The TRS could not be proven terminating. The proof attempt took 60019 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (60002ms)].
| mark#(U104(X1, X2, X3)) | → | U104#(mark(X1), X2, X3) | mark#(U102(X1, X2, X3)) | → | U102#(mark(X1), X2, X3) | |
| U51#(active(X)) | → | U51#(X) | U91#(X1, active(X2)) | → | U91#(X1, X2) | |
| mark#(U102(X1, X2, X3)) | → | active#(U102(mark(X1), X2, X3)) | U15#(X1, active(X2)) | → | U15#(X1, X2) | |
| active#(isNatKind(s(V1))) | → | U51#(isNatKind(V1)) | active#(U15(tt, V2)) | → | U16#(isNat(V2)) | |
| U34#(X1, X2, active(X3)) | → | U34#(X1, X2, X3) | mark#(U83(X1, X2, X3)) | → | active#(U83(mark(X1), X2, X3)) | |
| mark#(U33(X1, X2, X3)) | → | mark#(X1) | U21#(X1, active(X2)) | → | U21#(X1, X2) | |
| mark#(s(X)) | → | mark#(X) | active#(U34(tt, V1, V2)) | → | U35#(isNat(V1), V2) | |
| mark#(U31(X1, X2, X3)) | → | active#(U31(mark(X1), X2, X3)) | mark#(plus(X1, X2)) | → | active#(plus(mark(X1), mark(X2))) | |
| U102#(X1, X2, active(X3)) | → | U102#(X1, X2, X3) | U33#(X1, active(X2), X3) | → | U33#(X1, X2, X3) | |
| active#(U61(tt, V2)) | → | isNatKind#(V2) | U14#(X1, mark(X2), X3) | → | U14#(X1, X2, X3) | |
| mark#(U42(X)) | → | active#(U42(mark(X))) | U12#(X1, active(X2), X3) | → | U12#(X1, X2, X3) | |
| U12#(X1, X2, mark(X3)) | → | U12#(X1, X2, X3) | mark#(U84(X1, X2, X3)) | → | U84#(mark(X1), X2, X3) | |
| U81#(X1, active(X2), X3) | → | U81#(X1, X2, X3) | active#(U42(tt)) | → | mark#(tt) | |
| mark#(U11(X1, X2, X3)) | → | mark#(X1) | U102#(mark(X1), X2, X3) | → | U102#(X1, X2, X3) | |
| active#(U15(tt, V2)) | → | isNat#(V2) | mark#(U62(X)) | → | active#(U62(mark(X))) | |
| active#(U91(tt, N)) | → | isNatKind#(N) | mark#(U34(X1, X2, X3)) | → | U34#(mark(X1), X2, X3) | |
| U14#(X1, active(X2), X3) | → | U14#(X1, X2, X3) | U31#(active(X1), X2, X3) | → | U31#(X1, X2, X3) | |
| mark#(U16(X)) | → | mark#(X) | U91#(X1, mark(X2)) | → | U91#(X1, X2) | |
| active#(isNat(x(V1, V2))) | → | isNatKind#(V1) | mark#(U22(X1, X2)) | → | mark#(X1) | |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | active#(isNat(x(V1, V2))) | → | mark#(U31(isNatKind(V1), V1, V2)) | |
| U11#(active(X1), X2, X3) | → | U11#(X1, X2, X3) | mark#(U14(X1, X2, X3)) | → | active#(U14(mark(X1), X2, X3)) | |
| active#(U71(tt, N)) | → | mark#(U72(isNatKind(N), N)) | active#(U71(tt, N)) | → | U72#(isNatKind(N), N) | |
| mark#(U104(X1, X2, X3)) | → | active#(U104(mark(X1), X2, X3)) | mark#(U101(X1, X2, X3)) | → | U101#(mark(X1), X2, X3) | |
| U12#(X1, X2, active(X3)) | → | U12#(X1, X2, X3) | active#(U101(tt, M, N)) | → | mark#(U102(isNatKind(M), M, N)) | |
| U16#(active(X)) | → | U16#(X) | mark#(U36(X)) | → | mark#(X) | |
| active#(U84(tt, M, N)) | → | mark#(s(plus(N, M))) | active#(x(N, s(M))) | → | U101#(isNat(M), M, N) | |
| mark#(x(X1, X2)) | → | mark#(X1) | U83#(X1, active(X2), X3) | → | U83#(X1, X2, X3) | |
| mark#(U72(X1, X2)) | → | active#(U72(mark(X1), X2)) | U61#(active(X1), X2) | → | U61#(X1, X2) | |
| mark#(U11(X1, X2, X3)) | → | active#(U11(mark(X1), X2, X3)) | active#(U12(tt, V1, V2)) | → | mark#(U13(isNatKind(V2), V1, V2)) | |
| active#(U83(tt, M, N)) | → | isNatKind#(N) | U33#(X1, X2, active(X3)) | → | U33#(X1, X2, X3) | |
| U91#(mark(X1), X2) | → | U91#(X1, X2) | U61#(mark(X1), X2) | → | U61#(X1, X2) | |
| active#(U33(tt, V1, V2)) | → | mark#(U34(isNatKind(V2), V1, V2)) | U104#(active(X1), X2, X3) | → | U104#(X1, X2, X3) | |
| U13#(X1, active(X2), X3) | → | U13#(X1, X2, X3) | active#(U61(tt, V2)) | → | mark#(U62(isNatKind(V2))) | |
| active#(U62(tt)) | → | mark#(tt) | U41#(X1, mark(X2)) | → | U41#(X1, X2) | |
| active#(isNat(0)) | → | mark#(tt) | mark#(U15(X1, X2)) | → | U15#(mark(X1), X2) | |
| mark#(U71(X1, X2)) | → | mark#(X1) | mark#(U31(X1, X2, X3)) | → | mark#(X1) | |
| isNatKind#(active(X)) | → | isNatKind#(X) | U103#(X1, mark(X2), X3) | → | U103#(X1, X2, X3) | |
| U104#(X1, X2, mark(X3)) | → | U104#(X1, X2, X3) | U36#(active(X)) | → | U36#(X) | |
| U12#(X1, mark(X2), X3) | → | U12#(X1, X2, X3) | mark#(U42(X)) | → | mark#(X) | |
| mark#(U21(X1, X2)) | → | mark#(X1) | active#(U104(tt, M, N)) | → | mark#(plus(x(N, M), N)) | |
| U61#(X1, mark(X2)) | → | U61#(X1, X2) | active#(U84(tt, M, N)) | → | plus#(N, M) | |
| U14#(active(X1), X2, X3) | → | U14#(X1, X2, X3) | active#(U33(tt, V1, V2)) | → | U34#(isNatKind(V2), V1, V2) | |
| U23#(active(X)) | → | U23#(X) | U81#(active(X1), X2, X3) | → | U81#(X1, X2, X3) | |
| U101#(X1, X2, active(X3)) | → | U101#(X1, X2, X3) | U31#(X1, X2, mark(X3)) | → | U31#(X1, X2, X3) | |
| U41#(mark(X1), X2) | → | U41#(X1, X2) | mark#(U22(X1, X2)) | → | active#(U22(mark(X1), X2)) | |
| active#(U104(tt, M, N)) | → | x#(N, M) | U35#(active(X1), X2) | → | U35#(X1, X2) | |
| mark#(plus(X1, X2)) | → | plus#(mark(X1), mark(X2)) | active#(U102(tt, M, N)) | → | isNat#(N) | |
| mark#(U84(X1, X2, X3)) | → | active#(U84(mark(X1), X2, X3)) | mark#(U13(X1, X2, X3)) | → | U13#(mark(X1), X2, X3) | |
| s#(mark(X)) | → | s#(X) | mark#(U35(X1, X2)) | → | U35#(mark(X1), X2) | |
| U34#(X1, active(X2), X3) | → | U34#(X1, X2, X3) | U83#(mark(X1), X2, X3) | → | U83#(X1, X2, X3) | |
| U32#(mark(X1), X2, X3) | → | U32#(X1, X2, X3) | U34#(X1, X2, mark(X3)) | → | U34#(X1, X2, X3) | |
| active#(U35(tt, V2)) | → | U36#(isNat(V2)) | active#(isNatKind(0)) | → | mark#(tt) | |
| active#(isNatKind(plus(V1, V2))) | → | U41#(isNatKind(V1), V2) | U71#(X1, mark(X2)) | → | U71#(X1, X2) | |
| active#(isNatKind(x(V1, V2))) | → | U61#(isNatKind(V1), V2) | U83#(X1, mark(X2), X3) | → | U83#(X1, X2, X3) | |
| active#(U13(tt, V1, V2)) | → | U14#(isNatKind(V2), V1, V2) | U83#(X1, X2, active(X3)) | → | U83#(X1, X2, X3) | |
| mark#(U22(X1, X2)) | → | U22#(mark(X1), X2) | active#(x(N, 0)) | → | U91#(isNat(N), N) | |
| mark#(U31(X1, X2, X3)) | → | U31#(mark(X1), X2, X3) | active#(U11(tt, V1, V2)) | → | mark#(U12(isNatKind(V1), V1, V2)) | |
| x#(X1, mark(X2)) | → | x#(X1, X2) | active#(plus(N, 0)) | → | isNat#(N) | |
| active#(U102(tt, M, N)) | → | mark#(U103(isNat(N), M, N)) | active#(U22(tt, V1)) | → | isNat#(V1) | |
| active#(U32(tt, V1, V2)) | → | isNatKind#(V2) | mark#(U71(X1, X2)) | → | U71#(mark(X1), X2) | |
| mark#(U81(X1, X2, X3)) | → | U81#(mark(X1), X2, X3) | U12#(mark(X1), X2, X3) | → | U12#(X1, X2, X3) | |
| mark#(U13(X1, X2, X3)) | → | active#(U13(mark(X1), X2, X3)) | mark#(U82(X1, X2, X3)) | → | mark#(X1) | |
| active#(plus(N, s(M))) | → | U81#(isNat(M), M, N) | active#(U22(tt, V1)) | → | mark#(U23(isNat(V1))) | |
| mark#(U51(X)) | → | mark#(X) | mark#(U15(X1, X2)) | → | mark#(X1) | |
| active#(U11(tt, V1, V2)) | → | isNatKind#(V1) | U81#(X1, X2, active(X3)) | → | U81#(X1, X2, X3) | |
| active#(U14(tt, V1, V2)) | → | U15#(isNat(V1), V2) | U13#(X1, X2, active(X3)) | → | U13#(X1, X2, X3) | |
| U33#(mark(X1), X2, X3) | → | U33#(X1, X2, X3) | plus#(active(X1), X2) | → | plus#(X1, X2) | |
| mark#(U33(X1, X2, X3)) | → | U33#(mark(X1), X2, X3) | active#(U31(tt, V1, V2)) | → | isNatKind#(V1) | |
| U22#(mark(X1), X2) | → | U22#(X1, X2) | U34#(active(X1), X2, X3) | → | U34#(X1, X2, X3) | |
| mark#(U23(X)) | → | active#(U23(mark(X))) | U35#(X1, mark(X2)) | → | U35#(X1, X2) | |
| mark#(U81(X1, X2, X3)) | → | mark#(X1) | U104#(X1, X2, active(X3)) | → | U104#(X1, X2, X3) | |
| U82#(mark(X1), X2, X3) | → | U82#(X1, X2, X3) | x#(mark(X1), X2) | → | x#(X1, X2) | |
| U12#(active(X1), X2, X3) | → | U12#(X1, X2, X3) | U32#(X1, active(X2), X3) | → | U32#(X1, X2, X3) | |
| U61#(X1, active(X2)) | → | U61#(X1, X2) | active#(U101(tt, M, N)) | → | U102#(isNatKind(M), M, N) | |
| U101#(X1, X2, mark(X3)) | → | U101#(X1, X2, X3) | active#(U21(tt, V1)) | → | mark#(U22(isNatKind(V1), V1)) | |
| U32#(X1, X2, mark(X3)) | → | U32#(X1, X2, X3) | mark#(U91(X1, X2)) | → | U91#(mark(X1), X2) | |
| U13#(X1, mark(X2), X3) | → | U13#(X1, X2, X3) | mark#(0) | → | active#(0) | |
| mark#(U14(X1, X2, X3)) | → | U14#(mark(X1), X2, X3) | mark#(U62(X)) | → | U62#(mark(X)) | |
| mark#(x(X1, X2)) | → | x#(mark(X1), mark(X2)) | U11#(X1, X2, active(X3)) | → | U11#(X1, X2, X3) | |
| active#(U61(tt, V2)) | → | U62#(isNatKind(V2)) | active#(U72(tt, N)) | → | mark#(N) | |
| mark#(U103(X1, X2, X3)) | → | mark#(X1) | mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | |
| U42#(mark(X)) | → | U42#(X) | active#(U81(tt, M, N)) | → | isNatKind#(M) | |
| plus#(X1, mark(X2)) | → | plus#(X1, X2) | U84#(X1, mark(X2), X3) | → | U84#(X1, X2, X3) | |
| U15#(active(X1), X2) | → | U15#(X1, X2) | U82#(X1, X2, mark(X3)) | → | U82#(X1, X2, X3) | |
| active#(U31(tt, V1, V2)) | → | U32#(isNatKind(V1), V1, V2) | mark#(U41(X1, X2)) | → | U41#(mark(X1), X2) | |
| active#(U82(tt, M, N)) | → | isNat#(N) | active#(U32(tt, V1, V2)) | → | U33#(isNatKind(V2), V1, V2) | |
| active#(U34(tt, V1, V2)) | → | isNat#(V1) | mark#(U32(X1, X2, X3)) | → | U32#(mark(X1), X2, X3) | |
| mark#(U91(X1, X2)) | → | mark#(X1) | U104#(X1, mark(X2), X3) | → | U104#(X1, X2, X3) | |
| active#(U14(tt, V1, V2)) | → | mark#(U15(isNat(V1), V2)) | U22#(X1, mark(X2)) | → | U22#(X1, X2) | |
| U91#(active(X1), X2) | → | U91#(X1, X2) | U14#(X1, X2, mark(X3)) | → | U14#(X1, X2, X3) | |
| mark#(U71(X1, X2)) | → | active#(U71(mark(X1), X2)) | active#(isNatKind(s(V1))) | → | isNatKind#(V1) | |
| U82#(active(X1), X2, X3) | → | U82#(X1, X2, X3) | active#(U91(tt, N)) | → | U92#(isNatKind(N)) | |
| active#(U11(tt, V1, V2)) | → | U12#(isNatKind(V1), V1, V2) | U101#(X1, mark(X2), X3) | → | U101#(X1, X2, X3) | |
| active#(U23(tt)) | → | mark#(tt) | U21#(mark(X1), X2) | → | U21#(X1, X2) | |
| U71#(active(X1), X2) | → | U71#(X1, X2) | mark#(U34(X1, X2, X3)) | → | active#(U34(mark(X1), X2, X3)) | |
| U102#(active(X1), X2, X3) | → | U102#(X1, X2, X3) | active#(U35(tt, V2)) | → | isNat#(V2) | |
| mark#(U11(X1, X2, X3)) | → | U11#(mark(X1), X2, X3) | U31#(X1, active(X2), X3) | → | U31#(X1, X2, X3) | |
| x#(active(X1), X2) | → | x#(X1, X2) | active#(U103(tt, M, N)) | → | mark#(U104(isNatKind(N), M, N)) | |
| U102#(X1, X2, mark(X3)) | → | U102#(X1, X2, X3) | active#(U91(tt, N)) | → | mark#(U92(isNatKind(N))) | |
| x#(X1, active(X2)) | → | x#(X1, X2) | U72#(mark(X1), X2) | → | U72#(X1, X2) | |
| U33#(X1, mark(X2), X3) | → | U33#(X1, X2, X3) | U84#(X1, active(X2), X3) | → | U84#(X1, X2, X3) | |
| active#(plus(N, s(M))) | → | mark#(U81(isNat(M), M, N)) | mark#(U92(X)) | → | active#(U92(mark(X))) | |
| mark#(U12(X1, X2, X3)) | → | active#(U12(mark(X1), X2, X3)) | isNat#(active(X)) | → | isNat#(X) | |
| mark#(U13(X1, X2, X3)) | → | mark#(X1) | mark#(U36(X)) | → | active#(U36(mark(X))) | |
| U104#(X1, active(X2), X3) | → | U104#(X1, X2, X3) | U82#(X1, active(X2), X3) | → | U82#(X1, X2, X3) | |
| U36#(mark(X)) | → | U36#(X) | active#(U21(tt, V1)) | → | isNatKind#(V1) | |
| U103#(X1, active(X2), X3) | → | U103#(X1, X2, X3) | active#(U15(tt, V2)) | → | mark#(U16(isNat(V2))) | |
| mark#(U35(X1, X2)) | → | mark#(X1) | U15#(X1, mark(X2)) | → | U15#(X1, X2) | |
| U14#(mark(X1), X2, X3) | → | U14#(X1, X2, X3) | active#(U12(tt, V1, V2)) | → | U13#(isNatKind(V2), V1, V2) | |
| mark#(U41(X1, X2)) | → | mark#(X1) | U41#(X1, active(X2)) | → | U41#(X1, X2) | |
| mark#(isNatKind(X)) | → | isNatKind#(X) | isNatKind#(mark(X)) | → | isNatKind#(X) | |
| U15#(mark(X1), X2) | → | U15#(X1, X2) | U62#(active(X)) | → | U62#(X) | |
| mark#(x(X1, X2)) | → | active#(x(mark(X1), mark(X2))) | U21#(active(X1), X2) | → | U21#(X1, X2) | |
| active#(U83(tt, M, N)) | → | mark#(U84(isNatKind(N), M, N)) | U31#(X1, X2, active(X3)) | → | U31#(X1, X2, X3) | |
| U32#(X1, mark(X2), X3) | → | U32#(X1, X2, X3) | U82#(X1, mark(X2), X3) | → | U82#(X1, X2, X3) | |
| active#(x(N, s(M))) | → | isNat#(M) | active#(isNat(s(V1))) | → | U21#(isNatKind(V1), V1) | |
| U102#(X1, active(X2), X3) | → | U102#(X1, X2, X3) | U103#(X1, X2, active(X3)) | → | U103#(X1, X2, X3) | |
| active#(isNatKind(plus(V1, V2))) | → | mark#(U41(isNatKind(V1), V2)) | active#(U104(tt, M, N)) | → | plus#(x(N, M), N) | |
| active#(U82(tt, M, N)) | → | mark#(U83(isNat(N), M, N)) | active#(isNatKind(x(V1, V2))) | → | mark#(U61(isNatKind(V1), V2)) | |
| active#(U102(tt, M, N)) | → | U103#(isNat(N), M, N) | active#(U92(tt)) | → | mark#(0) | |
| active#(isNat(plus(V1, V2))) | → | U11#(isNatKind(V1), V1, V2) | mark#(s(X)) | → | s#(mark(X)) | |
| active#(U21(tt, V1)) | → | U22#(isNatKind(V1), V1) | U16#(mark(X)) | → | U16#(X) | |
| U34#(mark(X1), X2, X3) | → | U34#(X1, X2, X3) | active#(x(N, s(M))) | → | mark#(U101(isNat(M), M, N)) | |
| active#(U103(tt, M, N)) | → | U104#(isNatKind(N), M, N) | U102#(X1, mark(X2), X3) | → | U102#(X1, X2, X3) | |
| U101#(active(X1), X2, X3) | → | U101#(X1, X2, X3) | U11#(mark(X1), X2, X3) | → | U11#(X1, X2, X3) | |
| mark#(U61(X1, X2)) | → | active#(U61(mark(X1), X2)) | active#(U22(tt, V1)) | → | U23#(isNat(V1)) | |
| active#(U41(tt, V2)) | → | mark#(U42(isNatKind(V2))) | mark#(plus(X1, X2)) | → | mark#(X1) | |
| mark#(x(X1, X2)) | → | mark#(X2) | active#(plus(N, 0)) | → | mark#(U71(isNat(N), N)) | |
| mark#(U61(X1, X2)) | → | mark#(X1) | mark#(U51(X)) | → | U51#(mark(X)) | |
| mark#(U101(X1, X2, X3)) | → | active#(U101(mark(X1), X2, X3)) | mark#(U81(X1, X2, X3)) | → | active#(U81(mark(X1), X2, X3)) | |
| U101#(X1, active(X2), X3) | → | U101#(X1, X2, X3) | U13#(X1, X2, mark(X3)) | → | U13#(X1, X2, X3) | |
| mark#(U36(X)) | → | U36#(mark(X)) | mark#(U21(X1, X2)) | → | U21#(mark(X1), X2) | |
| mark#(isNat(X)) | → | isNat#(X) | active#(U34(tt, V1, V2)) | → | mark#(U35(isNat(V1), V2)) | |
| isNat#(mark(X)) | → | isNat#(X) | active#(U12(tt, V1, V2)) | → | isNatKind#(V2) | |
| active#(isNat(plus(V1, V2))) | → | isNatKind#(V1) | mark#(U83(X1, X2, X3)) | → | mark#(X1) | |
| U11#(X1, X2, mark(X3)) | → | U11#(X1, X2, X3) | mark#(U102(X1, X2, X3)) | → | mark#(X1) | |
| U82#(X1, X2, active(X3)) | → | U82#(X1, X2, X3) | mark#(U12(X1, X2, X3)) | → | mark#(X1) | |
| active#(U31(tt, V1, V2)) | → | mark#(U32(isNatKind(V1), V1, V2)) | active#(U36(tt)) | → | mark#(tt) | |
| U92#(active(X)) | → | U92#(X) | active#(U82(tt, M, N)) | → | U83#(isNat(N), M, N) | |
| U81#(X1, X2, mark(X3)) | → | U81#(X1, X2, X3) | U32#(active(X1), X2, X3) | → | U32#(X1, X2, X3) | |
| mark#(U33(X1, X2, X3)) | → | active#(U33(mark(X1), X2, X3)) | active#(isNat(x(V1, V2))) | → | U31#(isNatKind(V1), V1, V2) | |
| U104#(mark(X1), X2, X3) | → | U104#(X1, X2, X3) | active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1), V1)) | |
| U72#(active(X1), X2) | → | U72#(X1, X2) | U83#(active(X1), X2, X3) | → | U83#(X1, X2, X3) | |
| U84#(X1, X2, mark(X3)) | → | U84#(X1, X2, X3) | mark#(U103(X1, X2, X3)) | → | active#(U103(mark(X1), X2, X3)) | |
| U31#(X1, mark(X2), X3) | → | U31#(X1, X2, X3) | mark#(U82(X1, X2, X3)) | → | U82#(mark(X1), X2, X3) | |
| active#(U101(tt, M, N)) | → | isNatKind#(M) | mark#(U101(X1, X2, X3)) | → | mark#(X1) | |
| mark#(U84(X1, X2, X3)) | → | mark#(X1) | active#(isNatKind(plus(V1, V2))) | → | isNatKind#(V1) | |
| active#(U84(tt, M, N)) | → | s#(plus(N, M)) | active#(U35(tt, V2)) | → | mark#(U36(isNat(V2))) | |
| active#(U81(tt, M, N)) | → | mark#(U82(isNatKind(M), M, N)) | U72#(X1, active(X2)) | → | U72#(X1, X2) | |
| mark#(U42(X)) | → | U42#(mark(X)) | active#(U51(tt)) | → | mark#(tt) | |
| U22#(active(X1), X2) | → | U22#(X1, X2) | mark#(U72(X1, X2)) | → | mark#(X1) | |
| U11#(X1, active(X2), X3) | → | U11#(X1, X2, X3) | U81#(X1, mark(X2), X3) | → | U81#(X1, X2, X3) | |
| U41#(active(X1), X2) | → | U41#(X1, X2) | active#(isNat(s(V1))) | → | isNatKind#(V1) | |
| active#(U103(tt, M, N)) | → | isNatKind#(N) | mark#(U62(X)) | → | mark#(X) | |
| U51#(mark(X)) | → | U51#(X) | plus#(mark(X1), X2) | → | plus#(X1, X2) | |
| U13#(mark(X1), X2, X3) | → | U13#(X1, X2, X3) | mark#(U103(X1, X2, X3)) | → | U103#(mark(X1), X2, X3) | |
| U103#(mark(X1), X2, X3) | → | U103#(X1, X2, X3) | mark#(U92(X)) | → | U92#(mark(X)) | |
| active#(x(N, 0)) | → | isNat#(N) | mark#(U82(X1, X2, X3)) | → | active#(U82(mark(X1), X2, X3)) | |
| mark#(tt) | → | active#(tt) | mark#(U61(X1, X2)) | → | U61#(mark(X1), X2) | |
| mark#(U14(X1, X2, X3)) | → | mark#(X1) | U22#(X1, active(X2)) | → | U22#(X1, X2) | |
| U21#(X1, mark(X2)) | → | U21#(X1, X2) | mark#(U23(X)) | → | mark#(X) | |
| U62#(mark(X)) | → | U62#(X) | active#(U41(tt, V2)) | → | U42#(isNatKind(V2)) | |
| U71#(mark(X1), X2) | → | U71#(X1, X2) | active#(U33(tt, V1, V2)) | → | isNatKind#(V2) | |
| mark#(s(X)) | → | active#(s(mark(X))) | active#(U81(tt, M, N)) | → | U82#(isNatKind(M), M, N) | |
| mark#(U12(X1, X2, X3)) | → | U12#(mark(X1), X2, X3) | mark#(U51(X)) | → | active#(U51(mark(X))) | |
| mark#(U32(X1, X2, X3)) | → | active#(U32(mark(X1), X2, X3)) | active#(plus(N, s(M))) | → | isNat#(M) | |
| active#(U16(tt)) | → | mark#(tt) | mark#(U72(X1, X2)) | → | U72#(mark(X1), X2) | |
| U72#(X1, mark(X2)) | → | U72#(X1, X2) | mark#(U15(X1, X2)) | → | active#(U15(mark(X1), X2)) | |
| mark#(isNatKind(X)) | → | active#(isNatKind(X)) | U84#(X1, X2, active(X3)) | → | U84#(X1, X2, X3) | |
| U92#(mark(X)) | → | U92#(X) | mark#(U32(X1, X2, X3)) | → | mark#(X1) | |
| active#(isNat(plus(V1, V2))) | → | mark#(U11(isNatKind(V1), V1, V2)) | mark#(U104(X1, X2, X3)) | → | mark#(X1) | |
| U23#(mark(X)) | → | U23#(X) | U42#(active(X)) | → | U42#(X) | |
| U35#(X1, active(X2)) | → | U35#(X1, X2) | active#(U13(tt, V1, V2)) | → | isNatKind#(V2) | |
| mark#(U35(X1, X2)) | → | active#(U35(mark(X1), X2)) | mark#(U23(X)) | → | U23#(mark(X)) | |
| U14#(X1, X2, active(X3)) | → | U14#(X1, X2, X3) | mark#(U91(X1, X2)) | → | active#(U91(mark(X1), X2)) | |
| U103#(X1, X2, mark(X3)) | → | U103#(X1, X2, X3) | U81#(mark(X1), X2, X3) | → | U81#(X1, X2, X3) | |
| U84#(mark(X1), X2, X3) | → | U84#(X1, X2, X3) | U32#(X1, X2, active(X3)) | → | U32#(X1, X2, X3) | |
| U34#(X1, mark(X2), X3) | → | U34#(X1, X2, X3) | U33#(X1, X2, mark(X3)) | → | U33#(X1, X2, X3) | |
| U13#(active(X1), X2, X3) | → | U13#(X1, X2, X3) | mark#(U34(X1, X2, X3)) | → | mark#(X1) | |
| U71#(X1, active(X2)) | → | U71#(X1, X2) | active#(U71(tt, N)) | → | isNatKind#(N) | |
| plus#(X1, active(X2)) | → | plus#(X1, X2) | active#(x(N, 0)) | → | mark#(U91(isNat(N), N)) | |
| mark#(isNat(X)) | → | active#(isNat(X)) | mark#(U16(X)) | → | U16#(mark(X)) | |
| mark#(U16(X)) | → | active#(U16(mark(X))) | U101#(mark(X1), X2, X3) | → | U101#(X1, X2, X3) | |
| U83#(X1, X2, mark(X3)) | → | U83#(X1, X2, X3) | active#(U13(tt, V1, V2)) | → | mark#(U14(isNatKind(V2), V1, V2)) | |
| mark#(plus(X1, X2)) | → | mark#(X2) | active#(plus(N, 0)) | → | U71#(isNat(N), N) | |
| active#(isNatKind(x(V1, V2))) | → | isNatKind#(V1) | active#(U32(tt, V1, V2)) | → | mark#(U33(isNatKind(V2), V1, V2)) | |
| active#(U14(tt, V1, V2)) | → | isNat#(V1) | active#(isNatKind(s(V1))) | → | mark#(U51(isNatKind(V1))) | |
| U35#(mark(X1), X2) | → | U35#(X1, X2) | mark#(U83(X1, X2, X3)) | → | U83#(mark(X1), X2, X3) | |
| active#(U41(tt, V2)) | → | isNatKind#(V2) | active#(U83(tt, M, N)) | → | U84#(isNatKind(N), M, N) | |
| mark#(U92(X)) | → | mark#(X) | U11#(X1, mark(X2), X3) | → | U11#(X1, X2, X3) | |
| U33#(active(X1), X2, X3) | → | U33#(X1, X2, X3) | s#(active(X)) | → | s#(X) | |
| U31#(mark(X1), X2, X3) | → | U31#(X1, X2, X3) | U84#(active(X1), X2, X3) | → | U84#(X1, X2, X3) | |
| U103#(active(X1), X2, X3) | → | U103#(X1, X2, X3) |
| 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) |
Termination of terms over the following signature is verified: U104, isNat, U62, U61, U42, U92, U41, U91, U23, U21, U22, plus, isNatKind, U83, U84, mark, U71, U36, U72, 0, s, U51, U14, tt, U15, U82, U16, U81, U11, active, U12, U13, U31, U102, U32, U103, U33, U34, x, U101, U35