(U102'(z0, z1, z2))
U102'(active(z0), z1, z2) → c92(U102'(z0, z1, z2))
U102'(z0, active(z1), z2) → c93(U102'(z0, z1, z2))
U102'(z0, z1, active(z2)) → c94(U102'(z0, z1, z2))
ISNATKIND(mark(z0)) → c95(ISNATKIND(z0))
ISNATKIND(active(z0)) → c96(ISNATKIND(z0))
U103'(mark(z0), z1, z2) → c97(U103'(z0, z1, z2))
U103'(z0, mark(z1), z2) → c98(U103'(z0, z1, z2))
U103'(z0, z1, mark(z2)) → c99(U103'(z0, z1, z2))
U103'(active(z0), z1, z2) → c100(U103'(z0, z1, z2))
U103'(z0, active(z1), z2) → c101(U103'(z0, z1, z2))
U103'(z0, z1, active(z2)) → c102(U103'(z0, z1, z2))
ISNAT(mark(z0)) → c103(ISNAT(z0))
ISNAT(active(z0)) → c104(ISNAT(z0))
U104'(mark(z0), z1, z2) → c105(U104'(z0, z1, z2))
U104'(z0, mark(z1), z2) → c106(U104'(z0, z1, z2))
U104'(z0, z1, mark(z2)) → c107(U104'(z0, z1, z2))
U104'(active(z0), z1, z2) → c108(U104'(z0, z1, z2))
U104'(z0, active(z1), z2) → c109(U104'(z0, z1, z2))
U104'(z0, z1, active(z2)) → c110(U104'(z0, z1, z2))
PLUS(mark(z0), z1) → c111(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c112(PLUS(z0, z1))
PLUS(active(z0), z1) → c113(PLUS(z0, z1))
PLUS(z0, active(z1)) → c114(PLUS(z0, z1))
X(mark(z0), z1) → c115(X(z0, z1))
X(z0, mark(z1)) → c116(X(z0, z1))
X(active(z0), z1) → c117(X(z0, z1))
X(z0, active(z1)) → c118(X(z0, z1))
U11'(mark(z0), z1, z2) → c119(U11'(z0, z1, z2))
U11'(z0, mark(z1), z2) → c120(U11'(z0, z1, z2))
U11'(z0, z1, mark(z2)) → c121(U11'(z0, z1, z2))
U11'(active(z0), z1, z2) → c122(U11'(z0, z1, z2))
U11'(z0, active(z1), z2) → c123(U11'(z0, z1, z2))
U11'(z0, z1, active(z2)) → c124(U11'(z0, z1, z2))
U12'(mark(z0), z1, z2) → c125(U12'(z0, z1, z2))
U12'(z0, mark(z1), z2) → c126(U12'(z0, z1, z2))
U12'(z0, z1, mark(z2)) → c127(U12'(z0, z1, z2))
U12'(active(z0), z1, z2) → c128(U12'(z0, z1, z2))
U12'(z0, active(z1), z2) → c129(U12'(z0, z1, z2))
U12'(z0, z1, active(z2)) → c130(U12'(z0, z1, z2))
U13'(mark(z0), z1, z2) → c131(U13'(z0, z1, z2))
U13'(z0, mark(z1), z2) → c132(U13'(z0, z1, z2))
U13'(z0, z1, mark(z2)) → c133(U13'(z0, z1, z2))
U13'(active(z0), z1, z2) → c134(U13'(z0, z1, z2))
U13'(z0, active(z1), z2) → c135(U13'(z0, z1, z2))
U13'(z0, z1, active(z2)) → c136(U13'(z0, z1, z2))
U14'(mark(z0), z1, z2) → c137(U14'(z0, z1, z2))
U14'(z0, mark(z1), z2) → c138(U14'(z0, z1, z2))
U14'(z0, z1, mark(z2)) → c139(U14'(z0, z1, z2))
U14'(active(z0), z1, z2) → c140(U14'(z0, z1, z2))
U14'(z0, active(z1), z2) → c141(U14'(z0, z1, z2))
U14'(z0, z1, active(z2)) → c142(U14'(z0, z1, z2))
U15'(mark(z0), z1) → c143(U15'(z0, z1))
U15'(z0, mark(z1)) → c144(U15'(z0, z1))
U15'(active(z0), z1) → c145(U15'(z0, z1))
U15'(z0, active(z1)) → c146(U15'(z0, z1))
U16'(mark(z0)) → c147(U16'(z0))
U16'(active(z0)) → c148(U16'(z0))
U21'(mark(z0), z1) → c149(U21'(z0, z1))
U21'(z0, mark(z1)) → c150(U21'(z0, z1))
U21'(active(z0), z1) → c151(U21'(z0, z1))
U21'(z0, active(z1)) → c152(U21'(z0, z1))
U22'(mark(z0), z1) → c153(U22'(z0, z1))
U22'(z0, mark(z1)) → c154(U22'(z0, z1))
U22'(active(z0), z1) → c155(U22'(z0, z1))
U22'(z0, active(z1)) → c156(U22'(z0, z1))
U23'(mark(z0)) → c157(U23'(z0))
U23'(active(z0)) → c158(U23'(z0))
U31'(mark(z0), z1, z2) → c159(U31'(z0, z1, z2))
U31'(z0, mark(z1), z2) → c160(U31'(z0, z1, z2))
U31'(z0, z1, mark(z2)) → c161(U31'(z0, z1, z2))
U31'(active(z0), z1, z2) → c162(U31'(z0, z1, z2))
U31'(z0, active(z1), z2) → c163(U31'(z0, z1, z2))
U31'(z0, z1, active(z2)) → c164(U31'(z0, z1, z2))
U32'(mark(z0), z1, z2) → c165(U32'(z0, z1, z2))
U32'(z0, mark(z1), z2) → c166(U32'(z0, z1, z2))
U32'(z0, z1, mark(z2)) → c167(U32'(z0, z1, z2))
U32'(active(z0), z1, z2) → c168(U32'(z0, z1, z2))
U32'(z0, active(z1), z2) → c169(U32'(z0, z1, z2))
U32'(z0, z1, active(z2)) → c170(U32'(z0, z1, z2))
U33'(mark(z0), z1, z2) → c171(U33'(z0, z1, z2))
U33'(z0, mark(z1), z2) → c172(U33'(z0, z1, z2))
U33'(z0, z1, mark(z2)) → c173(U33'(z0, z1, z2))
U33'(active(z0), z1, z2) → c174(U33'(z0, z1, z2))
U33'(z0, active(z1), z2) → c175(U33'(z0, z1, z2))
U33'(z0, z1, active(z2)) → c176(U33'(z0, z1, z2))
U34'(mark(z0), z1, z2) → c177(U34'(z0, z1, z2))
U34'(z0, mark(z1), z2) → c178(U34'(z0, z1, z2))
U34'(z0, z1, mark(z2)) → c179(U34'(z0, z1, z2))
U34'(active(z0), z1, z2) → c180(U34'(z0, z1, z2))
U34'(z0, active(z1), z2) → c181(U34'(z0, z1, z2))
U34'(z0, z1, active(z2)) → c182(U34'(z0, z1, z2))
U35'(mark(z0), z1) → c183(U35'(z0, z1))
U35'(z0, mark(z1)) → c184(U35'(z0, z1))
U35'(active(z0), z1) → c185(U35'(z0, z1))
U35'(z0, active(z1)) → c186(U35'(z0, z1))
U36'(mark(z0)) → c187(U36'(z0))
U36'(active(z0)) → c188(U36'(z0))
U41'(mark(z0), z1) → c189(U41'(z0, z1))
U41'(z0, mark(z1)) → c190(U41'(z0, z1))
U41'(active(z0), z1) → c191(U41'(z0, z1))
U41'(z0, active(z1)) → c192(U41'(z0, z1))
U42'(mark(z0)) → c193(U42'(z0))
U42'(active(z0)) → c194(U42'(z0))
U51'(mark(z0)) → c195(U51'(z0))
U51'(active(z0)) → c196(U51'(z0))
U61'(mark(z0), z1) → c197(U61'(z0, z1))
U61'(z0, mark(z1)) → c198(U61'(z0, z1))
U61'(active(z0), z1) → c199(U61'(z0, z1))
U61'(z0, active(z1)) → c200(U61'(z0, z1))
U62'(mark(z0)) → c201(U62'(z0))
U62'(active(z0)) → c202(U62'(z0))
U71'(mark(z0), z1) → c203(U71'(z0, z1))
U71'(z0, mark(z1)) → c204(U71'(z0, z1))
U71'(active(z0), z1) → c205(U71'(z0, z1))
U71'(z0, active(z1)) → c206(U71'(z0, z1))
U72'(mark(z0), z1) → c207(U72'(z0, z1))
U72'(z0, mark(z1)) → c208(U72'(z0, z1))
U72'(active(z0), z1) → c209(U72'(z0, z1))
U72'(z0, active(z1)) → c210(U72'(z0, z1))
U81'(mark(z0), z1, z2) → c211(U81'(z0, z1, z2))
U81'(z0, mark(z1), z2) → c212(U81'(z0, z1, z2))
U81'(z0, z1, mark(z2)) → c213(U81'(z0, z1, z2))
U81'(active(z0), z1, z2) → c214(U81'(z0, z1, z2))
U81'(z0, active(z1), z2) → c215(U81'(z0, z1, z2))
U81'(z0, z1, active(z2)) → c216(U81'(z0, z1, z2))
U82'(mark(z0), z1, z2) → c217(U82'(z0, z1, z2))
U82'(z0, mark(z1), z2) → c218(U82'(z0, z1, z2))
U82'(z0, z1, mark(z2)) → c219(U82'(z0, z1, z2))
U82'(active(z0), z1, z2) → c220(U82'(z0, z1, z2))
U82'(z0, active(z1), z2) → c221(U82'(z0, z1, z2))
U82'(z0, z1, active(z2)) → c222(U82'(z0, z1, z2))
U83'(mark(z0), z1, z2) → c223(U83'(z0, z1, z2))
U83'(z0, mark(z1), z2) → c224(U83'(z0, z1, z2))
U83'(z0, z1, mark(z2)) → c225(U83'(z0, z1, z2))
U83'(active(z0), z1, z2) → c226(U83'(z0, z1, z2))
U83'(z0, active(z1), z2) → c227(U83'(z0, z1, z2))
U83'(z0, z1, active(z2)) → c228(U83'(z0, z1, z2))
U84'(mark(z0), z1, z2) → c229(U84'(z0, z1, z2))
U84'(z0, mark(z1), z2) → c230(U84'(z0, z1, z2))
U84'(z0, z1, mark(z2)) → c231(U84'(z0, z1, z2))
U84'(active(z0), z1, z2) → c232(U84'(z0, z1, z2))
U84'(z0, active(z1), z2) → c233(U84'(z0, z1, z2))
U84'(z0, z1, active(z2)) → c234(U84'(z0, z1, z2))
S(mark(z0)) → c235(S(z0))
S(active(z0)) → c236(S(z0))
U91'(mark(z0), z1) → c237(U91'(z0, z1))
U91'(z0, mark(z1)) → c238(U91'(z0, z1))
U91'(active(z0), z1) → c239(U91'(z0, z1))
U91'(z0, active(z1)) → c240(U91'(z0, z1))
U92'(mark(z0)) → c241(U92'(z0))
U92'(active(z0)) → c242(U92'(z0))

S tuples:

ACTIVE(U101(tt, z0, z1)) → c(MARK(U102(isNatKind(z0), z0, z1)), U102'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(U102(tt, z0, z1)) → c1(MARK(U103(isNat(z1), z0, z1)), U103'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U103(tt, z0, z1)) → c2(MARK(U104(isNatKind(z1), z0, z1)), U104'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U104(tt, z0, z1)) → c3(MARK(plus(x(z1, z0), z1)), PLUS(x(z1, z0), z1), X(z1, z0))
ACTIVE(U11(tt, z0, z1)) → c4(MARK(U12(isNatKind(z0), z0, z1)), U12'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(U12(tt, z0, z1)) → c5(MARK(U13(isNatKind(z1), z0, z1)), U13'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U13(tt, z0, z1)) → c6(MARK(U14(isNatKind(z1), z0, z1)), U14'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U14(tt, z0, z1)) → c7(MARK(U15(isNat(z0), z1)), U15'(isNat(z0), z1), ISNAT(z0))
ACTIVE(U15(tt, z0)) → c8(MARK(U16(isNat(z0))), U16'(isNat(z0)), ISNAT(z0))
ACTIVE(U16(tt)) → c9(MARK(tt))
ACTIVE(U21(tt, z0)) → c10(MARK(U22(isNatKind(z0), z0)), U22'(isNatKind(z0), z0), ISNATKIND(z0))
ACTIVE(U22(tt, z0)) → c11(MARK(U23(isNat(z0))), U23'(isNat(z0)), ISNAT(z0))
ACTIVE(U23(tt)) → c12(MARK(tt))
ACTIVE(U31(tt, z0, z1)) → c13(MARK(U32(isNatKind(z0), z0, z1)), U32'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(U32(tt, z0, z1)) → c14(MARK(U33(isNatKind(z1), z0, z1)), U33'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U33(tt, z0, z1)) → c15(MARK(U34(isNatKind(z1), z0, z1)), U34'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U34(tt, z0, z1)) → c16(MARK(U35(isNat(z0), z1)), U35'(isNat(z0), z1), ISNAT(z0))
ACTIVE(U35(tt, z0)) → c17(MARK(U36(isNat(z0))), U36'(isNat(z0)), ISNAT(z0))
ACTIVE(U36(tt)) → c18(MARK(tt))
ACTIVE(U41(tt, z0)) → c19(MARK(U42(isNatKind(z0))), U42'(isNatKind(z0)), ISNATKIND(z0))
ACTIVE(U42(tt)) → c20(MARK(tt))
ACTIVE(U51(tt)) → c21(MARK(tt))
ACTIVE(U61(tt, z0)) → c22(MARK(U62(isNatKind(z0))), U62'(isNatKind(z0)), ISNATKIND(z0))
ACTIVE(U62(tt)) → c23(MARK(tt))
ACTIVE(U71(tt, z0)) → c24(MARK(U72(isNatKind(z0), z0)), U72'(isNatKind(z0), z0), ISNATKIND(z0))
ACTIVE(U72(tt, z0)) → c25(MARK(z0))
ACTIVE(U81(tt, z0, z1)) → c26(MARK(U82(isNatKind(z0), z0, z1)), U82'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(U82(tt, z0, z1)) → c27(MARK(U83(isNat(z1), z0, z1)), U83'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U83(tt, z0, z1)) → c28(MARK(U84(isNatKind(z1), z0, z1)), U84'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U84(tt, z0, z1)) → c29(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0))
ACTIVE(U91(tt, z0)) → c30(MARK(U92(isNatKind(z0))), U92'(isNatKind(z0)), ISNATKIND(z0))
ACTIVE(U92(tt)) → c31(MARK(0))
ACTIVE(isNat(0)) → c32(MARK(tt))
ACTIVE(isNat(plus(z0, z1))) → c33(MARK(U11(isNatKind(z0), z0, z1)), U11'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(isNat(s(z0))) → c34(MARK(U21(isNatKind(z0), z0)), U21'(isNatKind(z0), z0), ISNATKIND(z0))
ACTIVE(isNat(x(z0, z1))) → c35(MARK(U31(isNatKind(z0), z0, z1)), U31'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(isNatKind(0)) → c36(MARK(tt))
ACTIVE(isNatKind(plus(z0, z1))) → c37(MARK(U41(isNatKind(z0), z1)), U41'(isNatKind(z0), z1), ISNATKIND(z0))
ACTIVE(isNatKind(s(z0))) → c38(MARK(U51(isNatKind(z0))), U51'(isNatKind(z0)), ISNATKIND(z0))
ACTIVE(isNatKind(x(z0, z1))) → c39(MARK(U61(isNatKind(z0), z1)), U61'(isNatKind(z0), z1), ISNATKIND(z0))
ACTIVE(plus(z0, 0)) → c40(MARK(U71(isNat(z0), z0)), U71'(isNat(z0), z0), ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c41(MARK(U81(isNat(z1), z1, z0)), U81'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(x(z0, 0)) → c42(MARK(U91(isNat(z0), z0)), U91'(isNat(z0), z0), ISNAT(z0))
ACTIVE(x(z0, s(z1))) → c43(MARK(U101(isNat(z1), z1, z0)), U101'(isNat(z1), z1, z0), ISNAT(z1))
MARK(U101(z0, z1, z2)) → c44(ACTIVE(U101(mark(z0), z1, z2)), U101'(mark(z0), z1, z2), MARK(z0))
MARK(tt) → c45(ACTIVE(tt))
MARK(U102(z0, z1, z2)) → c46(ACTIVE(U102(mark(z0), z1, z2)), U102'(mark(z0), z1, z2), MARK(z0))
MARK(isNatKind(z0)) → c47(ACTIVE(isNatKind(z0)), ISNATKIND(z0))
MARK(U103(z0, z1, z2)) → c48(ACTIVE(U103(mark(z0), z1, z2)), U103'(mark(z0), z1, z2), MARK(z0))
MARK(isNat(z0)) → c49(ACTIVE(isNat(z0)), ISNAT(z0))
MARK(U104(z0, z1, z2)) → c50(ACTIVE(U104(mark(z0), z1, z2)), U104'(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) → c51(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(x(z0, z1)) → c52(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U11(z0, z1, z2)) → c53(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) → c54(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0))
MARK(U13(z0, z1, z2)) → c55(ACTIVE(U13(mark(z0), z1, z2)), U13'(mark(z0), z1, z2), MARK(z0))
MARK(U14(z0, z1, z2)) → c56(ACTIVE(U14(mark(z0), z1, z2)), U14'(mark(z0), z1, z2), MARK(z0))
MARK(U15(z0, z1)) → c57(ACTIVE(U15(mark(z0), z1)), U15'(mark(z0), z1), MARK(z0))
MARK(U16(z0)) → c58(ACTIVE(U16(mark(z0))), U16'(mark(z0)), MARK(z0))
MARK(U21(z0, z1)) → c59(ACTIVE(U21(mark(z0), z1)), U21'(mark(z0), z1), MARK(z0))
MARK(U22(z0, z1)) → c60(ACTIVE(U22(mark(z0), z1)), U22'(mark(z0), z1), MARK(z0))
MARK(U23(z0)) → c61(ACTIVE(U23(mark(z0))), U23'(mark(z0)), MARK(z0))
MARK(U31(z0, z1, z2)) → c62(ACTIVE(U31(mark(z0), z1, z2)), U31'(mark(z0), z1, z2), MARK(z0))
MARK(U32(z0, z1, z2)) → c63(ACTIVE(U32(mark(z0), z1, z2)), U32'(mark(z0), z1, z2), MARK(z0))
MARK(U33(z0, z1, z2)) → c64(ACTIVE(U33(mark(z0), z1, z2)), U33'(mark(z0), z1, z2), MARK(z0))
MARK(U34(z0, z1, z2)) → c65(ACTIVE(U34(mark(z0), z1, z2)), U34'(mark(z0), z1, z2), MARK(z0))
MARK(U35(z0, z1)) → c66(ACTIVE(U35(mark(z0), z1)), U35'(mark(z0), z1), MARK(z0))
MARK(U36(z0)) → c67(ACTIVE(U36(mark(z0))), U36'(mark(z0)), MARK(z0))
MARK(U41(z0, z1)) → c68(ACTIVE(U41(mark(z0), z1)), U41'(mark(z0), z1), MARK(z0))
MARK(U42(z0)) → c69(ACTIVE(U42(mark(z0))), U42'(mark(z0)), MARK(z0))
MARK(U51(z0)) → c70(ACTIVE(U51(mark(z0))), U51'(mark(z0)), MARK(z0))
MARK(U61(z0, z1)) → c71(ACTIVE(U61(mark(z0), z1)), U61'(mark(z0), z1), MARK(z0))
MARK(U62(z0)) → c72(ACTIVE(U62(mark(z0))), U62'(mark(z0)), MARK(z0))
MARK(U71(z0, z1)) → c73(ACTIVE(U71(mark(z0), z1)), U71'(mark(z0), z1), MARK(z0))
MARK(U72(z0, z1)) → c74(ACTIVE(U72(mark(z0), z1)), U72'(mark(z0), z1), MARK(z0))
MARK(U81(z0, z1, z2)) → c75(ACTIVE(U81(mark(z0), z1, z2)), U81'(mark(z0), z1, z2), MARK(z0))
MARK(U82(z0, z1, z2)) → c76(ACTIVE(U82(mark(z0), z1, z2)), U82'(mark(z0), z1, z2), MARK(z0))
MARK(U83(z0, z1, z2)) → c77(ACTIVE(U83(mark(z0), z1, z2)), U83'(mark(z0), z1, z2), MARK(z0))
MARK(U84(z0, z1, z2)) → c78(ACTIVE(U84(mark(z0), z1, z2)), U84'(mark(z0), z1, z2), MARK(z0))
MARK(s(z0)) → c79(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0))
MARK(U91(z0, z1)) → c80(ACTIVE(U91(mark(z0), z1)), U91'(mark(z0), z1), MARK(z0))
MARK(U92(z0)) → c81(ACTIVE(U92(mark(z0))), U92'(mark(z0)), MARK(z0))
MARK(0) → c82(ACTIVE(0))
U101'(mark(z0), z1, z2) → c83(U101'(z0, z1, z2))
U101'(z0, mark(z1), z2) → c84(U101'(z0, z1, z2))
U101'(z0, z1, mark(z2)) → c85(U101'(z0, z1, z2))
U101'(active(z0), z1, z2) → c86(U101'(z0, z1, z2))
U101'(z0, active(z1), z2) → c87(U101'(z0, z1, z2))
U101'(z0, z1, active(z2)) → c88(U101'(z0, z1, z2))
U102'(mark(z0), z1, z2) → c89(U102'(z0, z1, z2))
U102'(z0, mark(z1), z2) → c90(U102'(z0, z1, z2))
U102'(z0, z1, mark(z2)) → c91(U102'(z0, z1, z2))
U102'(active(z0), z1, z2) → c92(U102'(z0, z1, z2))
U102'(z0, active(z1), z2) → c93(U102'(z0, z1, z2))
U102'(z0, z1, active(z2)) → c94(U102'(z0, z1, z2))
ISNATKIND(mark(z0)) → c95(ISNATKIND(z0))
ISNATKIND(active(z0)) → c96(ISNATKIND(z0))
U103'(mark(z0), z1, z2) → c97(U103'(z0, z1, z2))
U103'(z0, mark(z1), z2) → c98(U103'(z0, z1, z2))
U103'(z0, z1, mark(z2)) → c99(U103'(z0, z1, z2))
U103'(active(z0), z1, z2) → c100(U103'(z0, z1, z2))
U103'(z0, active(z1), z2) → c101(U103'(z0, z1, z2))
U103'(z0, z1, active(z2)) → c102(U103'(z0, z1, z2))
ISNAT(mark(z0)) → c103(ISNAT(z0))
ISNAT(active(z0)) → c104(ISNAT(z0))
U104'(mark(z0), z1, z2) → c105(U104'(z0, z1, z2))
U104'(z0, mark(z1), z2) → c106(U104'(z0, z1, z2))
U104'(z0, z1, mark(z2)) → c107(U104'(z0, z1, z2))
U104'(active(z0), z1, z2) → c108(U104'(z0, z1, z2))
U104'(z0, active(z1), z2) → c109(U104'(z0, z1, z2))
U104'(z0, z1, active(z2)) → c110(U104'(z0, z1, z2))
PLUS(mark(z0), z1) → c111(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c112(PLUS(z0, z1))
PLUS(active(z0), z1) → c113(PLUS(z0, z1))
PLUS(z0, active(z1)) → c114(PLUS(z0, z1))
X(mark(z0), z1) → c115(X(z0, z1))
X(z0, mark(z1)) → c116(X(z0, z1))
X(active(z0), z1) → c117(X(z0, z1))
X(z0, active(z1)) → c118(X(z0, z1))
U11'(mark(z0), z1, z2) → c119(U11'(z0, z1, z2))
U11'(z0, mark(z1), z2) → c120(U11'(z0, z1, z2))
U11'(z0, z1, mark(z2)) → c121(U11'(z0, z1, z2))
U11'(active(z0), z1, z2) → c122(U11'(z0, z1, z2))
U11'(z0, active(z1), z2) → c123(U11'(z0, z1, z2))
U11'(z0, z1, active(z2)) → c124(U11'(z0, z1, z2))
U12'(mark(z0), z1, z2) → c125(U12'(z0, z1, z2))
U12'(z0, mark(z1), z2) → c126(U12'(z0, z1, z2))
U12'(z0, z1, mark(z2)) → c127(U12'(z0, z1, z2))
U12'(active(z0), z1, z2) → c128(U12'(z0, z1, z2))
U12'(z0, active(z1), z2) → c129(U12'(z0, z1, z2))
U12'(z0, z1, active(z2)) → c130(U12'(z0, z1, z2))
U13'(mark(z0), z1, z2) → c131(U13'(z0, z1, z2))
U13'(z0, mark(z1), z2) → c132(U13'(z0, z1, z2))
U13'(z0, z1, mark(z2)) → c133(U13'(z0, z1, z2))
U13'(active(z0), z1, z2) → c134(U13'(z0, z1, z2))
U13'(z0, active(z1), z2) → c135(U13'(z0, z1, z2))
U13'(z0, z1, active(z2)) → c136(U13'(z0, z1, z2))
U14'(mark(z0), z1, z2) → c137(U14'(z0, z1, z2))
U14'(z0, mark(z1), z2) → c138(U14'(z0, z1, z2))
U14'(z0, z1, mark(z2)) → c139(U14'(z0, z1, z2))
U14'(active(z0), z1, z2) → c140(U14'(z0, z1, z2))
U14'(z0, active(z1), z2) → c141(U14'(z0, z1, z2))
U14'(z0, z1, active(z2)) → c142(U14'(z0, z1, z2))
U15'(mark(z0), z1) → c143(U15'(z0, z1))
U15'(z0, mark(z1)) → c144(U15'(z0, z1))
U15'(active(z0), z1) → c145(U15'(z0, z1))
U15'(z0, active(z1)) → c146(U15'(z0, z1))
U16'(mark(z0)) → c147(U16'(z0))
U16'(active(z0)) → c148(U16'(z0))
U21'(mark(z0), z1) → c149(U21'(z0, z1))
U21'(z0, mark(z1)) → c150(U21'(z0, z1))
U21'(active(z0), z1) → c151(U21'(z0, z1))
U21'(z0, active(z1)) → c152(U21'(z0, z1))
U22'(mark(z0), z1) → c153(U22'(z0, z1))
U22'(z0, mark(z1)) → c154(U22'(z0, z1))
U22'(active(z0), z1) → c155(U22'(z0, z1))
U22'(z0, active(z1)) → c156(U22'(z0, z1))
U23'(mark(z0)) → c157(U23'(z0))
U23'(active(z0)) → c158(U23'(z0))
U31'(mark(z0), z1, z2) → c159(U31'(z0, z1, z2))
U31'(z0, mark(z1), z2) → c160(U31'(z0, z1, z2))
U31'(z0, z1, mark(z2)) → c161(U31'(z0, z1, z2))
U31'(active(z0), z1, z2) → c162(U31'(z0, z1, z2))
U31'(z0, active(z1), z2) → c163(U31'(z0, z1, z2))
U31'(z0, z1, active(z2)) → c164(U31'(z0, z1, z2))
U32'(mark(z0), z1, z2) → c165(U32'(z0, z1, z2))
U32'(z0, mark(z1), z2) → c166(U32'(z0, z1, z2))
U32'(z0, z1, mark(z2)) → c167(U32'(z0, z1, z2))
U32'(active(z0), z1, z2) → c168(U32'(z0, z1, z2))
U32'(z0, active(z1), z2) → c169(U32'(z0, z1, z2))
U32'(z0, z1, active(z2)) → c170(U32'(z0, z1, z2))
U33'(mark(z0), z1, z2) → c171(U33'(z0, z1, z2))
U33'(z0, mark(z1), z2) → c172(U33'(z0, z1, z2))
U33'(z0, z1, mark(z2)) → c173(U33'(z0, z1, z2))
U33'(active(z0), z1, z2) → c174(U33'(z0, z1, z2))
U33'(z0, active(z1), z2) → c175(U33'(z0, z1, z2))
U33'(z0, z1, active(z2)) → c176(U33'(z0, z1, z2))
U34'(mark(z0), z1, z2) → c177(U34'(z0, z1, z2))
U34'(z0, mark(z1), z2) → c178(U34'(z0, z1, z2))
U34'(z0, z1, mark(z2)) → c179(U34'(z0, z1, z2))
U34'(active(z0), z1, z2) → c180(U34'(z0, z1, z2))
U34'(z0, active(z1), z2) → c181(U34'(z0, z1, z2))
U34'(z0, z1, active(z2)) → c182(U34'(z0, z1, z2))
U35'(mark(z0), z1) → c183(U35'(z0, z1))
U35'(z0, mark(z1)) → c184(U35'(z0, z1))
U35'(active(z0), z1) → c185(U35'(z0, z1))
U35'(z0, active(z1)) → c186(U35'(z0, z1))
U36'(mark(z0)) → c187(U36'(z0))
U36'(active(z0)) → c188(U36'(z0))
U41'(mark(z0), z1) → c189(U41'(z0, z1))
U41'(z0, mark(z1)) → c190(U41'(z0, z1))
U41'(active(z0), z1) → c191(U41'(z0, z1))
U41'(z0, active(z1)) → c192(U41'(z0, z1))
U42'(mark(z0)) → c193(U42'(z0))
U42'(active(z0)) → c194(U42'(z0))
U51'(mark(z0)) → c195(U51'(z0))
U51'(active(z0)) → c196(U51'(z0))
U61'(mark(z0), z1) → c197(U61'(z0, z1))
U61'(z0, mark(z1)) → c198(U61'(z0, z1))
U61'(active(z0), z1) → c199(U61'(z0, z1))
U61'(z0, active(z1)) → c200(U61'(z0, z1))
U62'(mark(z0)) → c201(U62'(z0))
U62'(active(z0)) → c202(U62'(z0))
U71'(mark(z0), z1) → c203(U71'(z0, z1))
U71'(z0, mark(z1)) → c204(U71'(z0, z1))
U71'(active(z0), z1) → c205(U71'(z0, z1))
U71'(z0, active(z1)) → c206(U71'(z0, z1))
U72'(mark(z0), z1) → c207(U72'(z0, z1))
U72'(z0, mark(z1)) → c208(U72'(z0, z1))
U72'(active(z0), z1) → c209(U72'(z0, z1))
U72'(z0, active(z1)) → c210(U72'(z0, z1))
U81'(mark(z0), z1, z2) → c211(U81'(z0, z1, z2))
U81'(z0, mark(z1), z2) → c212(U81'(z0, z1, z2))
U81'(z0, z1, mark(z2)) → c213(U81'(z0, z1, z2))
U81'(active(z0), z1, z2) → c214(U81'(z0, z1, z2))
U81'(z0, active(z1), z2) → c215(U81'(z0, z1, z2))
U81'(z0, z1, active(z2)) → c216(U81'(z0, z1, z2))
U82'(mark(z0), z1, z2) → c217(U82'(z0, z1, z2))
U82'(z0, mark(z1), z2) → c218(U82'(z0, z1, z2))
U82'(z0, z1, mark(z2)) → c219(U82'(z0, z1, z2))
U82'(active(z0), z1, z2) → c220(U82'(z0, z1, z2))
U82'(z0, active(z1), z2) → c221(U82'(z0, z1, z2))
U82'(z0, z1, active(z2)) → c222(U82'(z0, z1, z2))
U83'(mark(z0), z1, z2) → c223(U83'(z0, z1, z2))
U83'(z0, mark(z1), z2) → c224(U83'(z0, z1, z2))
U83'(z0, z1, mark(z2)) → c225(U83'(z0, z1, z2))
U83'(active(z0), z1, z2) → c226(U83'(z0, z1, z2))
U83'(z0, active(z1), z2) → c227(U83'(z0, z1, z2))
U83'(z0, z1, active(z2)) → c228(U83'(z0, z1, z2))
U84'(mark(z0), z1, z2) → c229(U84'(z0, z1, z2))
U84'(z0, mark(z1), z2) → c230(U84'(z0, z1, z2))
U84'(z0, z1, mark(z2)) → c231(U84'(z0, z1, z2))
U84'(active(z0), z1, z2) → c232(U84'(z0, z1, z2))
U84'(z0, active(z1), z2) → c233(U84'(z0, z1, z2))
U84'(z0, z1, active(z2)) → c234(U84'(z0, z1, z2))
S(mark(z0)) → c235(S(z0))
S(active(z0)) → c236(S(z0))
U91'(mark(z0), z1) → c237(U91'(z0, z1))
U91'(z0, mark(z1)) → c238(U91'(z0, z1))
U91'(active(z0), z1) → c239(U91'(z0, z1))
U91'(z0, active(z1)) → c240(U91'(z0, z1))
U92'(mark(z0)) → c241(U92'(z0))
U92'(active(z0)) → c242(U92'(z0))

K tuples:none
Defined Rule Symbols:

active, mark, U101, U102, isNatKind, U103, isNat, U104, plus, x, U11, U12, U13, U14, U15, U16, U21, U22, U23, U31, U32, U33, U34, U35, U36, U41, U42, U51, U61, U62, U71, U72, U81, U82, U83, U84, s, U91, U92

Defined Pair Symbols:

ACTIVE, MARK, U101', U102', ISNATKIND, U103', ISNAT, U104', PLUS, X, U11', U12', U13', U14', U15', U16', U21', U22', U23', U31', U32', U33', U34', U35', U36', U41', U42', U51', U61', U62', U71', U72', U81', U82', U83', U84', S, U91', U92'

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, c85, c86, c87, c88, c89, c90, c91, c92, c93, c94, c95, c96, c97, c98, c99, c100, c101, c102, c103, c104, c105, c106, c107, c108, c109, c110, c111, c112, c113, c114, c115, c116, c117, c118, c119, c120, c121, c122, c123, c124, c125, c126, c127, c128, c129, c130, c131, c132, c133, c134, c135, c136, c137, c138, c139, c140, c141, c142, c143, c144, c145, c146, c147, c148, c149, c150, c151, c152, c153, c154, c155, c156, c157, c158, c159, c160, c161, c162, c163, c164, c165, c166, c167, c168, c169, c170, c171, c172, c173, c174, c175, c176, c177, c178, c179, c180, c181, c182, c183, c184, c185, c186, c187, c188, c189, c190, c191, c192, c193, c194, c195, c196, c197, c198, c199, c200, c201, c202, c203, c204, c205, c206, c207, c208, c209, c210, c211, c212, c213, c214, c215, c216, c217, c218, c219, c220, c221, c222, c223, c224, c225, c226, c227, c228, c229, c230, c231, c232, c233, c234, c235, c236, c237, c238, c239, c240, c241, c242

(3) CdtUnreachableProof (EQUIVALENT transformation)

The following tuples could be removed as they are not reachable from basic start terms:

ACTIVE(U101(tt, z0, z1)) → c(MARK(U102(isNatKind(z0), z0, z1)), U102'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(U102(tt, z0, z1)) → c1(MARK(U103(isNat(z1), z0, z1)), U103'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U103(tt, z0, z1)) → c2(MARK(U104(isNatKind(z1), z0, z1)), U104'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U104(tt, z0, z1)) → c3(MARK(plus(x(z1, z0), z1)), PLUS(x(z1, z0), z1), X(z1, z0))
ACTIVE(U11(tt, z0, z1)) → c4(MARK(U12(isNatKind(z0), z0, z1)), U12'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(U12(tt, z0, z1)) → c5(MARK(U13(isNatKind(z1), z0, z1)), U13'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U13(tt, z0, z1)) → c6(MARK(U14(isNatKind(z1), z0, z1)), U14'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U14(tt, z0, z1)) → c7(MARK(U15(isNat(z0), z1)), U15'(isNat(z0), z1), ISNAT(z0))
ACTIVE(U15(tt, z0)) → c8(MARK(U16(isNat(z0))), U16'(isNat(z0)), ISNAT(z0))
ACTIVE(U16(tt)) → c9(MARK(tt))
ACTIVE(U21(tt, z0)) → c10(MARK(U22(isNatKind(z0), z0)), U22'(isNatKind(z0), z0), ISNATKIND(z0))
ACTIVE(U22(tt, z0)) → c11(MARK(U23(isNat(z0))), U23'(isNat(z0)), ISNAT(z0))
ACTIVE(U23(tt)) → c12(MARK(tt))
ACTIVE(U31(tt, z0, z1)) → c13(MARK(U32(isNatKind(z0), z0, z1)), U32'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(U32(tt, z0, z1)) → c14(MARK(U33(isNatKind(z1), z0, z1)), U33'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U33(tt, z0, z1)) → c15(MARK(U34(isNatKind(z1), z0, z1)), U34'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U34(tt, z0, z1)) → c16(MARK(U35(isNat(z0), z1)), U35'(isNat(z0), z1), ISNAT(z0))
ACTIVE(U35(tt, z0)) → c17(MARK(U36(isNat(z0))), U36'(isNat(z0)), ISNAT(z0))
ACTIVE(U36(tt)) → c18(MARK(tt))
ACTIVE(U41(tt, z0)) → c19(MARK(U42(isNatKind(z0))), U42'(isNatKind(z0)), ISNATKIND(z0))
ACTIVE(U42(tt)) → c20(MARK(tt))
ACTIVE(U51(tt)) → c21(MARK(tt))
ACTIVE(U61(tt, z0)) → c22(MARK(U62(isNatKind(z0))), U62'(isNatKind(z0)), ISNATKIND(z0))
ACTIVE(U62(tt)) → c23(MARK(tt))
ACTIVE(U71(tt, z0)) → c24(MARK(U72(isNatKind(z0), z0)), U72'(isNatKind(z0), z0), ISNATKIND(z0))
ACTIVE(U72(tt, z0)) → c25(MARK(z0))
ACTIVE(U81(tt, z0, z1)) → c26(MARK(U82(isNatKind(z0), z0, z1)), U82'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(U82(tt, z0, z1)) → c27(MARK(U83(isNat(z1), z0, z1)), U83'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U83(tt, z0, z1)) → c28(MARK(U84(isNatKind(z1), z0, z1)), U84'(isNatKind(z1), z0, z1), ISNATKIND(z1))
ACTIVE(U84(tt, z0, z1)) → c29(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0))
ACTIVE(U91(tt, z0)) → c30(MARK(U92(isNatKind(z0))), U92'(isNatKind(z0)), ISNATKIND(z0))
ACTIVE(U92(tt)) → c31(MARK(0))
ACTIVE(isNat(0)) → c32(MARK(tt))
ACTIVE(isNat(plus(z0, z1))) → c33(MARK(U11(isNatKind(z0), z0, z1)), U11'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(isNat(s(z0))) → c34(MARK(U21(isNatKind(z0), z0)), U21'(isNatKind(z0), z0), ISNATKIND(z0))
ACTIVE(isNat(x(z0, z1))) → c35(MARK(U31(isNatKind(z0), z0, z1)), U31'(isNatKind(z0), z0, z1), ISNATKIND(z0))
ACTIVE(isNatKind(0)) → c36(MARK(tt))
ACTIVE(isNatKind(plus(z0, z1))) → c37(MARK(U41(isNatKind(z0), z1)), U41'(isNatKind(z0), z1), ISNATKIND(z0))
ACTIVE(isNatKind(s(z0))) → c38(MARK(U51(isNatKind(z0))), U51'(isNatKind(z0)), ISNATKIND(z0))
ACTIVE(isNatKind(x(z0, z1))) → c39(MARK(U61(isNatKind(z0), z1)), U61'(isNatKind(z0), z1), ISNATKIND(z0))
ACTIVE(plus(z0, 0)) → c40(MARK(U71(isNat(z0), z0)), U71'(isNat(z0), z0), ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c41(MARK(U81(isNat(z1), z1, z0)), U81'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(x(z0, 0)) → c42(MARK(U91(isNat(z0), z0)), U91'(isNat(z0), z0), ISNAT(z0))
ACTIVE(x(z0, s(z1))) → c43(MARK(U101(isNat(z1), z1, z0)), U101'(isNat(z1), z1, z0), ISNAT(z1))
MARK(U101(z0, z1, z2)) → c44(ACTIVE(U101(mark(z0), z1, z2)), U101'(mark(z0), z1, z2), MARK(z0))
MARK(U102(z0, z1, z2)) → c46(ACTIVE(U102(mark(z0), z1, z2)), U102'(mark(z0), z1, z2), MARK(z0))
MARK(isNatKind(z0)) → c47(ACTIVE(isNatKind(z0)), ISNATKIND(z0))
MARK(U103(z0, z1, z2)) → c48(ACTIVE(U103(mark(z0), z1, z2)), U103'(mark(z0), z1, z2), MARK(z0))
MARK(isNat(z0)) → c49(ACTIVE(isNat(z0)), ISNAT(z0))
MARK(U104(z0, z1, z2)) → c50(ACTIVE(U104(mark(z0), z1, z2)), U104'(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) → c51(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(x(z0, z1)) → c52(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U11(z0, z1, z2)) → c53(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) → c54(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0))
MARK(U13(z0, z1, z2)) → c55(ACTIVE(U13(mark(z0), z1, z2)), U13'(mark(z0), z1, z2), MARK(z0))
MARK(U14(z0, z1, z2)) → c56(ACTIVE(U14(mark(z0), z1, z2)), U14'(mark(z0), z1, z2), MARK(z0))
MARK(U15(z0, z1)) → c57(ACTIVE(U15(mark(z0), z1)), U15'(mark(z0), z1), MARK(z0))
MARK(U16(z0)) → c58(ACTIVE(U16(mark(z0))), U16'(mark(z0)), MARK(z0))
MARK(U21(z0, z1)) → c59(ACTIVE(U21(mark(z0), z1)), U21'(mark(z0), z1), MARK(z0))
MARK(U22(z0, z1)) → c60(ACTIVE(U22(mark(z0), z1)), U22'(mark(z0), z1), MARK(z0))
MARK(U23(z0)) → c61(ACTIVE(U23(mark(z0))), U23'(mark(z0)), MARK(z0))
MARK(U31(z0, z1, z2)) → c62(ACTIVE(U31(mark(z0), z1, z2)), U31'(mark(z0), z1, z2), MARK(z0))
MARK(U32(z0, z1, z2)) → c63(ACTIVE(U32(mark(z0), z1, z2)), U32'(mark(z0), z1, z2), MARK(z0))
MARK(U33(z0, z1, z2)) → c64(ACTIVE(U33(mark(z0), z1, z2)), U33'(mark(z0), z1, z2), MARK(z0))
MARK(U34(z0, z1, z2)) → c65(ACTIVE(U34(mark(z0), z1, z2)), U34'(mark(z0), z1, z2), MARK(z0))
MARK(U35(z0, z1)) → c66(ACTIVE(U35(mark(z0), z1)), U35'(mark(z0), z1), MARK(z0))
MARK(U36(z0)) → c67(ACTIVE(U36(mark(z0))), U36'(mark(z0)), MARK(z0))
MARK(U41(z0, z1)) → c68(ACTIVE(U41(mark(z0), z1)), U41'(mark(z0), z1), MARK(z0))
MARK(U42(z0)) → c69(ACTIVE(U42(mark(z0))), U42'(mark(z0)), MARK(z0))
MARK(U51(z0)) → c70(ACTIVE(U51(mark(z0))), U51'(mark(z0)), MARK(z0))
MARK(U61(z0, z1)) → c71(ACTIVE(U61(mark(z0), z1)), U61'(mark(z0), z1), MARK(z0))
MARK(U62(z0)) → c72(ACTIVE(U62(mark(z0))), U62'(mark(z0)), MARK(z0))
MARK(U71(z0, z1)) → c73(ACTIVE(U71(mark(z0), z1)), U71'(mark(z0), z1), MARK(z0))
MARK(U72(z0, z1)) → c74(ACTIVE(U72(mark(z0), z1)), U72'(mark(z0), z1), MARK(z0))
MARK(U81(z0, z1, z2)) → c75(ACTIVE(U81(mark(z0), z1, z2)), U81'(mark(z0), z1, z2), MARK(z0))
MARK(U82(z0, z1, z2)) → c76(ACTIVE(U82(mark(z0), z1, z2)), U82'(mark(z0), z1, z2), MARK(z0))
MARK(U83(z0, z1, z2)) → c77(ACTIVE(U83(mark(z0), z1, z2)), U83'(mark(z0), z1, z2), MARK(z0))
MARK(U84(z0, z1, z2)) → c78(ACTIVE(U84(mark(z0), z1, z2)), U84'(mark(z0), z1, z2), MARK(z0))
MARK(s(z0)) → c79(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0))
MARK(U91(z0, z1)) → c80(ACTIVE(U91(mark(z0), z1)), U91'(mark(z0), z1), MARK(z0))
MARK(U92(z0)) → c81(ACTIVE(U92(mark(z0))), U92'(mark(z0)), MARK(z0))
U101'(mark(z0), z1, z2) → c83(U101'(z0, z1, z2))
U101'(z0, mark(z1), z2) → c84(U101'(z0, z1, z2))
U101'(z0, z1, mark(z2)) → c85(U101'(z0, z1, z2))
U101'(active(z0), z1, z2) → c86(U101'(z0, z1, z2))
U101'(z0, active(z1), z2) → c87(U101'(z0, z1, z2))
U101'(z0, z1, active(z2)) → c88(U101'(z0, z1, z2))
U102'(mark(z0), z1, z2) → c89(U102'(z0, z1, z2))
U102'(z0, mark(z1), z2) → c90(U102'(z0, z1, z2))
U102'(z0, z1, mark(z2)) → c91(U102'(z0, z1, z2))
U102'(active(z0), z1, z2) → c92(U102'(z0, z1, z2))
U102'(z0, active(z1), z2) → c93(U102'(z0, z1, z2))
U102'(z0, z1, active(z2)) → c94(U102'(z0, z1, z2))
ISNATKIND(mark(z0)) → c95(ISNATKIND(z0))
ISNATKIND(active(z0)) → c96(ISNATKIND(z0))
U103'(mark(z0), z1, z2) → c97(U103'(z0, z1, z2))
U103'(z0, mark(z1), z2) → c98(U103'(z0, z1, z2))
U103'(z0, z1, mark(z2)) → c99(U103'(z0, z1, z2))
U103'(active(z0), z1, z2) → c100(U103'(z0, z1, z2))
U103'(z0, active(z1), z2) → c101(U103'(z0, z1, z2))
U103'(z0, z1, active(z2)) → c102(U103'(z0, z1, z2))
ISNAT(mark(z0)) → c103(ISNAT(z0))
ISNAT(active(z0)) → c104(ISNAT(z0))
U104'(mark(z0), z1, z2) → c105(U104'(z0, z1, z2))
U104'(z0, mark(z1), z2) → c106(U104'(z0, z1, z2))
U104'(z0, z1, mark(z2)) → c107(U104'(z0, z1, z2))
U104'(active(z0), z1, z2) → c108(U104'(z0, z1, z2))
U104'(z0, active(z1), z2) → c109(U104'(z0, z1, z2))
U104'(z0, z1, active(z2)) → c110(U104'(z0, z1, z2))
PLUS(mark(z0), z1) → c111(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c112(PLUS(z0, z1))
PLUS(active(z0), z1) → c113(PLUS(z0, z1))
PLUS(z0, active(z1)) → c114(PLUS(z0, z1))
X(mark(z0), z1) → c115(X(z0, z1))
X(z0, mark(z1)) → c116(X(z0, z1))
X(active(z0), z1) → c117(X(z0, z1))
X(z0, active(z1)) → c118(X(z0, z1))
U11'(mark(z0), z1, z2) → c119(U11'(z0, z1, z2))
U11'(z0, mark(z1), z2) → c120(U11'(z0, z1, z2))
U11'(z0, z1, mark(z2)) → c121(U11'(z0, z1, z2))
U11'(active(z0), z1, z2) → c122(U11'(z0, z1, z2))
U11'(z0, active(z1), z2) → c123(U11'(z0, z1, z2))
U11'(z0, z1, active(z2)) → c124(U11'(z0, z1, z2))
U12'(mark(z0), z1, z2) → c125(U12'(z0, z1, z2))
U12'(z0, mark(z1), z2) → c126(U12'(z0, z1, z2))
U12'(z0, z1, mark(z2)) → c127(U12'(z0, z1, z2))
U12'(active(z0), z1, z2) → c128(U12'(z0, z1, z2))
U12'(z0, active(z1), z2) → c129(U12'(z0, z1, z2))
U12'(z0, z1, active(z2)) → c130(U12'(z0, z1, z2))
U13'(mark(z0), z1, z2) → c131(U13'(z0, z1, z2))
U13'(z0, mark(z1), z2) → c132(U13'(z0, z1, z2))
U13'(z0, z1, mark(z2)) → c133(U13'(z0, z1, z2))
U13'(active(z0), z1, z2) → c134(U13'(z0, z1, z2))
U13'(z0, active(z1), z2) → c135(U13'(z0, z1, z2))
U13'(z0, z1, active(z2)) → c136(U13'(z0, z1, z2))
U14'(mark(z0), z1, z2) → c137(U14'(z0, z1, z2))
U14'(z0, mark(z1), z2) → c138(U14'(z0, z1, z2))
U14'(z0, z1, mark(z2)) → c139(U14'(z0, z1, z2))
U14'(active(z0), z1, z2) → c140(U14'(z0, z1, z2))
U14'(z0, active(z1), z2) → c141(U14'(z0, z1, z2))
U14'(z0, z1, active(z2)) → c142(U14'(z0, z1, z2))
U15'(mark(z0), z1) → c143(U15'(z0, z1))
U15'(z0, mark(z1)) → c144(U15'(z0, z1))
U15'(active(z0), z1) → c145(U15'(z0, z1))
U15'(z0, active(z1)) → c146(U15'(z0, z1))
U16'(mark(z0)) → c147(U16'(z0))
U16'(active(z0)) → c148(U16'(z0))
U21'(mark(z0), z1) → c149(U21'(z0, z1))
U21'(z0, mark(z1)) → c150(U21'(z0, z1))
U21'(active(z0), z1) → c151(U21'(z0, z1))
U21'(z0, active(z1)) → c152(U21'(z0, z1))
U22'(mark(z0), z1) → c153(U22'(z0, z1))
U22'(z0, mark(z1)) → c154(U22'(z0, z1))
U22'(active(z0), z1) → c155(U22'(z0, z1))
U22'(z0, active(z1)) → c156(U22'(z0, z1))
U23'(mark(z0)) → c157(U23'(z0))
U23'(active(z0)) → c158(U23'(z0))
U31'(mark(z0), z1, z2) → c159(U31'(z0, z1, z2))
U31'(z0, mark(z1), z2) → c160(U31'(z0, z1, z2))
U31'(z0, z1, mark(z2)) → c161(U31'(z0, z1, z2))
U31'(active(z0), z1, z2) → c162(U31'(z0, z1, z2))
U31'(z0, active(z1), z2) → c163(U31'(z0, z1, z2))
U31'(z0, z1, active(z2)) → c164(U31'(z0, z1, z2))
U32'(mark(z0), z1, z2) → c165(U32'(z0, z1, z2))
U32'(z0, mark(z1), z2) → c166(U32'(z0, z1, z2))
U32'(z0, z1, mark(z2)) → c167(U32'(z0, z1, z2))
U32'(active(z0), z1, z2) → c168(U32'(z0, z1, z2))
U32'(z0, active(z1), z2) → c169(U32'(z0, z1, z2))
U32'(z0, z1, active(z2)) → c170(U32'(z0, z1, z2))
U33'(mark(z0), z1, z2) → c171(U33'(z0, z1, z2))
U33'(z0, mark(z1), z2) → c172(U33'(z0, z1, z2))
U33'(z0, z1, mark(z2)) → c173(U33'(z0, z1, z2))
U33'(active(z0), z1, z2) → c174(U33'(z0, z1, z2))
U33'(z0, active(z1), z2) → c175(U33'(z0, z1, z2))
U33'(z0, z1, active(z2)) → c176(U33'(z0, z1, z2))
U34'(mark(z0), z1, z2) → c177(U34'(z0, z1, z2))
U34'(z0, mark(z1), z2) → c178(U34'(z0, z1, z2))
U34'(z0, z1, mark(z2)) → c179(U34'(z0, z1, z2))
U34'(active(z0), z1, z2) → c180(U34'(z0, z1, z2))
U34'(z0, active(z1), z2) → c181(U34'(z0, z1, z2))
U34'(z0, z1, active(z2)) → c182(U34'(z0, z1, z2))
U35'(mark(z0), z1) → c183(U35'(z0, z1))
U35'(z0, mark(z1)) → c184(U35'(z0, z1))
U35'(active(z0), z1) → c185(U35'(z0, z1))
U35'(z0, active(z1)) → c186(U35'(z0, z1))
U36'(mark(z0)) → c187(U36'(z0))
U36'(active(z0)) → c188(U36'(z0))
U41'(mark(z0), z1) → c189(U41'(z0, z1))
U41'(z0, mark(z1)) → c190(U41'(z0, z1))
U41'(active(z0), z1) → c191(U41'(z0, z1))
U41'(z0, active(z1)) → c192(U41'(z0, z1))
U42'(mark(z0)) → c193(U42'(z0))
U42'(active(z0)) → c194(U42'(z0))
U51'(mark(z0)) → c195(U51'(z0))
U51'(active(z0)) → c196(U51'(z0))
U61'(mark(z0), z1) → c197(U61'(z0, z1))
U61'(z0, mark(z1)) → c198(U61'(z0, z1))
U61'(active(z0), z1) → c199(U61'(z0, z1))
U61'(z0, active(z1)) → c200(U61'(z0, z1))
U62'(mark(z0)) → c201(U62'(z0))
U62'(active(z0)) → c202(U62'(z0))
U71'(mark(z0), z1) → c203(U71'(z0, z1))
U71'(z0, mark(z1)) → c204(U71'(z0, z1))
U71'(active(z0), z1) → c205(U71'(z0, z1))
U71'(z0, active(z1)) → c206(U71'(z0, z1))
U72'(mark(z0), z1) → c207(U72'(z0, z1))
U72'(z0, mark(z1)) → c208(U72'(z0, z1))
U72'(active(z0), z1) → c209(U72'(z0, z1))
U72'(z0, active(z1)) → c210(U72'(z0, z1))
U81'(mark(z0), z1, z2) → c211(U81'(z0, z1, z2))
U81'(z0, mark(z1), z2) → c212(U81'(z0, z1, z2))
U81'(z0, z1, mark(z2)) → c213(U81'(z0, z1, z2))
U81'(active(z0), z1, z2) → c214(U81'(z0, z1, z2))
U81'(z0, active(z1), z2) → c215(U81'(z0, z1, z2))
U81'(z0, z1, active(z2)) → c216(U81'(z0, z1, z2))
U82'(mark(z0), z1, z2) → c217(U82'(z0, z1, z2))
U82'(z0, mark(z1), z2) → c218(U82'(z0, z1, z2))
U82'(z0, z1, mark(z2)) → c219(U82'(z0, z1, z2))
U82'(active(z0), z1, z2) → c220(U82'(z0, z1, z2))
U82'(z0, active(z1), z2) → c221(U82'(z0, z1, z2))
U82'(z0, z1, active(z2)) → c222(U82'(z0, z1, z2))
U83'(mark(z0), z1, z2) → c223(U83'(z0, z1, z2))
U83'(z0, mark(z1), z2) → c224(U83'(z0, z1, z2))
U83'(z0, z1, mark(z2)) → c225(U83'(z0, z1, z2))
U83'(active(z0), z1, z2) → c226(U83'(z0, z1, z2))
U83'(z0, active(z1), z2) → c227(U83'(z0, z1, z2))
U83'(z0, z1, active(z2)) → c228(U83'(z0, z1, z2))
U84'(mark(z0), z1, z2) → c229(U84'(z0, z1, z2))
U84'(z0, mark(z1), z2) → c230(U84'(z0, z1, z2))
U84'(z0, z1, mark(z2)) → c231(U84'(z0, z1, z2))
U84'(active(z0), z1, z2) → c232(U84'(z0, z1, z2))
U84'(z0, active(z1), z2) → c233(U84'(z0, z1, z2))
U84'(z0, z1, active(z2)) → c234(U84'(z0, z1, z2))
S(mark(z0)) → c235(S(z0))
S(active(z0)) → c236(S(z0))
U91'(mark(z0), z1) → c237(U91'(z0, z1))
U91'(z0, mark(z1)) → c238(U91'(z0, z1))
U91'(active(z0), z1) → c239(U91'(z0, z1))
U91'(z0, active(z1)) → c240(U91'(z0, z1))
U92'(mark(z0)) → c241(U92'(z0))
U92'(active(z0)) → c242(U92'(z0))

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U101(tt, z0, z1)) → mark(U102(isNatKind(z0), z0, z1))
active(U102(tt, z0, z1)) → mark(U103(isNat(z1), z0, z1))
active(U103(tt, z0, z1)) → mark(U104(isNatKind(z1), z0, z1))
active(U104(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(U11(tt, z0, z1)) → mark(U12(isNatKind(z0), z0, z1))
active(U12(tt, z0, z1)) → mark(U13(isNatKind(z1), z0, z1))
active(U13(tt, z0, z1)) → mark(U14(isNatKind(z1), z0, z1))
active(U14(tt, z0, z1)) → mark(U15(isNat(z0), z1))
active(U15(tt, z0)) → mark(U16(isNat(z0)))
active(U16(tt)) → mark(tt)
active(U21(tt, z0)) → mark(U22(isNatKind(z0), z0))
active(U22(tt, z0)) → mark(U23(isNat(z0)))
active(U23(tt)) → mark(tt)
active(U31(tt, z0, z1)) → mark(U32(isNatKind(z0), z0, z1))
active(U32(tt, z0, z1)) → mark(U33(isNatKind(z1), z0, z1))
active(U33(tt, z0, z1)) → mark(U34(isNatKind(z1), z0, z1))
active(U34(tt, z0, z1)) → mark(U35(isNat(z0), z1))
active(U35(tt, z0)) → mark(U36(isNat(z0)))
active(U36(tt)) → mark(tt)
active(U41(tt, z0)) → mark(U42(isNatKind(z0)))
active(U42(tt)) → mark(tt)
active(U51(tt)) → mark(tt)
active(U61(tt, z0)) → mark(U62(isNatKind(z0)))
active(U62(tt)) → mark(tt)
active(U71(tt, z0)) → mark(U72(isNatKind(z0), z0))
active(U72(tt, z0)) → mark(z0)
active(U81(tt, z0, z1)) → mark(U82(isNatKind(z0), z0, z1))
active(U82(tt, z0, z1)) → mark(U83(isNat(z1), z0, z1))
active(U83(tt, z0, z1)) → mark(U84(isNatKind(z1), z0, z1))
active(U84(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U91(tt, z0)) → mark(U92(isNatKind(z0)))
active(U92(tt)) → mark(0)
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNatKind(z0), z0, z1))
active(isNat(s(z0))) → mark(U21(isNatKind(z0), z0))
active(isNat(x(z0, z1))) → mark(U31(isNatKind(z0), z0, z1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(z0, z1))) → mark(U41(isNatKind(z0), z1))
active(isNatKind(s(z0))) → mark(U51(isNatKind(z0)))
active(isNatKind(x(z0, z1))) → mark(U61(isNatKind(z0), z1))
active(plus(z0, 0)) → mark(U71(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U81(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U91(isNat(z0), z0))
active(x(z0, s(z1))) → mark(U101(isNat(z1), z1, z0))
mark(U101(z0, z1, z2)) → active(U101(mark(z0), z1, z2))
mark(tt) → active(tt)
mark(U102(z0, z1, z2)) → active(U102(mark(z0), z1, z2))
mark(isNatKind(z0)) → active(isNatKind(z0))
mark(U103(z0, z1, z2)) → active(U103(mark(z0), z1, z2))
mark(isNat(z0)) → active(isNat(z0))
mark(U104(z0, z1, z2)) → active(U104(mark(z0), z1, z2))
mark(plus(z0, z1)) → active(plus(mark(z0), mark(z1)))
mark(x(z0, z1)) → active(x(mark(z0), mark(z1)))
mark(U11(z0, z1, z2)) → active(U11(mark(z0), z1, z2))
mark(U12(z0, z1, z2)) → active(U12(mark(z0), z1, z2))
mark(U13(z0, z1, z2)) → active(U13(mark(z0), z1, z2))
mark(U14(z0, z1, z2)) → active(U14(mark(z0), z1, z2))
mark(U15(z0, z1)) → active(U15(mark(z0), z1))
mark(U16(z0)) → active(U16(mark(z0)))
mark(U21(z0, z1)) → active(U21(mark(z0), z1))
mark(U22(z0, z1)) → active(U22(mark(z0), z1))
mark(U23(z0)) → active(U23(mark(z0)))
mark(U31(z0, z1, z2)) → active(U31(mark(z0), z1, z2))
mark(U32(z0, z1, z2)) → active(U32(mark(z0), z1, z2))
mark(U33(z0, z1, z2)) → active(U33(mark(z0), z1, z2))
mark(U34(z0, z1, z2)) → active(U34(mark(z0), z1, z2))
mark(U35(z0, z1)) → active(U35(mark(z0), z1))
mark(U36(z0)) → active(U36(mark(z0)))
mark(U41(z0, z1)) → active(U41(mark(z0), z1))
mark(U42(z0)) → active(U42(mark(z0)))
mark(U51(z0)) → active(U51(mark(z0)))
mark(U61(z0, z1)) → active(U61(mark(z0), z1))
mark(U62(z0)) → active(U62(mark(z0)))
mark(U71(z0, z1)) → active(U71(mark(z0), z1))
mark(U72(z0, z1)) → active(U72(mark(z0), z1))
mark(U81(z0, z1, z2)) → active(U81(mark(z0), z1, z2))
mark(U82(z0, z1, z2)) → active(U82(mark(z0), z1, z2))
mark(U83(z0, z1, z2)) → active(U83(mark(z0), z1, z2))
mark(U84(z0, z1, z2)) → active(U84(mark(z0), z1, z2))
mark(s(z0)) → active(s(mark(z0)))
mark(U91(z0, z1)) → active(U91(mark(z0), z1))
mark(U92(z0)) → active(U92(mark(z0)))
mark(0) → active(0)
U101(mark(z0), z1, z2) → U101(z0, z1, z2)
U101(z0, mark(z1), z2) → U101(z0, z1, z2)
U101(z0, z1, mark(z2)) → U101(z0, z1, z2)
U101(active(z0), z1, z2) → U101(z0, z1, z2)
U101(z0, active(z1), z2) → U101(z0, z1, z2)
U101(z0, z1, active(z2)) → U101(z0, z1, z2)
U102(mark(z0), z1, z2) → U102(z0, z1, z2)
U102(z0, mark(z1), z2) → U102(z0, z1, z2)
U102(z0, z1, mark(z2)) → U102(z0, z1, z2)
U102(active(z0), z1, z2) → U102(z0, z1, z2)
U102(z0, active(z1), z2) → U102(z0, z1, z2)
U102(z0, z1, active(z2)) → U102(z0, z1, z2)
isNatKind(mark(z0)) → isNatKind(z0)
isNatKind(active(z0)) → isNatKind(z0)
U103(mark(z0), z1, z2) → U103(z0, z1, z2)
U103(z0, mark(z1), z2) → U103(z0, z1, z2)
U103(z0, z1, mark(z2)) → U103(z0, z1, z2)
U103(active(z0), z1, z2) → U103(z0, z1, z2)
U103(z0, active(z1), z2) → U103(z0, z1, z2)
U103(z0, z1, active(z2)) → U103(z0, z1, z2)
isNat(mark(z0)) → isNat(z0)
isNat(active(z0)) → isNat(z0)
U104(mark(z0), z1, z2) → U104(z0, z1, z2)
U104(z0, mark(z1), z2) → U104(z0, z1, z2)
U104(z0, z1, mark(z2)) → U104(z0, z1, z2)
U104(active(z0), z1, z2) → U104(z0, z1, z2)
U104(z0, active(z1), z2) → U104(z0, z1, z2)
U104(z0, z1, active(z2)) → U104(z0, z1, z2)
plus(mark(z0), z1) → plus(z0, z1)
plus(z0, mark(z1)) → plus(z0, z1)
plus(active(z0), z1) → plus(z0, z1)
plus(z0, active(z1)) → plus(z0, z1)
x(mark(z0), z1) → x(z0, z1)
x(z0, mark(z1)) → x(z0, z1)
x(active(z0), z1) → x(z0, z1)
x(z0, active(z1)) → x(z0, z1)
U11(mark(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, mark(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, mark(z2)) → U11(z0, z1, z2)
U11(active(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, active(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, active(z2)) → U11(z0, z1, z2)
U12(mark(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, mark(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, mark(z2)) → U12(z0, z1, z2)
U12(active(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, active(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, active(z2)) → U12(z0, z1, z2)
U13(mark(z0), z1, z2) → U13(z0, z1, z2)
U13(z0, mark(z1), z2) → U13(z0, z1, z2)
U13(z0, z1, mark(z2)) → U13(z0, z1, z2)
U13(active(z0), z1, z2) → U13(z0, z1, z2)
U13(z0, active(z1), z2) → U13(z0, z1, z2)
U13(z0, z1, active(z2)) → U13(z0, z1, z2)
U14(mark(z0), z1, z2) → U14(z0, z1, z2)
U14(z0, mark(z1), z2) → U14(z0, z1, z2)
U14(z0, z1, mark(z2)) → U14(z0, z1, z2)
U14(active(z0), z1, z2) → U14(z0, z1, z2)
U14(z0, active(z1), z2) → U14(z0, z1, z2)
U14(z0, z1, active(z2)) → U14(z0, z1, z2)
U15(mark(z0), z1) → U15(z0, z1)
U15(z0, mark(z1)) → U15(z0, z1)
U15(active(z0), z1) → U15(z0, z1)
U15(z0, active(z1)) → U15(z0, z1)
U16(mark(z0)) → U16(z0)
U16(active(z0)) → U16(z0)
U21(mark(z0), z1) → U21(z0, z1)
U21(z0, mark(z1)) → U21(z0, z1)
U21(active(z0), z1) → U21(z0, z1)
U21(z0, active(z1)) → U21(z0, z1)
U22(mark(z0), z1) → U22(z0, z1)
U22(z0, mark(z1)) → U22(z0, z1)
U22(active(z0), z1) → U22(z0, z1)
U22(z0, active(z1)) → U22(z0, z1)
U23(mark(z0)) → U23(z0)
U23(active(z0)) → U23(z0)
U31(mark(z0), z1, z2) → U31(z0, z1, z2)
U31(z0, mark(z1), z2) → U31(z0, z1, z2)
U31(z0, z1, mark(z2)) → U31(z0, z1, z2)
U31(active(z0), z1, z2) → U31(z0, z1, z2)
U31(z0, active(z1), z2) → U31(z0, z1, z2)
U31(z0, z1, active(z2)) → U31(z0, z1, z2)
U32(mark(z0), z1, z2) → U32(z0, z1, z2)
U32(z0, mark(z1), z2) → U32(z0, z1, z2)
U32(z0, z1, mark(z2)) → U32(z0, z1, z2)
U32(active(z0), z1, z2) → U32(z0, z1, z2)
U32(z0, active(z1), z2) → U32(z0, z1, z2)
U32(z0, z1, active(z2)) → U32(z0, z1, z2)
U33(mark(z0), z1, z2) → U33(z0, z1, z2)
U33(z0, mark(z1), z2) → U33(z0, z1, z2)
U33(z0, z1, mark(z2)) → U33(z0, z1, z2)
U33(active(z0), z1, z2) → U33(z0, z1, z2)
U33(z0, active(z1), z2) → U33(z0, z1, z2)
U33(z0, z1, active(z2)) → U33(z0, z1, z2)
U34(mark(z0), z1, z2) → U34(z0, z1, z2)
U34(z0, mark(z1), z2) → U34(z0, z1, z2)
U34(z0, z1, mark(z2)) → U34(z0, z1, z2)
U34(active(z0), z1, z2) → U34(z0, z1, z2)
U34(z0, active(z1), z2) → U34(z0, z1, z2)
U34(z0, z1, active(z2)) → U34(z0, z1, z2)
U35(mark(z0), z1) → U35(z0, z1)
U35(z0, mark(z1)) → U35(z0, z1)
U35(active(z0), z1) → U35(z0, z1)
U35(z0, active(z1)) → U35(z0, z1)
U36(mark(z0)) → U36(z0)
U36(active(z0)) → U36(z0)
U41(mark(z0), z1) → U41(z0, z1)
U41(z0, mark(z1)) → U41(z0, z1)
U41(active(z0), z1) → U41(z0, z1)
U41(z0, active(z1)) → U41(z0, z1)
U42(mark(z0)) → U42(z0)
U42(active(z0)) → U42(z0)
U51(mark(z0)) → U51(z0)
U51(active(z0)) → U51(z0)
U61(mark(z0), z1) → U61(z0, z1)
U61(z0, mark(z1)) → U61(z0, z1)
U61(active(z0), z1) → U61(z0, z1)
U61(z0, active(z1)) → U61(z0, z1)
U62(mark(z0)) → U62(z0)
U62(active(z0)) → U62(z0)
U71(mark(z0), z1) → U71(z0, z1)
U71(z0, mark(z1)) → U71(z0, z1)
U71(active(z0), z1) → U71(z0, z1)
U71(z0, active(z1)) → U71(z0, z1)
U72(mark(z0), z1) → U72(z0, z1)
U72(z0, mark(z1)) → U72(z0, z1)
U72(active(z0), z1) → U72(z0, z1)
U72(z0, active(z1)) → U72(z0, z1)
U81(mark(z0), z1, z2) → U81(z0, z1, z2)
U81(z0, mark(z1), z2) → U81(z0, z1, z2)
U81(z0, z1, mark(z2)) → U81(z0, z1, z2)
U81(active(z0), z1, z2) → U81(z0, z1, z2)
U81(z0, active(z1), z2) → U81(z0, z1, z2)
U81(z0, z1, active(z2)) → U81(z0, z1, z2)
U82(mark(z0), z1, z2) → U82(z0, z1, z2)
U82(z0, mark(z1), z2) → U82(z0, z1, z2)
U82(z0, z1, mark(z2)) → U82(z0, z1, z2)
U82(active(z0), z1, z2) → U82(z0, z1, z2)
U82(z0, active(z1), z2) → U82(z0, z1, z2)
U82(z0, z1, active(z2)) → U82(z0, z1, z2)
U83(mark(z0), z1, z2) → U83(z0, z1, z2)
U83(z0, mark(z1), z2) → U83(z0, z1, z2)
U83(z0, z1, mark(z2)) → U83(z0, z1, z2)
U83(active(z0), z1, z2) → U83(z0, z1, z2)
U83(z0, active(z1), z2) → U83(z0, z1, z2)
U83(z0, z1, active(z2)) → U83(z0, z1, z2)
U84(mark(z0), z1, z2) → U84(z0, z1, z2)
U84(z0, mark(z1), z2) → U84(z0, z1, z2)
U84(z0, z1, mark(z2)) → U84(z0, z1, z2)
U84(active(z0), z1, z2) → U84(z0, z1, z2)
U84(z0, active(z1), z2) → U84(z0, z1, z2)
U84(z0, z1, active(z2)) → U84(z0, z1, z2)
s(mark(z0)) → s(z0)
s(active(z0)) → s(z0)
U91(mark(z0), z1) → U91(z0, z1)
U91(z0, mark(z1)) → U91(z0, z1)
U91(active(z0), z1) → U91(z0, z1)
U91(z0, active(z1)) → U91(z0, z1)
U92(mark(z0)) → U92(z0)
U92(active(z0)) → U92(z0)

Tuples:

MARK(tt) → c45(ACTIVE(tt))
MARK(0) → c82(ACTIVE(0))

S tuples:

MARK(tt) → c45(ACTIVE(tt))
MARK(0) → c82(ACTIVE(0))

K tuples:none
Defined Rule Symbols:

active, mark, U101, U102, isNatKind, U103, isNat, U104, plus, x, U11, U12, U13, U14, U15, U16, U21, U22, U23, U31, U32, U33, U34, U35, U36, U41, U42, U51, U61, U62, U71, U72, U81, U82, U83, U84, s, U91, U92

Defined Pair Symbols:

MARK

Compound Symbols:

c45, c82

(5) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing nodes:

MARK(tt) → c45(ACTIVE(tt))
MARK(0) → c82(ACTIVE(0))

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U101(tt, z0, z1)) → mark(U102(isNatKind(z0), z0, z1))
active(U102(tt, z0, z1)) → mark(U103(isNat(z1), z0, z1))
active(U103(tt, z0, z1)) → mark(U104(isNatKind(z1), z0, z1))
active(U104(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(U11(tt, z0, z1)) → mark(U12(isNatKind(z0), z0, z1))
active(U12(tt, z0, z1)) → mark(U13(isNatKind(z1), z0, z1))
active(U13(tt, z0, z1)) → mark(U14(isNatKind(z1), z0, z1))
active(U14(tt, z0, z1)) → mark(U15(isNat(z0), z1))
active(U15(tt, z0)) → mark(U16(isNat(z0)))
active(U16(tt)) → mark(tt)
active(U21(tt, z0)) → mark(U22(isNatKind(z0), z0))
active(U22(tt, z0)) → mark(U23(isNat(z0)))
active(U23(tt)) → mark(tt)
active(U31(tt, z0, z1)) → mark(U32(isNatKind(z0), z0, z1))
active(U32(tt, z0, z1)) → mark(U33(isNatKind(z1), z0, z1))
active(U33(tt, z0, z1)) → mark(U34(isNatKind(z1), z0, z1))
active(U34(tt, z0, z1)) → mark(U35(isNat(z0), z1))
active(U35(tt, z0)) → mark(U36(isNat(z0)))
active(U36(tt)) → mark(tt)
active(U41(tt, z0)) → mark(U42(isNatKind(z0)))
active(U42(tt)) → mark(tt)
active(U51(tt)) → mark(tt)
active(U61(tt, z0)) → mark(U62(isNatKind(z0)))
active(U62(tt)) → mark(tt)
active(U71(tt, z0)) → mark(U72(isNatKind(z0), z0))
active(U72(tt, z0)) → mark(z0)
active(U81(tt, z0, z1)) → mark(U82(isNatKind(z0), z0, z1))
active(U82(tt, z0, z1)) → mark(U83(isNat(z1), z0, z1))
active(U83(tt, z0, z1)) → mark(U84(isNatKind(z1), z0, z1))
active(U84(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U91(tt, z0)) → mark(U92(isNatKind(z0)))
active(U92(tt)) → mark(0)
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNatKind(z0), z0, z1))
active(isNat(s(z0))) → mark(U21(isNatKind(z0), z0))
active(isNat(x(z0, z1))) → mark(U31(isNatKind(z0), z0, z1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(z0, z1))) → mark(U41(isNatKind(z0), z1))
active(isNatKind(s(z0))) → mark(U51(isNatKind(z0)))
active(isNatKind(x(z0, z1))) → mark(U61(isNatKind(z0), z1))
active(plus(z0, 0)) → mark(U71(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U81(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U91(isNat(z0), z0))
active(x(z0, s(z1))) → mark(U101(isNat(z1), z1, z0))
mark(U101(z0, z1, z2)) → active(U101(mark(z0), z1, z2))
mark(tt) → active(tt)
mark(U102(z0, z1, z2)) → active(U102(mark(z0), z1, z2))
mark(isNatKind(z0)) → active(isNatKind(z0))
mark(U103(z0, z1, z2)) → active(U103(mark(z0), z1, z2))
mark(isNat(z0)) → active(isNat(z0))
mark(U104(z0, z1, z2)) → active(U104(mark(z0), z1, z2))
mark(plus(z0, z1)) → active(plus(mark(z0), mark(z1)))
mark(x(z0, z1)) → active(x(mark(z0), mark(z1)))
mark(U11(z0, z1, z2)) → active(U11(mark(z0), z1, z2))
mark(U12(z0, z1, z2)) → active(U12(mark(z0), z1, z2))
mark(U13(z0, z1, z2)) → active(U13(mark(z0), z1, z2))
mark(U14(z0, z1, z2)) → active(U14(mark(z0), z1, z2))
mark(U15(z0, z1)) → active(U15(mark(z0), z1))
mark(U16(z0)) → active(U16(mark(z0)))
mark(U21(z0, z1)) → active(U21(mark(z0), z1))
mark(U22(z0, z1)) → active(U22(mark(z0), z1))
mark(U23(z0)) → active(U23(mark(z0)))
mark(U31(z0, z1, z2)) → active(U31(mark(z0), z1, z2))
mark(U32(z0, z1, z2)) → active(U32(mark(z0), z1, z2))
mark(U33(z0, z1, z2)) → active(U33(mark(z0), z1, z2))
mark(U34(z0, z1, z2)) → active(U34(mark(z0), z1, z2))
mark(U35(z0, z1)) → active(U35(mark(z0), z1))
mark(U36(z0)) → active(U36(mark(z0)))
mark(U41(z0, z1)) → active(U41(mark(z0), z1))
mark(U42(z0)) → active(U42(mark(z0)))
mark(U51(z0)) → active(U51(mark(z0)))
mark(U61(z0, z1)) → active(U61(mark(z0), z1))
mark(U62(z0)) → active(U62(mark(z0)))
mark(U71(z0, z1)) → active(U71(mark(z0), z1))
mark(U72(z0, z1)) → active(U72(mark(z0), z1))
mark(U81(z0, z1, z2)) → active(U81(mark(z0), z1, z2))
mark(U82(z0, z1, z2)) → active(U82(mark(z0), z1, z2))
mark(U83(z0, z1, z2)) → active(U83(mark(z0), z1, z2))
mark(U84(z0, z1, z2)) → active(U84(mark(z0), z1, z2))
mark(s(z0)) → active(s(mark(z0)))
mark(U91(z0, z1)) → active(U91(mark(z0), z1))
mark(U92(z0)) → active(U92(mark(z0)))
mark(0) → active(0)
U101(mark(z0), z1, z2) → U101(z0, z1, z2)
U101(z0, mark(z1), z2) → U101(z0, z1, z2)
U101(z0, z1, mark(z2)) → U101(z0, z1, z2)
U101(active(z0), z1, z2) → U101(z0, z1, z2)
U101(z0, active(z1), z2) → U101(z0, z1, z2)
U101(z0, z1, active(z2)) → U101(z0, z1, z2)
U102(mark(z0), z1, z2) → U102(z0, z1, z2)
U102(z0, mark(z1), z2) → U102(z0, z1, z2)
U102(z0, z1, mark(z2)) → U102(z0, z1, z2)
U102(active(z0), z1, z2) → U102(z0, z1, z2)
U102(z0, active(z1), z2) → U102(z0, z1, z2)
U102(z0, z1, active(z2)) → U102(z0, z1, z2)
isNatKind(mark(z0)) → isNatKind(z0)
isNatKind(active(z0)) → isNatKind(z0)
U103(mark(z0), z1, z2) → U103(z0, z1, z2)
U103(z0, mark(z1), z2) → U103(z0, z1, z2)
U103(z0, z1, mark(z2)) → U103(z0, z1, z2)
U103(active(z0), z1, z2) → U103(z0, z1, z2)
U103(z0, active(z1), z2) → U103(z0, z1, z2)
U103(z0, z1, active(z2)) → U103(z0, z1, z2)
isNat(mark(z0)) → isNat(z0)
isNat(active(z0)) → isNat(z0)
U104(mark(z0), z1, z2) → U104(z0, z1, z2)
U104(z0, mark(z1), z2) → U104(z0, z1, z2)
U104(z0, z1, mark(z2)) → U104(z0, z1, z2)
U104(active(z0), z1, z2) → U104(z0, z1, z2)
U104(z0, active(z1), z2) → U104(z0, z1, z2)
U104(z0, z1, active(z2)) → U104(z0, z1, z2)
plus(mark(z0), z1) → plus(z0, z1)
plus(z0, mark(z1)) → plus(z0, z1)
plus(active(z0), z1) → plus(z0, z1)
plus(z0, active(z1)) → plus(z0, z1)
x(mark(z0), z1) → x(z0, z1)
x(z0, mark(z1)) → x(z0, z1)
x(active(z0), z1) → x(z0, z1)
x(z0, active(z1)) → x(z0, z1)
U11(mark(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, mark(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, mark(z2)) → U11(z0, z1, z2)
U11(active(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, active(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, active(z2)) → U11(z0, z1, z2)
U12(mark(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, mark(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, mark(z2)) → U12(z0, z1, z2)
U12(active(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, active(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, active(z2)) → U12(z0, z1, z2)
U13(mark(z0), z1, z2) → U13(z0, z1, z2)
U13(z0, mark(z1), z2) → U13(z0, z1, z2)
U13(z0, z1, mark(z2)) → U13(z0, z1, z2)
U13(active(z0), z1, z2) → U13(z0, z1, z2)
U13(z0, active(z1), z2) → U13(z0, z1, z2)
U13(z0, z1, active(z2)) → U13(z0, z1, z2)
U14(mark(z0), z1, z2) → U14(z0, z1, z2)
U14(z0, mark(z1), z2) → U14(z0, z1, z2)
U14(z0, z1, mark(z2)) → U14(z0, z1, z2)
U14(active(z0), z1, z2) → U14(z0, z1, z2)
U14(z0, active(z1), z2) → U14(z0, z1, z2)
U14(z0, z1, active(z2)) → U14(z0, z1, z2)
U15(mark(z0), z1) → U15(z0, z1)
U15(z0, mark(z1)) → U15(z0, z1)
U15(active(z0), z1) → U15(z0, z1)
U15(z0, active(z1)) → U15(z0, z1)
U16(mark(z0)) → U16(z0)
U16(active(z0)) → U16(z0)
U21(mark(z0), z1) → U21(z0, z1)
U21(z0, mark(z1)) → U21(z0, z1)
U21(active(z0), z1) → U21(z0, z1)
U21(z0, active(z1)) → U21(z0, z1)
U22(mark(z0), z1) → U22(z0, z1)
U22(z0, mark(z1)) → U22(z0, z1)
U22(active(z0), z1) → U22(z0, z1)
U22(z0, active(z1)) → U22(z0, z1)
U23(mark(z0)) → U23(z0)
U23(active(z0)) → U23(z0)
U31(mark(z0), z1, z2) → U31(z0, z1, z2)
U31(z0, mark(z1), z2) → U31(z0, z1, z2)
U31(z0, z1, mark(z2)) → U31(z0, z1, z2)
U31(active(z0), z1, z2) → U31(z0, z1, z2)
U31(z0, active(z1), z2) → U31(z0, z1, z2)
U31(z0, z1, active(z2)) → U31(z0, z1, z2)
U32(mark(z0), z1, z2) → U32(z0, z1, z2)
U32(z0, mark(z1), z2) → U32(z0, z1, z2)
U32(z0, z1, mark(z2)) → U32(z0, z1, z2)
U32(active(z0), z1, z2) → U32(z0, z1, z2)
U32(z0, active(z1), z2) → U32(z0, z1, z2)
U32(z0, z1, active(z2)) → U32(z0, z1, z2)
U33(mark(z0), z1, z2) → U33(z0, z1, z2)
U33(z0, mark(z1), z2) → U33(z0, z1, z2)
U33(z0, z1, mark(z2)) → U33(z0, z1, z2)
U33(active(z0), z1, z2) → U33(z0, z1, z2)
U33(z0, active(z1), z2) → U33(z0, z1, z2)
U33(z0, z1, active(z2)) → U33(z0, z1, z2)
U34(mark(z0), z1, z2) → U34(z0, z1, z2)
U34(z0, mark(z1), z2) → U34(z0, z1, z2)
U34(z0, z1, mark(z2)) → U34(z0, z1, z2)
U34(active(z0), z1, z2) → U34(z0, z1, z2)
U34(z0, active(z1), z2) → U34(z0, z1, z2)
U34(z0, z1, active(z2)) → U34(z0, z1, z2)
U35(mark(z0), z1) → U35(z0, z1)
U35(z0, mark(z1)) → U35(z0, z1)
U35(active(z0), z1) → U35(z0, z1)
U35(z0, active(z1)) → U35(z0, z1)
U36(mark(z0)) → U36(z0)
U36(active(z0)) → U36(z0)
U41(mark(z0), z1) → U41(z0, z1)
U41(z0, mark(z1)) → U41(z0, z1)
U41(active(z0), z1) → U41(z0, z1)
U41(z0, active(z1)) → U41(z0, z1)
U42(mark(z0)) → U42(z0)
U42(active(z0)) → U42(z0)
U51(mark(z0)) → U51(z0)
U51(active(z0)) → U51(z0)
U61(mark(z0), z1) → U61(z0, z1)
U61(z0, mark(z1)) → U61(z0, z1)
U61(active(z0), z1) → U61(z0, z1)
U61(z0, active(z1)) → U61(z0, z1)
U62(mark(z0)) → U62(z0)
U62(active(z0)) → U62(z0)
U71(mark(z0), z1) → U71(z0, z1)
U71(z0, mark(z1)) → U71(z0, z1)
U71(active(z0), z1) → U71(z0, z1)
U71(z0, active(z1)) → U71(z0, z1)
U72(mark(z0), z1) → U72(z0, z1)
U72(z0, mark(z1)) → U72(z0, z1)
U72(active(z0), z1) → U72(z0, z1)
U72(z0, active(z1)) → U72(z0, z1)
U81(mark(z0), z1, z2) → U81(z0, z1, z2)
U81(z0, mark(z1), z2) → U81(z0, z1, z2)
U81(z0, z1, mark(z2)) → U81(z0, z1, z2)
U81(active(z0), z1, z2) → U81(z0, z1, z2)
U81(z0, active(z1), z2) → U81(z0, z1, z2)
U81(z0, z1, active(z2)) → U81(z0, z1, z2)
U82(mark(z0), z1, z2) → U82(z0, z1, z2)
U82(z0, mark(z1), z2) → U82(z0, z1, z2)
U82(z0, z1, mark(z2)) → U82(z0, z1, z2)
U82(active(z0), z1, z2) → U82(z0, z1, z2)
U82(z0, active(z1), z2) → U82(z0, z1, z2)
U82(z0, z1, active(z2)) → U82(z0, z1, z2)
U83(mark(z0), z1, z2) → U83(z0, z1, z2)
U83(z0, mark(z1), z2) → U83(z0, z1, z2)
U83(z0, z1, mark(z2)) → U83(z0, z1, z2)
U83(active(z0), z1, z2) → U83(z0, z1, z2)
U83(z0, active(z1), z2) → U83(z0, z1, z2)
U83(z0, z1, active(z2)) → U83(z0, z1, z2)
U84(mark(z0), z1, z2) → U84(z0, z1, z2)
U84(z0, mark(z1), z2) → U84(z0, z1, z2)
U84(z0, z1, mark(z2)) → U84(z0, z1, z2)
U84(active(z0), z1, z2) → U84(z0, z1, z2)
U84(z0, active(z1), z2) → U84(z0, z1, z2)
U84(z0, z1, active(z2)) → U84(z0, z1, z2)
s(mark(z0)) → s(z0)
s(active(z0)) → s(z0)
U91(mark(z0), z1) → U91(z0, z1)
U91(z0, mark(z1)) → U91(z0, z1)
U91(active(z0), z1) → U91(z0, z1)
U91(z0, active(z1)) → U91(z0, z1)
U92(mark(z0)) → U92(z0)
U92(active(z0)) → U92(z0)

Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:

active, mark, U101, U102, isNatKind, U103, isNat, U104, plus, x, U11, U12, U13, U14, U15, U16, U21, U22, U23, U31, U32, U33, U34, U35, U36, U41, U42, U51, U61, U62, U71, U72, U81, U82, U83, U84, s, U91, U92

Defined Pair Symbols:none

Compound Symbols:none

(7) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

(8) BOUNDS(O(1), O(1))