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)

↳ QTRS

  ↳ DependencyPairsProof

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)

U32¹(X1, X2, active(X3)) → U32¹(X1, X2, X3)
U11¹(mark(X1), X2, X3) → U11¹(X1, X2, X3)
U91¹(mark(X1), X2) → U91¹(X1, X2)
U16¹(active(X)) → U16¹(X)
U71¹(mark(X1), X2) → U71¹(X1, X2)
U81¹(X1, X2, active(X3)) → U81¹(X1, X2, X3)
ACTIVE(U62(tt)) → MARK(tt)
U12¹(X1, mark(X2), X3) → U12¹(X1, X2, X3)
U41¹(X1, mark(X2)) → U41¹(X1, X2)
ACTIVE(U41(tt, V2)) → ISNATKIND(V2)
U34¹(X1, X2, active(X3)) → U34¹(X1, X2, X3)
ACTIVE(U104(tt, M, N)) → X(N, M)
U104¹(X1, active(X2), X3) → U104¹(X1, X2, X3)
U33¹(mark(X1), X2, X3) → U33¹(X1, X2, X3)
ACTIVE(U12(tt, V1, V2)) → MARK(U13(isNatKind(V2), V1, V2))
ACTIVE(U23(tt)) → MARK(tt)
ACTIVE(plus(N, s(M))) → ISNAT(M)
U81¹(mark(X1), X2, X3) → U81¹(X1, X2, X3)
ACTIVE(U91(tt, N)) → U92¹(isNatKind(N))
U14¹(X1, active(X2), X3) → U14¹(X1, X2, X3)
MARK(U15(X1, X2)) → U15¹(mark(X1), X2)
ACTIVE(U32(tt, V1, V2)) → MARK(U33(isNatKind(V2), V1, V2))
U82¹(X1, active(X2), X3) → U82¹(X1, X2, X3)
ACTIVE(U22(tt, V1)) → ISNAT(V1)
MARK(U31(X1, X2, X3)) → MARK(X1)
U15¹(mark(X1), X2) → U15¹(X1, X2)
U82¹(mark(X1), X2, X3) → U82¹(X1, X2, X3)
ACTIVE(U83(tt, M, N)) → ISNATKIND(N)
U84¹(X1, mark(X2), X3) → U84¹(X1, X2, X3)
U91¹(X1, active(X2)) → U91¹(X1, X2)
X(active(X1), X2) → X(X1, X2)
MARK(U13(X1, X2, X3)) → U13¹(mark(X1), X2, X3)
ACTIVE(U12(tt, V1, V2)) → U13¹(isNatKind(V2), V1, V2)
U82¹(active(X1), X2, X3) → U82¹(X1, X2, X3)
ACTIVE(U83(tt, M, N)) → U84¹(isNatKind(N), M, N)
MARK(U42(X)) → U42¹(mark(X))
MARK(U33(X1, X2, X3)) → ACTIVE(U33(mark(X1), X2, X3))
MARK(U41(X1, X2)) → MARK(X1)
U104¹(active(X1), X2, X3) → U104¹(X1, X2, X3)
U83¹(X1, X2, mark(X3)) → U83¹(X1, X2, X3)
ACTIVE(isNatKind(x(V1, V2))) → ISNATKIND(V1)
ACTIVE(U61(tt, V2)) → U62¹(isNatKind(V2))
MARK(U12(X1, X2, X3)) → MARK(X1)
ACTIVE(U32(tt, V1, V2)) → U33¹(isNatKind(V2), V1, V2)
MARK(U62(X)) → ACTIVE(U62(mark(X)))
ACTIVE(isNat(x(V1, V2))) → MARK(U31(isNatKind(V1), V1, V2))
U12¹(X1, X2, active(X3)) → U12¹(X1, X2, X3)
U101¹(active(X1), X2, X3) → U101¹(X1, X2, X3)
ACTIVE(plus(N, 0)) → ISNAT(N)
PLUS(mark(X1), X2) → PLUS(X1, X2)
MARK(U13(X1, X2, X3)) → ACTIVE(U13(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U81(isNat(M), M, N))
U102¹(X1, X2, mark(X3)) → U102¹(X1, X2, X3)
MARK(U61(X1, X2)) → ACTIVE(U61(mark(X1), X2))
ACTIVE(U82(tt, M, N)) → MARK(U83(isNat(N), M, N))
MARK(U34(X1, X2, X3)) → U34¹(mark(X1), X2, X3)
ACTIVE(U41(tt, V2)) → U42¹(isNatKind(V2))
MARK(s(X)) → ACTIVE(s(mark(X)))
ACTIVE(U31(tt, V1, V2)) → U32¹(isNatKind(V1), V1, V2)
MARK(U103(X1, X2, X3)) → MARK(X1)
ACTIVE(U92(tt)) → MARK(0)
U21¹(X1, mark(X2)) → U21¹(X1, X2)
MARK(U32(X1, X2, X3)) → ACTIVE(U32(mark(X1), X2, X3))
ACTIVE(U102(tt, M, N)) → MARK(U103(isNat(N), M, N))
ACTIVE(U35(tt, V2)) → MARK(U36(isNat(V2)))
U61¹(X1, active(X2)) → U61¹(X1, X2)
U31¹(active(X1), X2, X3) → U31¹(X1, X2, X3)
ACTIVE(U33(tt, V1, V2)) → MARK(U34(isNatKind(V2), V1, V2))
PLUS(X1, active(X2)) → PLUS(X1, X2)
S(mark(X)) → S(X)
ACTIVE(U101(tt, M, N)) → U102¹(isNatKind(M), M, N)
U15¹(active(X1), X2) → U15¹(X1, X2)
ACTIVE(U91(tt, N)) → MARK(U92(isNatKind(N)))
ACTIVE(U51(tt)) → MARK(tt)
MARK(U71(X1, X2)) → MARK(X1)
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
ACTIVE(U104(tt, M, N)) → MARK(plus(x(N, M), N))
MARK(U61(X1, X2)) → U61¹(mark(X1), X2)
U83¹(X1, X2, active(X3)) → U83¹(X1, X2, X3)
MARK(U81(X1, X2, X3)) → U81¹(mark(X1), X2, X3)
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
U15¹(X1, active(X2)) → U15¹(X1, X2)
MARK(U83(X1, X2, X3)) → U83¹(mark(X1), X2, X3)
U31¹(X1, X2, mark(X3)) → U31¹(X1, X2, X3)
U12¹(X1, X2, mark(X3)) → U12¹(X1, X2, X3)
ACTIVE(U36(tt)) → MARK(tt)
U33¹(X1, mark(X2), X3) → U33¹(X1, X2, X3)
U42¹(active(X)) → U42¹(X)
U23¹(mark(X)) → U23¹(X)
U22¹(X1, active(X2)) → U22¹(X1, X2)
MARK(isNat(X)) → ACTIVE(isNat(X))
MARK(U11(X1, X2, X3)) → U11¹(mark(X1), X2, X3)
U32¹(X1, mark(X2), X3) → U32¹(X1, X2, X3)
MARK(U42(X)) → ACTIVE(U42(mark(X)))
MARK(U41(X1, X2)) → ACTIVE(U41(mark(X1), X2))
U35¹(X1, mark(X2)) → U35¹(X1, X2)
U15¹(X1, mark(X2)) → U15¹(X1, X2)
U41¹(mark(X1), X2) → U41¹(X1, X2)
U33¹(X1, X2, active(X3)) → U33¹(X1, X2, X3)
ACTIVE(U101(tt, M, N)) → ISNATKIND(M)
U83¹(active(X1), X2, X3) → U83¹(X1, X2, X3)
MARK(U62(X)) → U62¹(mark(X))
ACTIVE(U14(tt, V1, V2)) → MARK(U15(isNat(V1), V2))
MARK(U84(X1, X2, X3)) → MARK(X1)
U61¹(X1, mark(X2)) → U61¹(X1, X2)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
MARK(U103(X1, X2, X3)) → ACTIVE(U103(mark(X1), X2, X3))
MARK(U92(X)) → ACTIVE(U92(mark(X)))
U16¹(mark(X)) → U16¹(X)
ACTIVE(isNatKind(plus(V1, V2))) → U41¹(isNatKind(V1), V2)
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U41(isNatKind(V1), V2))
U13¹(X1, X2, active(X3)) → U13¹(X1, X2, X3)
U31¹(X1, active(X2), X3) → U31¹(X1, X2, X3)
ACTIVE(U82(tt, M, N)) → U83¹(isNat(N), M, N)
S(active(X)) → S(X)
MARK(U11(X1, X2, X3)) → MARK(X1)
MARK(U51(X)) → MARK(X)
MARK(x(X1, X2)) → X(mark(X1), mark(X2))
U11¹(active(X1), X2, X3) → U11¹(X1, X2, X3)
U91¹(X1, mark(X2)) → U91¹(X1, X2)
MARK(U13(X1, X2, X3)) → MARK(X1)
ACTIVE(U102(tt, M, N)) → ISNAT(N)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U72(X1, X2)) → U72¹(mark(X1), X2)
U12¹(active(X1), X2, X3) → U12¹(X1, X2, X3)
MARK(U35(X1, X2)) → ACTIVE(U35(mark(X1), X2))
ACTIVE(U72(tt, N)) → MARK(N)
ACTIVE(isNatKind(s(V1))) → MARK(U51(isNatKind(V1)))
U35¹(X1, active(X2)) → U35¹(X1, X2)
ACTIVE(U14(tt, V1, V2)) → ISNAT(V1)
MARK(U15(X1, X2)) → MARK(X1)
ACTIVE(U33(tt, V1, V2)) → ISNATKIND(V2)
U83¹(X1, active(X2), X3) → U83¹(X1, X2, X3)
U33¹(active(X1), X2, X3) → U33¹(X1, X2, X3)
MARK(U11(X1, X2, X3)) → ACTIVE(U11(mark(X1), X2, X3))
MARK(U62(X)) → MARK(X)
U11¹(X1, active(X2), X3) → U11¹(X1, X2, X3)
MARK(U23(X)) → ACTIVE(U23(mark(X)))
PLUS(active(X1), X2) → PLUS(X1, X2)
U101¹(X1, X2, active(X3)) → U101¹(X1, X2, X3)
U101¹(X1, mark(X2), X3) → U101¹(X1, X2, X3)
ACTIVE(U11(tt, V1, V2)) → ISNATKIND(V1)
U81¹(X1, mark(X2), X3) → U81¹(X1, X2, X3)
MARK(U72(X1, X2)) → MARK(X1)
ACTIVE(x(N, 0)) → MARK(U91(isNat(N), N))
U84¹(X1, X2, mark(X3)) → U84¹(X1, X2, X3)
ACTIVE(U35(tt, V2)) → ISNAT(V2)
U11¹(X1, X2, active(X3)) → U11¹(X1, X2, X3)
U61¹(mark(X1), X2) → U61¹(X1, X2)
U32¹(mark(X1), X2, X3) → U32¹(X1, X2, X3)
MARK(U81(X1, X2, X3)) → ACTIVE(U81(mark(X1), X2, X3))
ACTIVE(U33(tt, V1, V2)) → U34¹(isNatKind(V2), V1, V2)
ACTIVE(U22(tt, V1)) → U23¹(isNat(V1))
U102¹(X1, X2, active(X3)) → U102¹(X1, X2, X3)
MARK(U91(X1, X2)) → ACTIVE(U91(mark(X1), X2))
MARK(U35(X1, X2)) → U35¹(mark(X1), X2)
U103¹(X1, X2, active(X3)) → U103¹(X1, X2, X3)
U35¹(active(X1), X2) → U35¹(X1, X2)
ACTIVE(isNatKind(s(V1))) → U51¹(isNatKind(V1))
U81¹(X1, X2, mark(X3)) → U81¹(X1, X2, X3)
U11¹(X1, X2, mark(X3)) → U11¹(X1, X2, X3)
U33¹(X1, X2, mark(X3)) → U33¹(X1, X2, X3)
X(X1, active(X2)) → X(X1, X2)
U101¹(X1, X2, mark(X3)) → U101¹(X1, X2, X3)
ISNAT(active(X)) → ISNAT(X)
ACTIVE(U103(tt, M, N)) → MARK(U104(isNatKind(N), M, N))
MARK(U101(X1, X2, X3)) → MARK(X1)
MARK(U34(X1, X2, X3)) → ACTIVE(U34(mark(X1), X2, X3))
ACTIVE(isNat(s(V1))) → U21¹(isNatKind(V1), V1)
ACTIVE(U84(tt, M, N)) → S(plus(N, M))
U13¹(X1, mark(X2), X3) → U13¹(X1, X2, X3)
ACTIVE(U15(tt, V2)) → U16¹(isNat(V2))
U42¹(mark(X)) → U42¹(X)
MARK(U23(X)) → MARK(X)
U91¹(active(X1), X2) → U91¹(X1, X2)
U31¹(mark(X1), X2, X3) → U31¹(X1, X2, X3)
U101¹(mark(X1), X2, X3) → U101¹(X1, X2, X3)
U72¹(X1, active(X2)) → U72¹(X1, X2)
MARK(U84(X1, X2, X3)) → ACTIVE(U84(mark(X1), X2, X3))
MARK(U83(X1, X2, X3)) → ACTIVE(U83(mark(X1), X2, X3))
U13¹(active(X1), X2, X3) → U13¹(X1, X2, X3)
MARK(U34(X1, X2, X3)) → MARK(X1)
ACTIVE(U61(tt, V2)) → MARK(U62(isNatKind(V2)))
ACTIVE(U11(tt, V1, V2)) → U12¹(isNatKind(V1), V1, V2)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
U84¹(active(X1), X2, X3) → U84¹(X1, X2, X3)
U31¹(X1, mark(X2), X3) → U31¹(X1, X2, X3)
U84¹(X1, X2, active(X3)) → U84¹(X1, X2, X3)
ISNATKIND(active(X)) → ISNATKIND(X)
ACTIVE(U13(tt, V1, V2)) → MARK(U14(isNatKind(V2), V1, V2))
ACTIVE(U13(tt, V1, V2)) → U14¹(isNatKind(V2), V1, V2)
U104¹(X1, mark(X2), X3) → U104¹(X1, X2, X3)
U81¹(X1, active(X2), X3) → U81¹(X1, X2, X3)
U34¹(X1, active(X2), X3) → U34¹(X1, X2, X3)
U34¹(active(X1), X2, X3) → U34¹(X1, X2, X3)
ACTIVE(x(N, s(M))) → MARK(U101(isNat(M), M, N))
U51¹(active(X)) → U51¹(X)
MARK(U104(X1, X2, X3)) → MARK(X1)
U82¹(X1, X2, active(X3)) → U82¹(X1, X2, X3)
U14¹(X1, X2, active(X3)) → U14¹(X1, X2, X3)
ACTIVE(U35(tt, V2)) → U36¹(isNat(V2))
U14¹(X1, mark(X2), X3) → U14¹(X1, X2, X3)
U103¹(X1, active(X2), X3) → U103¹(X1, X2, X3)
MARK(U82(X1, X2, X3)) → ACTIVE(U82(mark(X1), X2, X3))
U14¹(mark(X1), X2, X3) → U14¹(X1, X2, X3)
X(X1, mark(X2)) → X(X1, X2)
U21¹(mark(X1), X2) → U21¹(X1, X2)
U83¹(X1, mark(X2), X3) → U83¹(X1, X2, X3)
U23¹(active(X)) → U23¹(X)
MARK(U12(X1, X2, X3)) → U12¹(mark(X1), X2, X3)
U102¹(mark(X1), X2, X3) → U102¹(X1, X2, X3)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U36(X)) → ACTIVE(U36(mark(X)))
U32¹(active(X1), X2, X3) → U32¹(X1, X2, X3)
ACTIVE(U16(tt)) → MARK(tt)
MARK(U101(X1, X2, X3)) → ACTIVE(U101(mark(X1), X2, X3))
ACTIVE(U31(tt, V1, V2)) → ISNATKIND(V1)
U13¹(X1, X2, mark(X3)) → U13¹(X1, X2, X3)
U36¹(mark(X)) → U36¹(X)
U35¹(mark(X1), X2) → U35¹(X1, X2)
MARK(U81(X1, X2, X3)) → MARK(X1)
U14¹(active(X1), X2, X3) → U14¹(X1, X2, X3)
ACTIVE(U34(tt, V1, V2)) → U35¹(isNat(V1), V2)
ACTIVE(U84(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U84(X1, X2, X3)) → U84¹(mark(X1), X2, X3)
MARK(U82(X1, X2, X3)) → MARK(X1)
MARK(x(X1, X2)) → MARK(X2)
MARK(U32(X1, X2, X3)) → MARK(X1)
ACTIVE(U103(tt, M, N)) → ISNATKIND(N)
ACTIVE(isNat(plus(V1, V2))) → U11¹(isNatKind(V1), V1, V2)
MARK(U33(X1, X2, X3)) → MARK(X1)
U61¹(active(X1), X2) → U61¹(X1, X2)
ACTIVE(U41(tt, V2)) → MARK(U42(isNatKind(V2)))
U83¹(mark(X1), X2, X3) → U83¹(X1, X2, X3)
MARK(U51(X)) → U51¹(mark(X))
U51¹(mark(X)) → U51¹(X)
MARK(U92(X)) → U92¹(mark(X))
U103¹(mark(X1), X2, X3) → U103¹(X1, X2, X3)
MARK(s(X)) → MARK(X)
ACTIVE(U11(tt, V1, V2)) → MARK(U12(isNatKind(V1), V1, V2))
U103¹(active(X1), X2, X3) → U103¹(X1, X2, X3)
U12¹(mark(X1), X2, X3) → U12¹(X1, X2, X3)
MARK(U41(X1, X2)) → U41¹(mark(X1), X2)
ACTIVE(U91(tt, N)) → ISNATKIND(N)
MARK(plus(X1, X2)) → MARK(X2)
ACTIVE(isNatKind(x(V1, V2))) → MARK(U61(isNatKind(V1), V2))
X(mark(X1), X2) → X(X1, X2)
ACTIVE(isNat(0)) → MARK(tt)
ACTIVE(U103(tt, M, N)) → U104¹(isNatKind(N), M, N)
ACTIVE(U21(tt, V1)) → ISNATKIND(V1)
U72¹(mark(X1), X2) → U72¹(X1, X2)
U13¹(mark(X1), X2, X3) → U13¹(X1, X2, X3)
MARK(U33(X1, X2, X3)) → U33¹(mark(X1), X2, X3)
U92¹(active(X)) → U92¹(X)
ACTIVE(isNatKind(x(V1, V2))) → U61¹(isNatKind(V1), V2)
ACTIVE(isNat(plus(V1, V2))) → ISNATKIND(V1)
PLUS(X1, mark(X2)) → PLUS(X1, X2)
MARK(U104(X1, X2, X3)) → U104¹(mark(X1), X2, X3)
MARK(U32(X1, X2, X3)) → U32¹(mark(X1), X2, X3)
ACTIVE(U14(tt, V1, V2)) → U15¹(isNat(V1), V2)
U71¹(active(X1), X2) → U71¹(X1, X2)
U21¹(active(X1), X2) → U21¹(X1, X2)
ACTIVE(U82(tt, M, N)) → ISNAT(N)
MARK(U82(X1, X2, X3)) → U82¹(mark(X1), X2, X3)
MARK(plus(X1, X2)) → MARK(X1)
ISNAT(mark(X)) → ISNAT(X)
MARK(U35(X1, X2)) → MARK(X1)
MARK(U14(X1, X2, X3)) → MARK(X1)
U32¹(X1, active(X2), X3) → U32¹(X1, X2, X3)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
U101¹(X1, active(X2), X3) → U101¹(X1, X2, X3)
MARK(U92(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
U13¹(X1, active(X2), X3) → U13¹(X1, X2, X3)
MARK(U103(X1, X2, X3)) → U103¹(mark(X1), X2, X3)
U72¹(active(X1), X2) → U72¹(X1, X2)
U34¹(mark(X1), X2, X3) → U34¹(X1, X2, X3)
MARK(U16(X)) → MARK(X)
U104¹(X1, X2, active(X3)) → U104¹(X1, X2, X3)
MARK(U12(X1, X2, X3)) → ACTIVE(U12(mark(X1), X2, X3))
MARK(U102(X1, X2, X3)) → ACTIVE(U102(mark(X1), X2, X3))
U22¹(X1, mark(X2)) → U22¹(X1, X2)
MARK(U83(X1, X2, X3)) → MARK(X1)
U34¹(X1, X2, mark(X3)) → U34¹(X1, X2, X3)
ACTIVE(isNat(x(V1, V2))) → U31¹(isNatKind(V1), V1, V2)
MARK(tt) → ACTIVE(tt)
MARK(x(X1, X2)) → ACTIVE(x(mark(X1), mark(X2)))
MARK(U71(X1, X2)) → ACTIVE(U71(mark(X1), X2))
MARK(U101(X1, X2, X3)) → U101¹(mark(X1), X2, X3)
U34¹(X1, mark(X2), X3) → U34¹(X1, X2, X3)
ACTIVE(U21(tt, V1)) → U22¹(isNatKind(V1), V1)
MARK(U22(X1, X2)) → U22¹(mark(X1), X2)
U12¹(X1, active(X2), X3) → U12¹(X1, X2, X3)
MARK(U71(X1, X2)) → U71¹(mark(X1), X2)
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
ACTIVE(x(N, 0)) → U91¹(isNat(N), N)
MARK(U104(X1, X2, X3)) → ACTIVE(U104(mark(X1), X2, X3))
MARK(x(X1, X2)) → MARK(X1)
U41¹(active(X1), X2) → U41¹(X1, X2)
U14¹(X1, X2, mark(X3)) → U14¹(X1, X2, X3)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
U81¹(active(X1), X2, X3) → U81¹(X1, X2, X3)
U103¹(X1, mark(X2), X3) → U103¹(X1, X2, X3)
U104¹(mark(X1), X2, X3) → U104¹(X1, X2, X3)
U82¹(X1, mark(X2), X3) → U82¹(X1, X2, X3)
U41¹(X1, active(X2)) → U41¹(X1, X2)
MARK(U22(X1, X2)) → MARK(X1)
MARK(U16(X)) → U16¹(mark(X))
MARK(U21(X1, X2)) → U21¹(mark(X1), X2)
ACTIVE(U42(tt)) → MARK(tt)
U104¹(X1, X2, mark(X3)) → U104¹(X1, X2, X3)
U84¹(X1, active(X2), X3) → U84¹(X1, X2, X3)
MARK(U102(X1, X2, X3)) → U102¹(mark(X1), X2, X3)
MARK(U91(X1, X2)) → U91¹(mark(X1), X2)
ACTIVE(U81(tt, M, N)) → MARK(U82(isNatKind(M), M, N))
ACTIVE(isNat(s(V1))) → ISNATKIND(V1)
MARK(U21(X1, X2)) → MARK(X1)
MARK(U51(X)) → ACTIVE(U51(mark(X)))
ACTIVE(U102(tt, M, N)) → U103¹(isNat(N), M, N)
MARK(U31(X1, X2, X3)) → ACTIVE(U31(mark(X1), X2, X3))
U31¹(X1, X2, active(X3)) → U31¹(X1, X2, X3)
ACTIVE(U32(tt, V1, V2)) → ISNATKIND(V2)
ACTIVE(plus(N, 0)) → U71¹(isNat(N), N)
MARK(U42(X)) → MARK(X)
U102¹(active(X1), X2, X3) → U102¹(X1, X2, X3)
U22¹(mark(X1), X2) → U22¹(X1, X2)
U71¹(X1, active(X2)) → U71¹(X1, X2)
U21¹(X1, active(X2)) → U21¹(X1, X2)
ACTIVE(plus(N, s(M))) → U81¹(isNat(M), M, N)
U32¹(X1, X2, mark(X3)) → U32¹(X1, X2, X3)
ACTIVE(U84(tt, M, N)) → PLUS(N, M)
MARK(U72(X1, X2)) → ACTIVE(U72(mark(X1), X2))
U82¹(X1, X2, mark(X3)) → U82¹(X1, X2, X3)
U71¹(X1, mark(X2)) → U71¹(X1, X2)
U92¹(mark(X)) → U92¹(X)
U84¹(mark(X1), X2, X3) → U84¹(X1, X2, X3)
ACTIVE(U81(tt, M, N)) → ISNATKIND(M)
U62¹(mark(X)) → U62¹(X)
ACTIVE(U12(tt, V1, V2)) → ISNATKIND(V2)
U62¹(active(X)) → U62¹(X)
ACTIVE(isNatKind(plus(V1, V2))) → ISNATKIND(V1)
U103¹(X1, X2, mark(X3)) → U103¹(X1, X2, X3)
ACTIVE(U101(tt, M, N)) → MARK(U102(isNatKind(M), M, N))
U11¹(X1, mark(X2), X3) → U11¹(X1, X2, X3)
U102¹(X1, active(X2), X3) → U102¹(X1, X2, X3)
ACTIVE(U15(tt, V2)) → ISNAT(V2)
ACTIVE(x(N, s(M))) → ISNAT(M)
MARK(U31(X1, X2, X3)) → U31¹(mark(X1), X2, X3)
ACTIVE(U13(tt, V1, V2)) → ISNATKIND(V2)
MARK(U16(X)) → ACTIVE(U16(mark(X)))
U22¹(active(X1), X2) → U22¹(X1, X2)
ACTIVE(isNatKind(s(V1))) → ISNATKIND(V1)
ACTIVE(U34(tt, V1, V2)) → MARK(U35(isNat(V1), V2))
U102¹(X1, mark(X2), X3) → U102¹(X1, X2, X3)
MARK(s(X)) → S(mark(X))
ISNATKIND(mark(X)) → ISNATKIND(X)
ACTIVE(x(N, 0)) → ISNAT(N)
ACTIVE(x(N, s(M))) → U101¹(isNat(M), M, N)
U72¹(X1, mark(X2)) → U72¹(X1, X2)
ACTIVE(isNat(plus(V1, V2))) → MARK(U11(isNatKind(V1), V1, V2))
ACTIVE(U61(tt, V2)) → ISNATKIND(V2)
ACTIVE(isNatKind(0)) → MARK(tt)
ACTIVE(U71(tt, N)) → U72¹(isNatKind(N), N)
ACTIVE(U31(tt, V1, V2)) → MARK(U32(isNatKind(V1), V1, V2))
ACTIVE(U71(tt, N)) → ISNATKIND(N)
MARK(U36(X)) → MARK(X)
ACTIVE(U104(tt, M, N)) → PLUS(x(N, M), N)
ACTIVE(U83(tt, M, N)) → MARK(U84(isNatKind(N), M, N))
ACTIVE(U81(tt, M, N)) → U82¹(isNatKind(M), M, N)
MARK(U23(X)) → U23¹(mark(X))
ACTIVE(isNat(x(V1, V2))) → ISNATKIND(V1)
MARK(U102(X1, X2, X3)) → MARK(X1)
U33¹(X1, active(X2), X3) → U33¹(X1, X2, X3)
MARK(0) → ACTIVE(0)
ACTIVE(U34(tt, V1, V2)) → ISNAT(V1)
MARK(plus(X1, X2)) → PLUS(mark(X1), mark(X2))
ACTIVE(U71(tt, N)) → MARK(U72(isNatKind(N), N))
MARK(U14(X1, X2, X3)) → ACTIVE(U14(mark(X1), X2, X3))
ACTIVE(plus(N, 0)) → MARK(U71(isNat(N), N))
MARK(U36(X)) → U36¹(mark(X))
MARK(U14(X1, X2, X3)) → U14¹(mark(X1), X2, X3)
U36¹(active(X)) → U36¹(X)