The TRS could not be proven terminating. The proof attempt took 60001 ms.
Problem 1 was processed with processor DependencyGraph (11393ms). | – Problem 2 was processed with processor DependencyGraph (8350ms). | | – Problem 5 remains open; application of the following processors failed [PolynomialLinearRange4iUR (26ms), DependencyGraph (8556ms)]. | – Problem 3 was processed with processor DependencyGraph (8724ms). | | – Problem 6 remains open; application of the following processors failed [PolynomialLinearRange4iUR (10ms), DependencyGraph (timeout)]. | – Problem 4 remains open; application of the following processors failed [SubtermCriterion (5ms), DependencyGraph (8575ms), PolynomialLinearRange4iUR (3333ms), DependencyGraph (8301ms)].
| U81#(tt, M, N) | → | isNatKind#(activate(M)) | U91#(tt, N) | → | activate#(N) | |
| activate#(n__x(X1, X2)) | → | activate#(X1) | U34#(tt, V1, V2) | → | activate#(V1) | |
| U15#(tt, V2) | → | isNat#(activate(V2)) | U32#(tt, V1, V2) | → | isNatKind#(activate(V2)) | |
| U71#(tt, N) | → | U72#(isNatKind(activate(N)), activate(N)) | plus#(N, 0) | → | U71#(isNat(N), N) | |
| U33#(tt, V1, V2) | → | U34#(isNatKind(activate(V2)), activate(V1), activate(V2)) | activate#(n__x(X1, X2)) | → | activate#(X2) | |
| isNatKind#(n__plus(V1, V2)) | → | isNatKind#(activate(V1)) | U103#(tt, M, N) | → | U104#(isNatKind(activate(N)), activate(M), activate(N)) | |
| x#(N, s(M)) | → | isNat#(M) | U103#(tt, M, N) | → | isNatKind#(activate(N)) | |
| U84#(tt, M, N) | → | activate#(M) | U32#(tt, V1, V2) | → | U33#(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| isNatKind#(n__x(V1, V2)) | → | isNatKind#(activate(V1)) | isNat#(n__plus(V1, V2)) | → | activate#(V1) | |
| x#(N, s(M)) | → | U101#(isNat(M), M, N) | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) | |
| U34#(tt, V1, V2) | → | isNat#(activate(V1)) | isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | |
| isNatKind#(n__x(V1, V2)) | → | activate#(V1) | activate#(n__s(X)) | → | activate#(X) | |
| U82#(tt, M, N) | → | activate#(N) | U14#(tt, V1, V2) | → | U15#(isNat(activate(V1)), activate(V2)) | |
| isNatKind#(n__s(V1)) | → | activate#(V1) | U13#(tt, V1, V2) | → | activate#(V1) | |
| U81#(tt, M, N) | → | U82#(isNatKind(activate(M)), activate(M), activate(N)) | isNat#(n__plus(V1, V2)) | → | activate#(V2) | |
| plus#(N, 0) | → | isNat#(N) | U104#(tt, M, N) | → | activate#(N) | |
| x#(N, 0) | → | isNat#(N) | U11#(tt, V1, V2) | → | activate#(V2) | |
| activate#(n__plus(X1, X2)) | → | activate#(X2) | U11#(tt, V1, V2) | → | U12#(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| isNatKind#(n__plus(V1, V2)) | → | activate#(V2) | isNatKind#(n__x(V1, V2)) | → | activate#(V2) | |
| isNat#(n__x(V1, V2)) | → | activate#(V1) | U102#(tt, M, N) | → | isNat#(activate(N)) | |
| isNat#(n__x(V1, V2)) | → | U31#(isNatKind(activate(V1)), activate(V1), activate(V2)) | activate#(n__plus(X1, X2)) | → | activate#(X1) | |
| isNatKind#(n__plus(V1, V2)) | → | activate#(V1) | U84#(tt, M, N) | → | plus#(activate(N), activate(M)) | |
| U11#(tt, V1, V2) | → | isNatKind#(activate(V1)) | U21#(tt, V1) | → | activate#(V1) | |
| U35#(tt, V2) | → | activate#(V2) | U91#(tt, N) | → | isNatKind#(activate(N)) | |
| U31#(tt, V1, V2) | → | U32#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) | → | activate#(M) | |
| isNat#(n__plus(V1, V2)) | → | U11#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) | → | activate#(N) | |
| U34#(tt, V1, V2) | → | U35#(isNat(activate(V1)), activate(V2)) | U83#(tt, M, N) | → | isNatKind#(activate(N)) | |
| U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | U34#(tt, V1, V2) | → | activate#(V2) | |
| U82#(tt, M, N) | → | U83#(isNat(activate(N)), activate(M), activate(N)) | U81#(tt, M, N) | → | activate#(M) | |
| U104#(tt, M, N) | → | activate#(M) | isNat#(n__x(V1, V2)) | → | activate#(V2) | |
| U101#(tt, M, N) | → | isNatKind#(activate(M)) | isNatKind#(n__plus(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V2)) | |
| U21#(tt, V1) | → | isNatKind#(activate(V1)) | U82#(tt, M, N) | → | activate#(M) | |
| U12#(tt, V1, V2) | → | U13#(isNatKind(activate(V2)), activate(V1), activate(V2)) | U13#(tt, V1, V2) | → | isNatKind#(activate(V2)) | |
| isNatKind#(n__x(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | U14#(tt, V1, V2) | → | isNat#(activate(V1)) | |
| U32#(tt, V1, V2) | → | activate#(V1) | U12#(tt, V1, V2) | → | activate#(V1) | |
| U12#(tt, V1, V2) | → | isNatKind#(activate(V2)) | isNat#(n__s(V1)) | → | activate#(V1) | |
| U33#(tt, V1, V2) | → | activate#(V2) | U81#(tt, M, N) | → | activate#(N) | |
| plus#(N, s(M)) | → | U81#(isNat(M), M, N) | U33#(tt, V1, V2) | → | activate#(V1) | |
| U102#(tt, M, N) | → | activate#(N) | U32#(tt, V1, V2) | → | activate#(V2) | |
| U101#(tt, M, N) | → | U102#(isNatKind(activate(M)), activate(M), activate(N)) | U14#(tt, V1, V2) | → | activate#(V2) | |
| U31#(tt, V1, V2) | → | activate#(V2) | U15#(tt, V2) | → | activate#(V2) | |
| U11#(tt, V1, V2) | → | activate#(V1) | U104#(tt, M, N) | → | plus#(x(activate(N), activate(M)), activate(N)) | |
| U22#(tt, V1) | → | activate#(V1) | U41#(tt, V2) | → | isNatKind#(activate(V2)) | |
| U102#(tt, M, N) | → | activate#(M) | U102#(tt, M, N) | → | U103#(isNat(activate(N)), activate(M), activate(N)) | |
| isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | U84#(tt, M, N) | → | activate#(N) | |
| U101#(tt, M, N) | → | activate#(N) | U13#(tt, V1, V2) | → | activate#(V2) | |
| U31#(tt, V1, V2) | → | isNatKind#(activate(V1)) | isNat#(n__plus(V1, V2)) | → | isNatKind#(activate(V1)) | |
| U22#(tt, V1) | → | isNat#(activate(V1)) | isNat#(n__x(V1, V2)) | → | isNatKind#(activate(V1)) | |
| activate#(n__plus(X1, X2)) | → | plus#(activate(X1), activate(X2)) | U12#(tt, V1, V2) | → | activate#(V2) | |
| U83#(tt, M, N) | → | activate#(N) | U83#(tt, M, N) | → | activate#(M) | |
| activate#(n__x(X1, X2)) | → | x#(activate(X1), activate(X2)) | U41#(tt, V2) | → | activate#(V2) | |
| U13#(tt, V1, V2) | → | U14#(isNatKind(activate(V2)), activate(V1), activate(V2)) | U33#(tt, V1, V2) | → | isNatKind#(activate(V2)) | |
| U101#(tt, M, N) | → | activate#(M) | U35#(tt, V2) | → | isNat#(activate(V2)) | |
| U61#(tt, V2) | → | activate#(V2) | U31#(tt, V1, V2) | → | activate#(V1) | |
| U83#(tt, M, N) | → | U84#(isNatKind(activate(N)), activate(M), activate(N)) | U72#(tt, N) | → | activate#(N) | |
| x#(N, 0) | → | U91#(isNat(N), N) | U61#(tt, V2) | → | isNatKind#(activate(V2)) | |
| U71#(tt, N) | → | activate#(N) | plus#(N, s(M)) | → | isNat#(M) | |
| U71#(tt, N) | → | isNatKind#(activate(N)) | U82#(tt, M, N) | → | isNat#(activate(N)) | |
| U14#(tt, V1, V2) | → | activate#(V1) | U104#(tt, M, N) | → | x#(activate(N), activate(M)) |
| U101(tt, M, N) | → | U102(isNatKind(activate(M)), activate(M), activate(N)) | U102(tt, M, N) | → | U103(isNat(activate(N)), activate(M), activate(N)) | |
| U103(tt, M, N) | → | U104(isNatKind(activate(N)), activate(M), activate(N)) | U104(tt, M, N) | → | plus(x(activate(N), activate(M)), activate(N)) | |
| U11(tt, V1, V2) | → | U12(isNatKind(activate(V1)), activate(V1), activate(V2)) | U12(tt, V1, V2) | → | U13(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| U13(tt, V1, V2) | → | U14(isNatKind(activate(V2)), activate(V1), activate(V2)) | U14(tt, V1, V2) | → | U15(isNat(activate(V1)), activate(V2)) | |
| U15(tt, V2) | → | U16(isNat(activate(V2))) | U16(tt) | → | tt | |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | U22(tt, V1) | → | U23(isNat(activate(V1))) | |
| U23(tt) | → | tt | U31(tt, V1, V2) | → | U32(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| U32(tt, V1, V2) | → | U33(isNatKind(activate(V2)), activate(V1), activate(V2)) | U33(tt, V1, V2) | → | U34(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| U34(tt, V1, V2) | → | U35(isNat(activate(V1)), activate(V2)) | U35(tt, V2) | → | U36(isNat(activate(V2))) | |
| U36(tt) | → | tt | U41(tt, V2) | → | U42(isNatKind(activate(V2))) | |
| U42(tt) | → | tt | U51(tt) | → | tt | |
| U61(tt, V2) | → | U62(isNatKind(activate(V2))) | U62(tt) | → | tt | |
| U71(tt, N) | → | U72(isNatKind(activate(N)), activate(N)) | U72(tt, N) | → | activate(N) | |
| U81(tt, M, N) | → | U82(isNatKind(activate(M)), activate(M), activate(N)) | U82(tt, M, N) | → | U83(isNat(activate(N)), activate(M), activate(N)) | |
| U83(tt, M, N) | → | U84(isNatKind(activate(N)), activate(M), activate(N)) | U84(tt, M, N) | → | s(plus(activate(N), activate(M))) | |
| U91(tt, N) | → | U92(isNatKind(activate(N))) | U92(tt) | → | 0 | |
| isNat(n__0) | → | tt | isNat(n__plus(V1, V2)) | → | U11(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | isNat(n__x(V1, V2)) | → | U31(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| isNatKind(n__0) | → | tt | isNatKind(n__plus(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V2)) | |
| isNatKind(n__s(V1)) | → | U51(isNatKind(activate(V1))) | isNatKind(n__x(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) | |
| plus(N, 0) | → | U71(isNat(N), N) | plus(N, s(M)) | → | U81(isNat(M), M, N) | |
| x(N, 0) | → | U91(isNat(N), N) | x(N, s(M)) | → | U101(isNat(M), M, N) | |
| 0 | → | n__0 | plus(X1, X2) | → | n__plus(X1, X2) | |
| s(X) | → | n__s(X) | x(X1, X2) | → | n__x(X1, X2) | |
| activate(n__0) | → | 0 | activate(n__plus(X1, X2)) | → | plus(activate(X1), activate(X2)) | |
| activate(n__s(X)) | → | s(activate(X)) | activate(n__x(X1, X2)) | → | x(activate(X1), activate(X2)) | |
| activate(X) | → | X |
Termination of terms over the following signature is verified: U104, n__plus, n__s, isNat, activate, U62, n__0, U61, U42, U92, U41, U91, U23, U21, n__x, U22, plus, isNatKind, U83, U84, U71, U36, U72, 0, s, U51, U14, tt, U15, U82, U16, U81, U11, U12, U13, U31, U102, U32, U103, U33, U34, x, U101, U35
| U81#(tt, M, N) | → | isNatKind#(activate(M)) | U91#(tt, N) | → | activate#(N) | |
| activate#(n__x(X1, X2)) | → | activate#(X1) | U34#(tt, V1, V2) | → | activate#(V1) | |
| U15#(tt, V2) | → | isNat#(activate(V2)) | U32#(tt, V1, V2) | → | isNatKind#(activate(V2)) | |
| U71#(tt, N) | → | U72#(isNatKind(activate(N)), activate(N)) | plus#(N, 0) | → | U71#(isNat(N), N) | |
| U33#(tt, V1, V2) | → | U34#(isNatKind(activate(V2)), activate(V1), activate(V2)) | activate#(n__x(X1, X2)) | → | activate#(X2) | |
| isNatKind#(n__plus(V1, V2)) | → | isNatKind#(activate(V1)) | U103#(tt, M, N) | → | U104#(isNatKind(activate(N)), activate(M), activate(N)) | |
| x#(N, s(M)) | → | isNat#(M) | U103#(tt, M, N) | → | isNatKind#(activate(N)) | |
| U84#(tt, M, N) | → | activate#(M) | U32#(tt, V1, V2) | → | U33#(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| isNatKind#(n__x(V1, V2)) | → | isNatKind#(activate(V1)) | isNat#(n__plus(V1, V2)) | → | activate#(V1) | |
| x#(N, s(M)) | → | U101#(isNat(M), M, N) | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) | |
| U34#(tt, V1, V2) | → | isNat#(activate(V1)) | isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | |
| isNatKind#(n__x(V1, V2)) | → | activate#(V1) | activate#(n__s(X)) | → | activate#(X) | |
| U82#(tt, M, N) | → | activate#(N) | U14#(tt, V1, V2) | → | U15#(isNat(activate(V1)), activate(V2)) | |
| isNatKind#(n__s(V1)) | → | activate#(V1) | U13#(tt, V1, V2) | → | activate#(V1) | |
| U81#(tt, M, N) | → | U82#(isNatKind(activate(M)), activate(M), activate(N)) | isNat#(n__plus(V1, V2)) | → | activate#(V2) | |
| plus#(N, 0) | → | isNat#(N) | U104#(tt, M, N) | → | activate#(N) | |
| x#(N, 0) | → | isNat#(N) | U11#(tt, V1, V2) | → | activate#(V2) | |
| activate#(n__plus(X1, X2)) | → | activate#(X2) | U11#(tt, V1, V2) | → | U12#(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| isNatKind#(n__plus(V1, V2)) | → | activate#(V2) | isNatKind#(n__x(V1, V2)) | → | activate#(V2) | |
| isNat#(n__x(V1, V2)) | → | activate#(V1) | U102#(tt, M, N) | → | isNat#(activate(N)) | |
| isNat#(n__x(V1, V2)) | → | U31#(isNatKind(activate(V1)), activate(V1), activate(V2)) | activate#(n__plus(X1, X2)) | → | activate#(X1) | |
| isNatKind#(n__plus(V1, V2)) | → | activate#(V1) | U84#(tt, M, N) | → | plus#(activate(N), activate(M)) | |
| U11#(tt, V1, V2) | → | isNatKind#(activate(V1)) | U21#(tt, V1) | → | activate#(V1) | |
| U35#(tt, V2) | → | activate#(V2) | U91#(tt, N) | → | isNatKind#(activate(N)) | |
| U31#(tt, V1, V2) | → | U32#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) | → | activate#(M) | |
| isNat#(n__plus(V1, V2)) | → | U11#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) | → | activate#(N) | |
| U34#(tt, V1, V2) | → | U35#(isNat(activate(V1)), activate(V2)) | U83#(tt, M, N) | → | isNatKind#(activate(N)) | |
| U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | U34#(tt, V1, V2) | → | activate#(V2) | |
| U82#(tt, M, N) | → | U83#(isNat(activate(N)), activate(M), activate(N)) | U81#(tt, M, N) | → | activate#(M) | |
| U104#(tt, M, N) | → | activate#(M) | isNat#(n__x(V1, V2)) | → | activate#(V2) | |
| U101#(tt, M, N) | → | isNatKind#(activate(M)) | isNatKind#(n__plus(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V2)) | |
| U21#(tt, V1) | → | isNatKind#(activate(V1)) | U82#(tt, M, N) | → | activate#(M) | |
| U12#(tt, V1, V2) | → | U13#(isNatKind(activate(V2)), activate(V1), activate(V2)) | U13#(tt, V1, V2) | → | isNatKind#(activate(V2)) | |
| isNatKind#(n__x(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | U14#(tt, V1, V2) | → | isNat#(activate(V1)) | |
| U32#(tt, V1, V2) | → | activate#(V1) | U12#(tt, V1, V2) | → | activate#(V1) | |
| U12#(tt, V1, V2) | → | isNatKind#(activate(V2)) | isNat#(n__s(V1)) | → | activate#(V1) | |
| U33#(tt, V1, V2) | → | activate#(V2) | U81#(tt, M, N) | → | activate#(N) | |
| plus#(N, s(M)) | → | U81#(isNat(M), M, N) | U33#(tt, V1, V2) | → | activate#(V1) | |
| U102#(tt, M, N) | → | activate#(N) | U32#(tt, V1, V2) | → | activate#(V2) | |
| U101#(tt, M, N) | → | U102#(isNatKind(activate(M)), activate(M), activate(N)) | U14#(tt, V1, V2) | → | activate#(V2) | |
| U31#(tt, V1, V2) | → | activate#(V2) | U15#(tt, V2) | → | activate#(V2) | |
| U11#(tt, V1, V2) | → | activate#(V1) | U104#(tt, M, N) | → | plus#(x(activate(N), activate(M)), activate(N)) | |
| U22#(tt, V1) | → | activate#(V1) | U41#(tt, V2) | → | isNatKind#(activate(V2)) | |
| U102#(tt, M, N) | → | activate#(M) | U102#(tt, M, N) | → | U103#(isNat(activate(N)), activate(M), activate(N)) | |
| isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | U84#(tt, M, N) | → | activate#(N) | |
| U101#(tt, M, N) | → | activate#(N) | U13#(tt, V1, V2) | → | activate#(V2) | |
| U31#(tt, V1, V2) | → | isNatKind#(activate(V1)) | isNat#(n__plus(V1, V2)) | → | isNatKind#(activate(V1)) | |
| U22#(tt, V1) | → | isNat#(activate(V1)) | isNat#(n__x(V1, V2)) | → | isNatKind#(activate(V1)) | |
| activate#(n__plus(X1, X2)) | → | plus#(activate(X1), activate(X2)) | U12#(tt, V1, V2) | → | activate#(V2) | |
| U83#(tt, M, N) | → | activate#(N) | U83#(tt, M, N) | → | activate#(M) | |
| activate#(n__x(X1, X2)) | → | x#(activate(X1), activate(X2)) | U41#(tt, V2) | → | activate#(V2) | |
| U13#(tt, V1, V2) | → | U14#(isNatKind(activate(V2)), activate(V1), activate(V2)) | U33#(tt, V1, V2) | → | isNatKind#(activate(V2)) | |
| U101#(tt, M, N) | → | activate#(M) | U35#(tt, V2) | → | isNat#(activate(V2)) | |
| U61#(tt, V2) | → | activate#(V2) | U31#(tt, V1, V2) | → | activate#(V1) | |
| U83#(tt, M, N) | → | U84#(isNatKind(activate(N)), activate(M), activate(N)) | U72#(tt, N) | → | activate#(N) | |
| x#(N, 0) | → | U91#(isNat(N), N) | U61#(tt, V2) | → | isNatKind#(activate(V2)) | |
| U71#(tt, N) | → | activate#(N) | plus#(N, s(M)) | → | isNat#(M) | |
| U71#(tt, N) | → | isNatKind#(activate(N)) | U82#(tt, M, N) | → | isNat#(activate(N)) | |
| U14#(tt, V1, V2) | → | activate#(V1) | U104#(tt, M, N) | → | x#(activate(N), activate(M)) |
| U101(tt, M, N) | → | U102(isNatKind(activate(M)), activate(M), activate(N)) | U102(tt, M, N) | → | U103(isNat(activate(N)), activate(M), activate(N)) | |
| U103(tt, M, N) | → | U104(isNatKind(activate(N)), activate(M), activate(N)) | U104(tt, M, N) | → | plus(x(activate(N), activate(M)), activate(N)) | |
| U11(tt, V1, V2) | → | U12(isNatKind(activate(V1)), activate(V1), activate(V2)) | U12(tt, V1, V2) | → | U13(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| U13(tt, V1, V2) | → | U14(isNatKind(activate(V2)), activate(V1), activate(V2)) | U14(tt, V1, V2) | → | U15(isNat(activate(V1)), activate(V2)) | |
| U15(tt, V2) | → | U16(isNat(activate(V2))) | U16(tt) | → | tt | |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | U22(tt, V1) | → | U23(isNat(activate(V1))) | |
| U23(tt) | → | tt | U31(tt, V1, V2) | → | U32(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| U32(tt, V1, V2) | → | U33(isNatKind(activate(V2)), activate(V1), activate(V2)) | U33(tt, V1, V2) | → | U34(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| U34(tt, V1, V2) | → | U35(isNat(activate(V1)), activate(V2)) | U35(tt, V2) | → | U36(isNat(activate(V2))) | |
| U36(tt) | → | tt | U41(tt, V2) | → | U42(isNatKind(activate(V2))) | |
| U42(tt) | → | tt | U51(tt) | → | tt | |
| U61(tt, V2) | → | U62(isNatKind(activate(V2))) | U62(tt) | → | tt | |
| U71(tt, N) | → | U72(isNatKind(activate(N)), activate(N)) | U72(tt, N) | → | activate(N) | |
| U81(tt, M, N) | → | U82(isNatKind(activate(M)), activate(M), activate(N)) | U82(tt, M, N) | → | U83(isNat(activate(N)), activate(M), activate(N)) | |
| U83(tt, M, N) | → | U84(isNatKind(activate(N)), activate(M), activate(N)) | U84(tt, M, N) | → | s(plus(activate(N), activate(M))) | |
| U91(tt, N) | → | U92(isNatKind(activate(N))) | U92(tt) | → | 0 | |
| isNat(n__0) | → | tt | isNat(n__plus(V1, V2)) | → | U11(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | isNat(n__x(V1, V2)) | → | U31(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| isNatKind(n__0) | → | tt | isNatKind(n__plus(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V2)) | |
| isNatKind(n__s(V1)) | → | U51(isNatKind(activate(V1))) | isNatKind(n__x(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) | |
| plus(N, 0) | → | U71(isNat(N), N) | plus(N, s(M)) | → | U81(isNat(M), M, N) | |
| x(N, 0) | → | U91(isNat(N), N) | x(N, s(M)) | → | U101(isNat(M), M, N) | |
| 0 | → | n__0 | plus(X1, X2) | → | n__plus(X1, X2) | |
| s(X) | → | n__s(X) | x(X1, X2) | → | n__x(X1, X2) | |
| activate(n__0) | → | 0 | activate(n__plus(X1, X2)) | → | plus(activate(X1), activate(X2)) | |
| activate(n__s(X)) | → | s(activate(X)) | activate(n__x(X1, X2)) | → | x(activate(X1), activate(X2)) | |
| activate(X) | → | X |
Termination of terms over the following signature is verified: U104, n__plus, n__s, isNat, activate, U62, n__0, U61, U42, U92, U41, U91, U23, U21, n__x, U22, plus, isNatKind, U83, U84, U71, U36, U72, 0, s, U51, U14, tt, U15, U82, U16, U81, U11, U12, U13, U31, U102, U32, U103, U33, U34, x, U101, U35
| U81#(tt, M, N) | → | isNatKind#(activate(M)) | U91#(tt, N) | → | activate#(N) | |
| activate#(n__x(X1, X2)) | → | activate#(X1) | U34#(tt, V1, V2) | → | activate#(V1) | |
| U15#(tt, V2) | → | isNat#(activate(V2)) | U32#(tt, V1, V2) | → | isNatKind#(activate(V2)) | |
| U71#(tt, N) | → | U72#(isNatKind(activate(N)), activate(N)) | plus#(N, 0) | → | U71#(isNat(N), N) | |
| U33#(tt, V1, V2) | → | U34#(isNatKind(activate(V2)), activate(V1), activate(V2)) | activate#(n__x(X1, X2)) | → | activate#(X2) | |
| isNatKind#(n__plus(V1, V2)) | → | isNatKind#(activate(V1)) | U103#(tt, M, N) | → | U104#(isNatKind(activate(N)), activate(M), activate(N)) | |
| x#(N, s(M)) | → | isNat#(M) | U103#(tt, M, N) | → | isNatKind#(activate(N)) | |
| U84#(tt, M, N) | → | activate#(M) | U32#(tt, V1, V2) | → | U33#(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| isNatKind#(n__x(V1, V2)) | → | isNatKind#(activate(V1)) | isNat#(n__plus(V1, V2)) | → | activate#(V1) | |
| x#(N, s(M)) | → | U101#(isNat(M), M, N) | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) | |
| U34#(tt, V1, V2) | → | isNat#(activate(V1)) | isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | |
| isNatKind#(n__x(V1, V2)) | → | activate#(V1) | activate#(n__s(X)) | → | activate#(X) | |
| U82#(tt, M, N) | → | activate#(N) | U14#(tt, V1, V2) | → | U15#(isNat(activate(V1)), activate(V2)) | |
| isNatKind#(n__s(V1)) | → | activate#(V1) | U13#(tt, V1, V2) | → | activate#(V1) | |
| U81#(tt, M, N) | → | U82#(isNatKind(activate(M)), activate(M), activate(N)) | isNat#(n__plus(V1, V2)) | → | activate#(V2) | |
| plus#(N, 0) | → | isNat#(N) | U104#(tt, M, N) | → | activate#(N) | |
| x#(N, 0) | → | isNat#(N) | U11#(tt, V1, V2) | → | activate#(V2) | |
| activate#(n__plus(X1, X2)) | → | activate#(X2) | U11#(tt, V1, V2) | → | U12#(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| isNatKind#(n__plus(V1, V2)) | → | activate#(V2) | isNatKind#(n__x(V1, V2)) | → | activate#(V2) | |
| isNat#(n__x(V1, V2)) | → | activate#(V1) | U102#(tt, M, N) | → | isNat#(activate(N)) | |
| isNat#(n__x(V1, V2)) | → | U31#(isNatKind(activate(V1)), activate(V1), activate(V2)) | activate#(n__plus(X1, X2)) | → | activate#(X1) | |
| isNatKind#(n__plus(V1, V2)) | → | activate#(V1) | U84#(tt, M, N) | → | plus#(activate(N), activate(M)) | |
| U11#(tt, V1, V2) | → | isNatKind#(activate(V1)) | U21#(tt, V1) | → | activate#(V1) | |
| U35#(tt, V2) | → | activate#(V2) | U91#(tt, N) | → | isNatKind#(activate(N)) | |
| U31#(tt, V1, V2) | → | U32#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) | → | activate#(M) | |
| isNat#(n__plus(V1, V2)) | → | U11#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) | → | activate#(N) | |
| U34#(tt, V1, V2) | → | U35#(isNat(activate(V1)), activate(V2)) | U83#(tt, M, N) | → | isNatKind#(activate(N)) | |
| U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | U34#(tt, V1, V2) | → | activate#(V2) | |
| U82#(tt, M, N) | → | U83#(isNat(activate(N)), activate(M), activate(N)) | U81#(tt, M, N) | → | activate#(M) | |
| U104#(tt, M, N) | → | activate#(M) | isNat#(n__x(V1, V2)) | → | activate#(V2) | |
| U101#(tt, M, N) | → | isNatKind#(activate(M)) | isNatKind#(n__plus(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V2)) | |
| U21#(tt, V1) | → | isNatKind#(activate(V1)) | U82#(tt, M, N) | → | activate#(M) | |
| U12#(tt, V1, V2) | → | U13#(isNatKind(activate(V2)), activate(V1), activate(V2)) | U13#(tt, V1, V2) | → | isNatKind#(activate(V2)) | |
| isNatKind#(n__x(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | U14#(tt, V1, V2) | → | isNat#(activate(V1)) | |
| U32#(tt, V1, V2) | → | activate#(V1) | U12#(tt, V1, V2) | → | activate#(V1) | |
| U12#(tt, V1, V2) | → | isNatKind#(activate(V2)) | isNat#(n__s(V1)) | → | activate#(V1) | |
| U33#(tt, V1, V2) | → | activate#(V2) | U81#(tt, M, N) | → | activate#(N) | |
| plus#(N, s(M)) | → | U81#(isNat(M), M, N) | U33#(tt, V1, V2) | → | activate#(V1) | |
| U102#(tt, M, N) | → | activate#(N) | U32#(tt, V1, V2) | → | activate#(V2) | |
| U101#(tt, M, N) | → | U102#(isNatKind(activate(M)), activate(M), activate(N)) | U14#(tt, V1, V2) | → | activate#(V2) | |
| U31#(tt, V1, V2) | → | activate#(V2) | U15#(tt, V2) | → | activate#(V2) | |
| U11#(tt, V1, V2) | → | activate#(V1) | U104#(tt, M, N) | → | plus#(x(activate(N), activate(M)), activate(N)) | |
| U22#(tt, V1) | → | activate#(V1) | U41#(tt, V2) | → | isNatKind#(activate(V2)) | |
| U102#(tt, M, N) | → | activate#(M) | U102#(tt, M, N) | → | U103#(isNat(activate(N)), activate(M), activate(N)) | |
| isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | U84#(tt, M, N) | → | activate#(N) | |
| U101#(tt, M, N) | → | activate#(N) | U13#(tt, V1, V2) | → | activate#(V2) | |
| U31#(tt, V1, V2) | → | isNatKind#(activate(V1)) | isNat#(n__plus(V1, V2)) | → | isNatKind#(activate(V1)) | |
| U22#(tt, V1) | → | isNat#(activate(V1)) | isNat#(n__x(V1, V2)) | → | isNatKind#(activate(V1)) | |
| activate#(n__plus(X1, X2)) | → | plus#(activate(X1), activate(X2)) | U12#(tt, V1, V2) | → | activate#(V2) | |
| U83#(tt, M, N) | → | activate#(N) | U83#(tt, M, N) | → | activate#(M) | |
| activate#(n__x(X1, X2)) | → | x#(activate(X1), activate(X2)) | U41#(tt, V2) | → | activate#(V2) | |
| U13#(tt, V1, V2) | → | U14#(isNatKind(activate(V2)), activate(V1), activate(V2)) | U33#(tt, V1, V2) | → | isNatKind#(activate(V2)) | |
| U101#(tt, M, N) | → | activate#(M) | U35#(tt, V2) | → | isNat#(activate(V2)) | |
| U61#(tt, V2) | → | activate#(V2) | U31#(tt, V1, V2) | → | activate#(V1) | |
| U83#(tt, M, N) | → | U84#(isNatKind(activate(N)), activate(M), activate(N)) | U72#(tt, N) | → | activate#(N) | |
| x#(N, 0) | → | U91#(isNat(N), N) | U61#(tt, V2) | → | isNatKind#(activate(V2)) | |
| U71#(tt, N) | → | activate#(N) | plus#(N, s(M)) | → | isNat#(M) | |
| U71#(tt, N) | → | isNatKind#(activate(N)) | U82#(tt, M, N) | → | isNat#(activate(N)) | |
| U14#(tt, V1, V2) | → | activate#(V1) | U104#(tt, M, N) | → | x#(activate(N), activate(M)) |
| U101(tt, M, N) | → | U102(isNatKind(activate(M)), activate(M), activate(N)) | U102(tt, M, N) | → | U103(isNat(activate(N)), activate(M), activate(N)) | |
| U103(tt, M, N) | → | U104(isNatKind(activate(N)), activate(M), activate(N)) | U104(tt, M, N) | → | plus(x(activate(N), activate(M)), activate(N)) | |
| U11(tt, V1, V2) | → | U12(isNatKind(activate(V1)), activate(V1), activate(V2)) | U12(tt, V1, V2) | → | U13(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| U13(tt, V1, V2) | → | U14(isNatKind(activate(V2)), activate(V1), activate(V2)) | U14(tt, V1, V2) | → | U15(isNat(activate(V1)), activate(V2)) | |
| U15(tt, V2) | → | U16(isNat(activate(V2))) | U16(tt) | → | tt | |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | U22(tt, V1) | → | U23(isNat(activate(V1))) | |
| U23(tt) | → | tt | U31(tt, V1, V2) | → | U32(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| U32(tt, V1, V2) | → | U33(isNatKind(activate(V2)), activate(V1), activate(V2)) | U33(tt, V1, V2) | → | U34(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| U34(tt, V1, V2) | → | U35(isNat(activate(V1)), activate(V2)) | U35(tt, V2) | → | U36(isNat(activate(V2))) | |
| U36(tt) | → | tt | U41(tt, V2) | → | U42(isNatKind(activate(V2))) | |
| U42(tt) | → | tt | U51(tt) | → | tt | |
| U61(tt, V2) | → | U62(isNatKind(activate(V2))) | U62(tt) | → | tt | |
| U71(tt, N) | → | U72(isNatKind(activate(N)), activate(N)) | U72(tt, N) | → | activate(N) | |
| U81(tt, M, N) | → | U82(isNatKind(activate(M)), activate(M), activate(N)) | U82(tt, M, N) | → | U83(isNat(activate(N)), activate(M), activate(N)) | |
| U83(tt, M, N) | → | U84(isNatKind(activate(N)), activate(M), activate(N)) | U84(tt, M, N) | → | s(plus(activate(N), activate(M))) | |
| U91(tt, N) | → | U92(isNatKind(activate(N))) | U92(tt) | → | 0 | |
| isNat(n__0) | → | tt | isNat(n__plus(V1, V2)) | → | U11(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | isNat(n__x(V1, V2)) | → | U31(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| isNatKind(n__0) | → | tt | isNatKind(n__plus(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V2)) | |
| isNatKind(n__s(V1)) | → | U51(isNatKind(activate(V1))) | isNatKind(n__x(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) | |
| plus(N, 0) | → | U71(isNat(N), N) | plus(N, s(M)) | → | U81(isNat(M), M, N) | |
| x(N, 0) | → | U91(isNat(N), N) | x(N, s(M)) | → | U101(isNat(M), M, N) | |
| 0 | → | n__0 | plus(X1, X2) | → | n__plus(X1, X2) | |
| s(X) | → | n__s(X) | x(X1, X2) | → | n__x(X1, X2) | |
| activate(n__0) | → | 0 | activate(n__plus(X1, X2)) | → | plus(activate(X1), activate(X2)) | |
| activate(n__s(X)) | → | s(activate(X)) | activate(n__x(X1, X2)) | → | x(activate(X1), activate(X2)) | |
| activate(X) | → | X |
Termination of terms over the following signature is verified: U104, n__plus, n__s, isNat, activate, U62, n__0, U61, U42, U92, U41, U91, U23, U21, n__x, U22, plus, isNatKind, U83, U84, U71, U36, U72, 0, s, U51, U14, tt, U15, U82, U16, U81, U11, U12, U13, U31, U102, U32, U103, U33, U34, x, U101, U35
| U81#(tt, M, N) | → | isNatKind#(activate(M)) | U91#(tt, N) | → | activate#(N) | |
| activate#(n__x(X1, X2)) | → | activate#(X1) | U34#(tt, V1, V2) | → | activate#(V1) | |
| U15#(tt, V2) | → | isNat#(activate(V2)) | U32#(tt, V1, V2) | → | isNatKind#(activate(V2)) | |
| U71#(tt, N) | → | U72#(isNatKind(activate(N)), activate(N)) | plus#(N, 0) | → | U71#(isNat(N), N) | |
| U33#(tt, V1, V2) | → | U34#(isNatKind(activate(V2)), activate(V1), activate(V2)) | activate#(n__x(X1, X2)) | → | activate#(X2) | |
| isNatKind#(n__plus(V1, V2)) | → | isNatKind#(activate(V1)) | U103#(tt, M, N) | → | U104#(isNatKind(activate(N)), activate(M), activate(N)) | |
| x#(N, s(M)) | → | isNat#(M) | U103#(tt, M, N) | → | isNatKind#(activate(N)) | |
| U84#(tt, M, N) | → | activate#(M) | isNatKind#(n__x(V1, V2)) | → | isNatKind#(activate(V1)) | |
| U32#(tt, V1, V2) | → | U33#(isNatKind(activate(V2)), activate(V1), activate(V2)) | isNatKind#(n__s(V1)) | → | U51#(isNatKind(activate(V1))) | |
| U84#(tt, M, N) | → | s#(plus(activate(N), activate(M))) | isNat#(n__plus(V1, V2)) | → | activate#(V1) | |
| x#(N, s(M)) | → | U101#(isNat(M), M, N) | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) | |
| U34#(tt, V1, V2) | → | isNat#(activate(V1)) | isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | |
| isNatKind#(n__x(V1, V2)) | → | activate#(V1) | activate#(n__s(X)) | → | activate#(X) | |
| U82#(tt, M, N) | → | activate#(N) | U14#(tt, V1, V2) | → | U15#(isNat(activate(V1)), activate(V2)) | |
| isNatKind#(n__s(V1)) | → | activate#(V1) | U81#(tt, M, N) | → | U82#(isNatKind(activate(M)), activate(M), activate(N)) | |
| U13#(tt, V1, V2) | → | activate#(V1) | isNat#(n__plus(V1, V2)) | → | activate#(V2) | |
| U104#(tt, M, N) | → | activate#(N) | plus#(N, 0) | → | isNat#(N) | |
| U11#(tt, V1, V2) | → | activate#(V2) | x#(N, 0) | → | isNat#(N) | |
| activate#(n__plus(X1, X2)) | → | activate#(X2) | U11#(tt, V1, V2) | → | U12#(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| isNatKind#(n__plus(V1, V2)) | → | activate#(V2) | isNatKind#(n__x(V1, V2)) | → | activate#(V2) | |
| isNat#(n__x(V1, V2)) | → | activate#(V1) | U102#(tt, M, N) | → | isNat#(activate(N)) | |
| isNat#(n__x(V1, V2)) | → | U31#(isNatKind(activate(V1)), activate(V1), activate(V2)) | activate#(n__plus(X1, X2)) | → | activate#(X1) | |
| isNatKind#(n__plus(V1, V2)) | → | activate#(V1) | U84#(tt, M, N) | → | plus#(activate(N), activate(M)) | |
| U11#(tt, V1, V2) | → | isNatKind#(activate(V1)) | U21#(tt, V1) | → | activate#(V1) | |
| U35#(tt, V2) | → | activate#(V2) | U91#(tt, N) | → | isNatKind#(activate(N)) | |
| U31#(tt, V1, V2) | → | U32#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) | → | activate#(M) | |
| isNat#(n__plus(V1, V2)) | → | U11#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) | → | activate#(N) | |
| U34#(tt, V1, V2) | → | U35#(isNat(activate(V1)), activate(V2)) | U83#(tt, M, N) | → | isNatKind#(activate(N)) | |
| U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | activate#(n__s(X)) | → | s#(activate(X)) | |
| U34#(tt, V1, V2) | → | activate#(V2) | U82#(tt, M, N) | → | U83#(isNat(activate(N)), activate(M), activate(N)) | |
| U81#(tt, M, N) | → | activate#(M) | U104#(tt, M, N) | → | activate#(M) | |
| isNatKind#(n__plus(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V2)) | isNat#(n__x(V1, V2)) | → | activate#(V2) | |
| U101#(tt, M, N) | → | isNatKind#(activate(M)) | U21#(tt, V1) | → | isNatKind#(activate(V1)) | |
| U82#(tt, M, N) | → | activate#(M) | U12#(tt, V1, V2) | → | U13#(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| U13#(tt, V1, V2) | → | isNatKind#(activate(V2)) | isNatKind#(n__x(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | |
| U32#(tt, V1, V2) | → | activate#(V1) | U14#(tt, V1, V2) | → | isNat#(activate(V1)) | |
| U92#(tt) | → | 0# | U12#(tt, V1, V2) | → | activate#(V1) | |
| U12#(tt, V1, V2) | → | isNatKind#(activate(V2)) | U33#(tt, V1, V2) | → | activate#(V2) | |
| U81#(tt, M, N) | → | activate#(N) | isNat#(n__s(V1)) | → | activate#(V1) | |
| plus#(N, s(M)) | → | U81#(isNat(M), M, N) | U33#(tt, V1, V2) | → | activate#(V1) | |
| U32#(tt, V1, V2) | → | activate#(V2) | U102#(tt, M, N) | → | activate#(N) | |
| U101#(tt, M, N) | → | U102#(isNatKind(activate(M)), activate(M), activate(N)) | U14#(tt, V1, V2) | → | activate#(V2) | |
| U31#(tt, V1, V2) | → | activate#(V2) | U15#(tt, V2) | → | activate#(V2) | |
| U11#(tt, V1, V2) | → | activate#(V1) | U104#(tt, M, N) | → | plus#(x(activate(N), activate(M)), activate(N)) | |
| activate#(n__0) | → | 0# | U22#(tt, V1) | → | activate#(V1) | |
| U41#(tt, V2) | → | isNatKind#(activate(V2)) | U102#(tt, M, N) | → | activate#(M) | |
| U35#(tt, V2) | → | U36#(isNat(activate(V2))) | U102#(tt, M, N) | → | U103#(isNat(activate(N)), activate(M), activate(N)) | |
| U84#(tt, M, N) | → | activate#(N) | isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | |
| U101#(tt, M, N) | → | activate#(N) | U22#(tt, V1) | → | U23#(isNat(activate(V1))) | |
| U61#(tt, V2) | → | U62#(isNatKind(activate(V2))) | U13#(tt, V1, V2) | → | activate#(V2) | |
| U31#(tt, V1, V2) | → | isNatKind#(activate(V1)) | isNat#(n__plus(V1, V2)) | → | isNatKind#(activate(V1)) | |
| U22#(tt, V1) | → | isNat#(activate(V1)) | isNat#(n__x(V1, V2)) | → | isNatKind#(activate(V1)) | |
| activate#(n__plus(X1, X2)) | → | plus#(activate(X1), activate(X2)) | U83#(tt, M, N) | → | activate#(N) | |
| U12#(tt, V1, V2) | → | activate#(V2) | U83#(tt, M, N) | → | activate#(M) | |
| activate#(n__x(X1, X2)) | → | x#(activate(X1), activate(X2)) | U41#(tt, V2) | → | activate#(V2) | |
| U13#(tt, V1, V2) | → | U14#(isNatKind(activate(V2)), activate(V1), activate(V2)) | U33#(tt, V1, V2) | → | isNatKind#(activate(V2)) | |
| U35#(tt, V2) | → | isNat#(activate(V2)) | U101#(tt, M, N) | → | activate#(M) | |
| U61#(tt, V2) | → | activate#(V2) | U31#(tt, V1, V2) | → | activate#(V1) | |
| U83#(tt, M, N) | → | U84#(isNatKind(activate(N)), activate(M), activate(N)) | U91#(tt, N) | → | U92#(isNatKind(activate(N))) | |
| U72#(tt, N) | → | activate#(N) | x#(N, 0) | → | U91#(isNat(N), N) | |
| U15#(tt, V2) | → | U16#(isNat(activate(V2))) | U61#(tt, V2) | → | isNatKind#(activate(V2)) | |
| U71#(tt, N) | → | activate#(N) | plus#(N, s(M)) | → | isNat#(M) | |
| U71#(tt, N) | → | isNatKind#(activate(N)) | U82#(tt, M, N) | → | isNat#(activate(N)) | |
| U14#(tt, V1, V2) | → | activate#(V1) | U104#(tt, M, N) | → | x#(activate(N), activate(M)) | |
| U41#(tt, V2) | → | U42#(isNatKind(activate(V2))) |
| U101(tt, M, N) | → | U102(isNatKind(activate(M)), activate(M), activate(N)) | U102(tt, M, N) | → | U103(isNat(activate(N)), activate(M), activate(N)) | |
| U103(tt, M, N) | → | U104(isNatKind(activate(N)), activate(M), activate(N)) | U104(tt, M, N) | → | plus(x(activate(N), activate(M)), activate(N)) | |
| U11(tt, V1, V2) | → | U12(isNatKind(activate(V1)), activate(V1), activate(V2)) | U12(tt, V1, V2) | → | U13(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| U13(tt, V1, V2) | → | U14(isNatKind(activate(V2)), activate(V1), activate(V2)) | U14(tt, V1, V2) | → | U15(isNat(activate(V1)), activate(V2)) | |
| U15(tt, V2) | → | U16(isNat(activate(V2))) | U16(tt) | → | tt | |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | U22(tt, V1) | → | U23(isNat(activate(V1))) | |
| U23(tt) | → | tt | U31(tt, V1, V2) | → | U32(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| U32(tt, V1, V2) | → | U33(isNatKind(activate(V2)), activate(V1), activate(V2)) | U33(tt, V1, V2) | → | U34(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| U34(tt, V1, V2) | → | U35(isNat(activate(V1)), activate(V2)) | U35(tt, V2) | → | U36(isNat(activate(V2))) | |
| U36(tt) | → | tt | U41(tt, V2) | → | U42(isNatKind(activate(V2))) | |
| U42(tt) | → | tt | U51(tt) | → | tt | |
| U61(tt, V2) | → | U62(isNatKind(activate(V2))) | U62(tt) | → | tt | |
| U71(tt, N) | → | U72(isNatKind(activate(N)), activate(N)) | U72(tt, N) | → | activate(N) | |
| U81(tt, M, N) | → | U82(isNatKind(activate(M)), activate(M), activate(N)) | U82(tt, M, N) | → | U83(isNat(activate(N)), activate(M), activate(N)) | |
| U83(tt, M, N) | → | U84(isNatKind(activate(N)), activate(M), activate(N)) | U84(tt, M, N) | → | s(plus(activate(N), activate(M))) | |
| U91(tt, N) | → | U92(isNatKind(activate(N))) | U92(tt) | → | 0 | |
| isNat(n__0) | → | tt | isNat(n__plus(V1, V2)) | → | U11(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | isNat(n__x(V1, V2)) | → | U31(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| isNatKind(n__0) | → | tt | isNatKind(n__plus(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V2)) | |
| isNatKind(n__s(V1)) | → | U51(isNatKind(activate(V1))) | isNatKind(n__x(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) | |
| plus(N, 0) | → | U71(isNat(N), N) | plus(N, s(M)) | → | U81(isNat(M), M, N) | |
| x(N, 0) | → | U91(isNat(N), N) | x(N, s(M)) | → | U101(isNat(M), M, N) | |
| 0 | → | n__0 | plus(X1, X2) | → | n__plus(X1, X2) | |
| s(X) | → | n__s(X) | x(X1, X2) | → | n__x(X1, X2) | |
| activate(n__0) | → | 0 | activate(n__plus(X1, X2)) | → | plus(activate(X1), activate(X2)) | |
| activate(n__s(X)) | → | s(activate(X)) | activate(n__x(X1, X2)) | → | x(activate(X1), activate(X2)) | |
| activate(X) | → | X |
Termination of terms over the following signature is verified: U104, n__plus, activate, isNat, n__s, U62, U61, n__0, U42, U41, U92, U91, U23, U21, n__x, U22, plus, isNatKind, U83, U84, U71, U36, U72, 0, U14, U51, s, U15, tt, U16, U82, U81, U11, U12, U31, U13, U32, U102, U33, U103, U34, U35, U101, x
| U81#(tt, M, N) → isNatKind#(activate(M)) | activate#(n__x(X1, X2)) → activate#(X1) |
| U91#(tt, N) → activate#(N) | U34#(tt, V1, V2) → activate#(V1) |
| U32#(tt, V1, V2) → isNatKind#(activate(V2)) | U15#(tt, V2) → isNat#(activate(V2)) |
| U71#(tt, N) → U72#(isNatKind(activate(N)), activate(N)) | plus#(N, 0) → U71#(isNat(N), N) |
| U33#(tt, V1, V2) → U34#(isNatKind(activate(V2)), activate(V1), activate(V2)) | activate#(n__x(X1, X2)) → activate#(X2) |
| isNatKind#(n__plus(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, M, N) → U104#(isNatKind(activate(N)), activate(M), activate(N)) |
| x#(N, s(M)) → isNat#(M) | U84#(tt, M, N) → activate#(M) |
| U103#(tt, M, N) → isNatKind#(activate(N)) | isNatKind#(n__x(V1, V2)) → isNatKind#(activate(V1)) |
| U32#(tt, V1, V2) → U33#(isNatKind(activate(V2)), activate(V1), activate(V2)) | isNat#(n__plus(V1, V2)) → activate#(V1) |
| x#(N, s(M)) → U101#(isNat(M), M, N) | isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) |
| U34#(tt, V1, V2) → isNat#(activate(V1)) | isNat#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatKind#(n__x(V1, V2)) → activate#(V1) | activate#(n__s(X)) → activate#(X) |
| U82#(tt, M, N) → activate#(N) | U14#(tt, V1, V2) → U15#(isNat(activate(V1)), activate(V2)) |
| isNatKind#(n__s(V1)) → activate#(V1) | U81#(tt, M, N) → U82#(isNatKind(activate(M)), activate(M), activate(N)) |
| U13#(tt, V1, V2) → activate#(V1) | U104#(tt, M, N) → activate#(N) |
| plus#(N, 0) → isNat#(N) | isNat#(n__plus(V1, V2)) → activate#(V2) |
| U11#(tt, V1, V2) → activate#(V2) | x#(N, 0) → isNat#(N) |
| activate#(n__plus(X1, X2)) → activate#(X2) | U11#(tt, V1, V2) → U12#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatKind#(n__plus(V1, V2)) → activate#(V2) | isNatKind#(n__x(V1, V2)) → activate#(V2) |
| isNat#(n__x(V1, V2)) → activate#(V1) | isNat#(n__x(V1, V2)) → U31#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102#(tt, M, N) → isNat#(activate(N)) | activate#(n__plus(X1, X2)) → activate#(X1) |
| isNatKind#(n__plus(V1, V2)) → activate#(V1) | U84#(tt, M, N) → plus#(activate(N), activate(M)) |
| U11#(tt, V1, V2) → isNatKind#(activate(V1)) | U21#(tt, V1) → activate#(V1) |
| U91#(tt, N) → isNatKind#(activate(N)) | U35#(tt, V2) → activate#(V2) |
| U31#(tt, V1, V2) → U32#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) → activate#(M) |
| isNat#(n__plus(V1, V2)) → U11#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) → activate#(N) |
| U34#(tt, V1, V2) → U35#(isNat(activate(V1)), activate(V2)) | U83#(tt, M, N) → isNatKind#(activate(N)) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | U34#(tt, V1, V2) → activate#(V2) |
| U82#(tt, M, N) → U83#(isNat(activate(N)), activate(M), activate(N)) | U81#(tt, M, N) → activate#(M) |
| U104#(tt, M, N) → activate#(M) | isNatKind#(n__plus(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V2)) |
| U101#(tt, M, N) → isNatKind#(activate(M)) | isNat#(n__x(V1, V2)) → activate#(V2) |
| U82#(tt, M, N) → activate#(M) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U12#(tt, V1, V2) → U13#(isNatKind(activate(V2)), activate(V1), activate(V2)) | U13#(tt, V1, V2) → isNatKind#(activate(V2)) |
| isNatKind#(n__x(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U32#(tt, V1, V2) → activate#(V1) |
| U14#(tt, V1, V2) → isNat#(activate(V1)) | U12#(tt, V1, V2) → activate#(V1) |
| U12#(tt, V1, V2) → isNatKind#(activate(V2)) | U81#(tt, M, N) → activate#(N) |
| U33#(tt, V1, V2) → activate#(V2) | isNat#(n__s(V1)) → activate#(V1) |
| plus#(N, s(M)) → U81#(isNat(M), M, N) | U33#(tt, V1, V2) → activate#(V1) |
| U32#(tt, V1, V2) → activate#(V2) | U102#(tt, M, N) → activate#(N) |
| U101#(tt, M, N) → U102#(isNatKind(activate(M)), activate(M), activate(N)) | U14#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V1, V2) → activate#(V2) | U15#(tt, V2) → activate#(V2) |
| U11#(tt, V1, V2) → activate#(V1) | U104#(tt, M, N) → plus#(x(activate(N), activate(M)), activate(N)) |
| U41#(tt, V2) → isNatKind#(activate(V2)) | U22#(tt, V1) → activate#(V1) |
| U102#(tt, M, N) → activate#(M) | U102#(tt, M, N) → U103#(isNat(activate(N)), activate(M), activate(N)) |
| U84#(tt, M, N) → activate#(N) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U101#(tt, M, N) → activate#(N) | U31#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U13#(tt, V1, V2) → activate#(V2) | isNat#(n__plus(V1, V2)) → isNatKind#(activate(V1)) |
| U22#(tt, V1) → isNat#(activate(V1)) | activate#(n__plus(X1, X2)) → plus#(activate(X1), activate(X2)) |
| isNat#(n__x(V1, V2)) → isNatKind#(activate(V1)) | U83#(tt, M, N) → activate#(N) |
| U12#(tt, V1, V2) → activate#(V2) | U83#(tt, M, N) → activate#(M) |
| activate#(n__x(X1, X2)) → x#(activate(X1), activate(X2)) | U41#(tt, V2) → activate#(V2) |
| U13#(tt, V1, V2) → U14#(isNatKind(activate(V2)), activate(V1), activate(V2)) | U33#(tt, V1, V2) → isNatKind#(activate(V2)) |
| U35#(tt, V2) → isNat#(activate(V2)) | U101#(tt, M, N) → activate#(M) |
| U61#(tt, V2) → activate#(V2) | U31#(tt, V1, V2) → activate#(V1) |
| U83#(tt, M, N) → U84#(isNatKind(activate(N)), activate(M), activate(N)) | U72#(tt, N) → activate#(N) |
| x#(N, 0) → U91#(isNat(N), N) | U61#(tt, V2) → isNatKind#(activate(V2)) |
| U71#(tt, N) → activate#(N) | plus#(N, s(M)) → isNat#(M) |
| U71#(tt, N) → isNatKind#(activate(N)) | U82#(tt, M, N) → isNat#(activate(N)) |
| U14#(tt, V1, V2) → activate#(V1) | U104#(tt, M, N) → x#(activate(N), activate(M)) |
| U81#(tt, M, N) → isNatKind#(activate(M)) | activate#(n__x(X1, X2)) → activate#(X1) |
| U91#(tt, N) → activate#(N) | U34#(tt, V1, V2) → activate#(V1) |
| U32#(tt, V1, V2) → isNatKind#(activate(V2)) | U15#(tt, V2) → isNat#(activate(V2)) |
| U71#(tt, N) → U72#(isNatKind(activate(N)), activate(N)) | plus#(N, 0) → U71#(isNat(N), N) |
| U33#(tt, V1, V2) → U34#(isNatKind(activate(V2)), activate(V1), activate(V2)) | activate#(n__x(X1, X2)) → activate#(X2) |
| isNatKind#(n__plus(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, M, N) → U104#(isNatKind(activate(N)), activate(M), activate(N)) |
| x#(N, s(M)) → isNat#(M) | U84#(tt, M, N) → activate#(M) |
| U103#(tt, M, N) → isNatKind#(activate(N)) | isNatKind#(n__x(V1, V2)) → isNatKind#(activate(V1)) |
| U32#(tt, V1, V2) → U33#(isNatKind(activate(V2)), activate(V1), activate(V2)) | isNat#(n__plus(V1, V2)) → activate#(V1) |
| x#(N, s(M)) → U101#(isNat(M), M, N) | isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) |
| U34#(tt, V1, V2) → isNat#(activate(V1)) | isNat#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatKind#(n__x(V1, V2)) → activate#(V1) | activate#(n__s(X)) → activate#(X) |
| U82#(tt, M, N) → activate#(N) | U14#(tt, V1, V2) → U15#(isNat(activate(V1)), activate(V2)) |
| isNatKind#(n__s(V1)) → activate#(V1) | U81#(tt, M, N) → U82#(isNatKind(activate(M)), activate(M), activate(N)) |
| U13#(tt, V1, V2) → activate#(V1) | U104#(tt, M, N) → activate#(N) |
| plus#(N, 0) → isNat#(N) | isNat#(n__plus(V1, V2)) → activate#(V2) |
| U11#(tt, V1, V2) → activate#(V2) | x#(N, 0) → isNat#(N) |
| activate#(n__plus(X1, X2)) → activate#(X2) | U11#(tt, V1, V2) → U12#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatKind#(n__plus(V1, V2)) → activate#(V2) | isNatKind#(n__x(V1, V2)) → activate#(V2) |
| isNat#(n__x(V1, V2)) → activate#(V1) | isNat#(n__x(V1, V2)) → U31#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102#(tt, M, N) → isNat#(activate(N)) | activate#(n__plus(X1, X2)) → activate#(X1) |
| isNatKind#(n__plus(V1, V2)) → activate#(V1) | U84#(tt, M, N) → plus#(activate(N), activate(M)) |
| U11#(tt, V1, V2) → isNatKind#(activate(V1)) | U21#(tt, V1) → activate#(V1) |
| U91#(tt, N) → isNatKind#(activate(N)) | U35#(tt, V2) → activate#(V2) |
| U31#(tt, V1, V2) → U32#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) → activate#(M) |
| isNat#(n__plus(V1, V2)) → U11#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) → activate#(N) |
| U34#(tt, V1, V2) → U35#(isNat(activate(V1)), activate(V2)) | U83#(tt, M, N) → isNatKind#(activate(N)) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | U34#(tt, V1, V2) → activate#(V2) |
| U82#(tt, M, N) → U83#(isNat(activate(N)), activate(M), activate(N)) | U81#(tt, M, N) → activate#(M) |
| U104#(tt, M, N) → activate#(M) | isNatKind#(n__plus(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V2)) |
| U101#(tt, M, N) → isNatKind#(activate(M)) | isNat#(n__x(V1, V2)) → activate#(V2) |
| U82#(tt, M, N) → activate#(M) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U12#(tt, V1, V2) → U13#(isNatKind(activate(V2)), activate(V1), activate(V2)) | U13#(tt, V1, V2) → isNatKind#(activate(V2)) |
| isNatKind#(n__x(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U32#(tt, V1, V2) → activate#(V1) |
| U14#(tt, V1, V2) → isNat#(activate(V1)) | U12#(tt, V1, V2) → activate#(V1) |
| U12#(tt, V1, V2) → isNatKind#(activate(V2)) | U81#(tt, M, N) → activate#(N) |
| U33#(tt, V1, V2) → activate#(V2) | isNat#(n__s(V1)) → activate#(V1) |
| plus#(N, s(M)) → U81#(isNat(M), M, N) | U33#(tt, V1, V2) → activate#(V1) |
| U32#(tt, V1, V2) → activate#(V2) | U102#(tt, M, N) → activate#(N) |
| U101#(tt, M, N) → U102#(isNatKind(activate(M)), activate(M), activate(N)) | U14#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V1, V2) → activate#(V2) | U15#(tt, V2) → activate#(V2) |
| U11#(tt, V1, V2) → activate#(V1) | U104#(tt, M, N) → plus#(x(activate(N), activate(M)), activate(N)) |
| U22#(tt, V1) → activate#(V1) | U41#(tt, V2) → isNatKind#(activate(V2)) |
| U102#(tt, M, N) → activate#(M) | U102#(tt, M, N) → U103#(isNat(activate(N)), activate(M), activate(N)) |
| U84#(tt, M, N) → activate#(N) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U22#(tt, V1) → U23#(isNat(activate(V1))) | U101#(tt, M, N) → activate#(N) |
| U31#(tt, V1, V2) → isNatKind#(activate(V1)) | U13#(tt, V1, V2) → activate#(V2) |
| isNat#(n__plus(V1, V2)) → isNatKind#(activate(V1)) | U22#(tt, V1) → isNat#(activate(V1)) |
| activate#(n__plus(X1, X2)) → plus#(activate(X1), activate(X2)) | isNat#(n__x(V1, V2)) → isNatKind#(activate(V1)) |
| U83#(tt, M, N) → activate#(N) | U12#(tt, V1, V2) → activate#(V2) |
| U83#(tt, M, N) → activate#(M) | activate#(n__x(X1, X2)) → x#(activate(X1), activate(X2)) |
| U41#(tt, V2) → activate#(V2) | U13#(tt, V1, V2) → U14#(isNatKind(activate(V2)), activate(V1), activate(V2)) |
| U33#(tt, V1, V2) → isNatKind#(activate(V2)) | U35#(tt, V2) → isNat#(activate(V2)) |
| U101#(tt, M, N) → activate#(M) | U61#(tt, V2) → activate#(V2) |
| U31#(tt, V1, V2) → activate#(V1) | U83#(tt, M, N) → U84#(isNatKind(activate(N)), activate(M), activate(N)) |
| U72#(tt, N) → activate#(N) | x#(N, 0) → U91#(isNat(N), N) |
| U61#(tt, V2) → isNatKind#(activate(V2)) | U71#(tt, N) → activate#(N) |
| plus#(N, s(M)) → isNat#(M) | U71#(tt, N) → isNatKind#(activate(N)) |
| U82#(tt, M, N) → isNat#(activate(N)) | U14#(tt, V1, V2) → activate#(V1) |
| U104#(tt, M, N) → x#(activate(N), activate(M)) |
| U81#(tt, M, N) → isNatKind#(activate(M)) | U91#(tt, N) → activate#(N) |
| activate#(n__x(X1, X2)) → activate#(X1) | U34#(tt, V1, V2) → activate#(V1) |
| U32#(tt, V1, V2) → isNatKind#(activate(V2)) | U15#(tt, V2) → isNat#(activate(V2)) |
| U71#(tt, N) → U72#(isNatKind(activate(N)), activate(N)) | plus#(N, 0) → U71#(isNat(N), N) |
| U33#(tt, V1, V2) → U34#(isNatKind(activate(V2)), activate(V1), activate(V2)) | activate#(n__x(X1, X2)) → activate#(X2) |
| isNatKind#(n__plus(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, M, N) → U104#(isNatKind(activate(N)), activate(M), activate(N)) |
| x#(N, s(M)) → isNat#(M) | U103#(tt, M, N) → isNatKind#(activate(N)) |
| U84#(tt, M, N) → activate#(M) | isNatKind#(n__x(V1, V2)) → isNatKind#(activate(V1)) |
| U32#(tt, V1, V2) → U33#(isNatKind(activate(V2)), activate(V1), activate(V2)) | U84#(tt, M, N) → s#(plus(activate(N), activate(M))) |
| isNat#(n__plus(V1, V2)) → activate#(V1) | x#(N, s(M)) → U101#(isNat(M), M, N) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | U34#(tt, V1, V2) → isNat#(activate(V1)) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatKind#(n__x(V1, V2)) → activate#(V1) |
| activate#(n__s(X)) → activate#(X) | U82#(tt, M, N) → activate#(N) |
| U14#(tt, V1, V2) → U15#(isNat(activate(V1)), activate(V2)) | isNatKind#(n__s(V1)) → activate#(V1) |
| U81#(tt, M, N) → U82#(isNatKind(activate(M)), activate(M), activate(N)) | U13#(tt, V1, V2) → activate#(V1) |
| U104#(tt, M, N) → activate#(N) | plus#(N, 0) → isNat#(N) |
| isNat#(n__plus(V1, V2)) → activate#(V2) | x#(N, 0) → isNat#(N) |
| U11#(tt, V1, V2) → activate#(V2) | activate#(n__plus(X1, X2)) → activate#(X2) |
| U11#(tt, V1, V2) → U12#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatKind#(n__plus(V1, V2)) → activate#(V2) |
| isNatKind#(n__x(V1, V2)) → activate#(V2) | isNat#(n__x(V1, V2)) → activate#(V1) |
| isNat#(n__x(V1, V2)) → U31#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U102#(tt, M, N) → isNat#(activate(N)) |
| activate#(n__plus(X1, X2)) → activate#(X1) | isNatKind#(n__plus(V1, V2)) → activate#(V1) |
| U84#(tt, M, N) → plus#(activate(N), activate(M)) | U11#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U21#(tt, V1) → activate#(V1) | U91#(tt, N) → isNatKind#(activate(N)) |
| U35#(tt, V2) → activate#(V2) | U31#(tt, V1, V2) → U32#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U103#(tt, M, N) → activate#(M) | isNat#(n__plus(V1, V2)) → U11#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U103#(tt, M, N) → activate#(N) | U34#(tt, V1, V2) → U35#(isNat(activate(V1)), activate(V2)) |
| U83#(tt, M, N) → isNatKind#(activate(N)) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| U34#(tt, V1, V2) → activate#(V2) | U82#(tt, M, N) → U83#(isNat(activate(N)), activate(M), activate(N)) |
| U81#(tt, M, N) → activate#(M) | U104#(tt, M, N) → activate#(M) |
| isNatKind#(n__plus(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V2)) | U101#(tt, M, N) → isNatKind#(activate(M)) |
| isNat#(n__x(V1, V2)) → activate#(V2) | U82#(tt, M, N) → activate#(M) |
| U21#(tt, V1) → isNatKind#(activate(V1)) | U12#(tt, V1, V2) → U13#(isNatKind(activate(V2)), activate(V1), activate(V2)) |
| U13#(tt, V1, V2) → isNatKind#(activate(V2)) | isNatKind#(n__x(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) |
| U32#(tt, V1, V2) → activate#(V1) | U14#(tt, V1, V2) → isNat#(activate(V1)) |
| U12#(tt, V1, V2) → activate#(V1) | U12#(tt, V1, V2) → isNatKind#(activate(V2)) |
| U33#(tt, V1, V2) → activate#(V2) | U81#(tt, M, N) → activate#(N) |
| isNat#(n__s(V1)) → activate#(V1) | plus#(N, s(M)) → U81#(isNat(M), M, N) |
| U33#(tt, V1, V2) → activate#(V1) | U32#(tt, V1, V2) → activate#(V2) |
| U102#(tt, M, N) → activate#(N) | U101#(tt, M, N) → U102#(isNatKind(activate(M)), activate(M), activate(N)) |
| U14#(tt, V1, V2) → activate#(V2) | U31#(tt, V1, V2) → activate#(V2) |
| U15#(tt, V2) → activate#(V2) | U11#(tt, V1, V2) → activate#(V1) |
| U104#(tt, M, N) → plus#(x(activate(N), activate(M)), activate(N)) | U41#(tt, V2) → isNatKind#(activate(V2)) |
| U22#(tt, V1) → activate#(V1) | U102#(tt, M, N) → activate#(M) |
| U102#(tt, M, N) → U103#(isNat(activate(N)), activate(M), activate(N)) | U84#(tt, M, N) → activate#(N) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U101#(tt, M, N) → activate#(N) |
| U31#(tt, V1, V2) → isNatKind#(activate(V1)) | U13#(tt, V1, V2) → activate#(V2) |
| isNat#(n__plus(V1, V2)) → isNatKind#(activate(V1)) | U22#(tt, V1) → isNat#(activate(V1)) |
| activate#(n__plus(X1, X2)) → plus#(activate(X1), activate(X2)) | isNat#(n__x(V1, V2)) → isNatKind#(activate(V1)) |
| U83#(tt, M, N) → activate#(N) | U12#(tt, V1, V2) → activate#(V2) |
| U83#(tt, M, N) → activate#(M) | activate#(n__x(X1, X2)) → x#(activate(X1), activate(X2)) |
| U41#(tt, V2) → activate#(V2) | U13#(tt, V1, V2) → U14#(isNatKind(activate(V2)), activate(V1), activate(V2)) |
| U33#(tt, V1, V2) → isNatKind#(activate(V2)) | U101#(tt, M, N) → activate#(M) |
| U35#(tt, V2) → isNat#(activate(V2)) | U61#(tt, V2) → activate#(V2) |
| U31#(tt, V1, V2) → activate#(V1) | U83#(tt, M, N) → U84#(isNatKind(activate(N)), activate(M), activate(N)) |
| U72#(tt, N) → activate#(N) | x#(N, 0) → U91#(isNat(N), N) |
| U61#(tt, V2) → isNatKind#(activate(V2)) | U71#(tt, N) → activate#(N) |
| plus#(N, s(M)) → isNat#(M) | U71#(tt, N) → isNatKind#(activate(N)) |
| U82#(tt, M, N) → isNat#(activate(N)) | U14#(tt, V1, V2) → activate#(V1) |
| U104#(tt, M, N) → x#(activate(N), activate(M)) |
| U81#(tt, M, N) | → | isNatKind#(activate(M)) | activate#(n__x(X1, X2)) | → | activate#(X1) | |
| U91#(tt, N) | → | activate#(N) | U34#(tt, V1, V2) | → | activate#(V1) | |
| U32#(tt, V1, V2) | → | isNatKind#(activate(V2)) | U15#(tt, V2) | → | isNat#(activate(V2)) | |
| U71#(tt, N) | → | U72#(isNatKind(activate(N)), activate(N)) | plus#(N, 0) | → | U71#(isNat(N), N) | |
| U33#(tt, V1, V2) | → | U34#(isNatKind(activate(V2)), activate(V1), activate(V2)) | activate#(n__x(X1, X2)) | → | activate#(X2) | |
| isNatKind#(n__plus(V1, V2)) | → | isNatKind#(activate(V1)) | U103#(tt, M, N) | → | U104#(isNatKind(activate(N)), activate(M), activate(N)) | |
| x#(N, s(M)) | → | isNat#(M) | U103#(tt, M, N) | → | isNatKind#(activate(N)) | |
| U84#(tt, M, N) | → | activate#(M) | U32#(tt, V1, V2) | → | U33#(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| isNatKind#(n__x(V1, V2)) | → | isNatKind#(activate(V1)) | isNat#(n__plus(V1, V2)) | → | activate#(V1) | |
| x#(N, s(M)) | → | U101#(isNat(M), M, N) | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) | |
| U34#(tt, V1, V2) | → | isNat#(activate(V1)) | isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | |
| isNatKind#(n__x(V1, V2)) | → | activate#(V1) | activate#(n__s(X)) | → | activate#(X) | |
| U82#(tt, M, N) | → | activate#(N) | U14#(tt, V1, V2) | → | U15#(isNat(activate(V1)), activate(V2)) | |
| isNatKind#(n__s(V1)) | → | activate#(V1) | U81#(tt, M, N) | → | U82#(isNatKind(activate(M)), activate(M), activate(N)) | |
| U13#(tt, V1, V2) | → | activate#(V1) | U104#(tt, M, N) | → | activate#(N) | |
| plus#(N, 0) | → | isNat#(N) | isNat#(n__plus(V1, V2)) | → | activate#(V2) | |
| U11#(tt, V1, V2) | → | activate#(V2) | x#(N, 0) | → | isNat#(N) | |
| activate#(n__plus(X1, X2)) | → | activate#(X2) | U11#(tt, V1, V2) | → | U12#(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| isNatKind#(n__plus(V1, V2)) | → | activate#(V2) | isNatKind#(n__x(V1, V2)) | → | activate#(V2) | |
| isNat#(n__x(V1, V2)) | → | activate#(V1) | isNat#(n__x(V1, V2)) | → | U31#(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| U102#(tt, M, N) | → | isNat#(activate(N)) | activate#(n__plus(X1, X2)) | → | activate#(X1) | |
| isNatKind#(n__plus(V1, V2)) | → | activate#(V1) | U84#(tt, M, N) | → | plus#(activate(N), activate(M)) | |
| U11#(tt, V1, V2) | → | isNatKind#(activate(V1)) | U21#(tt, V1) | → | activate#(V1) | |
| U91#(tt, N) | → | isNatKind#(activate(N)) | U35#(tt, V2) | → | activate#(V2) | |
| U31#(tt, V1, V2) | → | U32#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) | → | activate#(M) | |
| isNat#(n__plus(V1, V2)) | → | U11#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) | → | activate#(N) | |
| U34#(tt, V1, V2) | → | U35#(isNat(activate(V1)), activate(V2)) | U83#(tt, M, N) | → | isNatKind#(activate(N)) | |
| U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | U34#(tt, V1, V2) | → | activate#(V2) | |
| U82#(tt, M, N) | → | U83#(isNat(activate(N)), activate(M), activate(N)) | U81#(tt, M, N) | → | activate#(M) | |
| U104#(tt, M, N) | → | activate#(M) | isNat#(n__x(V1, V2)) | → | activate#(V2) | |
| U101#(tt, M, N) | → | isNatKind#(activate(M)) | isNatKind#(n__plus(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V2)) | |
| U21#(tt, V1) | → | isNatKind#(activate(V1)) | U82#(tt, M, N) | → | activate#(M) | |
| U12#(tt, V1, V2) | → | U13#(isNatKind(activate(V2)), activate(V1), activate(V2)) | U13#(tt, V1, V2) | → | isNatKind#(activate(V2)) | |
| isNatKind#(n__x(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | U14#(tt, V1, V2) | → | isNat#(activate(V1)) | |
| U32#(tt, V1, V2) | → | activate#(V1) | U12#(tt, V1, V2) | → | activate#(V1) | |
| U12#(tt, V1, V2) | → | isNatKind#(activate(V2)) | isNat#(n__s(V1)) | → | activate#(V1) | |
| U33#(tt, V1, V2) | → | activate#(V2) | U81#(tt, M, N) | → | activate#(N) | |
| plus#(N, s(M)) | → | U81#(isNat(M), M, N) | U33#(tt, V1, V2) | → | activate#(V1) | |
| U102#(tt, M, N) | → | activate#(N) | U32#(tt, V1, V2) | → | activate#(V2) | |
| U101#(tt, M, N) | → | U102#(isNatKind(activate(M)), activate(M), activate(N)) | U14#(tt, V1, V2) | → | activate#(V2) | |
| U31#(tt, V1, V2) | → | activate#(V2) | U15#(tt, V2) | → | activate#(V2) | |
| U11#(tt, V1, V2) | → | activate#(V1) | U104#(tt, M, N) | → | plus#(x(activate(N), activate(M)), activate(N)) | |
| U41#(tt, V2) | → | isNatKind#(activate(V2)) | U22#(tt, V1) | → | activate#(V1) | |
| U102#(tt, M, N) | → | activate#(M) | U102#(tt, M, N) | → | U103#(isNat(activate(N)), activate(M), activate(N)) | |
| isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | U84#(tt, M, N) | → | activate#(N) | |
| U101#(tt, M, N) | → | activate#(N) | U22#(tt, V1) | → | U23#(isNat(activate(V1))) | |
| U13#(tt, V1, V2) | → | activate#(V2) | U31#(tt, V1, V2) | → | isNatKind#(activate(V1)) | |
| isNat#(n__plus(V1, V2)) | → | isNatKind#(activate(V1)) | U22#(tt, V1) | → | isNat#(activate(V1)) | |
| activate#(n__plus(X1, X2)) | → | plus#(activate(X1), activate(X2)) | isNat#(n__x(V1, V2)) | → | isNatKind#(activate(V1)) | |
| U83#(tt, M, N) | → | activate#(N) | U12#(tt, V1, V2) | → | activate#(V2) | |
| U83#(tt, M, N) | → | activate#(M) | activate#(n__x(X1, X2)) | → | x#(activate(X1), activate(X2)) | |
| U41#(tt, V2) | → | activate#(V2) | U13#(tt, V1, V2) | → | U14#(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| U33#(tt, V1, V2) | → | isNatKind#(activate(V2)) | U35#(tt, V2) | → | isNat#(activate(V2)) | |
| U101#(tt, M, N) | → | activate#(M) | U61#(tt, V2) | → | activate#(V2) | |
| U31#(tt, V1, V2) | → | activate#(V1) | U83#(tt, M, N) | → | U84#(isNatKind(activate(N)), activate(M), activate(N)) | |
| U72#(tt, N) | → | activate#(N) | x#(N, 0) | → | U91#(isNat(N), N) | |
| U61#(tt, V2) | → | isNatKind#(activate(V2)) | U71#(tt, N) | → | activate#(N) | |
| plus#(N, s(M)) | → | isNat#(M) | U71#(tt, N) | → | isNatKind#(activate(N)) | |
| U82#(tt, M, N) | → | isNat#(activate(N)) | U14#(tt, V1, V2) | → | activate#(V1) | |
| U104#(tt, M, N) | → | x#(activate(N), activate(M)) |
| U101(tt, M, N) | → | U102(isNatKind(activate(M)), activate(M), activate(N)) | U102(tt, M, N) | → | U103(isNat(activate(N)), activate(M), activate(N)) | |
| U103(tt, M, N) | → | U104(isNatKind(activate(N)), activate(M), activate(N)) | U104(tt, M, N) | → | plus(x(activate(N), activate(M)), activate(N)) | |
| U11(tt, V1, V2) | → | U12(isNatKind(activate(V1)), activate(V1), activate(V2)) | U12(tt, V1, V2) | → | U13(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| U13(tt, V1, V2) | → | U14(isNatKind(activate(V2)), activate(V1), activate(V2)) | U14(tt, V1, V2) | → | U15(isNat(activate(V1)), activate(V2)) | |
| U15(tt, V2) | → | U16(isNat(activate(V2))) | U16(tt) | → | tt | |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | U22(tt, V1) | → | U23(isNat(activate(V1))) | |
| U23(tt) | → | tt | U31(tt, V1, V2) | → | U32(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| U32(tt, V1, V2) | → | U33(isNatKind(activate(V2)), activate(V1), activate(V2)) | U33(tt, V1, V2) | → | U34(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| U34(tt, V1, V2) | → | U35(isNat(activate(V1)), activate(V2)) | U35(tt, V2) | → | U36(isNat(activate(V2))) | |
| U36(tt) | → | tt | U41(tt, V2) | → | U42(isNatKind(activate(V2))) | |
| U42(tt) | → | tt | U51(tt) | → | tt | |
| U61(tt, V2) | → | U62(isNatKind(activate(V2))) | U62(tt) | → | tt | |
| U71(tt, N) | → | U72(isNatKind(activate(N)), activate(N)) | U72(tt, N) | → | activate(N) | |
| U81(tt, M, N) | → | U82(isNatKind(activate(M)), activate(M), activate(N)) | U82(tt, M, N) | → | U83(isNat(activate(N)), activate(M), activate(N)) | |
| U83(tt, M, N) | → | U84(isNatKind(activate(N)), activate(M), activate(N)) | U84(tt, M, N) | → | s(plus(activate(N), activate(M))) | |
| U91(tt, N) | → | U92(isNatKind(activate(N))) | U92(tt) | → | 0 | |
| isNat(n__0) | → | tt | isNat(n__plus(V1, V2)) | → | U11(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | isNat(n__x(V1, V2)) | → | U31(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| isNatKind(n__0) | → | tt | isNatKind(n__plus(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V2)) | |
| isNatKind(n__s(V1)) | → | U51(isNatKind(activate(V1))) | isNatKind(n__x(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) | |
| plus(N, 0) | → | U71(isNat(N), N) | plus(N, s(M)) | → | U81(isNat(M), M, N) | |
| x(N, 0) | → | U91(isNat(N), N) | x(N, s(M)) | → | U101(isNat(M), M, N) | |
| 0 | → | n__0 | plus(X1, X2) | → | n__plus(X1, X2) | |
| s(X) | → | n__s(X) | x(X1, X2) | → | n__x(X1, X2) | |
| activate(n__0) | → | 0 | activate(n__plus(X1, X2)) | → | plus(activate(X1), activate(X2)) | |
| activate(n__s(X)) | → | s(activate(X)) | activate(n__x(X1, X2)) | → | x(activate(X1), activate(X2)) | |
| activate(X) | → | X |
Termination of terms over the following signature is verified: U104, n__plus, activate, isNat, n__s, U62, U61, n__0, U42, U41, U92, U91, U23, U21, n__x, U22, plus, isNatKind, U83, U84, U71, U36, U72, 0, U14, U51, s, U15, tt, U16, U82, U81, U11, U12, U31, U13, U32, U102, U33, U103, U34, U35, U101, x
| U81#(tt, M, N) → isNatKind#(activate(M)) | activate#(n__x(X1, X2)) → activate#(X1) |
| U91#(tt, N) → activate#(N) | U34#(tt, V1, V2) → activate#(V1) |
| U32#(tt, V1, V2) → isNatKind#(activate(V2)) | U15#(tt, V2) → isNat#(activate(V2)) |
| U71#(tt, N) → U72#(isNatKind(activate(N)), activate(N)) | plus#(N, 0) → U71#(isNat(N), N) |
| U33#(tt, V1, V2) → U34#(isNatKind(activate(V2)), activate(V1), activate(V2)) | activate#(n__x(X1, X2)) → activate#(X2) |
| isNatKind#(n__plus(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, M, N) → U104#(isNatKind(activate(N)), activate(M), activate(N)) |
| x#(N, s(M)) → isNat#(M) | U84#(tt, M, N) → activate#(M) |
| U103#(tt, M, N) → isNatKind#(activate(N)) | isNatKind#(n__x(V1, V2)) → isNatKind#(activate(V1)) |
| U32#(tt, V1, V2) → U33#(isNatKind(activate(V2)), activate(V1), activate(V2)) | isNat#(n__plus(V1, V2)) → activate#(V1) |
| x#(N, s(M)) → U101#(isNat(M), M, N) | isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) |
| U34#(tt, V1, V2) → isNat#(activate(V1)) | isNat#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatKind#(n__x(V1, V2)) → activate#(V1) | activate#(n__s(X)) → activate#(X) |
| U82#(tt, M, N) → activate#(N) | U14#(tt, V1, V2) → U15#(isNat(activate(V1)), activate(V2)) |
| isNatKind#(n__s(V1)) → activate#(V1) | U81#(tt, M, N) → U82#(isNatKind(activate(M)), activate(M), activate(N)) |
| U13#(tt, V1, V2) → activate#(V1) | U104#(tt, M, N) → activate#(N) |
| plus#(N, 0) → isNat#(N) | isNat#(n__plus(V1, V2)) → activate#(V2) |
| U11#(tt, V1, V2) → activate#(V2) | x#(N, 0) → isNat#(N) |
| activate#(n__plus(X1, X2)) → activate#(X2) | U11#(tt, V1, V2) → U12#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatKind#(n__plus(V1, V2)) → activate#(V2) | isNatKind#(n__x(V1, V2)) → activate#(V2) |
| isNat#(n__x(V1, V2)) → activate#(V1) | isNat#(n__x(V1, V2)) → U31#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102#(tt, M, N) → isNat#(activate(N)) | activate#(n__plus(X1, X2)) → activate#(X1) |
| isNatKind#(n__plus(V1, V2)) → activate#(V1) | U84#(tt, M, N) → plus#(activate(N), activate(M)) |
| U11#(tt, V1, V2) → isNatKind#(activate(V1)) | U21#(tt, V1) → activate#(V1) |
| U91#(tt, N) → isNatKind#(activate(N)) | U35#(tt, V2) → activate#(V2) |
| U31#(tt, V1, V2) → U32#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) → activate#(M) |
| isNat#(n__plus(V1, V2)) → U11#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) → activate#(N) |
| U34#(tt, V1, V2) → U35#(isNat(activate(V1)), activate(V2)) | U83#(tt, M, N) → isNatKind#(activate(N)) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | U34#(tt, V1, V2) → activate#(V2) |
| U82#(tt, M, N) → U83#(isNat(activate(N)), activate(M), activate(N)) | U81#(tt, M, N) → activate#(M) |
| U104#(tt, M, N) → activate#(M) | isNatKind#(n__plus(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V2)) |
| U101#(tt, M, N) → isNatKind#(activate(M)) | isNat#(n__x(V1, V2)) → activate#(V2) |
| U82#(tt, M, N) → activate#(M) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U12#(tt, V1, V2) → U13#(isNatKind(activate(V2)), activate(V1), activate(V2)) | U13#(tt, V1, V2) → isNatKind#(activate(V2)) |
| isNatKind#(n__x(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U32#(tt, V1, V2) → activate#(V1) |
| U14#(tt, V1, V2) → isNat#(activate(V1)) | U12#(tt, V1, V2) → activate#(V1) |
| U12#(tt, V1, V2) → isNatKind#(activate(V2)) | U81#(tt, M, N) → activate#(N) |
| U33#(tt, V1, V2) → activate#(V2) | isNat#(n__s(V1)) → activate#(V1) |
| plus#(N, s(M)) → U81#(isNat(M), M, N) | U33#(tt, V1, V2) → activate#(V1) |
| U32#(tt, V1, V2) → activate#(V2) | U102#(tt, M, N) → activate#(N) |
| U101#(tt, M, N) → U102#(isNatKind(activate(M)), activate(M), activate(N)) | U14#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V1, V2) → activate#(V2) | U15#(tt, V2) → activate#(V2) |
| U11#(tt, V1, V2) → activate#(V1) | U104#(tt, M, N) → plus#(x(activate(N), activate(M)), activate(N)) |
| U41#(tt, V2) → isNatKind#(activate(V2)) | U22#(tt, V1) → activate#(V1) |
| U102#(tt, M, N) → activate#(M) | U102#(tt, M, N) → U103#(isNat(activate(N)), activate(M), activate(N)) |
| U84#(tt, M, N) → activate#(N) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U101#(tt, M, N) → activate#(N) | U31#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U13#(tt, V1, V2) → activate#(V2) | isNat#(n__plus(V1, V2)) → isNatKind#(activate(V1)) |
| U22#(tt, V1) → isNat#(activate(V1)) | activate#(n__plus(X1, X2)) → plus#(activate(X1), activate(X2)) |
| isNat#(n__x(V1, V2)) → isNatKind#(activate(V1)) | U83#(tt, M, N) → activate#(N) |
| U12#(tt, V1, V2) → activate#(V2) | U83#(tt, M, N) → activate#(M) |
| activate#(n__x(X1, X2)) → x#(activate(X1), activate(X2)) | U41#(tt, V2) → activate#(V2) |
| U13#(tt, V1, V2) → U14#(isNatKind(activate(V2)), activate(V1), activate(V2)) | U33#(tt, V1, V2) → isNatKind#(activate(V2)) |
| U35#(tt, V2) → isNat#(activate(V2)) | U101#(tt, M, N) → activate#(M) |
| U61#(tt, V2) → activate#(V2) | U31#(tt, V1, V2) → activate#(V1) |
| U83#(tt, M, N) → U84#(isNatKind(activate(N)), activate(M), activate(N)) | U72#(tt, N) → activate#(N) |
| x#(N, 0) → U91#(isNat(N), N) | U61#(tt, V2) → isNatKind#(activate(V2)) |
| U71#(tt, N) → activate#(N) | plus#(N, s(M)) → isNat#(M) |
| U71#(tt, N) → isNatKind#(activate(N)) | U82#(tt, M, N) → isNat#(activate(N)) |
| U14#(tt, V1, V2) → activate#(V1) | U104#(tt, M, N) → x#(activate(N), activate(M)) |
| U81#(tt, M, N) | → | isNatKind#(activate(M)) | U91#(tt, N) | → | activate#(N) | |
| activate#(n__x(X1, X2)) | → | activate#(X1) | U34#(tt, V1, V2) | → | activate#(V1) | |
| U32#(tt, V1, V2) | → | isNatKind#(activate(V2)) | U15#(tt, V2) | → | isNat#(activate(V2)) | |
| U71#(tt, N) | → | U72#(isNatKind(activate(N)), activate(N)) | plus#(N, 0) | → | U71#(isNat(N), N) | |
| U33#(tt, V1, V2) | → | U34#(isNatKind(activate(V2)), activate(V1), activate(V2)) | activate#(n__x(X1, X2)) | → | activate#(X2) | |
| isNatKind#(n__plus(V1, V2)) | → | isNatKind#(activate(V1)) | U103#(tt, M, N) | → | U104#(isNatKind(activate(N)), activate(M), activate(N)) | |
| x#(N, s(M)) | → | isNat#(M) | U84#(tt, M, N) | → | activate#(M) | |
| U103#(tt, M, N) | → | isNatKind#(activate(N)) | U32#(tt, V1, V2) | → | U33#(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| isNatKind#(n__x(V1, V2)) | → | isNatKind#(activate(V1)) | isNat#(n__plus(V1, V2)) | → | activate#(V1) | |
| U84#(tt, M, N) | → | s#(plus(activate(N), activate(M))) | x#(N, s(M)) | → | U101#(isNat(M), M, N) | |
| isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) | U34#(tt, V1, V2) | → | isNat#(activate(V1)) | |
| isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | isNatKind#(n__x(V1, V2)) | → | activate#(V1) | |
| activate#(n__s(X)) | → | activate#(X) | U82#(tt, M, N) | → | activate#(N) | |
| U14#(tt, V1, V2) | → | U15#(isNat(activate(V1)), activate(V2)) | isNatKind#(n__s(V1)) | → | activate#(V1) | |
| U81#(tt, M, N) | → | U82#(isNatKind(activate(M)), activate(M), activate(N)) | U13#(tt, V1, V2) | → | activate#(V1) | |
| U104#(tt, M, N) | → | activate#(N) | plus#(N, 0) | → | isNat#(N) | |
| isNat#(n__plus(V1, V2)) | → | activate#(V2) | x#(N, 0) | → | isNat#(N) | |
| U11#(tt, V1, V2) | → | activate#(V2) | activate#(n__plus(X1, X2)) | → | activate#(X2) | |
| U11#(tt, V1, V2) | → | U12#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatKind#(n__plus(V1, V2)) | → | activate#(V2) | |
| isNatKind#(n__x(V1, V2)) | → | activate#(V2) | isNat#(n__x(V1, V2)) | → | activate#(V1) | |
| isNat#(n__x(V1, V2)) | → | U31#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U102#(tt, M, N) | → | isNat#(activate(N)) | |
| activate#(n__plus(X1, X2)) | → | activate#(X1) | isNatKind#(n__plus(V1, V2)) | → | activate#(V1) | |
| U84#(tt, M, N) | → | plus#(activate(N), activate(M)) | U11#(tt, V1, V2) | → | isNatKind#(activate(V1)) | |
| U21#(tt, V1) | → | activate#(V1) | U91#(tt, N) | → | isNatKind#(activate(N)) | |
| U35#(tt, V2) | → | activate#(V2) | U31#(tt, V1, V2) | → | U32#(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| U103#(tt, M, N) | → | activate#(M) | isNat#(n__plus(V1, V2)) | → | U11#(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| U103#(tt, M, N) | → | activate#(N) | U34#(tt, V1, V2) | → | U35#(isNat(activate(V1)), activate(V2)) | |
| U83#(tt, M, N) | → | isNatKind#(activate(N)) | U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | |
| U34#(tt, V1, V2) | → | activate#(V2) | U82#(tt, M, N) | → | U83#(isNat(activate(N)), activate(M), activate(N)) | |
| U81#(tt, M, N) | → | activate#(M) | U104#(tt, M, N) | → | activate#(M) | |
| isNat#(n__x(V1, V2)) | → | activate#(V2) | U101#(tt, M, N) | → | isNatKind#(activate(M)) | |
| isNatKind#(n__plus(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V2)) | U21#(tt, V1) | → | isNatKind#(activate(V1)) | |
| U82#(tt, M, N) | → | activate#(M) | U12#(tt, V1, V2) | → | U13#(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| U13#(tt, V1, V2) | → | isNatKind#(activate(V2)) | isNatKind#(n__x(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | |
| U14#(tt, V1, V2) | → | isNat#(activate(V1)) | U32#(tt, V1, V2) | → | activate#(V1) | |
| U12#(tt, V1, V2) | → | activate#(V1) | U12#(tt, V1, V2) | → | isNatKind#(activate(V2)) | |
| isNat#(n__s(V1)) | → | activate#(V1) | U81#(tt, M, N) | → | activate#(N) | |
| U33#(tt, V1, V2) | → | activate#(V2) | plus#(N, s(M)) | → | U81#(isNat(M), M, N) | |
| U33#(tt, V1, V2) | → | activate#(V1) | U102#(tt, M, N) | → | activate#(N) | |
| U32#(tt, V1, V2) | → | activate#(V2) | U101#(tt, M, N) | → | U102#(isNatKind(activate(M)), activate(M), activate(N)) | |
| U14#(tt, V1, V2) | → | activate#(V2) | U31#(tt, V1, V2) | → | activate#(V2) | |
| U15#(tt, V2) | → | activate#(V2) | U11#(tt, V1, V2) | → | activate#(V1) | |
| U104#(tt, M, N) | → | plus#(x(activate(N), activate(M)), activate(N)) | U22#(tt, V1) | → | activate#(V1) | |
| U41#(tt, V2) | → | isNatKind#(activate(V2)) | U102#(tt, M, N) | → | activate#(M) | |
| U102#(tt, M, N) | → | U103#(isNat(activate(N)), activate(M), activate(N)) | isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | |
| U84#(tt, M, N) | → | activate#(N) | U101#(tt, M, N) | → | activate#(N) | |
| U13#(tt, V1, V2) | → | activate#(V2) | U31#(tt, V1, V2) | → | isNatKind#(activate(V1)) | |
| isNat#(n__plus(V1, V2)) | → | isNatKind#(activate(V1)) | U22#(tt, V1) | → | isNat#(activate(V1)) | |
| activate#(n__plus(X1, X2)) | → | plus#(activate(X1), activate(X2)) | isNat#(n__x(V1, V2)) | → | isNatKind#(activate(V1)) | |
| U83#(tt, M, N) | → | activate#(N) | U12#(tt, V1, V2) | → | activate#(V2) | |
| U83#(tt, M, N) | → | activate#(M) | activate#(n__x(X1, X2)) | → | x#(activate(X1), activate(X2)) | |
| U41#(tt, V2) | → | activate#(V2) | U13#(tt, V1, V2) | → | U14#(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| U33#(tt, V1, V2) | → | isNatKind#(activate(V2)) | U101#(tt, M, N) | → | activate#(M) | |
| U35#(tt, V2) | → | isNat#(activate(V2)) | U61#(tt, V2) | → | activate#(V2) | |
| U31#(tt, V1, V2) | → | activate#(V1) | U83#(tt, M, N) | → | U84#(isNatKind(activate(N)), activate(M), activate(N)) | |
| U72#(tt, N) | → | activate#(N) | x#(N, 0) | → | U91#(isNat(N), N) | |
| U61#(tt, V2) | → | isNatKind#(activate(V2)) | U71#(tt, N) | → | activate#(N) | |
| plus#(N, s(M)) | → | isNat#(M) | U71#(tt, N) | → | isNatKind#(activate(N)) | |
| U82#(tt, M, N) | → | isNat#(activate(N)) | U14#(tt, V1, V2) | → | activate#(V1) | |
| U104#(tt, M, N) | → | x#(activate(N), activate(M)) |
| U101(tt, M, N) | → | U102(isNatKind(activate(M)), activate(M), activate(N)) | U102(tt, M, N) | → | U103(isNat(activate(N)), activate(M), activate(N)) | |
| U103(tt, M, N) | → | U104(isNatKind(activate(N)), activate(M), activate(N)) | U104(tt, M, N) | → | plus(x(activate(N), activate(M)), activate(N)) | |
| U11(tt, V1, V2) | → | U12(isNatKind(activate(V1)), activate(V1), activate(V2)) | U12(tt, V1, V2) | → | U13(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| U13(tt, V1, V2) | → | U14(isNatKind(activate(V2)), activate(V1), activate(V2)) | U14(tt, V1, V2) | → | U15(isNat(activate(V1)), activate(V2)) | |
| U15(tt, V2) | → | U16(isNat(activate(V2))) | U16(tt) | → | tt | |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | U22(tt, V1) | → | U23(isNat(activate(V1))) | |
| U23(tt) | → | tt | U31(tt, V1, V2) | → | U32(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| U32(tt, V1, V2) | → | U33(isNatKind(activate(V2)), activate(V1), activate(V2)) | U33(tt, V1, V2) | → | U34(isNatKind(activate(V2)), activate(V1), activate(V2)) | |
| U34(tt, V1, V2) | → | U35(isNat(activate(V1)), activate(V2)) | U35(tt, V2) | → | U36(isNat(activate(V2))) | |
| U36(tt) | → | tt | U41(tt, V2) | → | U42(isNatKind(activate(V2))) | |
| U42(tt) | → | tt | U51(tt) | → | tt | |
| U61(tt, V2) | → | U62(isNatKind(activate(V2))) | U62(tt) | → | tt | |
| U71(tt, N) | → | U72(isNatKind(activate(N)), activate(N)) | U72(tt, N) | → | activate(N) | |
| U81(tt, M, N) | → | U82(isNatKind(activate(M)), activate(M), activate(N)) | U82(tt, M, N) | → | U83(isNat(activate(N)), activate(M), activate(N)) | |
| U83(tt, M, N) | → | U84(isNatKind(activate(N)), activate(M), activate(N)) | U84(tt, M, N) | → | s(plus(activate(N), activate(M))) | |
| U91(tt, N) | → | U92(isNatKind(activate(N))) | U92(tt) | → | 0 | |
| isNat(n__0) | → | tt | isNat(n__plus(V1, V2)) | → | U11(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | isNat(n__x(V1, V2)) | → | U31(isNatKind(activate(V1)), activate(V1), activate(V2)) | |
| isNatKind(n__0) | → | tt | isNatKind(n__plus(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V2)) | |
| isNatKind(n__s(V1)) | → | U51(isNatKind(activate(V1))) | isNatKind(n__x(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) | |
| plus(N, 0) | → | U71(isNat(N), N) | plus(N, s(M)) | → | U81(isNat(M), M, N) | |
| x(N, 0) | → | U91(isNat(N), N) | x(N, s(M)) | → | U101(isNat(M), M, N) | |
| 0 | → | n__0 | plus(X1, X2) | → | n__plus(X1, X2) | |
| s(X) | → | n__s(X) | x(X1, X2) | → | n__x(X1, X2) | |
| activate(n__0) | → | 0 | activate(n__plus(X1, X2)) | → | plus(activate(X1), activate(X2)) | |
| activate(n__s(X)) | → | s(activate(X)) | activate(n__x(X1, X2)) | → | x(activate(X1), activate(X2)) | |
| activate(X) | → | X |
Termination of terms over the following signature is verified: U104, n__plus, activate, isNat, n__s, U62, U61, n__0, U42, U41, U92, U91, U23, U21, n__x, U22, plus, isNatKind, U83, U84, U71, U36, U72, 0, U14, U51, s, U15, tt, U16, U82, U81, U11, U12, U31, U13, U32, U102, U33, U103, U34, U35, U101, x
| U81#(tt, M, N) → isNatKind#(activate(M)) | activate#(n__x(X1, X2)) → activate#(X1) |
| U91#(tt, N) → activate#(N) | U34#(tt, V1, V2) → activate#(V1) |
| U32#(tt, V1, V2) → isNatKind#(activate(V2)) | U15#(tt, V2) → isNat#(activate(V2)) |
| U71#(tt, N) → U72#(isNatKind(activate(N)), activate(N)) | plus#(N, 0) → U71#(isNat(N), N) |
| U33#(tt, V1, V2) → U34#(isNatKind(activate(V2)), activate(V1), activate(V2)) | activate#(n__x(X1, X2)) → activate#(X2) |
| isNatKind#(n__plus(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, M, N) → U104#(isNatKind(activate(N)), activate(M), activate(N)) |
| x#(N, s(M)) → isNat#(M) | U84#(tt, M, N) → activate#(M) |
| U103#(tt, M, N) → isNatKind#(activate(N)) | isNatKind#(n__x(V1, V2)) → isNatKind#(activate(V1)) |
| U32#(tt, V1, V2) → U33#(isNatKind(activate(V2)), activate(V1), activate(V2)) | isNat#(n__plus(V1, V2)) → activate#(V1) |
| x#(N, s(M)) → U101#(isNat(M), M, N) | isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) |
| U34#(tt, V1, V2) → isNat#(activate(V1)) | isNat#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatKind#(n__x(V1, V2)) → activate#(V1) | activate#(n__s(X)) → activate#(X) |
| U82#(tt, M, N) → activate#(N) | U14#(tt, V1, V2) → U15#(isNat(activate(V1)), activate(V2)) |
| isNatKind#(n__s(V1)) → activate#(V1) | U81#(tt, M, N) → U82#(isNatKind(activate(M)), activate(M), activate(N)) |
| U13#(tt, V1, V2) → activate#(V1) | U104#(tt, M, N) → activate#(N) |
| plus#(N, 0) → isNat#(N) | isNat#(n__plus(V1, V2)) → activate#(V2) |
| U11#(tt, V1, V2) → activate#(V2) | x#(N, 0) → isNat#(N) |
| activate#(n__plus(X1, X2)) → activate#(X2) | U11#(tt, V1, V2) → U12#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatKind#(n__plus(V1, V2)) → activate#(V2) | isNatKind#(n__x(V1, V2)) → activate#(V2) |
| isNat#(n__x(V1, V2)) → activate#(V1) | isNat#(n__x(V1, V2)) → U31#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102#(tt, M, N) → isNat#(activate(N)) | activate#(n__plus(X1, X2)) → activate#(X1) |
| isNatKind#(n__plus(V1, V2)) → activate#(V1) | U84#(tt, M, N) → plus#(activate(N), activate(M)) |
| U11#(tt, V1, V2) → isNatKind#(activate(V1)) | U21#(tt, V1) → activate#(V1) |
| U91#(tt, N) → isNatKind#(activate(N)) | U35#(tt, V2) → activate#(V2) |
| U31#(tt, V1, V2) → U32#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) → activate#(M) |
| isNat#(n__plus(V1, V2)) → U11#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U103#(tt, M, N) → activate#(N) |
| U34#(tt, V1, V2) → U35#(isNat(activate(V1)), activate(V2)) | U83#(tt, M, N) → isNatKind#(activate(N)) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | U34#(tt, V1, V2) → activate#(V2) |
| U82#(tt, M, N) → U83#(isNat(activate(N)), activate(M), activate(N)) | U81#(tt, M, N) → activate#(M) |
| U104#(tt, M, N) → activate#(M) | isNatKind#(n__plus(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V2)) |
| U101#(tt, M, N) → isNatKind#(activate(M)) | isNat#(n__x(V1, V2)) → activate#(V2) |
| U82#(tt, M, N) → activate#(M) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U12#(tt, V1, V2) → U13#(isNatKind(activate(V2)), activate(V1), activate(V2)) | U13#(tt, V1, V2) → isNatKind#(activate(V2)) |
| isNatKind#(n__x(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U32#(tt, V1, V2) → activate#(V1) |
| U14#(tt, V1, V2) → isNat#(activate(V1)) | U12#(tt, V1, V2) → activate#(V1) |
| U12#(tt, V1, V2) → isNatKind#(activate(V2)) | U81#(tt, M, N) → activate#(N) |
| U33#(tt, V1, V2) → activate#(V2) | isNat#(n__s(V1)) → activate#(V1) |
| plus#(N, s(M)) → U81#(isNat(M), M, N) | U33#(tt, V1, V2) → activate#(V1) |
| U32#(tt, V1, V2) → activate#(V2) | U102#(tt, M, N) → activate#(N) |
| U101#(tt, M, N) → U102#(isNatKind(activate(M)), activate(M), activate(N)) | U14#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V1, V2) → activate#(V2) | U15#(tt, V2) → activate#(V2) |
| U11#(tt, V1, V2) → activate#(V1) | U104#(tt, M, N) → plus#(x(activate(N), activate(M)), activate(N)) |
| U41#(tt, V2) → isNatKind#(activate(V2)) | U22#(tt, V1) → activate#(V1) |
| U102#(tt, M, N) → activate#(M) | U102#(tt, M, N) → U103#(isNat(activate(N)), activate(M), activate(N)) |
| U84#(tt, M, N) → activate#(N) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U101#(tt, M, N) → activate#(N) | U31#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U13#(tt, V1, V2) → activate#(V2) | isNat#(n__plus(V1, V2)) → isNatKind#(activate(V1)) |
| U22#(tt, V1) → isNat#(activate(V1)) | activate#(n__plus(X1, X2)) → plus#(activate(X1), activate(X2)) |
| isNat#(n__x(V1, V2)) → isNatKind#(activate(V1)) | U83#(tt, M, N) → activate#(N) |
| U12#(tt, V1, V2) → activate#(V2) | U83#(tt, M, N) → activate#(M) |
| activate#(n__x(X1, X2)) → x#(activate(X1), activate(X2)) | U41#(tt, V2) → activate#(V2) |
| U13#(tt, V1, V2) → U14#(isNatKind(activate(V2)), activate(V1), activate(V2)) | U33#(tt, V1, V2) → isNatKind#(activate(V2)) |
| U35#(tt, V2) → isNat#(activate(V2)) | U101#(tt, M, N) → activate#(M) |
| U61#(tt, V2) → activate#(V2) | U31#(tt, V1, V2) → activate#(V1) |
| U83#(tt, M, N) → U84#(isNatKind(activate(N)), activate(M), activate(N)) | U72#(tt, N) → activate#(N) |
| x#(N, 0) → U91#(isNat(N), N) | U61#(tt, V2) → isNatKind#(activate(V2)) |
| U71#(tt, N) → activate#(N) | plus#(N, s(M)) → isNat#(M) |
| U71#(tt, N) → isNatKind#(activate(N)) | U82#(tt, M, N) → isNat#(activate(N)) |
| U14#(tt, V1, V2) → activate#(V1) | U104#(tt, M, N) → x#(activate(N), activate(M)) |