The TRS could not be proven terminating. The proof attempt took 60021 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (timeout)].
| active#(U11(tt, V1)) | → | mark#(U12(isNatIListKind(V1), V1)) | U91#(X1, active(X2), X3) | → | U91#(X1, X2, X3) | |
| U12#(active(X1), X2) | → | U12#(X1, X2) | mark#(U61(X)) | → | U61#(mark(X)) | |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | U11#(mark(X1), X2) | → | U11#(X1, X2) | |
| active#(isNatIListKind(cons(V1, V2))) | → | U51#(isNatKind(V1), V2) | mark#(U85(X1, X2)) | → | active#(U85(mark(X1), X2)) | |
| active#(isNatList(cons(V1, V2))) | → | U81#(isNatKind(V1), V1, V2) | U91#(mark(X1), X2, X3) | → | U91#(X1, X2, X3) | |
| U51#(mark(X1), X2) | → | U51#(X1, X2) | mark#(U83(X1, X2, X3)) | → | active#(U83(mark(X1), X2, X3)) | |
| active#(isNatIListKind(cons(V1, V2))) | → | isNatKind#(V1) | U84#(X1, active(X2), X3) | → | U84#(X1, X2, X3) | |
| isNat#(active(X)) | → | isNat#(X) | U21#(X1, active(X2)) | → | U21#(X1, X2) | |
| active#(isNatIList(cons(V1, V2))) | → | U41#(isNatKind(V1), V1, V2) | mark#(s(X)) | → | mark#(X) | |
| mark#(U11(X1, X2)) | → | active#(U11(mark(X1), X2)) | active#(U94(tt, L)) | → | mark#(s(length(L))) | |
| mark#(U12(X1, X2)) | → | mark#(X1) | length#(mark(X)) | → | length#(X) | |
| U86#(mark(X)) | → | U86#(X) | U43#(mark(X1), X2, X3) | → | U43#(X1, X2, X3) | |
| active#(U42(tt, V1, V2)) | → | mark#(U43(isNatIListKind(V2), V1, V2)) | active#(isNatIListKind(cons(V1, V2))) | → | mark#(U51(isNatKind(V1), V2)) | |
| active#(U41(tt, V1, V2)) | → | isNatKind#(V1) | active#(U82(tt, V1, V2)) | → | U83#(isNatIListKind(V2), V1, V2) | |
| U82#(X1, active(X2), X3) | → | U82#(X1, X2, X3) | mark#(U52(X)) | → | mark#(X) | |
| active#(U93(tt, L, N)) | → | mark#(U94(isNatKind(N), L)) | U11#(X1, mark(X2)) | → | U11#(X1, X2) | |
| active#(U21(tt, V1)) | → | isNatKind#(V1) | U41#(X1, active(X2), X3) | → | U41#(X1, X2, X3) | |
| U43#(active(X1), X2, X3) | → | U43#(X1, X2, X3) | mark#(U41(X1, X2, X3)) | → | mark#(X1) | |
| active#(U85(tt, V2)) | → | isNatList#(V2) | mark#(U93(X1, X2, X3)) | → | mark#(X1) | |
| mark#(U71(X)) | → | U71#(mark(X)) | active#(U31(tt, V)) | → | mark#(U32(isNatIListKind(V), V)) | |
| U81#(X1, active(X2), X3) | → | U81#(X1, X2, X3) | mark#(U84(X1, X2, X3)) | → | U84#(mark(X1), X2, X3) | |
| active#(U32(tt, V)) | → | U33#(isNatList(V)) | mark#(U45(X1, X2)) | → | mark#(X1) | |
| mark#(U13(X)) | → | U13#(mark(X)) | U12#(X1, active(X2)) | → | U12#(X1, X2) | |
| active#(U43(tt, V1, V2)) | → | U44#(isNatIListKind(V2), V1, V2) | mark#(U43(X1, X2, X3)) | → | mark#(X1) | |
| active#(U44(tt, V1, V2)) | → | U45#(isNat(V1), V2) | active#(U32(tt, V)) | → | mark#(U33(isNatList(V))) | |
| active#(U91(tt, L, N)) | → | isNatIListKind#(L) | active#(U84(tt, V1, V2)) | → | U85#(isNat(V1), V2) | |
| mark#(U22(X1, X2)) | → | mark#(X1) | U32#(X1, active(X2)) | → | U32#(X1, X2) | |
| mark#(U21(X1, X2)) | → | active#(U21(mark(X1), X2)) | active#(U45(tt, V2)) | → | U46#(isNatIList(V2)) | |
| mark#(U33(X)) | → | active#(U33(mark(X))) | active#(U81(tt, V1, V2)) | → | U82#(isNatKind(V1), V1, V2) | |
| active#(isNatKind(s(V1))) | → | U71#(isNatKind(V1)) | cons#(X1, mark(X2)) | → | cons#(X1, X2) | |
| U93#(X1, X2, mark(X3)) | → | U93#(X1, X2, X3) | U41#(X1, X2, active(X3)) | → | U41#(X1, X2, X3) | |
| active#(U93(tt, L, N)) | → | isNatKind#(N) | mark#(U61(X)) | → | mark#(X) | |
| isNatKind#(mark(X)) | → | isNatKind#(X) | mark#(isNatKind(X)) | → | isNatKind#(X) | |
| active#(U12(tt, V1)) | → | mark#(U13(isNatList(V1))) | mark#(U46(X)) | → | active#(U46(mark(X))) | |
| active#(U12(tt, V1)) | → | isNatList#(V1) | mark#(U92(X1, X2, X3)) | → | mark#(X1) | |
| mark#(U93(X1, X2, X3)) | → | U93#(mark(X1), X2, X3) | U45#(X1, mark(X2)) | → | U45#(X1, X2) | |
| U21#(active(X1), X2) | → | U21#(X1, X2) | active#(U94(tt, L)) | → | s#(length(L)) | |
| U33#(mark(X)) | → | U33#(X) | cons#(active(X1), X2) | → | cons#(X1, X2) | |
| active#(U92(tt, L, N)) | → | isNat#(N) | U51#(X1, mark(X2)) | → | U51#(X1, X2) | |
| U82#(X1, mark(X2), X3) | → | U82#(X1, X2, X3) | isNatList#(mark(X)) | → | isNatList#(X) | |
| active#(isNat(s(V1))) | → | U21#(isNatKind(V1), V1) | mark#(isNatList(X)) | → | isNatList#(X) | |
| U33#(active(X)) | → | U33#(X) | active#(U51(tt, V2)) | → | isNatIListKind#(V2) | |
| mark#(U41(X1, X2, X3)) | → | active#(U41(mark(X1), X2, X3)) | U42#(X1, X2, mark(X3)) | → | U42#(X1, X2, X3) | |
| active#(U41(tt, V1, V2)) | → | U42#(isNatKind(V1), V1, V2) | U83#(X1, active(X2), X3) | → | U83#(X1, X2, X3) | |
| active#(U31(tt, V)) | → | U32#(isNatIListKind(V), V) | mark#(U91(X1, X2, X3)) | → | U91#(mark(X1), X2, X3) | |
| mark#(U45(X1, X2)) | → | active#(U45(mark(X1), X2)) | U71#(active(X)) | → | U71#(X) | |
| U93#(X1, active(X2), X3) | → | U93#(X1, X2, X3) | mark#(s(X)) | → | s#(mark(X)) | |
| active#(U21(tt, V1)) | → | U22#(isNatKind(V1), V1) | U85#(mark(X1), X2) | → | U85#(X1, X2) | |
| U52#(active(X)) | → | U52#(X) | U12#(mark(X1), X2) | → | U12#(X1, X2) | |
| mark#(U46(X)) | → | U46#(mark(X)) | U91#(X1, X2, active(X3)) | → | U91#(X1, X2, X3) | |
| isNatList#(active(X)) | → | isNatList#(X) | mark#(U93(X1, X2, X3)) | → | active#(U93(mark(X1), X2, X3)) | |
| active#(U85(tt, V2)) | → | U86#(isNatList(V2)) | U93#(X1, mark(X2), X3) | → | U93#(X1, X2, X3) | |
| U93#(active(X1), X2, X3) | → | U93#(X1, X2, X3) | U92#(X1, X2, active(X3)) | → | U92#(X1, X2, X3) | |
| U71#(mark(X)) | → | U71#(X) | active#(U51(tt, V2)) | → | mark#(U52(isNatIListKind(V2))) | |
| U42#(active(X1), X2, X3) | → | U42#(X1, X2, X3) | active#(isNat(0)) | → | mark#(tt) | |
| active#(U11(tt, V1)) | → | isNatIListKind#(V1) | U85#(active(X1), X2) | → | U85#(X1, X2) | |
| mark#(U94(X1, X2)) | → | active#(U94(mark(X1), X2)) | isNatIList#(mark(X)) | → | isNatIList#(X) | |
| active#(U22(tt, V1)) | → | U23#(isNat(V1)) | mark#(isNatIList(X)) | → | isNatIList#(X) | |
| U43#(X1, X2, mark(X3)) | → | U43#(X1, X2, X3) | active#(U84(tt, V1, V2)) | → | mark#(U85(isNat(V1), V2)) | |
| cons#(X1, active(X2)) | → | cons#(X1, X2) | isNatKind#(active(X)) | → | isNatKind#(X) | |
| active#(U51(tt, V2)) | → | U52#(isNatIListKind(V2)) | active#(isNat(length(V1))) | → | U11#(isNatIListKind(V1), V1) | |
| active#(U52(tt)) | → | mark#(tt) | mark#(U46(X)) | → | mark#(X) | |
| U92#(X1, X2, mark(X3)) | → | U92#(X1, X2, X3) | active#(U46(tt)) | → | mark#(tt) | |
| mark#(U41(X1, X2, X3)) | → | U41#(mark(X1), X2, X3) | active#(U43(tt, V1, V2)) | → | isNatIListKind#(V2) | |
| mark#(U81(X1, X2, X3)) | → | active#(U81(mark(X1), X2, X3)) | active#(U86(tt)) | → | mark#(tt) | |
| mark#(U21(X1, X2)) | → | U21#(mark(X1), X2) | mark#(U21(X1, X2)) | → | mark#(X1) | |
| isNat#(mark(X)) | → | isNat#(X) | mark#(isNat(X)) | → | isNat#(X) | |
| active#(length(cons(N, L))) | → | isNatList#(L) | active#(U61(tt)) | → | mark#(tt) | |
| active#(isNatList(nil)) | → | mark#(tt) | mark#(U42(X1, X2, X3)) | → | active#(U42(mark(X1), X2, X3)) | |
| mark#(nil) | → | active#(nil) | mark#(U83(X1, X2, X3)) | → | mark#(X1) | |
| active#(U83(tt, V1, V2)) | → | mark#(U84(isNatIListKind(V2), V1, V2)) | mark#(U61(X)) | → | active#(U61(mark(X))) | |
| U23#(active(X)) | → | U23#(X) | U82#(X1, X2, active(X3)) | → | U82#(X1, X2, X3) | |
| U81#(active(X1), X2, X3) | → | U81#(X1, X2, X3) | active#(U83(tt, V1, V2)) | → | U84#(isNatIListKind(V2), V1, V2) | |
| mark#(isNatIListKind(X)) | → | active#(isNatIListKind(X)) | active#(U11(tt, V1)) | → | U12#(isNatIListKind(V1), V1) | |
| active#(isNatIList(zeros)) | → | mark#(tt) | active#(U13(tt)) | → | mark#(tt) | |
| mark#(cons(X1, X2)) | → | cons#(mark(X1), X2) | mark#(U22(X1, X2)) | → | active#(U22(mark(X1), X2)) | |
| U12#(X1, mark(X2)) | → | U12#(X1, X2) | active#(U81(tt, V1, V2)) | → | mark#(U82(isNatKind(V1), V1, V2)) | |
| mark#(U44(X1, X2, X3)) | → | active#(U44(mark(X1), X2, X3)) | U81#(X1, X2, mark(X3)) | → | U81#(X1, X2, X3) | |
| mark#(length(X)) | → | length#(mark(X)) | active#(length(cons(N, L))) | → | U91#(isNatList(L), L, N) | |
| U94#(mark(X1), X2) | → | U94#(X1, X2) | mark#(U32(X1, X2)) | → | active#(U32(mark(X1), X2)) | |
| active#(isNatKind(length(V1))) | → | U61#(isNatIListKind(V1)) | U92#(active(X1), X2, X3) | → | U92#(X1, X2, X3) | |
| U92#(X1, active(X2), X3) | → | U92#(X1, X2, X3) | active#(U71(tt)) | → | mark#(tt) | |
| active#(isNat(s(V1))) | → | mark#(U21(isNatKind(V1), V1)) | U84#(X1, X2, mark(X3)) | → | U84#(X1, X2, X3) | |
| U83#(active(X1), X2, X3) | → | U83#(X1, X2, X3) | mark#(U84(X1, X2, X3)) | → | active#(U84(mark(X1), X2, X3)) | |
| mark#(U12(X1, X2)) | → | U12#(mark(X1), X2) | s#(mark(X)) | → | s#(X) | |
| active#(U31(tt, V)) | → | isNatIListKind#(V) | U32#(active(X1), X2) | → | U32#(X1, X2) | |
| mark#(U31(X1, X2)) | → | U31#(mark(X1), X2) | U83#(mark(X1), X2, X3) | → | U83#(X1, X2, X3) | |
| U52#(mark(X)) | → | U52#(X) | active#(isNatIList(V)) | → | U31#(isNatIListKind(V), V) | |
| mark#(length(X)) | → | active#(length(mark(X))) | mark#(U82(X1, X2, X3)) | → | U82#(mark(X1), X2, X3) | |
| mark#(U13(X)) | → | mark#(X) | active#(isNatKind(0)) | → | mark#(tt) | |
| mark#(U11(X1, X2)) | → | mark#(X1) | isNatIListKind#(active(X)) | → | isNatIListKind#(X) | |
| active#(U41(tt, V1, V2)) | → | mark#(U42(isNatKind(V1), V1, V2)) | mark#(U84(X1, X2, X3)) | → | mark#(X1) | |
| active#(isNatIList(V)) | → | isNatIListKind#(V) | U46#(active(X)) | → | U46#(X) | |
| U44#(active(X1), X2, X3) | → | U44#(X1, X2, X3) | active#(U32(tt, V)) | → | isNatList#(V) | |
| active#(length(nil)) | → | mark#(0) | U83#(X1, mark(X2), X3) | → | U83#(X1, X2, X3) | |
| mark#(U85(X1, X2)) | → | mark#(X1) | mark#(U94(X1, X2)) | → | mark#(X1) | |
| U94#(X1, active(X2)) | → | U94#(X1, X2) | U83#(X1, X2, active(X3)) | → | U83#(X1, X2, X3) | |
| mark#(U44(X1, X2, X3)) | → | U44#(mark(X1), X2, X3) | active#(U42(tt, V1, V2)) | → | isNatIListKind#(V2) | |
| mark#(U22(X1, X2)) | → | U22#(mark(X1), X2) | active#(isNat(length(V1))) | → | mark#(U11(isNatIListKind(V1), V1)) | |
| active#(U45(tt, V2)) | → | mark#(U46(isNatIList(V2))) | active#(length(cons(N, L))) | → | mark#(U91(isNatList(L), L, N)) | |
| active#(U83(tt, V1, V2)) | → | isNatIListKind#(V2) | active#(U22(tt, V1)) | → | isNat#(V1) | |
| U44#(mark(X1), X2, X3) | → | U44#(X1, X2, X3) | U22#(active(X1), X2) | → | U22#(X1, X2) | |
| U11#(active(X1), X2) | → | U11#(X1, X2) | active#(U42(tt, V1, V2)) | → | U43#(isNatIListKind(V2), V1, V2) | |
| mark#(U81(X1, X2, X3)) | → | U81#(mark(X1), X2, X3) | active#(U43(tt, V1, V2)) | → | mark#(U44(isNatIListKind(V2), V1, V2)) | |
| U81#(X1, mark(X2), X3) | → | U81#(X1, X2, X3) | mark#(cons(X1, X2)) | → | mark#(X1) | |
| mark#(U91(X1, X2, X3)) | → | active#(U91(mark(X1), X2, X3)) | mark#(U42(X1, X2, X3)) | → | mark#(X1) | |
| mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | mark#(U82(X1, X2, X3)) | → | mark#(X1) | |
| active#(U22(tt, V1)) | → | mark#(U23(isNat(V1))) | U43#(X1, X2, active(X3)) | → | U43#(X1, X2, X3) | |
| U42#(X1, active(X2), X3) | → | U42#(X1, X2, X3) | mark#(U33(X)) | → | U33#(mark(X)) | |
| U11#(X1, active(X2)) | → | U11#(X1, X2) | active#(isNatKind(length(V1))) | → | isNatIListKind#(V1) | |
| active#(isNat(s(V1))) | → | isNatKind#(V1) | U81#(X1, X2, active(X3)) | → | U81#(X1, X2, X3) | |
| U85#(X1, active(X2)) | → | U85#(X1, X2) | U91#(X1, mark(X2), X3) | → | U91#(X1, X2, X3) | |
| mark#(U45(X1, X2)) | → | U45#(mark(X1), X2) | U61#(active(X)) | → | U61#(X) | |
| mark#(U32(X1, X2)) | → | mark#(X1) | active#(U91(tt, L, N)) | → | U92#(isNatIListKind(L), L, N) | |
| U86#(active(X)) | → | U86#(X) | U51#(X1, active(X2)) | → | U51#(X1, X2) | |
| mark#(U91(X1, X2, X3)) | → | mark#(X1) | U43#(X1, active(X2), X3) | → | U43#(X1, X2, X3) | |
| active#(U93(tt, L, N)) | → | U94#(isNatKind(N), L) | U22#(mark(X1), X2) | → | U22#(X1, X2) | |
| mark#(U82(X1, X2, X3)) | → | active#(U82(mark(X1), X2, X3)) | U43#(X1, mark(X2), X3) | → | U43#(X1, X2, X3) | |
| cons#(mark(X1), X2) | → | cons#(X1, X2) | active#(U82(tt, V1, V2)) | → | mark#(U83(isNatIListKind(V2), V1, V2)) | |
| mark#(tt) | → | active#(tt) | U31#(X1, active(X2)) | → | U31#(X1, X2) | |
| U44#(X1, X2, active(X3)) | → | U44#(X1, X2, X3) | mark#(U23(X)) | → | active#(U23(mark(X))) | |
| mark#(U33(X)) | → | mark#(X) | U45#(X1, active(X2)) | → | U45#(X1, X2) | |
| U22#(X1, active(X2)) | → | U22#(X1, X2) | mark#(U81(X1, X2, X3)) | → | mark#(X1) | |
| mark#(U52(X)) | → | active#(U52(mark(X))) | U82#(mark(X1), X2, X3) | → | U82#(X1, X2, X3) | |
| U21#(X1, mark(X2)) | → | U21#(X1, X2) | mark#(U23(X)) | → | mark#(X) | |
| U45#(active(X1), X2) | → | U45#(X1, X2) | U45#(mark(X1), X2) | → | U45#(X1, X2) | |
| U13#(mark(X)) | → | U13#(X) | mark#(length(X)) | → | mark#(X) | |
| active#(U94(tt, L)) | → | length#(L) | mark#(U13(X)) | → | active#(U13(mark(X))) | |
| mark#(zeros) | → | active#(zeros) | mark#(U31(X1, X2)) | → | active#(U31(mark(X1), X2)) | |
| active#(U21(tt, V1)) | → | mark#(U22(isNatKind(V1), V1)) | active#(isNat(length(V1))) | → | isNatIListKind#(V1) | |
| mark#(0) | → | active#(0) | mark#(s(X)) | → | active#(s(mark(X))) | |
| U61#(mark(X)) | → | U61#(X) | U92#(X1, mark(X2), X3) | → | U92#(X1, X2, X3) | |
| U41#(X1, X2, mark(X3)) | → | U41#(X1, X2, X3) | mark#(U43(X1, X2, X3)) | → | active#(U43(mark(X1), X2, X3)) | |
| mark#(U71(X)) | → | active#(U71(mark(X))) | mark#(U86(X)) | → | U86#(mark(X)) | |
| active#(isNatIListKind(nil)) | → | mark#(tt) | active#(zeros) | → | cons#(0, zeros) | |
| mark#(U12(X1, X2)) | → | active#(U12(mark(X1), X2)) | U13#(active(X)) | → | U13#(X) | |
| active#(isNatList(cons(V1, V2))) | → | mark#(U81(isNatKind(V1), V1, V2)) | mark#(U71(X)) | → | mark#(X) | |
| isNatIListKind#(mark(X)) | → | isNatIListKind#(X) | active#(U85(tt, V2)) | → | mark#(U86(isNatList(V2))) | |
| mark#(isNatIListKind(X)) | → | isNatIListKind#(X) | active#(U44(tt, V1, V2)) | → | mark#(U45(isNat(V1), V2)) | |
| U42#(X1, X2, active(X3)) | → | U42#(X1, X2, X3) | mark#(cons(X1, X2)) | → | active#(cons(mark(X1), X2)) | |
| active#(isNatIListKind(zeros)) | → | mark#(tt) | mark#(isNatKind(X)) | → | active#(isNatKind(X)) | |
| U84#(X1, X2, active(X3)) | → | U84#(X1, X2, X3) | active#(isNatIList(V)) | → | mark#(U31(isNatIListKind(V), V)) | |
| U92#(mark(X1), X2, X3) | → | U92#(X1, X2, X3) | U23#(mark(X)) | → | U23#(X) | |
| mark#(U43(X1, X2, X3)) | → | U43#(mark(X1), X2, X3) | active#(isNatKind(length(V1))) | → | mark#(U61(isNatIListKind(V1))) | |
| U44#(X1, mark(X2), X3) | → | U44#(X1, X2, X3) | mark#(U94(X1, X2)) | → | U94#(mark(X1), X2) | |
| mark#(U52(X)) | → | U52#(mark(X)) | U91#(X1, X2, mark(X3)) | → | U91#(X1, X2, X3) | |
| active#(U45(tt, V2)) | → | isNatIList#(V2) | U91#(active(X1), X2, X3) | → | U91#(X1, X2, X3) | |
| active#(U33(tt)) | → | mark#(tt) | length#(active(X)) | → | length#(X) | |
| mark#(U92(X1, X2, X3)) | → | active#(U92(mark(X1), X2, X3)) | U31#(active(X1), X2) | → | U31#(X1, X2) | |
| active#(U81(tt, V1, V2)) | → | isNatKind#(V1) | U93#(mark(X1), X2, X3) | → | U93#(X1, X2, X3) | |
| U84#(X1, mark(X2), X3) | → | U84#(X1, X2, X3) | mark#(U31(X1, X2)) | → | mark#(X1) | |
| mark#(U23(X)) | → | U23#(mark(X)) | U93#(X1, X2, active(X3)) | → | U93#(X1, X2, X3) | |
| mark#(isNatIList(X)) | → | active#(isNatIList(X)) | U84#(mark(X1), X2, X3) | → | U84#(X1, X2, X3) | |
| U81#(mark(X1), X2, X3) | → | U81#(X1, X2, X3) | active#(U82(tt, V1, V2)) | → | isNatIListKind#(V2) | |
| U82#(X1, X2, mark(X3)) | → | U82#(X1, X2, X3) | mark#(U32(X1, X2)) | → | U32#(mark(X1), X2) | |
| U42#(mark(X1), X2, X3) | → | U42#(X1, X2, X3) | isNatIList#(active(X)) | → | isNatIList#(X) | |
| mark#(U85(X1, X2)) | → | U85#(mark(X1), X2) | mark#(U86(X)) | → | active#(U86(mark(X))) | |
| U42#(X1, mark(X2), X3) | → | U42#(X1, X2, X3) | active#(U84(tt, V1, V2)) | → | isNat#(V1) | |
| mark#(U42(X1, X2, X3)) | → | U42#(mark(X1), X2, X3) | U41#(active(X1), X2, X3) | → | U41#(X1, X2, X3) | |
| U44#(X1, X2, mark(X3)) | → | U44#(X1, X2, X3) | mark#(isNat(X)) | → | active#(isNat(X)) | |
| U94#(X1, mark(X2)) | → | U94#(X1, X2) | active#(isNatIList(cons(V1, V2))) | → | mark#(U41(isNatKind(V1), V1, V2)) | |
| U22#(X1, mark(X2)) | → | U22#(X1, X2) | U51#(active(X1), X2) | → | U51#(X1, X2) | |
| U83#(X1, X2, mark(X3)) | → | U83#(X1, X2, X3) | mark#(U51(X1, X2)) | → | mark#(X1) | |
| U31#(X1, mark(X2)) | → | U31#(X1, X2) | mark#(U44(X1, X2, X3)) | → | mark#(X1) | |
| U94#(active(X1), X2) | → | U94#(X1, X2) | U32#(X1, mark(X2)) | → | U32#(X1, X2) | |
| mark#(U86(X)) | → | mark#(X) | mark#(U92(X1, X2, X3)) | → | U92#(mark(X1), X2, X3) | |
| mark#(U11(X1, X2)) | → | U11#(mark(X1), X2) | U41#(mark(X1), X2, X3) | → | U41#(X1, X2, X3) | |
| active#(U92(tt, L, N)) | → | mark#(U93(isNat(N), L, N)) | active#(U44(tt, V1, V2)) | → | isNat#(V1) | |
| active#(isNatKind(s(V1))) | → | isNatKind#(V1) | U82#(active(X1), X2, X3) | → | U82#(X1, X2, X3) | |
| active#(U92(tt, L, N)) | → | U93#(isNat(N), L, N) | active#(isNatIList(cons(V1, V2))) | → | isNatKind#(V1) | |
| active#(U91(tt, L, N)) | → | mark#(U92(isNatIListKind(L), L, N)) | mark#(U83(X1, X2, X3)) | → | U83#(mark(X1), X2, X3) | |
| U41#(X1, mark(X2), X3) | → | U41#(X1, X2, X3) | U46#(mark(X)) | → | U46#(X) | |
| U31#(mark(X1), X2) | → | U31#(X1, X2) | active#(U23(tt)) | → | mark#(tt) | |
| U44#(X1, active(X2), X3) | → | U44#(X1, X2, X3) | active#(U12(tt, V1)) | → | U13#(isNatList(V1)) | |
| U21#(mark(X1), X2) | → | U21#(X1, X2) | U32#(mark(X1), X2) | → | U32#(X1, X2) | |
| active#(isNatKind(s(V1))) | → | mark#(U71(isNatKind(V1))) | active#(isNatList(cons(V1, V2))) | → | isNatKind#(V1) | |
| active#(zeros) | → | mark#(cons(0, zeros)) | s#(active(X)) | → | s#(X) | |
| U85#(X1, mark(X2)) | → | U85#(X1, X2) | mark#(isNatList(X)) | → | active#(isNatList(X)) | |
| U84#(active(X1), X2, X3) | → | U84#(X1, X2, X3) |
| active(zeros) | → | mark(cons(0, zeros)) | active(U11(tt, V1)) | → | mark(U12(isNatIListKind(V1), V1)) | |
| active(U12(tt, V1)) | → | mark(U13(isNatList(V1))) | active(U13(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, V)) | → | mark(U32(isNatIListKind(V), V)) | |
| active(U32(tt, V)) | → | mark(U33(isNatList(V))) | active(U33(tt)) | → | mark(tt) | |
| active(U41(tt, V1, V2)) | → | mark(U42(isNatKind(V1), V1, V2)) | active(U42(tt, V1, V2)) | → | mark(U43(isNatIListKind(V2), V1, V2)) | |
| active(U43(tt, V1, V2)) | → | mark(U44(isNatIListKind(V2), V1, V2)) | active(U44(tt, V1, V2)) | → | mark(U45(isNat(V1), V2)) | |
| active(U45(tt, V2)) | → | mark(U46(isNatIList(V2))) | active(U46(tt)) | → | mark(tt) | |
| active(U51(tt, V2)) | → | mark(U52(isNatIListKind(V2))) | active(U52(tt)) | → | mark(tt) | |
| active(U61(tt)) | → | mark(tt) | active(U71(tt)) | → | mark(tt) | |
| active(U81(tt, V1, V2)) | → | mark(U82(isNatKind(V1), V1, V2)) | active(U82(tt, V1, V2)) | → | mark(U83(isNatIListKind(V2), V1, V2)) | |
| active(U83(tt, V1, V2)) | → | mark(U84(isNatIListKind(V2), V1, V2)) | active(U84(tt, V1, V2)) | → | mark(U85(isNat(V1), V2)) | |
| active(U85(tt, V2)) | → | mark(U86(isNatList(V2))) | active(U86(tt)) | → | mark(tt) | |
| active(U91(tt, L, N)) | → | mark(U92(isNatIListKind(L), L, N)) | active(U92(tt, L, N)) | → | mark(U93(isNat(N), L, N)) | |
| active(U93(tt, L, N)) | → | mark(U94(isNatKind(N), L)) | active(U94(tt, L)) | → | mark(s(length(L))) | |
| active(isNat(0)) | → | mark(tt) | active(isNat(length(V1))) | → | mark(U11(isNatIListKind(V1), V1)) | |
| active(isNat(s(V1))) | → | mark(U21(isNatKind(V1), V1)) | active(isNatIList(V)) | → | mark(U31(isNatIListKind(V), V)) | |
| active(isNatIList(zeros)) | → | mark(tt) | active(isNatIList(cons(V1, V2))) | → | mark(U41(isNatKind(V1), V1, V2)) | |
| active(isNatIListKind(nil)) | → | mark(tt) | active(isNatIListKind(zeros)) | → | mark(tt) | |
| active(isNatIListKind(cons(V1, V2))) | → | mark(U51(isNatKind(V1), V2)) | active(isNatKind(0)) | → | mark(tt) | |
| active(isNatKind(length(V1))) | → | mark(U61(isNatIListKind(V1))) | active(isNatKind(s(V1))) | → | mark(U71(isNatKind(V1))) | |
| active(isNatList(nil)) | → | mark(tt) | active(isNatList(cons(V1, V2))) | → | mark(U81(isNatKind(V1), V1, V2)) | |
| active(length(nil)) | → | mark(0) | active(length(cons(N, L))) | → | mark(U91(isNatList(L), L, N)) | |
| mark(zeros) | → | active(zeros) | mark(cons(X1, X2)) | → | active(cons(mark(X1), X2)) | |
| mark(0) | → | active(0) | mark(U11(X1, X2)) | → | active(U11(mark(X1), X2)) | |
| mark(tt) | → | active(tt) | mark(U12(X1, X2)) | → | active(U12(mark(X1), X2)) | |
| mark(isNatIListKind(X)) | → | active(isNatIListKind(X)) | mark(U13(X)) | → | active(U13(mark(X))) | |
| mark(isNatList(X)) | → | active(isNatList(X)) | mark(U21(X1, X2)) | → | active(U21(mark(X1), X2)) | |
| mark(U22(X1, X2)) | → | active(U22(mark(X1), X2)) | mark(isNatKind(X)) | → | active(isNatKind(X)) | |
| mark(U23(X)) | → | active(U23(mark(X))) | mark(isNat(X)) | → | active(isNat(X)) | |
| mark(U31(X1, X2)) | → | active(U31(mark(X1), X2)) | mark(U32(X1, X2)) | → | active(U32(mark(X1), X2)) | |
| mark(U33(X)) | → | active(U33(mark(X))) | mark(U41(X1, X2, X3)) | → | active(U41(mark(X1), X2, X3)) | |
| mark(U42(X1, X2, X3)) | → | active(U42(mark(X1), X2, X3)) | mark(U43(X1, X2, X3)) | → | active(U43(mark(X1), X2, X3)) | |
| mark(U44(X1, X2, X3)) | → | active(U44(mark(X1), X2, X3)) | mark(U45(X1, X2)) | → | active(U45(mark(X1), X2)) | |
| mark(U46(X)) | → | active(U46(mark(X))) | mark(isNatIList(X)) | → | active(isNatIList(X)) | |
| mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) | mark(U52(X)) | → | active(U52(mark(X))) | |
| mark(U61(X)) | → | active(U61(mark(X))) | mark(U71(X)) | → | active(U71(mark(X))) | |
| 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(U85(X1, X2)) | → | active(U85(mark(X1), X2)) | mark(U86(X)) | → | active(U86(mark(X))) | |
| mark(U91(X1, X2, X3)) | → | active(U91(mark(X1), X2, X3)) | mark(U92(X1, X2, X3)) | → | active(U92(mark(X1), X2, X3)) | |
| mark(U93(X1, X2, X3)) | → | active(U93(mark(X1), X2, X3)) | mark(U94(X1, X2)) | → | active(U94(mark(X1), X2)) | |
| mark(s(X)) | → | active(s(mark(X))) | mark(length(X)) | → | active(length(mark(X))) | |
| mark(nil) | → | active(nil) | cons(mark(X1), X2) | → | cons(X1, X2) | |
| cons(X1, mark(X2)) | → | cons(X1, X2) | cons(active(X1), X2) | → | cons(X1, X2) | |
| cons(X1, active(X2)) | → | cons(X1, X2) | U11(mark(X1), X2) | → | U11(X1, X2) | |
| U11(X1, mark(X2)) | → | U11(X1, X2) | U11(active(X1), X2) | → | U11(X1, X2) | |
| U11(X1, active(X2)) | → | U11(X1, X2) | U12(mark(X1), X2) | → | U12(X1, X2) | |
| U12(X1, mark(X2)) | → | U12(X1, X2) | U12(active(X1), X2) | → | U12(X1, X2) | |
| U12(X1, active(X2)) | → | U12(X1, X2) | isNatIListKind(mark(X)) | → | isNatIListKind(X) | |
| isNatIListKind(active(X)) | → | isNatIListKind(X) | U13(mark(X)) | → | U13(X) | |
| U13(active(X)) | → | U13(X) | isNatList(mark(X)) | → | isNatList(X) | |
| isNatList(active(X)) | → | isNatList(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) | isNatKind(mark(X)) | → | isNatKind(X) | |
| isNatKind(active(X)) | → | isNatKind(X) | U23(mark(X)) | → | U23(X) | |
| U23(active(X)) | → | U23(X) | isNat(mark(X)) | → | isNat(X) | |
| isNat(active(X)) | → | isNat(X) | U31(mark(X1), X2) | → | U31(X1, X2) | |
| U31(X1, mark(X2)) | → | U31(X1, X2) | U31(active(X1), X2) | → | U31(X1, X2) | |
| U31(X1, active(X2)) | → | U31(X1, X2) | U32(mark(X1), X2) | → | U32(X1, X2) | |
| U32(X1, mark(X2)) | → | U32(X1, X2) | U32(active(X1), X2) | → | U32(X1, X2) | |
| U32(X1, active(X2)) | → | U32(X1, X2) | U33(mark(X)) | → | U33(X) | |
| U33(active(X)) | → | U33(X) | U41(mark(X1), X2, X3) | → | U41(X1, X2, X3) | |
| U41(X1, mark(X2), X3) | → | U41(X1, X2, X3) | U41(X1, X2, mark(X3)) | → | U41(X1, X2, X3) | |
| U41(active(X1), X2, X3) | → | U41(X1, X2, X3) | U41(X1, active(X2), X3) | → | U41(X1, X2, X3) | |
| U41(X1, X2, active(X3)) | → | U41(X1, X2, X3) | U42(mark(X1), X2, X3) | → | U42(X1, X2, X3) | |
| U42(X1, mark(X2), X3) | → | U42(X1, X2, X3) | U42(X1, X2, mark(X3)) | → | U42(X1, X2, X3) | |
| U42(active(X1), X2, X3) | → | U42(X1, X2, X3) | U42(X1, active(X2), X3) | → | U42(X1, X2, X3) | |
| U42(X1, X2, active(X3)) | → | U42(X1, X2, X3) | U43(mark(X1), X2, X3) | → | U43(X1, X2, X3) | |
| U43(X1, mark(X2), X3) | → | U43(X1, X2, X3) | U43(X1, X2, mark(X3)) | → | U43(X1, X2, X3) | |
| U43(active(X1), X2, X3) | → | U43(X1, X2, X3) | U43(X1, active(X2), X3) | → | U43(X1, X2, X3) | |
| U43(X1, X2, active(X3)) | → | U43(X1, X2, X3) | U44(mark(X1), X2, X3) | → | U44(X1, X2, X3) | |
| U44(X1, mark(X2), X3) | → | U44(X1, X2, X3) | U44(X1, X2, mark(X3)) | → | U44(X1, X2, X3) | |
| U44(active(X1), X2, X3) | → | U44(X1, X2, X3) | U44(X1, active(X2), X3) | → | U44(X1, X2, X3) | |
| U44(X1, X2, active(X3)) | → | U44(X1, X2, X3) | U45(mark(X1), X2) | → | U45(X1, X2) | |
| U45(X1, mark(X2)) | → | U45(X1, X2) | U45(active(X1), X2) | → | U45(X1, X2) | |
| U45(X1, active(X2)) | → | U45(X1, X2) | U46(mark(X)) | → | U46(X) | |
| U46(active(X)) | → | U46(X) | isNatIList(mark(X)) | → | isNatIList(X) | |
| isNatIList(active(X)) | → | isNatIList(X) | U51(mark(X1), X2) | → | U51(X1, X2) | |
| U51(X1, mark(X2)) | → | U51(X1, X2) | U51(active(X1), X2) | → | U51(X1, X2) | |
| U51(X1, active(X2)) | → | U51(X1, X2) | U52(mark(X)) | → | U52(X) | |
| U52(active(X)) | → | U52(X) | U61(mark(X)) | → | U61(X) | |
| U61(active(X)) | → | U61(X) | U71(mark(X)) | → | U71(X) | |
| U71(active(X)) | → | U71(X) | 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) | U85(mark(X1), X2) | → | U85(X1, X2) | |
| U85(X1, mark(X2)) | → | U85(X1, X2) | U85(active(X1), X2) | → | U85(X1, X2) | |
| U85(X1, active(X2)) | → | U85(X1, X2) | U86(mark(X)) | → | U86(X) | |
| U86(active(X)) | → | U86(X) | U91(mark(X1), X2, X3) | → | U91(X1, X2, X3) | |
| U91(X1, mark(X2), X3) | → | U91(X1, X2, X3) | U91(X1, X2, mark(X3)) | → | U91(X1, X2, X3) | |
| U91(active(X1), X2, X3) | → | U91(X1, X2, X3) | U91(X1, active(X2), X3) | → | U91(X1, X2, X3) | |
| U91(X1, X2, active(X3)) | → | U91(X1, X2, X3) | U92(mark(X1), X2, X3) | → | U92(X1, X2, X3) | |
| U92(X1, mark(X2), X3) | → | U92(X1, X2, X3) | U92(X1, X2, mark(X3)) | → | U92(X1, X2, X3) | |
| U92(active(X1), X2, X3) | → | U92(X1, X2, X3) | U92(X1, active(X2), X3) | → | U92(X1, X2, X3) | |
| U92(X1, X2, active(X3)) | → | U92(X1, X2, X3) | U93(mark(X1), X2, X3) | → | U93(X1, X2, X3) | |
| U93(X1, mark(X2), X3) | → | U93(X1, X2, X3) | U93(X1, X2, mark(X3)) | → | U93(X1, X2, X3) | |
| U93(active(X1), X2, X3) | → | U93(X1, X2, X3) | U93(X1, active(X2), X3) | → | U93(X1, X2, X3) | |
| U93(X1, X2, active(X3)) | → | U93(X1, X2, X3) | U94(mark(X1), X2) | → | U94(X1, X2) | |
| U94(X1, mark(X2)) | → | U94(X1, X2) | U94(active(X1), X2) | → | U94(X1, X2) | |
| U94(X1, active(X2)) | → | U94(X1, X2) | s(mark(X)) | → | s(X) | |
| s(active(X)) | → | s(X) | length(mark(X)) | → | length(X) | |
| length(active(X)) | → | length(X) |
Termination of terms over the following signature is verified: isNatIListKind, U94, isNat, U46, U45, U44, U61, U43, U93, U42, U92, U41, U91, length, U23, U21, cons, U22, isNatIList, isNatKind, U83, U84, U85, mark, U86, U71, 0, s, U51, isNatList, tt, zeros, U82, U81, U52, U11, active, U12, U13, U31, U32, U33, nil