TIMEOUT
The TRS could not be proven terminating. The proof attempt took 60001 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (28931ms).
| – Problem 2 was processed with processor DependencyGraph (21840ms).
| | – Problem 23 remains open; application of the following processors failed [].
| | – Problem 24 remains open; application of the following processors failed [].
| | – Problem 25 remains open; application of the following processors failed [].
| | – Problem 26 remains open; application of the following processors failed [].
| | – Problem 27 remains open; application of the following processors failed [].
| | – Problem 28 remains open; application of the following processors failed [].
| | – Problem 29 remains open; application of the following processors failed [].
| | – Problem 30 remains open; application of the following processors failed [].
| | – Problem 31 remains open; application of the following processors failed [].
| | – Problem 32 remains open; application of the following processors failed [].
| | – Problem 33 remains open; application of the following processors failed [].
| – Problem 3 remains open; application of the following processors failed [SubtermCriterion (1ms), DependencyGraph (timeout)].
| – Problem 4 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 5 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 6 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 7 remains open; application of the following processors failed [SubtermCriterion (3ms)].
| – Problem 8 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 9 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 10 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 11 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 12 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 13 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 14 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 15 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 16 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 17 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 18 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 19 remains open; application of the following processors failed [SubtermCriterion (2ms)].
| – Problem 20 remains open; application of the following processors failed [SubtermCriterion (3ms)].
| – Problem 21 remains open; application of the following processors failed [SubtermCriterion (1ms)].
| – Problem 22 remains open; application of the following processors failed [SubtermCriterion (1ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U94#(tt, V1, V2) | → | activate#(V1) | | U121#(tt, IL) | → | activate#(IL) |
| U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | | U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U31#(tt, V) | → | isNatIListKind#(activate(V)) |
| U51#(tt, V2) | → | activate#(V2) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | length#(nil) | → | 0# |
| U111#(tt, L, N) | → | isNatIListKind#(activate(L)) | | U44#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U105#(tt, V2) | → | isNatIList#(activate(V2)) | | U113#(tt, L, N) | → | activate#(L) |
| U113#(tt, L, N) | → | isNatKind#(activate(N)) | | U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) | → | activate#(M) | | length#(cons(N, L)) | → | isNatList#(activate(L)) |
| U136#(tt, IL, M, N) | → | activate#(IL) | | isNatList#(n__take(V1, V2)) | → | activate#(V2) |
| U95#(tt, V2) | → | isNatList#(activate(V2)) | | U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) | → | activate#(N) | | isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | | U132#(tt, IL, M, N) | → | activate#(M) |
| take#(s(M), cons(N, IL)) | → | activate#(IL) | | isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) |
| isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) | | U114#(tt, L) | → | activate#(L) |
| isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V2) |
| U92#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) | → | activate#(V1) | | U32#(tt, V) | → | isNatList#(activate(V)) |
| isNatKind#(n__s(V1)) | → | activate#(V1) | | U93#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U105#(tt, V2) | → | activate#(V2) | | U131#(tt, IL, M, N) | → | activate#(N) |
| isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U31#(tt, V) | → | activate#(V) |
| U132#(tt, IL, M, N) | → | activate#(IL) | | U131#(tt, IL, M, N) | → | activate#(IL) |
| U114#(tt, L) | → | length#(activate(L)) | | U91#(tt, V1, V2) | → | activate#(V2) |
| U122#(tt) | → | nil# | | U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) |
| U102#(tt, V1, V2) | → | activate#(V2) | | U112#(tt, L, N) | → | isNat#(activate(N)) |
| U93#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | activate#(V1) |
| U32#(tt, V) | → | activate#(V) | | U11#(tt, V1) | → | activate#(V1) |
| U41#(tt, V1, V2) | → | activate#(V2) | | U11#(tt, V1) | → | isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) | | U131#(tt, IL, M, N) | → | activate#(M) |
| isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U134#(tt, IL, M, N) | → | activate#(IL) |
| U113#(tt, L, N) | → | activate#(N) | | U43#(tt, V1, V2) | → | activate#(V2) |
| isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(IL) |
| U91#(tt, V1, V2) | → | activate#(V1) | | U44#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V1) |
| activate#(n__take(X1, X2)) | → | take#(X1, X2) | | isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| take#(0, IL) | → | isNatIList#(IL) | | U121#(tt, IL) | → | isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) | → | activate#(M) | | U12#(tt, V1) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | activate#(V2) | | U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U21#(tt, V1) | → | isNatKind#(activate(V1)) | | U45#(tt, V2) | → | activate#(V2) |
| U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) | | U95#(tt, V2) | → | activate#(V2) |
| length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) | | U45#(tt, V2) | → | isNatIList#(activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(M) | | U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) | | U44#(tt, V1, V2) | → | activate#(V1) |
| U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U101#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U105#(tt, V2) | → | U106#(isNatIList(activate(V2))) | | U134#(tt, IL, M, N) | → | isNat#(activate(N)) |
| isNat#(n__s(V1)) | → | activate#(V1) | | U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | isNatIListKind#(activate(V)) |
| isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U103#(tt, V1, V2) | → | activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U42#(tt, V1, V2) | → | activate#(V1) |
| U112#(tt, L, N) | → | activate#(N) | | U133#(tt, IL, M, N) | → | activate#(IL) |
| U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) |
| U112#(tt, L, N) | → | activate#(L) | | U41#(tt, V1, V2) | → | activate#(V1) |
| U42#(tt, V1, V2) | → | activate#(V2) | | U103#(tt, V1, V2) | → | activate#(V1) |
| U22#(tt, V1) | → | activate#(V1) | | U92#(tt, V1, V2) | → | activate#(V2) |
| U12#(tt, V1) | → | isNatList#(activate(V1)) | | U121#(tt, IL) | → | U122#(isNatIListKind(activate(IL))) |
| isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | | U136#(tt, IL, M, N) | → | activate#(N) |
| U22#(tt, V1) | → | U23#(isNat(activate(V1))) | | U111#(tt, L, N) | → | activate#(N) |
| isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(M) | | U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U22#(tt, V1) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | activate#(L) |
| U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(N) |
| U51#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U101#(tt, V1, V2) | → | activate#(V2) |
| U61#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) |
| U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(N) |
| U132#(tt, IL, M, N) | → | activate#(N) | | U104#(tt, V1, V2) | → | activate#(V1) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | activate#(V) |
| U61#(tt, V2) | → | activate#(V2) | | U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) | | take#(0, IL) | → | U121#(isNatIList(IL), IL) |
| U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) | | isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U94#(tt, V1, V2) | → | isNat#(activate(V1)) | | U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) | → | activate#(V1) | | U104#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | | activate#(n__length(X)) | → | length#(X) |
| U114#(tt, L) | → | s#(length(activate(L))) | | U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V1) |
| length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 3
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U94#(tt, V1, V2) | → | activate#(V1) | | U121#(tt, IL) | → | activate#(IL) |
| U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U31#(tt, V) | → | isNatIListKind#(activate(V)) |
| U51#(tt, V2) | → | activate#(V2) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | U111#(tt, L, N) | → | isNatIListKind#(activate(L)) |
| length#(nil) | → | 0# | | U44#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U105#(tt, V2) | → | isNatIList#(activate(V2)) | | U113#(tt, L, N) | → | activate#(L) |
| U113#(tt, L, N) | → | isNatKind#(activate(N)) | | U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| length#(cons(N, L)) | → | isNatList#(activate(L)) | | U134#(tt, IL, M, N) | → | activate#(M) |
| U136#(tt, IL, M, N) | → | activate#(IL) | | isNatList#(n__take(V1, V2)) | → | activate#(V2) |
| U95#(tt, V2) | → | isNatList#(activate(V2)) | | U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) | → | activate#(N) | | isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) | → | activate#(M) | | U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| take#(s(M), cons(N, IL)) | → | activate#(IL) | | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) | | U114#(tt, L) | → | activate#(L) |
| isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V2) |
| U92#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) | → | activate#(V1) | | U32#(tt, V) | → | isNatList#(activate(V)) |
| isNatKind#(n__s(V1)) | → | activate#(V1) | | U93#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U105#(tt, V2) | → | activate#(V2) | | isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) | → | activate#(N) | | U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U31#(tt, V) | → | activate#(V) |
| U132#(tt, IL, M, N) | → | activate#(IL) | | U131#(tt, IL, M, N) | → | activate#(IL) |
| U114#(tt, L) | → | length#(activate(L)) | | U91#(tt, V1, V2) | → | activate#(V2) |
| U102#(tt, V1, V2) | → | activate#(V2) | | U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) |
| U112#(tt, L, N) | → | isNat#(activate(N)) | | U93#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | activate#(V1) | | U11#(tt, V1) | → | activate#(V1) |
| U32#(tt, V) | → | activate#(V) | | U41#(tt, V1, V2) | → | activate#(V2) |
| U11#(tt, V1) | → | isNatIListKind#(activate(V1)) | | U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) |
| U131#(tt, IL, M, N) | → | activate#(M) | | isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | activate#(IL) | | U113#(tt, L, N) | → | activate#(N) |
| U43#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(IL) | | U91#(tt, V1, V2) | → | activate#(V1) |
| U44#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V1) | | activate#(n__take(X1, X2)) | → | take#(X1, X2) |
| isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | take#(0, IL) | → | isNatIList#(IL) |
| U121#(tt, IL) | → | isNatIListKind#(activate(IL)) | | U136#(tt, IL, M, N) | → | activate#(M) |
| U12#(tt, V1) | → | activate#(V1) | | U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U104#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | isNatKind#(activate(V1)) |
| U45#(tt, V2) | → | activate#(V2) | | U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) |
| U95#(tt, V2) | → | activate#(V2) | | length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) |
| U45#(tt, V2) | → | isNatIList#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(M) |
| U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) | | U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) | → | activate#(V1) | | U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNat#(n__s(V1)) | → | activate#(V1) | | U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U105#(tt, V2) | → | U106#(isNatIList(activate(V2))) | | U134#(tt, IL, M, N) | → | isNat#(activate(N)) |
| U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | isNatIList#(V) | → | isNatIListKind#(activate(V)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V2) | | isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | activate#(V2) | | isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U42#(tt, V1, V2) | → | activate#(V1) | | U112#(tt, L, N) | → | activate#(N) |
| U133#(tt, IL, M, N) | → | activate#(IL) | | U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) | | U112#(tt, L, N) | → | activate#(L) |
| U41#(tt, V1, V2) | → | activate#(V1) | | U42#(tt, V1, V2) | → | activate#(V2) |
| U103#(tt, V1, V2) | → | activate#(V1) | | U22#(tt, V1) | → | activate#(V1) |
| U12#(tt, V1) | → | isNatList#(activate(V1)) | | U92#(tt, V1, V2) | → | activate#(V2) |
| isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | | U111#(tt, L, N) | → | activate#(N) |
| U136#(tt, IL, M, N) | → | activate#(N) | | isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(M) |
| U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U22#(tt, V1) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | activate#(L) | | U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(N) | | U51#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) | → | activate#(V2) | | U61#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) | | U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U132#(tt, IL, M, N) | → | activate#(N) | | U135#(tt, IL, M, N) | → | activate#(N) |
| U104#(tt, V1, V2) | → | activate#(V1) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) |
| isNatIList#(V) | → | activate#(V) | | U61#(tt, V2) | → | activate#(V2) |
| U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) |
| take#(0, IL) | → | U121#(isNatIList(IL), IL) | | U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) |
| isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) | | U94#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) | | U43#(tt, V1, V2) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| activate#(n__length(X)) | → | length#(X) | | U114#(tt, L) | → | s#(length(activate(L))) |
| U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | activate#(V1) | | length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 4
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U94#(tt, V1, V2) | → | activate#(V1) | | U121#(tt, IL) | → | activate#(IL) |
| U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U51#(tt, V2) | → | activate#(V2) |
| U31#(tt, V) | → | isNatIListKind#(activate(V)) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | U111#(tt, L, N) | → | isNatIListKind#(activate(L)) |
| length#(nil) | → | 0# | | U44#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U105#(tt, V2) | → | isNatIList#(activate(V2)) | | U113#(tt, L, N) | → | activate#(L) |
| U113#(tt, L, N) | → | isNatKind#(activate(N)) | | U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| length#(cons(N, L)) | → | isNatList#(activate(L)) | | U134#(tt, IL, M, N) | → | activate#(M) |
| isNatList#(n__take(V1, V2)) | → | activate#(V2) | | U136#(tt, IL, M, N) | → | activate#(IL) |
| U95#(tt, V2) | → | isNatList#(activate(V2)) | | U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) | → | activate#(N) | | isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | | U132#(tt, IL, M, N) | → | activate#(M) |
| take#(s(M), cons(N, IL)) | → | activate#(IL) | | isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) |
| isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) | | U114#(tt, L) | → | activate#(L) |
| isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V2) |
| U92#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) | → | activate#(V1) | | U32#(tt, V) | → | isNatList#(activate(V)) |
| isNatKind#(n__s(V1)) | → | activate#(V1) | | U93#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U105#(tt, V2) | → | activate#(V2) | | isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) | → | activate#(N) | | U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U31#(tt, V) | → | activate#(V) |
| U132#(tt, IL, M, N) | → | activate#(IL) | | U131#(tt, IL, M, N) | → | activate#(IL) |
| U114#(tt, L) | → | length#(activate(L)) | | U91#(tt, V1, V2) | → | activate#(V2) |
| U122#(tt) | → | nil# | | U102#(tt, V1, V2) | → | activate#(V2) |
| U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) | | U32#(tt, V) | → | U33#(isNatList(activate(V))) |
| U112#(tt, L, N) | → | isNat#(activate(N)) | | U93#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | activate#(V1) | | U11#(tt, V1) | → | activate#(V1) |
| U32#(tt, V) | → | activate#(V) | | U41#(tt, V1, V2) | → | activate#(V2) |
| U11#(tt, V1) | → | isNatIListKind#(activate(V1)) | | U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) |
| U131#(tt, IL, M, N) | → | activate#(M) | | isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | activate#(IL) | | U113#(tt, L, N) | → | activate#(N) |
| U43#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(IL) | | U91#(tt, V1, V2) | → | activate#(V1) |
| U44#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V1) | | activate#(n__take(X1, X2)) | → | take#(X1, X2) |
| isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | take#(0, IL) | → | isNatIList#(IL) |
| U121#(tt, IL) | → | isNatIListKind#(activate(IL)) | | U136#(tt, IL, M, N) | → | activate#(M) |
| U12#(tt, V1) | → | activate#(V1) | | U104#(tt, V1, V2) | → | activate#(V2) |
| U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U21#(tt, V1) | → | isNatKind#(activate(V1)) |
| U45#(tt, V2) | → | activate#(V2) | | U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) |
| U95#(tt, V2) | → | activate#(V2) | | length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) |
| U45#(tt, V2) | → | isNatIList#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(M) |
| U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) | | U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) | → | activate#(V1) | | U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U134#(tt, IL, M, N) | → | isNat#(activate(N)) |
| isNat#(n__s(V1)) | → | activate#(V1) | | U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | isNatIListKind#(activate(V)) |
| isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U103#(tt, V1, V2) | → | activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U42#(tt, V1, V2) | → | activate#(V1) |
| U112#(tt, L, N) | → | activate#(N) | | U133#(tt, IL, M, N) | → | activate#(IL) |
| U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) |
| U112#(tt, L, N) | → | activate#(L) | | U41#(tt, V1, V2) | → | activate#(V1) |
| U42#(tt, V1, V2) | → | activate#(V2) | | U103#(tt, V1, V2) | → | activate#(V1) |
| U22#(tt, V1) | → | activate#(V1) | | U92#(tt, V1, V2) | → | activate#(V2) |
| U12#(tt, V1) | → | isNatList#(activate(V1)) | | U121#(tt, IL) | → | U122#(isNatIListKind(activate(IL))) |
| isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | | U111#(tt, L, N) | → | activate#(N) |
| U136#(tt, IL, M, N) | → | activate#(N) | | isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(M) |
| U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U22#(tt, V1) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | activate#(L) | | U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(N) | | U51#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) | → | activate#(V2) | | U61#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) | | U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(N) | | U132#(tt, IL, M, N) | → | activate#(N) |
| U104#(tt, V1, V2) | → | activate#(V1) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) |
| U61#(tt, V2) | → | activate#(V2) | | isNatIList#(V) | → | activate#(V) |
| U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) |
| take#(0, IL) | → | U121#(isNatIList(IL), IL) | | U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) |
| isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) | | U94#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) | | U43#(tt, V1, V2) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| activate#(n__length(X)) | → | length#(X) | | U114#(tt, L) | → | s#(length(activate(L))) |
| U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | activate#(V1) | | length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 5
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U94#(tt, V1, V2) | → | activate#(V1) | | U121#(tt, IL) | → | activate#(IL) |
| U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | | U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U31#(tt, V) | → | isNatIListKind#(activate(V)) |
| U51#(tt, V2) | → | activate#(V2) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | length#(nil) | → | 0# |
| U111#(tt, L, N) | → | isNatIListKind#(activate(L)) | | U44#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U105#(tt, V2) | → | isNatIList#(activate(V2)) | | U113#(tt, L, N) | → | activate#(L) |
| U113#(tt, L, N) | → | isNatKind#(activate(N)) | | U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) | → | activate#(M) | | length#(cons(N, L)) | → | isNatList#(activate(L)) |
| U136#(tt, IL, M, N) | → | activate#(IL) | | isNatList#(n__take(V1, V2)) | → | activate#(V2) |
| U95#(tt, V2) | → | isNatList#(activate(V2)) | | U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) | → | activate#(N) | | isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | | U132#(tt, IL, M, N) | → | activate#(M) |
| take#(s(M), cons(N, IL)) | → | activate#(IL) | | isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) |
| isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) | | U114#(tt, L) | → | activate#(L) |
| isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V2) |
| U92#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) | → | activate#(V1) | | U32#(tt, V) | → | isNatList#(activate(V)) |
| isNatKind#(n__s(V1)) | → | activate#(V1) | | U93#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U105#(tt, V2) | → | activate#(V2) | | U131#(tt, IL, M, N) | → | activate#(N) |
| isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U31#(tt, V) | → | activate#(V) |
| U132#(tt, IL, M, N) | → | activate#(IL) | | U131#(tt, IL, M, N) | → | activate#(IL) |
| U114#(tt, L) | → | length#(activate(L)) | | U91#(tt, V1, V2) | → | activate#(V2) |
| U122#(tt) | → | nil# | | U102#(tt, V1, V2) | → | activate#(V2) |
| U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) | | U32#(tt, V) | → | U33#(isNatList(activate(V))) |
| U112#(tt, L, N) | → | isNat#(activate(N)) | | U93#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | activate#(V1) | | U32#(tt, V) | → | activate#(V) |
| U11#(tt, V1) | → | activate#(V1) | | U41#(tt, V1, V2) | → | activate#(V2) |
| U11#(tt, V1) | → | isNatIListKind#(activate(V1)) | | U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) |
| U131#(tt, IL, M, N) | → | activate#(M) | | isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | activate#(IL) | | U113#(tt, L, N) | → | activate#(N) |
| U43#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(IL) | | U91#(tt, V1, V2) | → | activate#(V1) |
| U44#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V1) | | activate#(n__take(X1, X2)) | → | take#(X1, X2) |
| isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | take#(0, IL) | → | isNatIList#(IL) |
| U121#(tt, IL) | → | isNatIListKind#(activate(IL)) | | U136#(tt, IL, M, N) | → | activate#(M) |
| U12#(tt, V1) | → | activate#(V1) | | U104#(tt, V1, V2) | → | activate#(V2) |
| U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U21#(tt, V1) | → | isNatKind#(activate(V1)) |
| U45#(tt, V2) | → | activate#(V2) | | U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) |
| U95#(tt, V2) | → | activate#(V2) | | length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) |
| U45#(tt, V2) | → | isNatIList#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(M) |
| U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) | | U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) | → | activate#(V1) | | U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNat#(n__s(V1)) | → | activate#(V1) | | U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U105#(tt, V2) | → | U106#(isNatIList(activate(V2))) | | U134#(tt, IL, M, N) | → | isNat#(activate(N)) |
| U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V2) |
| isNatIList#(V) | → | isNatIListKind#(activate(V)) | | isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | activate#(V2) | | isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U42#(tt, V1, V2) | → | activate#(V1) | | U112#(tt, L, N) | → | activate#(N) |
| U133#(tt, IL, M, N) | → | activate#(IL) | | U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) | | U112#(tt, L, N) | → | activate#(L) |
| U41#(tt, V1, V2) | → | activate#(V1) | | U42#(tt, V1, V2) | → | activate#(V2) |
| U103#(tt, V1, V2) | → | activate#(V1) | | U22#(tt, V1) | → | activate#(V1) |
| U92#(tt, V1, V2) | → | activate#(V2) | | U12#(tt, V1) | → | isNatList#(activate(V1)) |
| U121#(tt, IL) | → | U122#(isNatIListKind(activate(IL))) | | isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) |
| U136#(tt, IL, M, N) | → | activate#(N) | | U111#(tt, L, N) | → | activate#(N) |
| isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(M) | | U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U22#(tt, V1) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | activate#(L) |
| U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(N) |
| U51#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U101#(tt, V1, V2) | → | activate#(V2) |
| U61#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) |
| U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(N) |
| U132#(tt, IL, M, N) | → | activate#(N) | | U104#(tt, V1, V2) | → | activate#(V1) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | activate#(V) |
| U61#(tt, V2) | → | activate#(V2) | | U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) | | take#(0, IL) | → | U121#(isNatIList(IL), IL) |
| U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) | | isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U94#(tt, V1, V2) | → | isNat#(activate(V1)) | | U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) | → | activate#(V1) | | U104#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | | activate#(n__length(X)) | → | length#(X) |
| U114#(tt, L) | → | s#(length(activate(L))) | | U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V1) |
| length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 6
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U94#(tt, V1, V2) | → | activate#(V1) | | U121#(tt, IL) | → | activate#(IL) |
| U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | | U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U31#(tt, V) | → | isNatIListKind#(activate(V)) |
| U51#(tt, V2) | → | activate#(V2) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | U111#(tt, L, N) | → | isNatIListKind#(activate(L)) |
| U44#(tt, V1, V2) | → | isNat#(activate(V1)) | | U105#(tt, V2) | → | isNatIList#(activate(V2)) |
| U113#(tt, L, N) | → | isNatKind#(activate(N)) | | U113#(tt, L, N) | → | activate#(L) |
| U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) | | U134#(tt, IL, M, N) | → | activate#(M) |
| length#(cons(N, L)) | → | isNatList#(activate(L)) | | U136#(tt, IL, M, N) | → | activate#(IL) |
| isNatList#(n__take(V1, V2)) | → | activate#(V2) | | U95#(tt, V2) | → | isNatList#(activate(V2)) |
| U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134#(tt, IL, M, N) | → | activate#(N) |
| isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U132#(tt, IL, M, N) | → | activate#(M) | | take#(s(M), cons(N, IL)) | → | activate#(IL) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) | | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| U114#(tt, L) | → | activate#(L) | | isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) | → | activate#(V2) | | U92#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | isNatKind#(n__length(V1)) | → | activate#(V1) |
| U32#(tt, V) | → | isNatList#(activate(V)) | | isNatKind#(n__s(V1)) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U105#(tt, V2) | → | activate#(V2) |
| U131#(tt, IL, M, N) | → | activate#(N) | | isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U31#(tt, V) | → | activate#(V) | | U132#(tt, IL, M, N) | → | activate#(IL) |
| U131#(tt, IL, M, N) | → | activate#(IL) | | U114#(tt, L) | → | length#(activate(L)) |
| U91#(tt, V1, V2) | → | activate#(V2) | | U122#(tt) | → | nil# |
| U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) | | U102#(tt, V1, V2) | → | activate#(V2) |
| U112#(tt, L, N) | → | isNat#(activate(N)) | | U93#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | activate#(V1) | | U32#(tt, V) | → | activate#(V) |
| U11#(tt, V1) | → | activate#(V1) | | U41#(tt, V1, V2) | → | activate#(V2) |
| U95#(tt, V2) | → | U96#(isNatList(activate(V2))) | | U11#(tt, V1) | → | isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) | | U131#(tt, IL, M, N) | → | activate#(M) |
| isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U134#(tt, IL, M, N) | → | activate#(IL) |
| U113#(tt, L, N) | → | activate#(N) | | U43#(tt, V1, V2) | → | activate#(V2) |
| isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(IL) |
| U91#(tt, V1, V2) | → | activate#(V1) | | U44#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V1) |
| activate#(n__take(X1, X2)) | → | take#(X1, X2) | | isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| take#(0, IL) | → | isNatIList#(IL) | | U121#(tt, IL) | → | isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) | → | activate#(M) | | U12#(tt, V1) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | activate#(V2) | | U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U21#(tt, V1) | → | isNatKind#(activate(V1)) | | U45#(tt, V2) | → | activate#(V2) |
| U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) | | U95#(tt, V2) | → | activate#(V2) |
| length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) | | U45#(tt, V2) | → | isNatIList#(activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(M) | | U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) | | U44#(tt, V1, V2) | → | activate#(V1) |
| U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U101#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | isNat#(n__s(V1)) | → | activate#(V1) |
| U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U134#(tt, IL, M, N) | → | isNat#(activate(N)) |
| U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V2) |
| isNatIList#(V) | → | isNatIListKind#(activate(V)) | | isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | activate#(V2) | | isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U42#(tt, V1, V2) | → | activate#(V1) | | U112#(tt, L, N) | → | activate#(N) |
| U133#(tt, IL, M, N) | → | activate#(IL) | | U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) | | U112#(tt, L, N) | → | activate#(L) |
| U41#(tt, V1, V2) | → | activate#(V1) | | U42#(tt, V1, V2) | → | activate#(V2) |
| U103#(tt, V1, V2) | → | activate#(V1) | | U22#(tt, V1) | → | activate#(V1) |
| U92#(tt, V1, V2) | → | activate#(V2) | | U12#(tt, V1) | → | isNatList#(activate(V1)) |
| U121#(tt, IL) | → | U122#(isNatIListKind(activate(IL))) | | isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) |
| U22#(tt, V1) | → | U23#(isNat(activate(V1))) | | U136#(tt, IL, M, N) | → | activate#(N) |
| U111#(tt, L, N) | → | activate#(N) | | isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(M) |
| U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U22#(tt, V1) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | activate#(L) | | U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(N) | | U51#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) | → | activate#(V2) | | U61#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) | | U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(N) | | U132#(tt, IL, M, N) | → | activate#(N) |
| U104#(tt, V1, V2) | → | activate#(V1) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) |
| isNatIList#(V) | → | activate#(V) | | U61#(tt, V2) | → | activate#(V2) |
| U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) |
| take#(0, IL) | → | U121#(isNatIList(IL), IL) | | U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) |
| isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) | | U94#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) | | U43#(tt, V1, V2) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| activate#(n__length(X)) | → | length#(X) | | U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V1) |
| length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 7
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U12#(tt, V1) | → | U13#(isNatList(activate(V1))) | | U94#(tt, V1, V2) | → | activate#(V2) |
| isNatList#(n__take(V1, V2)) | → | activate#(V1) | | U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) | | U94#(tt, V1, V2) | → | activate#(V1) |
| U121#(tt, IL) | → | activate#(IL) | | U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) |
| U31#(tt, V) | → | isNatIListKind#(activate(V)) | | U51#(tt, V2) | → | activate#(V2) |
| isNat#(n__length(V1)) | → | activate#(V1) | | isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) |
| length#(nil) | → | 0# | | U111#(tt, L, N) | → | isNatIListKind#(activate(L)) |
| U44#(tt, V1, V2) | → | isNat#(activate(V1)) | | U105#(tt, V2) | → | isNatIList#(activate(V2)) |
| U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U113#(tt, L, N) | → | activate#(L) |
| U113#(tt, L, N) | → | isNatKind#(activate(N)) | | isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) | | U134#(tt, IL, M, N) | → | activate#(M) |
| length#(cons(N, L)) | → | isNatList#(activate(L)) | | U136#(tt, IL, M, N) | → | activate#(IL) |
| isNatList#(n__take(V1, V2)) | → | activate#(V2) | | U95#(tt, V2) | → | isNatList#(activate(V2)) |
| U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134#(tt, IL, M, N) | → | activate#(N) |
| U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | | U132#(tt, IL, M, N) | → | activate#(M) |
| isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | take#(s(M), cons(N, IL)) | → | activate#(IL) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) | | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| U114#(tt, L) | → | activate#(L) | | isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) | → | activate#(V2) | | U92#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | isNatKind#(n__length(V1)) | → | activate#(V1) |
| U32#(tt, V) | → | isNatList#(activate(V)) | | isNatKind#(n__s(V1)) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U105#(tt, V2) | → | activate#(V2) |
| U131#(tt, IL, M, N) | → | activate#(N) | | isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U31#(tt, V) | → | activate#(V) | | U132#(tt, IL, M, N) | → | activate#(IL) |
| U131#(tt, IL, M, N) | → | activate#(IL) | | U114#(tt, L) | → | length#(activate(L)) |
| U91#(tt, V1, V2) | → | activate#(V2) | | U122#(tt) | → | nil# |
| U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) | | U102#(tt, V1, V2) | → | activate#(V2) |
| U112#(tt, L, N) | → | isNat#(activate(N)) | | U93#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | activate#(V1) | | U32#(tt, V) | → | activate#(V) |
| U11#(tt, V1) | → | activate#(V1) | | U41#(tt, V1, V2) | → | activate#(V2) |
| U11#(tt, V1) | → | isNatIListKind#(activate(V1)) | | U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) |
| U131#(tt, IL, M, N) | → | activate#(M) | | isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | activate#(IL) | | U113#(tt, L, N) | → | activate#(N) |
| U43#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(IL) | | U91#(tt, V1, V2) | → | activate#(V1) |
| U44#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V1) | | activate#(n__take(X1, X2)) | → | take#(X1, X2) |
| isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| take#(0, IL) | → | isNatIList#(IL) | | U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U121#(tt, IL) | → | isNatIListKind#(activate(IL)) | | U136#(tt, IL, M, N) | → | activate#(M) |
| U12#(tt, V1) | → | activate#(V1) | | U104#(tt, V1, V2) | → | activate#(V2) |
| U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U21#(tt, V1) | → | isNatKind#(activate(V1)) |
| U45#(tt, V2) | → | activate#(V2) | | U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) |
| U95#(tt, V2) | → | activate#(V2) | | length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) |
| U45#(tt, V2) | → | isNatIList#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(M) |
| U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) | | U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) | → | activate#(V1) | | U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U105#(tt, V2) | → | U106#(isNatIList(activate(V2))) |
| U134#(tt, IL, M, N) | → | isNat#(activate(N)) | | isNat#(n__s(V1)) | → | activate#(V1) |
| U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V2) |
| isNatIList#(V) | → | isNatIListKind#(activate(V)) | | isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | activate#(V2) | | isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U42#(tt, V1, V2) | → | activate#(V1) | | U112#(tt, L, N) | → | activate#(N) |
| U133#(tt, IL, M, N) | → | activate#(IL) | | U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) | | U112#(tt, L, N) | → | activate#(L) |
| U41#(tt, V1, V2) | → | activate#(V1) | | U42#(tt, V1, V2) | → | activate#(V2) |
| U103#(tt, V1, V2) | → | activate#(V1) | | U22#(tt, V1) | → | activate#(V1) |
| U92#(tt, V1, V2) | → | activate#(V2) | | U12#(tt, V1) | → | isNatList#(activate(V1)) |
| U121#(tt, IL) | → | U122#(isNatIListKind(activate(IL))) | | isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) |
| U136#(tt, IL, M, N) | → | activate#(N) | | U111#(tt, L, N) | → | activate#(N) |
| isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(M) | | U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U22#(tt, V1) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | activate#(L) |
| U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(N) |
| U51#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U101#(tt, V1, V2) | → | activate#(V2) |
| U61#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) | | U135#(tt, IL, M, N) | → | activate#(N) |
| U132#(tt, IL, M, N) | → | activate#(N) | | U104#(tt, V1, V2) | → | activate#(V1) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | activate#(V) |
| U61#(tt, V2) | → | activate#(V2) | | U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) | | take#(0, IL) | → | U121#(isNatIList(IL), IL) |
| isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) | | U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) | → | isNat#(activate(V1)) | | U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) | → | activate#(V1) | | U104#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | | activate#(n__length(X)) | → | length#(X) |
| U114#(tt, L) | → | s#(length(activate(L))) | | U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V1) |
| length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 8
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U94#(tt, V1, V2) | → | activate#(V1) | | U121#(tt, IL) | → | activate#(IL) |
| U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U31#(tt, V) | → | isNatIListKind#(activate(V)) |
| U51#(tt, V2) | → | activate#(V2) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | length#(nil) | → | 0# |
| U111#(tt, L, N) | → | isNatIListKind#(activate(L)) | | U44#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U105#(tt, V2) | → | isNatIList#(activate(V2)) | | U113#(tt, L, N) | → | isNatKind#(activate(N)) |
| U113#(tt, L, N) | → | activate#(L) | | U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| length#(cons(N, L)) | → | isNatList#(activate(L)) | | U134#(tt, IL, M, N) | → | activate#(M) |
| isNatList#(n__take(V1, V2)) | → | activate#(V2) | | U136#(tt, IL, M, N) | → | activate#(IL) |
| U95#(tt, V2) | → | isNatList#(activate(V2)) | | U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) | → | activate#(N) | | U132#(tt, IL, M, N) | → | activate#(M) |
| U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | | isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(s(M), cons(N, IL)) | → | activate#(IL) | | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) | | U114#(tt, L) | → | activate#(L) |
| isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V2) |
| U92#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) | → | activate#(V1) | | U32#(tt, V) | → | isNatList#(activate(V)) |
| isNatKind#(n__s(V1)) | → | activate#(V1) | | U93#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U105#(tt, V2) | → | activate#(V2) | | isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) | → | activate#(N) | | U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U31#(tt, V) | → | activate#(V) |
| U132#(tt, IL, M, N) | → | activate#(IL) | | U131#(tt, IL, M, N) | → | activate#(IL) |
| U114#(tt, L) | → | length#(activate(L)) | | U91#(tt, V1, V2) | → | activate#(V2) |
| U102#(tt, V1, V2) | → | activate#(V2) | | U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) |
| U112#(tt, L, N) | → | isNat#(activate(N)) | | U93#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | activate#(V1) | | U11#(tt, V1) | → | activate#(V1) |
| U32#(tt, V) | → | activate#(V) | | U41#(tt, V1, V2) | → | activate#(V2) |
| U11#(tt, V1) | → | isNatIListKind#(activate(V1)) | | U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) |
| U131#(tt, IL, M, N) | → | activate#(M) | | isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | activate#(IL) | | U113#(tt, L, N) | → | activate#(N) |
| U43#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(IL) | | U91#(tt, V1, V2) | → | activate#(V1) |
| U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | | U44#(tt, V1, V2) | → | activate#(V2) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V1) | | activate#(n__take(X1, X2)) | → | take#(X1, X2) |
| isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | take#(0, IL) | → | isNatIList#(IL) |
| U121#(tt, IL) | → | isNatIListKind#(activate(IL)) | | U136#(tt, IL, M, N) | → | activate#(M) |
| U12#(tt, V1) | → | activate#(V1) | | U104#(tt, V1, V2) | → | activate#(V2) |
| U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U21#(tt, V1) | → | isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) | | U45#(tt, V2) | → | activate#(V2) |
| U95#(tt, V2) | → | activate#(V2) | | length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) |
| U135#(tt, IL, M, N) | → | activate#(M) | | U45#(tt, V2) | → | isNatIList#(activate(V2)) |
| U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) | | U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) | → | activate#(V1) | | U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNat#(n__s(V1)) | → | activate#(V1) | | U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | isNat#(activate(N)) | | U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | isNatIListKind#(activate(V)) |
| isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U103#(tt, V1, V2) | → | activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U112#(tt, L, N) | → | activate#(N) |
| U42#(tt, V1, V2) | → | activate#(V1) | | U133#(tt, IL, M, N) | → | activate#(IL) |
| U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) |
| U112#(tt, L, N) | → | activate#(L) | | U41#(tt, V1, V2) | → | activate#(V1) |
| U42#(tt, V1, V2) | → | activate#(V2) | | U103#(tt, V1, V2) | → | activate#(V1) |
| U22#(tt, V1) | → | activate#(V1) | | U92#(tt, V1, V2) | → | activate#(V2) |
| U12#(tt, V1) | → | isNatList#(activate(V1)) | | isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) |
| U136#(tt, IL, M, N) | → | activate#(N) | | U111#(tt, L, N) | → | activate#(N) |
| isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(M) | | U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U22#(tt, V1) | → | isNat#(activate(V1)) | | U45#(tt, V2) | → | U46#(isNatIList(activate(V2))) |
| U111#(tt, L, N) | → | activate#(L) | | U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(N) | | U51#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) | → | activate#(V2) | | U61#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) | | U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U132#(tt, IL, M, N) | → | activate#(N) | | U135#(tt, IL, M, N) | → | activate#(N) |
| U104#(tt, V1, V2) | → | activate#(V1) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) |
| isNatIList#(V) | → | activate#(V) | | U61#(tt, V2) | → | activate#(V2) |
| U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) |
| take#(0, IL) | → | U121#(isNatIList(IL), IL) | | U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) |
| isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) | | U94#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) | | U43#(tt, V1, V2) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| activate#(n__length(X)) | → | length#(X) | | U114#(tt, L) | → | s#(length(activate(L))) |
| U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | activate#(V1) | | length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 9
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U94#(tt, V1, V2) | → | activate#(V1) | | U121#(tt, IL) | → | activate#(IL) |
| U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | | U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U31#(tt, V) | → | isNatIListKind#(activate(V)) |
| U51#(tt, V2) | → | activate#(V2) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | length#(nil) | → | 0# |
| U111#(tt, L, N) | → | isNatIListKind#(activate(L)) | | U44#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U105#(tt, V2) | → | isNatIList#(activate(V2)) | | U113#(tt, L, N) | → | isNatKind#(activate(N)) |
| U113#(tt, L, N) | → | activate#(L) | | U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) | → | activate#(M) | | length#(cons(N, L)) | → | isNatList#(activate(L)) |
| U136#(tt, IL, M, N) | → | activate#(IL) | | isNatList#(n__take(V1, V2)) | → | activate#(V2) |
| U95#(tt, V2) | → | isNatList#(activate(V2)) | | U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) | → | activate#(N) | | isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | | U132#(tt, IL, M, N) | → | activate#(M) |
| take#(s(M), cons(N, IL)) | → | activate#(IL) | | isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) |
| isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) | | U114#(tt, L) | → | activate#(L) |
| isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V2) |
| U92#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) | → | activate#(V1) | | U32#(tt, V) | → | isNatList#(activate(V)) |
| isNatKind#(n__s(V1)) | → | activate#(V1) | | U102#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U105#(tt, V2) | → | activate#(V2) | | U131#(tt, IL, M, N) | → | activate#(N) |
| isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U31#(tt, V) | → | activate#(V) |
| U132#(tt, IL, M, N) | → | activate#(IL) | | U131#(tt, IL, M, N) | → | activate#(IL) |
| U114#(tt, L) | → | length#(activate(L)) | | U91#(tt, V1, V2) | → | activate#(V2) |
| U122#(tt) | → | nil# | | U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) |
| U102#(tt, V1, V2) | → | activate#(V2) | | U112#(tt, L, N) | → | isNat#(activate(N)) |
| U93#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | activate#(V1) |
| U32#(tt, V) | → | activate#(V) | | U11#(tt, V1) | → | activate#(V1) |
| U41#(tt, V1, V2) | → | activate#(V2) | | U95#(tt, V2) | → | U96#(isNatList(activate(V2))) |
| U11#(tt, V1) | → | isNatIListKind#(activate(V1)) | | U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) |
| U131#(tt, IL, M, N) | → | activate#(M) | | isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | activate#(IL) | | U113#(tt, L, N) | → | activate#(N) |
| U43#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(IL) | | U91#(tt, V1, V2) | → | activate#(V1) |
| U44#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V1) | | activate#(n__take(X1, X2)) | → | take#(X1, X2) |
| isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | take#(0, IL) | → | isNatIList#(IL) |
| U121#(tt, IL) | → | isNatIListKind#(activate(IL)) | | U136#(tt, IL, M, N) | → | activate#(M) |
| U12#(tt, V1) | → | activate#(V1) | | U104#(tt, V1, V2) | → | activate#(V2) |
| U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U21#(tt, V1) | → | isNatKind#(activate(V1)) |
| U45#(tt, V2) | → | activate#(V2) | | U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) |
| U95#(tt, V2) | → | activate#(V2) | | length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) |
| U45#(tt, V2) | → | isNatIList#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(M) |
| U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) | | U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) | → | activate#(V1) | | U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNat#(n__s(V1)) | → | activate#(V1) | | U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | isNat#(activate(N)) | | U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | isNatIListKind#(activate(V)) |
| isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U103#(tt, V1, V2) | → | activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U42#(tt, V1, V2) | → | activate#(V1) |
| U112#(tt, L, N) | → | activate#(N) | | U133#(tt, IL, M, N) | → | activate#(IL) |
| U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) |
| U112#(tt, L, N) | → | activate#(L) | | U41#(tt, V1, V2) | → | activate#(V1) |
| U42#(tt, V1, V2) | → | activate#(V2) | | U103#(tt, V1, V2) | → | activate#(V1) |
| U22#(tt, V1) | → | activate#(V1) | | U92#(tt, V1, V2) | → | activate#(V2) |
| U12#(tt, V1) | → | isNatList#(activate(V1)) | | U121#(tt, IL) | → | U122#(isNatIListKind(activate(IL))) |
| isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | | U22#(tt, V1) | → | U23#(isNat(activate(V1))) |
| U136#(tt, IL, M, N) | → | activate#(N) | | U111#(tt, L, N) | → | activate#(N) |
| isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(M) | | U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U22#(tt, V1) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | activate#(L) |
| U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(N) |
| U51#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U101#(tt, V1, V2) | → | activate#(V2) |
| U61#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) |
| U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(N) |
| U132#(tt, IL, M, N) | → | activate#(N) | | U104#(tt, V1, V2) | → | activate#(V1) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | activate#(V) |
| U61#(tt, V2) | → | activate#(V2) | | U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) | | take#(0, IL) | → | U121#(isNatIList(IL), IL) |
| U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) | | isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U94#(tt, V1, V2) | → | isNat#(activate(V1)) | | U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) | → | activate#(V1) | | U104#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | | activate#(n__length(X)) | → | length#(X) |
| U114#(tt, L) | → | s#(length(activate(L))) | | U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V1) |
| length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 10
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U12#(tt, V1) | → | U13#(isNatList(activate(V1))) | | U94#(tt, V1, V2) | → | activate#(V2) |
| isNatList#(n__take(V1, V2)) | → | activate#(V1) | | U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) | | U94#(tt, V1, V2) | → | activate#(V1) |
| U121#(tt, IL) | → | activate#(IL) | | U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) |
| U31#(tt, V) | → | isNatIListKind#(activate(V)) | | U51#(tt, V2) | → | activate#(V2) |
| isNat#(n__length(V1)) | → | activate#(V1) | | isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) |
| U111#(tt, L, N) | → | isNatIListKind#(activate(L)) | | U44#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U105#(tt, V2) | → | isNatIList#(activate(V2)) | | U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) | → | activate#(L) | | U113#(tt, L, N) | → | isNatKind#(activate(N)) |
| isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| length#(cons(N, L)) | → | isNatList#(activate(L)) | | U134#(tt, IL, M, N) | → | activate#(M) |
| isNatList#(n__take(V1, V2)) | → | activate#(V2) | | U136#(tt, IL, M, N) | → | activate#(IL) |
| U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U95#(tt, V2) | → | isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) | → | activate#(N) | | isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | | U132#(tt, IL, M, N) | → | activate#(M) |
| take#(s(M), cons(N, IL)) | → | activate#(IL) | | isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) |
| isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) | | U114#(tt, L) | → | activate#(L) |
| isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V2) |
| U92#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) | → | activate#(V1) | | U32#(tt, V) | → | isNatList#(activate(V)) |
| isNatKind#(n__s(V1)) | → | activate#(V1) | | U102#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U105#(tt, V2) | → | activate#(V2) | | isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) | → | activate#(N) | | U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U31#(tt, V) | → | activate#(V) |
| U132#(tt, IL, M, N) | → | activate#(IL) | | U131#(tt, IL, M, N) | → | activate#(IL) |
| U114#(tt, L) | → | length#(activate(L)) | | U91#(tt, V1, V2) | → | activate#(V2) |
| U122#(tt) | → | nil# | | U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) |
| U102#(tt, V1, V2) | → | activate#(V2) | | U112#(tt, L, N) | → | isNat#(activate(N)) |
| U93#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | activate#(V1) |
| U32#(tt, V) | → | activate#(V) | | U11#(tt, V1) | → | activate#(V1) |
| U41#(tt, V1, V2) | → | activate#(V2) | | U95#(tt, V2) | → | U96#(isNatList(activate(V2))) |
| U11#(tt, V1) | → | isNatIListKind#(activate(V1)) | | U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) |
| U131#(tt, IL, M, N) | → | activate#(M) | | isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | activate#(IL) | | U113#(tt, L, N) | → | activate#(N) |
| U43#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(IL) | | U91#(tt, V1, V2) | → | activate#(V1) |
| U44#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V1) | | activate#(n__take(X1, X2)) | → | take#(X1, X2) |
| isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | take#(0, IL) | → | isNatIList#(IL) |
| U121#(tt, IL) | → | isNatIListKind#(activate(IL)) | | U136#(tt, IL, M, N) | → | activate#(M) |
| U104#(tt, V1, V2) | → | activate#(V2) | | U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U12#(tt, V1) | → | activate#(V1) | | U21#(tt, V1) | → | isNatKind#(activate(V1)) |
| U45#(tt, V2) | → | activate#(V2) | | U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) |
| U95#(tt, V2) | → | activate#(V2) | | length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) |
| U45#(tt, V2) | → | isNatIList#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(M) |
| U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) | | U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) | → | activate#(V1) | | U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U105#(tt, V2) | → | U106#(isNatIList(activate(V2))) |
| U134#(tt, IL, M, N) | → | isNat#(activate(N)) | | isNat#(n__s(V1)) | → | activate#(V1) |
| U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V2) |
| isNatIList#(V) | → | isNatIListKind#(activate(V)) | | isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | activate#(V2) | | isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U42#(tt, V1, V2) | → | activate#(V1) | | U112#(tt, L, N) | → | activate#(N) |
| U133#(tt, IL, M, N) | → | activate#(IL) | | U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) | | U112#(tt, L, N) | → | activate#(L) |
| U41#(tt, V1, V2) | → | activate#(V1) | | U42#(tt, V1, V2) | → | activate#(V2) |
| U103#(tt, V1, V2) | → | activate#(V1) | | U22#(tt, V1) | → | activate#(V1) |
| U92#(tt, V1, V2) | → | activate#(V2) | | U12#(tt, V1) | → | isNatList#(activate(V1)) |
| U121#(tt, IL) | → | U122#(isNatIListKind(activate(IL))) | | isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) |
| U136#(tt, IL, M, N) | → | activate#(N) | | U111#(tt, L, N) | → | activate#(N) |
| isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(M) | | U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U22#(tt, V1) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | activate#(L) |
| U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(N) |
| U51#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U101#(tt, V1, V2) | → | activate#(V2) |
| U61#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) |
| U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(N) |
| U132#(tt, IL, M, N) | → | activate#(N) | | U104#(tt, V1, V2) | → | activate#(V1) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | activate#(V) |
| U61#(tt, V2) | → | activate#(V2) | | U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) | | take#(0, IL) | → | U121#(isNatIList(IL), IL) |
| U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) | | isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U94#(tt, V1, V2) | → | isNat#(activate(V1)) | | U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) | → | activate#(V1) | | U104#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | | activate#(n__length(X)) | → | length#(X) |
| U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | activate#(V1) | | length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 11
Dependency Pairs
| take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) | | U132#(tt, IL, M, N) | → | isNat#(activate(M)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U94#(tt, V1, V2) | → | activate#(V1) | | U121#(tt, IL) | → | activate#(IL) |
| U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | | U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U31#(tt, V) | → | isNatIListKind#(activate(V)) |
| U51#(tt, V2) | → | activate#(V2) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | length#(nil) | → | 0# |
| U111#(tt, L, N) | → | isNatIListKind#(activate(L)) | | U44#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U105#(tt, V2) | → | isNatIList#(activate(V2)) | | U113#(tt, L, N) | → | activate#(L) |
| U113#(tt, L, N) | → | isNatKind#(activate(N)) | | U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) | → | activate#(M) | | length#(cons(N, L)) | → | isNatList#(activate(L)) |
| U136#(tt, IL, M, N) | → | activate#(IL) | | isNatList#(n__take(V1, V2)) | → | activate#(V2) |
| U95#(tt, V2) | → | isNatList#(activate(V2)) | | U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) | → | activate#(N) | | isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | | U132#(tt, IL, M, N) | → | activate#(M) |
| take#(s(M), cons(N, IL)) | → | activate#(IL) | | isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) |
| isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) | | U114#(tt, L) | → | activate#(L) |
| isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V2) |
| U92#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) | → | activate#(V1) | | U32#(tt, V) | → | isNatList#(activate(V)) |
| isNatKind#(n__s(V1)) | → | activate#(V1) | | U93#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U105#(tt, V2) | → | activate#(V2) | | U131#(tt, IL, M, N) | → | activate#(N) |
| isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U31#(tt, V) | → | activate#(V) |
| U132#(tt, IL, M, N) | → | activate#(IL) | | U131#(tt, IL, M, N) | → | activate#(IL) |
| U114#(tt, L) | → | length#(activate(L)) | | U91#(tt, V1, V2) | → | activate#(V2) |
| U122#(tt) | → | nil# | | U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) |
| U102#(tt, V1, V2) | → | activate#(V2) | | U112#(tt, L, N) | → | isNat#(activate(N)) |
| U93#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | activate#(V1) |
| U32#(tt, V) | → | activate#(V) | | U11#(tt, V1) | → | activate#(V1) |
| U41#(tt, V1, V2) | → | activate#(V2) | | U11#(tt, V1) | → | isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) | | U131#(tt, IL, M, N) | → | activate#(M) |
| isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U134#(tt, IL, M, N) | → | activate#(IL) |
| U113#(tt, L, N) | → | activate#(N) | | U43#(tt, V1, V2) | → | activate#(V2) |
| isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(IL) |
| U91#(tt, V1, V2) | → | activate#(V1) | | U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__cons(V1, V2)) | → | activate#(V1) |
| activate#(n__take(X1, X2)) | → | take#(X1, X2) | | isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| take#(0, IL) | → | isNatIList#(IL) | | U121#(tt, IL) | → | isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) | → | activate#(M) | | U12#(tt, V1) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | activate#(V2) | | U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U21#(tt, V1) | → | isNatKind#(activate(V1)) | | U45#(tt, V2) | → | activate#(V2) |
| U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) | | U95#(tt, V2) | → | activate#(V2) |
| length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) | | U45#(tt, V2) | → | isNatIList#(activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(M) | | U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) | | U44#(tt, V1, V2) | → | activate#(V1) |
| U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U101#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | isNat#(n__s(V1)) | → | activate#(V1) |
| U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U134#(tt, IL, M, N) | → | isNat#(activate(N)) |
| U105#(tt, V2) | → | U106#(isNatIList(activate(V2))) | | U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | isNatIListKind#(activate(V)) |
| isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U103#(tt, V1, V2) | → | activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U42#(tt, V1, V2) | → | activate#(V1) |
| U112#(tt, L, N) | → | activate#(N) | | U133#(tt, IL, M, N) | → | activate#(IL) |
| U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) |
| U112#(tt, L, N) | → | activate#(L) | | U41#(tt, V1, V2) | → | activate#(V1) |
| U42#(tt, V1, V2) | → | activate#(V2) | | U103#(tt, V1, V2) | → | activate#(V1) |
| U22#(tt, V1) | → | activate#(V1) | | U92#(tt, V1, V2) | → | activate#(V2) |
| U12#(tt, V1) | → | isNatList#(activate(V1)) | | U121#(tt, IL) | → | U122#(isNatIListKind(activate(IL))) |
| isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | | U136#(tt, IL, M, N) | → | activate#(N) |
| U111#(tt, L, N) | → | activate#(N) | | isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(M) |
| U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U22#(tt, V1) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | activate#(L) | | U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(N) | | U51#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) | → | activate#(V2) | | U61#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) | | U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(N) | | U132#(tt, IL, M, N) | → | activate#(N) |
| U104#(tt, V1, V2) | → | activate#(V1) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) |
| isNatIList#(V) | → | activate#(V) | | U61#(tt, V2) | → | activate#(V2) |
| U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) |
| take#(0, IL) | → | U121#(isNatIList(IL), IL) | | U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) |
| isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) | | U94#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) | | U43#(tt, V1, V2) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| activate#(n__length(X)) | → | length#(X) | | U114#(tt, L) | → | s#(length(activate(L))) |
| U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | activate#(V1) | | length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 12
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U12#(tt, V1) | → | U13#(isNatList(activate(V1))) | | U94#(tt, V1, V2) | → | activate#(V2) |
| isNatList#(n__take(V1, V2)) | → | activate#(V1) | | U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) | | U94#(tt, V1, V2) | → | activate#(V1) |
| U121#(tt, IL) | → | activate#(IL) | | U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) |
| U31#(tt, V) | → | isNatIListKind#(activate(V)) | | U51#(tt, V2) | → | activate#(V2) |
| isNat#(n__length(V1)) | → | activate#(V1) | | isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) |
| length#(nil) | → | 0# | | U111#(tt, L, N) | → | isNatIListKind#(activate(L)) |
| U44#(tt, V1, V2) | → | isNat#(activate(V1)) | | U105#(tt, V2) | → | isNatIList#(activate(V2)) |
| U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U113#(tt, L, N) | → | activate#(L) |
| U113#(tt, L, N) | → | isNatKind#(activate(N)) | | isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) | | U134#(tt, IL, M, N) | → | activate#(M) |
| length#(cons(N, L)) | → | isNatList#(activate(L)) | | isNatList#(n__take(V1, V2)) | → | activate#(V2) |
| U136#(tt, IL, M, N) | → | activate#(IL) | | U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U95#(tt, V2) | → | isNatList#(activate(V2)) | | U134#(tt, IL, M, N) | → | activate#(N) |
| isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U132#(tt, IL, M, N) | → | activate#(M) | | take#(s(M), cons(N, IL)) | → | activate#(IL) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) | | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| U114#(tt, L) | → | activate#(L) | | isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) | → | activate#(V2) | | U92#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | isNatKind#(n__length(V1)) | → | activate#(V1) |
| U32#(tt, V) | → | isNatList#(activate(V)) | | isNatKind#(n__s(V1)) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U105#(tt, V2) | → | activate#(V2) |
| isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U131#(tt, IL, M, N) | → | activate#(N) |
| U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U31#(tt, V) | → | activate#(V) | | U132#(tt, IL, M, N) | → | activate#(IL) |
| U114#(tt, L) | → | length#(activate(L)) | | U131#(tt, IL, M, N) | → | activate#(IL) |
| U91#(tt, V1, V2) | → | activate#(V2) | | U122#(tt) | → | nil# |
| U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) | | U102#(tt, V1, V2) | → | activate#(V2) |
| U112#(tt, L, N) | → | isNat#(activate(N)) | | U93#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | activate#(V1) | | U32#(tt, V) | → | activate#(V) |
| U11#(tt, V1) | → | activate#(V1) | | U41#(tt, V1, V2) | → | activate#(V2) |
| U95#(tt, V2) | → | U96#(isNatList(activate(V2))) | | U11#(tt, V1) | → | isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) | | U131#(tt, IL, M, N) | → | activate#(M) |
| isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U134#(tt, IL, M, N) | → | activate#(IL) |
| U113#(tt, L, N) | → | activate#(N) | | U43#(tt, V1, V2) | → | activate#(V2) |
| isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(IL) |
| U91#(tt, V1, V2) | → | activate#(V1) | | U44#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V1) |
| activate#(n__take(X1, X2)) | → | take#(X1, X2) | | isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| take#(0, IL) | → | isNatIList#(IL) | | U121#(tt, IL) | → | isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) | → | activate#(M) | | U104#(tt, V1, V2) | → | activate#(V2) |
| U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U12#(tt, V1) | → | activate#(V1) |
| U21#(tt, V1) | → | isNatKind#(activate(V1)) | | U45#(tt, V2) | → | activate#(V2) |
| U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) | | U95#(tt, V2) | → | activate#(V2) |
| length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) | | U45#(tt, V2) | → | isNatIList#(activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(M) | | U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) | | U44#(tt, V1, V2) | → | activate#(V1) |
| U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U101#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U105#(tt, V2) | → | U106#(isNatIList(activate(V2))) | | U134#(tt, IL, M, N) | → | isNat#(activate(N)) |
| isNat#(n__s(V1)) | → | activate#(V1) | | U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | isNatIListKind#(activate(V)) |
| isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U103#(tt, V1, V2) | → | activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U42#(tt, V1, V2) | → | activate#(V1) |
| U112#(tt, L, N) | → | activate#(N) | | U133#(tt, IL, M, N) | → | activate#(IL) |
| U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) |
| U112#(tt, L, N) | → | activate#(L) | | U41#(tt, V1, V2) | → | activate#(V1) |
| U42#(tt, V1, V2) | → | activate#(V2) | | U103#(tt, V1, V2) | → | activate#(V1) |
| U22#(tt, V1) | → | activate#(V1) | | U92#(tt, V1, V2) | → | activate#(V2) |
| U12#(tt, V1) | → | isNatList#(activate(V1)) | | U121#(tt, IL) | → | U122#(isNatIListKind(activate(IL))) |
| isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | | U136#(tt, IL, M, N) | → | activate#(N) |
| U111#(tt, L, N) | → | activate#(N) | | isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(M) |
| U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U22#(tt, V1) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | activate#(L) | | U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(N) | | U51#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) | → | activate#(V2) | | U61#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) | | U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(N) | | U132#(tt, IL, M, N) | → | activate#(N) |
| U104#(tt, V1, V2) | → | activate#(V1) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) |
| isNatIList#(V) | → | activate#(V) | | U61#(tt, V2) | → | activate#(V2) |
| U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) |
| take#(0, IL) | → | U121#(isNatIList(IL), IL) | | U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) |
| isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) | | U94#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) | | U43#(tt, V1, V2) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| activate#(n__length(X)) | → | length#(X) | | U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V1) |
| length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 13
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U94#(tt, V1, V2) | → | activate#(V1) | | U121#(tt, IL) | → | activate#(IL) |
| U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | | U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U31#(tt, V) | → | isNatIListKind#(activate(V)) |
| U51#(tt, V2) | → | activate#(V2) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | U111#(tt, L, N) | → | isNatIListKind#(activate(L)) |
| length#(nil) | → | 0# | | U44#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U105#(tt, V2) | → | isNatIList#(activate(V2)) | | U113#(tt, L, N) | → | activate#(L) |
| U113#(tt, L, N) | → | isNatKind#(activate(N)) | | U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| length#(cons(N, L)) | → | isNatList#(activate(L)) | | U134#(tt, IL, M, N) | → | activate#(M) |
| isNatList#(n__take(V1, V2)) | → | activate#(V2) | | U136#(tt, IL, M, N) | → | activate#(IL) |
| U95#(tt, V2) | → | isNatList#(activate(V2)) | | U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) | → | activate#(N) | | isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | | U132#(tt, IL, M, N) | → | activate#(M) |
| take#(s(M), cons(N, IL)) | → | activate#(IL) | | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) | | U114#(tt, L) | → | activate#(L) |
| isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V2) |
| U92#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) | → | activate#(V1) | | U32#(tt, V) | → | isNatList#(activate(V)) |
| isNatKind#(n__s(V1)) | → | activate#(V1) | | U93#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U105#(tt, V2) | → | activate#(V2) | | isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) | → | activate#(N) | | U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U31#(tt, V) | → | activate#(V) |
| U132#(tt, IL, M, N) | → | activate#(IL) | | U131#(tt, IL, M, N) | → | activate#(IL) |
| U114#(tt, L) | → | length#(activate(L)) | | U91#(tt, V1, V2) | → | activate#(V2) |
| U102#(tt, V1, V2) | → | activate#(V2) | | U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) |
| U32#(tt, V) | → | U33#(isNatList(activate(V))) | | U112#(tt, L, N) | → | isNat#(activate(N)) |
| U93#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | activate#(V1) |
| U11#(tt, V1) | → | activate#(V1) | | U32#(tt, V) | → | activate#(V) |
| U41#(tt, V1, V2) | → | activate#(V2) | | U11#(tt, V1) | → | isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) | | U131#(tt, IL, M, N) | → | activate#(M) |
| isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U134#(tt, IL, M, N) | → | activate#(IL) |
| U113#(tt, L, N) | → | activate#(N) | | U43#(tt, V1, V2) | → | activate#(V2) |
| isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(IL) |
| U91#(tt, V1, V2) | → | activate#(V1) | | U44#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V1) |
| activate#(n__take(X1, X2)) | → | take#(X1, X2) | | isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| take#(0, IL) | → | isNatIList#(IL) | | U121#(tt, IL) | → | isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) | → | activate#(M) | | U12#(tt, V1) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | activate#(V2) | | U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U21#(tt, V1) | → | isNatKind#(activate(V1)) | | U45#(tt, V2) | → | activate#(V2) |
| U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) | | U95#(tt, V2) | → | activate#(V2) |
| length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) | | U45#(tt, V2) | → | isNatIList#(activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(M) | | U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) | | U44#(tt, V1, V2) | → | activate#(V1) |
| U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U101#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | isNat#(activate(N)) | | isNat#(n__s(V1)) | → | activate#(V1) |
| U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V2) |
| isNatIList#(V) | → | isNatIListKind#(activate(V)) | | isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | activate#(V2) | | isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U42#(tt, V1, V2) | → | activate#(V1) | | U112#(tt, L, N) | → | activate#(N) |
| U133#(tt, IL, M, N) | → | activate#(IL) | | U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) | | U112#(tt, L, N) | → | activate#(L) |
| U41#(tt, V1, V2) | → | activate#(V1) | | U42#(tt, V1, V2) | → | activate#(V2) |
| U103#(tt, V1, V2) | → | activate#(V1) | | U22#(tt, V1) | → | activate#(V1) |
| U92#(tt, V1, V2) | → | activate#(V2) | | U12#(tt, V1) | → | isNatList#(activate(V1)) |
| isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | | U111#(tt, L, N) | → | activate#(N) |
| U136#(tt, IL, M, N) | → | activate#(N) | | isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(M) |
| U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U22#(tt, V1) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | activate#(L) | | U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(N) | | U51#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) | → | activate#(V2) | | U61#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U61#(tt, V2) | → | U62#(isNatIListKind(activate(V2))) | | U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) |
| U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(N) |
| U132#(tt, IL, M, N) | → | activate#(N) | | U104#(tt, V1, V2) | → | activate#(V1) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | activate#(V) |
| U61#(tt, V2) | → | activate#(V2) | | U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) | | take#(0, IL) | → | U121#(isNatIList(IL), IL) |
| U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) | | isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U94#(tt, V1, V2) | → | isNat#(activate(V1)) | | U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) | → | activate#(V1) | | U104#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | | activate#(n__length(X)) | → | length#(X) |
| U114#(tt, L) | → | s#(length(activate(L))) | | U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V1) |
| length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 14
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U94#(tt, V1, V2) | → | activate#(V1) | | U121#(tt, IL) | → | activate#(IL) |
| U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U31#(tt, V) | → | isNatIListKind#(activate(V)) |
| U51#(tt, V2) | → | activate#(V2) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | length#(nil) | → | 0# |
| U111#(tt, L, N) | → | isNatIListKind#(activate(L)) | | U44#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U105#(tt, V2) | → | isNatIList#(activate(V2)) | | U113#(tt, L, N) | → | isNatKind#(activate(N)) |
| U113#(tt, L, N) | → | activate#(L) | | U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| length#(cons(N, L)) | → | isNatList#(activate(L)) | | U134#(tt, IL, M, N) | → | activate#(M) |
| isNatList#(n__take(V1, V2)) | → | activate#(V2) | | U136#(tt, IL, M, N) | → | activate#(IL) |
| U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U95#(tt, V2) | → | isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) | → | activate#(N) | | U132#(tt, IL, M, N) | → | activate#(M) |
| U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | | isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(s(M), cons(N, IL)) | → | activate#(IL) | | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) | | U114#(tt, L) | → | activate#(L) |
| isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V2) |
| U92#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) | → | activate#(V1) | | U32#(tt, V) | → | isNatList#(activate(V)) |
| isNatKind#(n__s(V1)) | → | activate#(V1) | | U102#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U105#(tt, V2) | → | activate#(V2) | | isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) | → | activate#(N) | | U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U31#(tt, V) | → | activate#(V) |
| U132#(tt, IL, M, N) | → | activate#(IL) | | U131#(tt, IL, M, N) | → | activate#(IL) |
| U114#(tt, L) | → | length#(activate(L)) | | U91#(tt, V1, V2) | → | activate#(V2) |
| U102#(tt, V1, V2) | → | activate#(V2) | | U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) |
| U112#(tt, L, N) | → | isNat#(activate(N)) | | U93#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | activate#(V1) | | U11#(tt, V1) | → | activate#(V1) |
| U32#(tt, V) | → | activate#(V) | | U41#(tt, V1, V2) | → | activate#(V2) |
| U95#(tt, V2) | → | U96#(isNatList(activate(V2))) | | U11#(tt, V1) | → | isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) | | U131#(tt, IL, M, N) | → | activate#(M) |
| isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U134#(tt, IL, M, N) | → | activate#(IL) |
| U113#(tt, L, N) | → | activate#(N) | | U43#(tt, V1, V2) | → | activate#(V2) |
| isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(IL) |
| U91#(tt, V1, V2) | → | activate#(V1) | | U44#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V1) |
| activate#(n__take(X1, X2)) | → | take#(X1, X2) | | isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| take#(0, IL) | → | isNatIList#(IL) | | U121#(tt, IL) | → | isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) | → | activate#(M) | | U12#(tt, V1) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | activate#(V2) | | U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U21#(tt, V1) | → | isNatKind#(activate(V1)) | | U45#(tt, V2) | → | activate#(V2) |
| U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) | | U95#(tt, V2) | → | activate#(V2) |
| length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) | | U45#(tt, V2) | → | isNatIList#(activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(M) | | U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) | | U44#(tt, V1, V2) | → | activate#(V1) |
| U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U101#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | isNat#(activate(N)) | | isNat#(n__s(V1)) | → | activate#(V1) |
| U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | isNatIList#(V) | → | isNatIListKind#(activate(V)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V2) | | isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | activate#(V2) | | isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U42#(tt, V1, V2) | → | activate#(V1) | | U112#(tt, L, N) | → | activate#(N) |
| U133#(tt, IL, M, N) | → | activate#(IL) | | U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) |
| U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U112#(tt, L, N) | → | activate#(L) |
| U41#(tt, V1, V2) | → | activate#(V1) | | U42#(tt, V1, V2) | → | activate#(V2) |
| U103#(tt, V1, V2) | → | activate#(V1) | | U22#(tt, V1) | → | activate#(V1) |
| U12#(tt, V1) | → | isNatList#(activate(V1)) | | U92#(tt, V1, V2) | → | activate#(V2) |
| isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | | U136#(tt, IL, M, N) | → | activate#(N) |
| U111#(tt, L, N) | → | activate#(N) | | isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) |
| isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(M) |
| U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U22#(tt, V1) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | activate#(L) | | U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(N) | | U51#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) | → | activate#(V2) | | U61#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) |
| U132#(tt, IL, M, N) | → | activate#(N) | | U135#(tt, IL, M, N) | → | activate#(N) |
| U104#(tt, V1, V2) | → | activate#(V1) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) |
| isNatIList#(V) | → | activate#(V) | | U61#(tt, V2) | → | activate#(V2) |
| U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) |
| take#(0, IL) | → | U121#(isNatIList(IL), IL) | | U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) |
| isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) | | U94#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) | | U43#(tt, V1, V2) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| activate#(n__length(X)) | → | length#(X) | | U114#(tt, L) | → | s#(length(activate(L))) |
| U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | activate#(V1) | | length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 15
Dependency Pairs
| take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) | | U132#(tt, IL, M, N) | → | isNat#(activate(M)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U94#(tt, V1, V2) | → | activate#(V1) | | U121#(tt, IL) | → | activate#(IL) |
| U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | | U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U31#(tt, V) | → | isNatIListKind#(activate(V)) |
| U51#(tt, V2) | → | activate#(V2) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | U111#(tt, L, N) | → | isNatIListKind#(activate(L)) |
| U44#(tt, V1, V2) | → | isNat#(activate(V1)) | | U105#(tt, V2) | → | isNatIList#(activate(V2)) |
| U113#(tt, L, N) | → | isNatKind#(activate(N)) | | U113#(tt, L, N) | → | activate#(L) |
| U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) | | U134#(tt, IL, M, N) | → | activate#(M) |
| length#(cons(N, L)) | → | isNatList#(activate(L)) | | U136#(tt, IL, M, N) | → | activate#(IL) |
| isNatList#(n__take(V1, V2)) | → | activate#(V2) | | U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U95#(tt, V2) | → | isNatList#(activate(V2)) | | U134#(tt, IL, M, N) | → | activate#(N) |
| isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U132#(tt, IL, M, N) | → | activate#(M) | | take#(s(M), cons(N, IL)) | → | activate#(IL) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) | | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| U114#(tt, L) | → | activate#(L) | | isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) | → | activate#(V2) | | U92#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | isNatKind#(n__length(V1)) | → | activate#(V1) |
| U32#(tt, V) | → | isNatList#(activate(V)) | | isNatKind#(n__s(V1)) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U105#(tt, V2) | → | activate#(V2) |
| U131#(tt, IL, M, N) | → | activate#(N) | | isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U31#(tt, V) | → | activate#(V) | | U132#(tt, IL, M, N) | → | activate#(IL) |
| U131#(tt, IL, M, N) | → | activate#(IL) | | U114#(tt, L) | → | length#(activate(L)) |
| U91#(tt, V1, V2) | → | activate#(V2) | | U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) |
| U102#(tt, V1, V2) | → | activate#(V2) | | U112#(tt, L, N) | → | isNat#(activate(N)) |
| U93#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | activate#(V1) |
| U32#(tt, V) | → | activate#(V) | | U11#(tt, V1) | → | activate#(V1) |
| U41#(tt, V1, V2) | → | activate#(V2) | | U95#(tt, V2) | → | U96#(isNatList(activate(V2))) |
| U11#(tt, V1) | → | isNatIListKind#(activate(V1)) | | U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) |
| U131#(tt, IL, M, N) | → | activate#(M) | | isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | activate#(IL) | | U113#(tt, L, N) | → | activate#(N) |
| U43#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(IL) | | U91#(tt, V1, V2) | → | activate#(V1) |
| U44#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V1) | | activate#(n__take(X1, X2)) | → | take#(X1, X2) |
| isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | take#(0, IL) | → | isNatIList#(IL) |
| U121#(tt, IL) | → | isNatIListKind#(activate(IL)) | | U136#(tt, IL, M, N) | → | activate#(M) |
| U104#(tt, V1, V2) | → | activate#(V2) | | U12#(tt, V1) | → | activate#(V1) |
| U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U21#(tt, V1) | → | isNatKind#(activate(V1)) |
| U45#(tt, V2) | → | activate#(V2) | | U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) |
| U95#(tt, V2) | → | activate#(V2) | | length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) |
| U45#(tt, V2) | → | isNatIList#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(M) |
| U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) | | U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) | → | activate#(V1) | | U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U105#(tt, V2) | → | U106#(isNatIList(activate(V2))) |
| U134#(tt, IL, M, N) | → | isNat#(activate(N)) | | isNat#(n__s(V1)) | → | activate#(V1) |
| U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | isNatIList#(V) | → | isNatIListKind#(activate(V)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V2) | | isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | activate#(V2) | | isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U112#(tt, L, N) | → | activate#(N) | | U42#(tt, V1, V2) | → | activate#(V1) |
| U133#(tt, IL, M, N) | → | activate#(IL) | | U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) | | U112#(tt, L, N) | → | activate#(L) |
| U41#(tt, V1, V2) | → | activate#(V1) | | U42#(tt, V1, V2) | → | activate#(V2) |
| U103#(tt, V1, V2) | → | activate#(V1) | | U22#(tt, V1) | → | activate#(V1) |
| U92#(tt, V1, V2) | → | activate#(V2) | | U12#(tt, V1) | → | isNatList#(activate(V1)) |
| isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | | U136#(tt, IL, M, N) | → | activate#(N) |
| U111#(tt, L, N) | → | activate#(N) | | isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(M) |
| U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U22#(tt, V1) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | activate#(L) | | U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(N) | | U51#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) | → | activate#(V2) | | U61#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) | | U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(N) | | U132#(tt, IL, M, N) | → | activate#(N) |
| U104#(tt, V1, V2) | → | activate#(V1) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) |
| isNatIList#(V) | → | activate#(V) | | U61#(tt, V2) | → | activate#(V2) |
| U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) |
| take#(0, IL) | → | U121#(isNatIList(IL), IL) | | U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) |
| isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) | | U94#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) | | U43#(tt, V1, V2) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| activate#(n__length(X)) | → | length#(X) | | U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V1) |
| length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 17
Dependency Pairs
| take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) | | U132#(tt, IL, M, N) | → | isNat#(activate(M)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U94#(tt, V1, V2) | → | activate#(V1) | | U121#(tt, IL) | → | activate#(IL) |
| U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | | U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U31#(tt, V) | → | isNatIListKind#(activate(V)) |
| U51#(tt, V2) | → | activate#(V2) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | U111#(tt, L, N) | → | isNatIListKind#(activate(L)) |
| U44#(tt, V1, V2) | → | isNat#(activate(V1)) | | U105#(tt, V2) | → | isNatIList#(activate(V2)) |
| U113#(tt, L, N) | → | isNatKind#(activate(N)) | | U113#(tt, L, N) | → | activate#(L) |
| U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) | | U134#(tt, IL, M, N) | → | activate#(M) |
| length#(cons(N, L)) | → | isNatList#(activate(L)) | | U136#(tt, IL, M, N) | → | activate#(IL) |
| isNatList#(n__take(V1, V2)) | → | activate#(V2) | | U95#(tt, V2) | → | isNatList#(activate(V2)) |
| U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134#(tt, IL, M, N) | → | activate#(N) |
| isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U132#(tt, IL, M, N) | → | activate#(M) | | take#(s(M), cons(N, IL)) | → | activate#(IL) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) | | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| U114#(tt, L) | → | activate#(L) | | isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) | → | activate#(V2) | | U92#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | isNatKind#(n__length(V1)) | → | activate#(V1) |
| U32#(tt, V) | → | isNatList#(activate(V)) | | isNatKind#(n__s(V1)) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U105#(tt, V2) | → | activate#(V2) |
| U131#(tt, IL, M, N) | → | activate#(N) | | isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U31#(tt, V) | → | activate#(V) | | U132#(tt, IL, M, N) | → | activate#(IL) |
| U131#(tt, IL, M, N) | → | activate#(IL) | | U114#(tt, L) | → | length#(activate(L)) |
| U91#(tt, V1, V2) | → | activate#(V2) | | U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) |
| U102#(tt, V1, V2) | → | activate#(V2) | | U112#(tt, L, N) | → | isNat#(activate(N)) |
| U93#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | activate#(V1) |
| U32#(tt, V) | → | activate#(V) | | U11#(tt, V1) | → | activate#(V1) |
| U41#(tt, V1, V2) | → | activate#(V2) | | U11#(tt, V1) | → | isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) | | U131#(tt, IL, M, N) | → | activate#(M) |
| isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U134#(tt, IL, M, N) | → | activate#(IL) |
| U113#(tt, L, N) | → | activate#(N) | | U43#(tt, V1, V2) | → | activate#(V2) |
| isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(IL) |
| U91#(tt, V1, V2) | → | activate#(V1) | | U44#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V1) |
| activate#(n__take(X1, X2)) | → | take#(X1, X2) | | isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| take#(0, IL) | → | isNatIList#(IL) | | U121#(tt, IL) | → | isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) | → | activate#(M) | | U104#(tt, V1, V2) | → | activate#(V2) |
| U12#(tt, V1) | → | activate#(V1) | | U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U21#(tt, V1) | → | isNatKind#(activate(V1)) | | U45#(tt, V2) | → | activate#(V2) |
| U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) | | U95#(tt, V2) | → | activate#(V2) |
| length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) | | U45#(tt, V2) | → | isNatIList#(activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(M) | | U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) | | U44#(tt, V1, V2) | → | activate#(V1) |
| U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U101#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U105#(tt, V2) | → | U106#(isNatIList(activate(V2))) | | U134#(tt, IL, M, N) | → | isNat#(activate(N)) |
| isNat#(n__s(V1)) | → | activate#(V1) | | U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIList#(V) | → | isNatIListKind#(activate(V)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V2) |
| isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U103#(tt, V1, V2) | → | activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U112#(tt, L, N) | → | activate#(N) |
| U42#(tt, V1, V2) | → | activate#(V1) | | U133#(tt, IL, M, N) | → | activate#(IL) |
| U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) |
| U112#(tt, L, N) | → | activate#(L) | | U41#(tt, V1, V2) | → | activate#(V1) |
| U42#(tt, V1, V2) | → | activate#(V2) | | U103#(tt, V1, V2) | → | activate#(V1) |
| U22#(tt, V1) | → | activate#(V1) | | U92#(tt, V1, V2) | → | activate#(V2) |
| U12#(tt, V1) | → | isNatList#(activate(V1)) | | isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) |
| U136#(tt, IL, M, N) | → | activate#(N) | | U111#(tt, L, N) | → | activate#(N) |
| isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(M) | | U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U22#(tt, V1) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | activate#(L) |
| U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(N) |
| U51#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U101#(tt, V1, V2) | → | activate#(V2) |
| U61#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) |
| U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(N) |
| U132#(tt, IL, M, N) | → | activate#(N) | | U104#(tt, V1, V2) | → | activate#(V1) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | activate#(V) |
| U61#(tt, V2) | → | activate#(V2) | | U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) | | take#(0, IL) | → | U121#(isNatIList(IL), IL) |
| U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) | | isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U94#(tt, V1, V2) | → | isNat#(activate(V1)) | | U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) | → | activate#(V1) | | U104#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | | activate#(n__length(X)) | → | length#(X) |
| U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | activate#(V1) | | length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 16
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U94#(tt, V1, V2) | → | activate#(V1) | | U121#(tt, IL) | → | activate#(IL) |
| U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | | U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U31#(tt, V) | → | isNatIListKind#(activate(V)) |
| U51#(tt, V2) | → | activate#(V2) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | U111#(tt, L, N) | → | isNatIListKind#(activate(L)) |
| length#(nil) | → | 0# | | U44#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U105#(tt, V2) | → | isNatIList#(activate(V2)) | | U113#(tt, L, N) | → | activate#(L) |
| U113#(tt, L, N) | → | isNatKind#(activate(N)) | | U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| length#(cons(N, L)) | → | isNatList#(activate(L)) | | U134#(tt, IL, M, N) | → | activate#(M) |
| isNatList#(n__take(V1, V2)) | → | activate#(V2) | | U136#(tt, IL, M, N) | → | activate#(IL) |
| U95#(tt, V2) | → | isNatList#(activate(V2)) | | U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) | → | activate#(N) | | isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | | U132#(tt, IL, M, N) | → | activate#(M) |
| take#(s(M), cons(N, IL)) | → | activate#(IL) | | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) | | U114#(tt, L) | → | activate#(L) |
| isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V2) |
| U92#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) | → | activate#(V1) | | U32#(tt, V) | → | isNatList#(activate(V)) |
| isNatKind#(n__s(V1)) | → | activate#(V1) | | U93#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U105#(tt, V2) | → | activate#(V2) | | isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) | → | activate#(N) | | U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U31#(tt, V) | → | activate#(V) |
| U132#(tt, IL, M, N) | → | activate#(IL) | | U114#(tt, L) | → | length#(activate(L)) |
| U131#(tt, IL, M, N) | → | activate#(IL) | | U91#(tt, V1, V2) | → | activate#(V2) |
| U102#(tt, V1, V2) | → | activate#(V2) | | U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) |
| U32#(tt, V) | → | U33#(isNatList(activate(V))) | | U112#(tt, L, N) | → | isNat#(activate(N)) |
| U93#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | activate#(V1) |
| U11#(tt, V1) | → | activate#(V1) | | U32#(tt, V) | → | activate#(V) |
| U41#(tt, V1, V2) | → | activate#(V2) | | U11#(tt, V1) | → | isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) | | U131#(tt, IL, M, N) | → | activate#(M) |
| isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U134#(tt, IL, M, N) | → | activate#(IL) |
| U113#(tt, L, N) | → | activate#(N) | | U43#(tt, V1, V2) | → | activate#(V2) |
| isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(IL) |
| U91#(tt, V1, V2) | → | activate#(V1) | | U44#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V1) |
| activate#(n__take(X1, X2)) | → | take#(X1, X2) | | isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| take#(0, IL) | → | isNatIList#(IL) | | U121#(tt, IL) | → | isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) | → | activate#(M) | | U12#(tt, V1) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | activate#(V2) | | U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U21#(tt, V1) | → | isNatKind#(activate(V1)) | | U45#(tt, V2) | → | activate#(V2) |
| U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) | | U95#(tt, V2) | → | activate#(V2) |
| length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) | | U45#(tt, V2) | → | isNatIList#(activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(M) | | U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) | | U44#(tt, V1, V2) | → | activate#(V1) |
| U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U101#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | isNat#(activate(N)) | | isNat#(n__s(V1)) | → | activate#(V1) |
| U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V2) |
| isNatIList#(V) | → | isNatIListKind#(activate(V)) | | isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | activate#(V2) | | isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U42#(tt, V1, V2) | → | activate#(V1) | | U112#(tt, L, N) | → | activate#(N) |
| U133#(tt, IL, M, N) | → | activate#(IL) | | U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) | | U112#(tt, L, N) | → | activate#(L) |
| U41#(tt, V1, V2) | → | activate#(V1) | | U42#(tt, V1, V2) | → | activate#(V2) |
| U103#(tt, V1, V2) | → | activate#(V1) | | U22#(tt, V1) | → | activate#(V1) |
| U92#(tt, V1, V2) | → | activate#(V2) | | U12#(tt, V1) | → | isNatList#(activate(V1)) |
| isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | | U111#(tt, L, N) | → | activate#(N) |
| U136#(tt, IL, M, N) | → | activate#(N) | | isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(M) |
| U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U22#(tt, V1) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | activate#(L) | | U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(N) | | U51#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) | → | activate#(V2) | | U61#(tt, V2) | → | isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) | | U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(N) | | U132#(tt, IL, M, N) | → | activate#(N) |
| U104#(tt, V1, V2) | → | activate#(V1) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) |
| isNatIList#(V) | → | activate#(V) | | U61#(tt, V2) | → | activate#(V2) |
| U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) |
| take#(0, IL) | → | U121#(isNatIList(IL), IL) | | U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) |
| isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) | | U94#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) | | U43#(tt, V1, V2) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| activate#(n__length(X)) | → | length#(X) | | U114#(tt, L) | → | s#(length(activate(L))) |
| U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | activate#(V1) | | length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 19
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U12#(tt, V1) | → | U13#(isNatList(activate(V1))) |
| isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) | | U94#(tt, V1, V2) | → | activate#(V2) |
| isNatList#(n__take(V1, V2)) | → | activate#(V1) | | U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) | | U94#(tt, V1, V2) | → | activate#(V1) |
| U121#(tt, IL) | → | activate#(IL) | | U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) |
| U31#(tt, V) | → | isNatIListKind#(activate(V)) | | U51#(tt, V2) | → | activate#(V2) |
| isNat#(n__length(V1)) | → | activate#(V1) | | isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) |
| U111#(tt, L, N) | → | isNatIListKind#(activate(L)) | | length#(nil) | → | 0# |
| U44#(tt, V1, V2) | → | isNat#(activate(V1)) | | U105#(tt, V2) | → | isNatIList#(activate(V2)) |
| U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U113#(tt, L, N) | → | activate#(L) |
| U113#(tt, L, N) | → | isNatKind#(activate(N)) | | isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) | | length#(cons(N, L)) | → | isNatList#(activate(L)) |
| U134#(tt, IL, M, N) | → | activate#(M) | | isNatList#(n__take(V1, V2)) | → | activate#(V2) |
| U136#(tt, IL, M, N) | → | activate#(IL) | | U95#(tt, V2) | → | isNatList#(activate(V2)) |
| U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134#(tt, IL, M, N) | → | activate#(N) |
| U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | | U132#(tt, IL, M, N) | → | activate#(M) |
| isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | take#(s(M), cons(N, IL)) | → | activate#(IL) |
| isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) | | isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) |
| U114#(tt, L) | → | activate#(L) | | isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) | → | activate#(V2) | | U92#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | isNatKind#(n__length(V1)) | → | activate#(V1) |
| U32#(tt, V) | → | isNatList#(activate(V)) | | isNatKind#(n__s(V1)) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U105#(tt, V2) | → | activate#(V2) |
| isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U131#(tt, IL, M, N) | → | activate#(N) |
| U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U31#(tt, V) | → | activate#(V) | | U132#(tt, IL, M, N) | → | activate#(IL) |
| U131#(tt, IL, M, N) | → | activate#(IL) | | U114#(tt, L) | → | length#(activate(L)) |
| U91#(tt, V1, V2) | → | activate#(V2) | | U102#(tt, V1, V2) | → | activate#(V2) |
| U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) | | U32#(tt, V) | → | U33#(isNatList(activate(V))) |
| U112#(tt, L, N) | → | isNat#(activate(N)) | | U93#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | activate#(V1) | | U11#(tt, V1) | → | activate#(V1) |
| U32#(tt, V) | → | activate#(V) | | U41#(tt, V1, V2) | → | activate#(V2) |
| U11#(tt, V1) | → | isNatIListKind#(activate(V1)) | | U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) |
| U131#(tt, IL, M, N) | → | activate#(M) | | isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | activate#(IL) | | U113#(tt, L, N) | → | activate#(N) |
| U43#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(IL) | | U91#(tt, V1, V2) | → | activate#(V1) |
| U44#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V1) | | activate#(n__take(X1, X2)) | → | take#(X1, X2) |
| isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| take#(0, IL) | → | isNatIList#(IL) | | U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U121#(tt, IL) | → | isNatIListKind#(activate(IL)) | | U136#(tt, IL, M, N) | → | activate#(M) |
| U104#(tt, V1, V2) | → | activate#(V2) | | U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U12#(tt, V1) | → | activate#(V1) | | U21#(tt, V1) | → | isNatKind#(activate(V1)) |
| U45#(tt, V2) | → | activate#(V2) | | U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) |
| U95#(tt, V2) | → | activate#(V2) | | length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) |
| U45#(tt, V2) | → | isNatIList#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(M) |
| U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) | | U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) | → | activate#(V1) | | U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U134#(tt, IL, M, N) | → | isNat#(activate(N)) |
| isNat#(n__s(V1)) | → | activate#(V1) | | U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIList#(V) | → | isNatIListKind#(activate(V)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V2) |
| isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U103#(tt, V1, V2) | → | activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U42#(tt, V1, V2) | → | activate#(V1) |
| U112#(tt, L, N) | → | activate#(N) | | U133#(tt, IL, M, N) | → | activate#(IL) |
| U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) | | U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) | → | activate#(L) | | U41#(tt, V1, V2) | → | activate#(V1) |
| U42#(tt, V1, V2) | → | activate#(V2) | | U103#(tt, V1, V2) | → | activate#(V1) |
| U22#(tt, V1) | → | activate#(V1) | | U92#(tt, V1, V2) | → | activate#(V2) |
| U12#(tt, V1) | → | isNatList#(activate(V1)) | | isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) |
| U111#(tt, L, N) | → | activate#(N) | | U136#(tt, IL, M, N) | → | activate#(N) |
| isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(M) | | U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U22#(tt, V1) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | activate#(L) |
| U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(N) |
| U51#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U101#(tt, V1, V2) | → | activate#(V2) |
| U61#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) | | U135#(tt, IL, M, N) | → | activate#(N) |
| U132#(tt, IL, M, N) | → | activate#(N) | | U104#(tt, V1, V2) | → | activate#(V1) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | activate#(V) |
| U61#(tt, V2) | → | activate#(V2) | | U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) | | take#(0, IL) | → | U121#(isNatIList(IL), IL) |
| U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) | | isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U94#(tt, V1, V2) | → | isNat#(activate(V1)) | | U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) | → | activate#(V1) | | U104#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | | activate#(n__length(X)) | → | length#(X) |
| U114#(tt, L) | → | s#(length(activate(L))) | | U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V1) |
| length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 18
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U94#(tt, V1, V2) | → | activate#(V1) | | U121#(tt, IL) | → | activate#(IL) |
| U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U31#(tt, V) | → | isNatIListKind#(activate(V)) |
| U51#(tt, V2) | → | activate#(V2) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | length#(nil) | → | 0# |
| U111#(tt, L, N) | → | isNatIListKind#(activate(L)) | | U44#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U105#(tt, V2) | → | isNatIList#(activate(V2)) | | U113#(tt, L, N) | → | isNatKind#(activate(N)) |
| U113#(tt, L, N) | → | activate#(L) | | U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| length#(cons(N, L)) | → | isNatList#(activate(L)) | | U134#(tt, IL, M, N) | → | activate#(M) |
| isNatList#(n__take(V1, V2)) | → | activate#(V2) | | U136#(tt, IL, M, N) | → | activate#(IL) |
| U95#(tt, V2) | → | isNatList#(activate(V2)) | | U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) | → | activate#(N) | | isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | | U132#(tt, IL, M, N) | → | activate#(M) |
| take#(s(M), cons(N, IL)) | → | activate#(IL) | | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) | | U114#(tt, L) | → | activate#(L) |
| isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V2) |
| U92#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) | → | activate#(V1) | | U32#(tt, V) | → | isNatList#(activate(V)) |
| isNatKind#(n__s(V1)) | → | activate#(V1) | | U93#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U105#(tt, V2) | → | activate#(V2) | | isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) | → | activate#(N) | | U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U31#(tt, V) | → | activate#(V) |
| U132#(tt, IL, M, N) | → | activate#(IL) | | U114#(tt, L) | → | length#(activate(L)) |
| U131#(tt, IL, M, N) | → | activate#(IL) | | U91#(tt, V1, V2) | → | activate#(V2) |
| U102#(tt, V1, V2) | → | activate#(V2) | | U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) |
| U32#(tt, V) | → | U33#(isNatList(activate(V))) | | U112#(tt, L, N) | → | isNat#(activate(N)) |
| U93#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | activate#(V1) |
| U11#(tt, V1) | → | activate#(V1) | | U32#(tt, V) | → | activate#(V) |
| U41#(tt, V1, V2) | → | activate#(V2) | | U11#(tt, V1) | → | isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) | | U131#(tt, IL, M, N) | → | activate#(M) |
| isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U134#(tt, IL, M, N) | → | activate#(IL) |
| U113#(tt, L, N) | → | activate#(N) | | U43#(tt, V1, V2) | → | activate#(V2) |
| isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(IL) |
| U91#(tt, V1, V2) | → | activate#(V1) | | U44#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V1) |
| activate#(n__take(X1, X2)) | → | take#(X1, X2) | | isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| take#(0, IL) | → | isNatIList#(IL) | | U121#(tt, IL) | → | isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) | → | activate#(M) | | U12#(tt, V1) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | activate#(V2) | | U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U21#(tt, V1) | → | isNatKind#(activate(V1)) | | U45#(tt, V2) | → | activate#(V2) |
| U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) | | U95#(tt, V2) | → | activate#(V2) |
| length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) | | U45#(tt, V2) | → | isNatIList#(activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(M) | | U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) | | U44#(tt, V1, V2) | → | activate#(V1) |
| U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U101#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | isNat#(n__s(V1)) | → | activate#(V1) |
| U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U105#(tt, V2) | → | U106#(isNatIList(activate(V2))) |
| U134#(tt, IL, M, N) | → | isNat#(activate(N)) | | U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | isNatIListKind#(activate(V)) |
| isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U103#(tt, V1, V2) | → | activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U42#(tt, V1, V2) | → | activate#(V1) |
| U112#(tt, L, N) | → | activate#(N) | | U133#(tt, IL, M, N) | → | activate#(IL) |
| U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) |
| U112#(tt, L, N) | → | activate#(L) | | U41#(tt, V1, V2) | → | activate#(V1) |
| U42#(tt, V1, V2) | → | activate#(V2) | | U103#(tt, V1, V2) | → | activate#(V1) |
| U22#(tt, V1) | → | activate#(V1) | | U92#(tt, V1, V2) | → | activate#(V2) |
| U12#(tt, V1) | → | isNatList#(activate(V1)) | | isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) |
| U136#(tt, IL, M, N) | → | activate#(N) | | U111#(tt, L, N) | → | activate#(N) |
| isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(M) | | U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U22#(tt, V1) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | activate#(L) |
| U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(N) |
| U51#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U101#(tt, V1, V2) | → | activate#(V2) |
| U61#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) |
| U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(N) |
| U132#(tt, IL, M, N) | → | activate#(N) | | U104#(tt, V1, V2) | → | activate#(V1) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | activate#(V) |
| U61#(tt, V2) | → | activate#(V2) | | U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) | | take#(0, IL) | → | U121#(isNatIList(IL), IL) |
| U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) | | isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U94#(tt, V1, V2) | → | isNat#(activate(V1)) | | U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) | → | activate#(V1) | | U104#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | | activate#(n__length(X)) | → | length#(X) |
| U114#(tt, L) | → | s#(length(activate(L))) | | U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V1) |
| length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 21
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | U51#(tt, V2) | → | U52#(isNatIListKind(activate(V2))) |
| isNatList#(n__take(V1, V2)) | → | activate#(V1) | | U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) | | U94#(tt, V1, V2) | → | activate#(V1) |
| U121#(tt, IL) | → | activate#(IL) | | U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) |
| U31#(tt, V) | → | isNatIListKind#(activate(V)) | | U51#(tt, V2) | → | activate#(V2) |
| isNat#(n__length(V1)) | → | activate#(V1) | | isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) |
| length#(nil) | → | 0# | | U111#(tt, L, N) | → | isNatIListKind#(activate(L)) |
| U44#(tt, V1, V2) | → | isNat#(activate(V1)) | | U105#(tt, V2) | → | isNatIList#(activate(V2)) |
| U113#(tt, L, N) | → | activate#(L) | | U113#(tt, L, N) | → | isNatKind#(activate(N)) |
| U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) | | U134#(tt, IL, M, N) | → | activate#(M) |
| length#(cons(N, L)) | → | isNatList#(activate(L)) | | U136#(tt, IL, M, N) | → | activate#(IL) |
| isNatList#(n__take(V1, V2)) | → | activate#(V2) | | U95#(tt, V2) | → | isNatList#(activate(V2)) |
| U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134#(tt, IL, M, N) | → | activate#(N) |
| isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U132#(tt, IL, M, N) | → | activate#(M) | | take#(s(M), cons(N, IL)) | → | activate#(IL) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) | | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| U114#(tt, L) | → | activate#(L) | | isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) | → | activate#(V2) | | U92#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | isNatKind#(n__length(V1)) | → | activate#(V1) |
| U32#(tt, V) | → | isNatList#(activate(V)) | | isNatKind#(n__s(V1)) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U105#(tt, V2) | → | activate#(V2) |
| U131#(tt, IL, M, N) | → | activate#(N) | | isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U31#(tt, V) | → | activate#(V) | | U132#(tt, IL, M, N) | → | activate#(IL) |
| U131#(tt, IL, M, N) | → | activate#(IL) | | U114#(tt, L) | → | length#(activate(L)) |
| U91#(tt, V1, V2) | → | activate#(V2) | | U122#(tt) | → | nil# |
| U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) | | U102#(tt, V1, V2) | → | activate#(V2) |
| U112#(tt, L, N) | → | isNat#(activate(N)) | | U93#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | activate#(V1) | | U32#(tt, V) | → | activate#(V) |
| U11#(tt, V1) | → | activate#(V1) | | U41#(tt, V1, V2) | → | activate#(V2) |
| U11#(tt, V1) | → | isNatIListKind#(activate(V1)) | | U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) |
| U131#(tt, IL, M, N) | → | activate#(M) | | isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | activate#(IL) | | U113#(tt, L, N) | → | activate#(N) |
| U43#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(IL) | | U91#(tt, V1, V2) | → | activate#(V1) |
| U44#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V1) | | activate#(n__take(X1, X2)) | → | take#(X1, X2) |
| isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | take#(0, IL) | → | isNatIList#(IL) |
| U121#(tt, IL) | → | isNatIListKind#(activate(IL)) | | U136#(tt, IL, M, N) | → | activate#(M) |
| U12#(tt, V1) | → | activate#(V1) | | U104#(tt, V1, V2) | → | activate#(V2) |
| U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U21#(tt, V1) | → | isNatKind#(activate(V1)) |
| U45#(tt, V2) | → | activate#(V2) | | U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) |
| U95#(tt, V2) | → | activate#(V2) | | length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) |
| U45#(tt, V2) | → | isNatIList#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(M) |
| U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) | | U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) | → | activate#(V1) | | U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNat#(n__s(V1)) | → | activate#(V1) | | U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U105#(tt, V2) | → | U106#(isNatIList(activate(V2))) | | U134#(tt, IL, M, N) | → | isNat#(activate(N)) |
| U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V2) |
| isNatIList#(V) | → | isNatIListKind#(activate(V)) | | isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | activate#(V2) | | isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U42#(tt, V1, V2) | → | activate#(V1) | | U112#(tt, L, N) | → | activate#(N) |
| U133#(tt, IL, M, N) | → | activate#(IL) | | U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) | | U112#(tt, L, N) | → | activate#(L) |
| U41#(tt, V1, V2) | → | activate#(V1) | | U42#(tt, V1, V2) | → | activate#(V2) |
| U103#(tt, V1, V2) | → | activate#(V1) | | U22#(tt, V1) | → | activate#(V1) |
| U92#(tt, V1, V2) | → | activate#(V2) | | U12#(tt, V1) | → | isNatList#(activate(V1)) |
| U121#(tt, IL) | → | U122#(isNatIListKind(activate(IL))) | | isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) |
| U136#(tt, IL, M, N) | → | activate#(N) | | U111#(tt, L, N) | → | activate#(N) |
| isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(M) | | U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U22#(tt, V1) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | activate#(L) |
| U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(N) |
| U51#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U101#(tt, V1, V2) | → | activate#(V2) |
| U61#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) |
| U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(N) |
| U132#(tt, IL, M, N) | → | activate#(N) | | U104#(tt, V1, V2) | → | activate#(V1) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | activate#(V) |
| U61#(tt, V2) | → | activate#(V2) | | U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) | | take#(0, IL) | → | U121#(isNatIList(IL), IL) |
| U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) | | isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U94#(tt, V1, V2) | → | isNat#(activate(V1)) | | U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) | → | activate#(V1) | | U104#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | | activate#(n__length(X)) | → | length#(X) |
| U114#(tt, L) | → | s#(length(activate(L))) | | U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V1) |
| length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 20
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U94#(tt, V1, V2) | → | activate#(V1) | | U121#(tt, IL) | → | activate#(IL) |
| U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U31#(tt, V) | → | isNatIListKind#(activate(V)) |
| U51#(tt, V2) | → | activate#(V2) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | length#(nil) | → | 0# |
| U111#(tt, L, N) | → | isNatIListKind#(activate(L)) | | U44#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U105#(tt, V2) | → | isNatIList#(activate(V2)) | | U113#(tt, L, N) | → | isNatKind#(activate(N)) |
| U113#(tt, L, N) | → | activate#(L) | | U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) | → | activate#(M) | | length#(cons(N, L)) | → | isNatList#(activate(L)) |
| isNatList#(n__take(V1, V2)) | → | activate#(V2) | | U136#(tt, IL, M, N) | → | activate#(IL) |
| U95#(tt, V2) | → | isNatList#(activate(V2)) | | U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) | → | activate#(N) | | U132#(tt, IL, M, N) | → | activate#(M) |
| U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | | isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(s(M), cons(N, IL)) | → | activate#(IL) | | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) | | U114#(tt, L) | → | activate#(L) |
| isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V2) |
| U92#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) | → | activate#(V1) | | U32#(tt, V) | → | isNatList#(activate(V)) |
| isNatKind#(n__s(V1)) | → | activate#(V1) | | U93#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U105#(tt, V2) | → | activate#(V2) | | isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) | → | activate#(N) | | U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U31#(tt, V) | → | activate#(V) |
| U132#(tt, IL, M, N) | → | activate#(IL) | | U131#(tt, IL, M, N) | → | activate#(IL) |
| U114#(tt, L) | → | length#(activate(L)) | | U91#(tt, V1, V2) | → | activate#(V2) |
| U102#(tt, V1, V2) | → | activate#(V2) | | U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) |
| U112#(tt, L, N) | → | isNat#(activate(N)) | | U93#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | activate#(V1) | | U11#(tt, V1) | → | activate#(V1) |
| U32#(tt, V) | → | activate#(V) | | U41#(tt, V1, V2) | → | activate#(V2) |
| U11#(tt, V1) | → | isNatIListKind#(activate(V1)) | | U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) |
| U131#(tt, IL, M, N) | → | activate#(M) | | isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | activate#(IL) | | U113#(tt, L, N) | → | activate#(N) |
| U43#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(IL) | | U91#(tt, V1, V2) | → | activate#(V1) |
| U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | | U44#(tt, V1, V2) | → | activate#(V2) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V1) | | activate#(n__take(X1, X2)) | → | take#(X1, X2) |
| isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | take#(0, IL) | → | isNatIList#(IL) |
| U121#(tt, IL) | → | isNatIListKind#(activate(IL)) | | U136#(tt, IL, M, N) | → | activate#(M) |
| U12#(tt, V1) | → | activate#(V1) | | U104#(tt, V1, V2) | → | activate#(V2) |
| U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U21#(tt, V1) | → | isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) | | U45#(tt, V2) | → | activate#(V2) |
| U95#(tt, V2) | → | activate#(V2) | | length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) |
| U135#(tt, IL, M, N) | → | activate#(M) | | U45#(tt, V2) | → | isNatIList#(activate(V2)) |
| U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) | | U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) | → | activate#(V1) | | U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNat#(n__s(V1)) | → | activate#(V1) | | U134#(tt, IL, M, N) | → | isNat#(activate(N)) |
| U105#(tt, V2) | → | U106#(isNatIList(activate(V2))) | | U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V2) |
| isNatIList#(V) | → | isNatIListKind#(activate(V)) | | isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | activate#(V2) | | isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U112#(tt, L, N) | → | activate#(N) | | U42#(tt, V1, V2) | → | activate#(V1) |
| U133#(tt, IL, M, N) | → | activate#(IL) | | U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) | | U112#(tt, L, N) | → | activate#(L) |
| U41#(tt, V1, V2) | → | activate#(V1) | | U42#(tt, V1, V2) | → | activate#(V2) |
| U103#(tt, V1, V2) | → | activate#(V1) | | U22#(tt, V1) | → | activate#(V1) |
| U92#(tt, V1, V2) | → | activate#(V2) | | U12#(tt, V1) | → | isNatList#(activate(V1)) |
| isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | | U136#(tt, IL, M, N) | → | activate#(N) |
| U111#(tt, L, N) | → | activate#(N) | | isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(M) |
| U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U22#(tt, V1) | → | isNat#(activate(V1)) |
| U45#(tt, V2) | → | U46#(isNatIList(activate(V2))) | | U111#(tt, L, N) | → | activate#(L) |
| U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(N) |
| U51#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U101#(tt, V1, V2) | → | activate#(V2) |
| U61#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) |
| U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U132#(tt, IL, M, N) | → | activate#(N) |
| U135#(tt, IL, M, N) | → | activate#(N) | | U104#(tt, V1, V2) | → | activate#(V1) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | activate#(V) |
| U61#(tt, V2) | → | activate#(V2) | | U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) | | take#(0, IL) | → | U121#(isNatIList(IL), IL) |
| U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) | | isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U94#(tt, V1, V2) | → | isNat#(activate(V1)) | | U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) | → | activate#(V1) | | U104#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | | activate#(n__length(X)) | → | length#(X) |
| U114#(tt, L) | → | s#(length(activate(L))) | | U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V1) |
| length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Open Dependency Pair Problem 22
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U94#(tt, V1, V2) | → | activate#(V1) | | U121#(tt, IL) | → | activate#(IL) |
| U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | | U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U31#(tt, V) | → | isNatIListKind#(activate(V)) |
| U51#(tt, V2) | → | activate#(V2) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | U111#(tt, L, N) | → | isNatIListKind#(activate(L)) |
| length#(nil) | → | 0# | | U44#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U105#(tt, V2) | → | isNatIList#(activate(V2)) | | U113#(tt, L, N) | → | activate#(L) |
| U113#(tt, L, N) | → | isNatKind#(activate(N)) | | U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| length#(cons(N, L)) | → | isNatList#(activate(L)) | | U134#(tt, IL, M, N) | → | activate#(M) |
| isNatList#(n__take(V1, V2)) | → | activate#(V2) | | U136#(tt, IL, M, N) | → | activate#(IL) |
| U95#(tt, V2) | → | isNatList#(activate(V2)) | | U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) | → | activate#(N) | | isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | | U132#(tt, IL, M, N) | → | activate#(M) |
| take#(s(M), cons(N, IL)) | → | activate#(IL) | | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) | | U114#(tt, L) | → | activate#(L) |
| isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V2) |
| U92#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) | → | activate#(V1) | | U32#(tt, V) | → | isNatList#(activate(V)) |
| isNatKind#(n__s(V1)) | → | activate#(V1) | | U93#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U105#(tt, V2) | → | activate#(V2) | | isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) | → | activate#(N) | | U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U31#(tt, V) | → | activate#(V) |
| U132#(tt, IL, M, N) | → | activate#(IL) | | U131#(tt, IL, M, N) | → | activate#(IL) |
| U114#(tt, L) | → | length#(activate(L)) | | U91#(tt, V1, V2) | → | activate#(V2) |
| U102#(tt, V1, V2) | → | activate#(V2) | | U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) |
| U32#(tt, V) | → | U33#(isNatList(activate(V))) | | U112#(tt, L, N) | → | isNat#(activate(N)) |
| U93#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | activate#(V1) |
| U11#(tt, V1) | → | activate#(V1) | | U32#(tt, V) | → | activate#(V) |
| U41#(tt, V1, V2) | → | activate#(V2) | | U11#(tt, V1) | → | isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) | | U131#(tt, IL, M, N) | → | activate#(M) |
| isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U134#(tt, IL, M, N) | → | activate#(IL) |
| U113#(tt, L, N) | → | activate#(N) | | U43#(tt, V1, V2) | → | activate#(V2) |
| isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(IL) |
| U91#(tt, V1, V2) | → | activate#(V1) | | U44#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V1) |
| activate#(n__take(X1, X2)) | → | take#(X1, X2) | | isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| take#(0, IL) | → | isNatIList#(IL) | | U121#(tt, IL) | → | isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) | → | activate#(M) | | U12#(tt, V1) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | activate#(V2) | | U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U21#(tt, V1) | → | isNatKind#(activate(V1)) | | U45#(tt, V2) | → | activate#(V2) |
| U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) | | U95#(tt, V2) | → | activate#(V2) |
| length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) | | U45#(tt, V2) | → | isNatIList#(activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(M) | | U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) | | U44#(tt, V1, V2) | → | activate#(V1) |
| U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U101#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | isNat#(activate(N)) | | isNat#(n__s(V1)) | → | activate#(V1) |
| U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V2) |
| isNatIList#(V) | → | isNatIListKind#(activate(V)) | | isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | activate#(V2) | | isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U42#(tt, V1, V2) | → | activate#(V1) | | U112#(tt, L, N) | → | activate#(N) |
| U133#(tt, IL, M, N) | → | activate#(IL) | | U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) | | U112#(tt, L, N) | → | activate#(L) |
| U41#(tt, V1, V2) | → | activate#(V1) | | U42#(tt, V1, V2) | → | activate#(V2) |
| U103#(tt, V1, V2) | → | activate#(V1) | | U22#(tt, V1) | → | activate#(V1) |
| U92#(tt, V1, V2) | → | activate#(V2) | | U12#(tt, V1) | → | isNatList#(activate(V1)) |
| isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | | U111#(tt, L, N) | → | activate#(N) |
| U22#(tt, V1) | → | U23#(isNat(activate(V1))) | | U136#(tt, IL, M, N) | → | activate#(N) |
| isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(M) | | U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U22#(tt, V1) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | activate#(L) |
| U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(N) |
| U51#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U101#(tt, V1, V2) | → | activate#(V2) |
| U61#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) |
| U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(N) |
| U132#(tt, IL, M, N) | → | activate#(N) | | U104#(tt, V1, V2) | → | activate#(V1) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) | | isNatIList#(V) | → | activate#(V) |
| U61#(tt, V2) | → | activate#(V2) | | U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) | | take#(0, IL) | → | U121#(isNatIList(IL), IL) |
| U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) | | isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U94#(tt, V1, V2) | → | isNat#(activate(V1)) | | U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) | → | activate#(V1) | | U104#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | | activate#(n__length(X)) | → | length#(X) |
| U114#(tt, L) | → | s#(length(activate(L))) | | U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V1) |
| length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, 0, U122, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, isNatList, s, U51, tt, take, U81, U52, U11, U12, U13, U102, U103, U101, nil
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| U132#(tt, IL, M, N) | → | isNat#(activate(M)) | | take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U12#(tt, V1) | → | U13#(isNatList(activate(V1))) |
| isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) | | U94#(tt, V1, V2) | → | activate#(V2) |
| U51#(tt, V2) | → | U52#(isNatIListKind(activate(V2))) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U121#(tt, IL) | → | activate#(IL) | | U94#(tt, V1, V2) | → | activate#(V1) |
| U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U51#(tt, V2) | → | activate#(V2) |
| U31#(tt, V) | → | isNatIListKind#(activate(V)) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | length#(nil) | → | 0# |
| U111#(tt, L, N) | → | isNatIListKind#(activate(L)) | | U44#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U105#(tt, V2) | → | isNatIList#(activate(V2)) | | U113#(tt, L, N) | → | isNatKind#(activate(N)) |
| U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U113#(tt, L, N) | → | activate#(L) |
| isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) | → | activate#(M) | | length#(cons(N, L)) | → | isNatList#(activate(L)) |
| U136#(tt, IL, M, N) | → | activate#(IL) | | isNatList#(n__take(V1, V2)) | → | activate#(V2) |
| U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U95#(tt, V2) | → | isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) | → | activate#(N) | | U132#(tt, IL, M, N) | → | activate#(M) |
| U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | | isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(s(M), cons(N, IL)) | → | activate#(IL) | | isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) |
| isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) | | U114#(tt, L) | → | activate#(L) |
| isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V2) |
| activate#(n__zeros) | → | zeros# | | U92#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | isNatKind#(n__length(V1)) | → | activate#(V1) |
| isNatKind#(n__s(V1)) | → | activate#(V1) | | U32#(tt, V) | → | isNatList#(activate(V)) |
| U93#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | activate#(V1) |
| U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U105#(tt, V2) | → | activate#(V2) |
| isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U131#(tt, IL, M, N) | → | activate#(N) |
| isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatKind#(n__length(V1)) | → | U71#(isNatIListKind(activate(V1))) | | U31#(tt, V) | → | activate#(V) |
| U132#(tt, IL, M, N) | → | activate#(IL) | | U131#(tt, IL, M, N) | → | activate#(IL) |
| U114#(tt, L) | → | length#(activate(L)) | | U91#(tt, V1, V2) | → | activate#(V2) |
| U122#(tt) | → | nil# | | U102#(tt, V1, V2) | → | activate#(V2) |
| U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) | | U32#(tt, V) | → | U33#(isNatList(activate(V))) |
| U112#(tt, L, N) | → | isNat#(activate(N)) | | U93#(tt, V1, V2) | → | activate#(V2) |
| zeros# | → | cons#(0, n__zeros) | | U21#(tt, V1) | → | activate#(V1) |
| U11#(tt, V1) | → | activate#(V1) | | U32#(tt, V) | → | activate#(V) |
| U41#(tt, V1, V2) | → | activate#(V2) | | U95#(tt, V2) | → | U96#(isNatList(activate(V2))) |
| U11#(tt, V1) | → | isNatIListKind#(activate(V1)) | | U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) |
| isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U131#(tt, IL, M, N) | → | activate#(M) |
| U134#(tt, IL, M, N) | → | activate#(IL) | | U113#(tt, L, N) | → | activate#(N) |
| U43#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) | → | activate#(IL) | | U91#(tt, V1, V2) | → | activate#(V1) |
| U44#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V1) | | activate#(n__take(X1, X2)) | → | take#(X1, X2) |
| isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | take#(0, IL) | → | isNatIList#(IL) |
| U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U121#(tt, IL) | → | isNatIListKind#(activate(IL)) | | U136#(tt, IL, M, N) | → | activate#(M) |
| U104#(tt, V1, V2) | → | activate#(V2) | | U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U12#(tt, V1) | → | activate#(V1) | | zeros# | → | 0# |
| U21#(tt, V1) | → | isNatKind#(activate(V1)) | | U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) |
| U45#(tt, V2) | → | activate#(V2) | | U95#(tt, V2) | → | activate#(V2) |
| length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) | | U135#(tt, IL, M, N) | → | activate#(M) |
| U45#(tt, V2) | → | isNatIList#(activate(V2)) | | U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) | | U44#(tt, V1, V2) | → | activate#(V1) |
| U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U101#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) | → | isNat#(activate(N)) | | U105#(tt, V2) | → | U106#(isNatIList(activate(V2))) |
| isNat#(n__s(V1)) | → | activate#(V1) | | U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIList#(V) | → | isNatIListKind#(activate(V)) | | isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V2) | | U103#(tt, V1, V2) | → | activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U42#(tt, V1, V2) | → | activate#(V1) |
| U112#(tt, L, N) | → | activate#(N) | | U133#(tt, IL, M, N) | → | activate#(IL) |
| U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) |
| U112#(tt, L, N) | → | activate#(L) | | U41#(tt, V1, V2) | → | activate#(V1) |
| U42#(tt, V1, V2) | → | activate#(V2) | | U103#(tt, V1, V2) | → | activate#(V1) |
| U22#(tt, V1) | → | activate#(V1) | | activate#(n__0) | → | 0# |
| U12#(tt, V1) | → | isNatList#(activate(V1)) | | U92#(tt, V1, V2) | → | activate#(V2) |
| U121#(tt, IL) | → | U122#(isNatIListKind(activate(IL))) | | isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) |
| U22#(tt, V1) | → | U23#(isNat(activate(V1))) | | U136#(tt, IL, M, N) | → | activate#(N) |
| U111#(tt, L, N) | → | activate#(N) | | isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) |
| isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(M) |
| U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U22#(tt, V1) | → | isNat#(activate(V1)) |
| U111#(tt, L, N) | → | activate#(L) | | U45#(tt, V2) | → | U46#(isNatIList(activate(V2))) |
| U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(N) |
| U51#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U101#(tt, V1, V2) | → | activate#(V2) |
| U61#(tt, V2) | → | isNatIListKind#(activate(V2)) | | isNatKind#(n__s(V1)) | → | U81#(isNatKind(activate(V1))) |
| U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) | | U61#(tt, V2) | → | U62#(isNatIListKind(activate(V2))) |
| U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(N) |
| U132#(tt, IL, M, N) | → | activate#(N) | | U104#(tt, V1, V2) | → | activate#(V1) |
| isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) | | U61#(tt, V2) | → | activate#(V2) |
| isNatIList#(V) | → | activate#(V) | | activate#(n__cons(X1, X2)) | → | cons#(X1, X2) |
| U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) |
| take#(0, IL) | → | U121#(isNatIList(IL), IL) | | U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) |
| isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) | | U94#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) | | U43#(tt, V1, V2) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | isNat#(activate(V1)) | | activate#(n__s(X)) | → | s#(X) |
| U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | | activate#(n__length(X)) | → | length#(X) |
| activate#(n__nil) | → | nil# | | U114#(tt, L) | → | s#(length(activate(L))) |
| U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) | | U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | activate#(V1) | | length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, U122, 0, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, U51, s, isNatList, tt, take, U52, U81, U11, U12, U13, U102, U103, nil, U101
Strategy
The following SCCs where found
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U12#(tt, V1) → U13#(isNatList(activate(V1))) | U94#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → activate#(V1) | U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V1) | U121#(tt, IL) → activate#(IL) |
| U94#(tt, V1, V2) → activate#(V1) | U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) |
| U51#(tt, V2) → activate#(V2) | U31#(tt, V) → isNatIListKind#(activate(V)) |
| isNat#(n__length(V1)) → activate#(V1) | isNatIListKind#(n__cons(V1, V2)) → activate#(V2) |
| length#(nil) → 0# | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| U44#(tt, V1, V2) → isNat#(activate(V1)) | U105#(tt, V2) → isNatIList#(activate(V2)) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | U113#(tt, L, N) → activate#(L) |
| U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) | U134#(tt, IL, M, N) → activate#(M) |
| length#(cons(N, L)) → isNatList#(activate(L)) | U136#(tt, IL, M, N) → activate#(IL) |
| isNatList#(n__take(V1, V2)) → activate#(V2) | U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U95#(tt, V2) → isNatList#(activate(V2)) | U134#(tt, IL, M, N) → activate#(N) |
| isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U132#(tt, IL, M, N) → activate#(M) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | take#(s(M), cons(N, IL)) → activate#(IL) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V1) | isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) |
| U114#(tt, L) → activate#(L) | isNat#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V2) | U92#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) | isNatKind#(n__length(V1)) → activate#(V1) |
| isNatKind#(n__s(V1)) → activate#(V1) | U32#(tt, V) → isNatList#(activate(V)) |
| U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U93#(tt, V1, V2) → activate#(V1) |
| U102#(tt, V1, V2) → activate#(V1) | U105#(tt, V2) → activate#(V2) |
| U131#(tt, IL, M, N) → activate#(N) | isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U31#(tt, V) → activate#(V) | U132#(tt, IL, M, N) → activate#(IL) |
| U114#(tt, L) → length#(activate(L)) | U131#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V2) | U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) |
| U102#(tt, V1, V2) → activate#(V2) | U32#(tt, V) → U33#(isNatList(activate(V))) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U11#(tt, V1) → activate#(V1) | U41#(tt, V1, V2) → activate#(V2) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) |
| isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(M) |
| U134#(tt, IL, M, N) → activate#(IL) | U113#(tt, L, N) → activate#(N) |
| U43#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V1) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → activate#(V1) | activate#(n__take(X1, X2)) → take#(X1, X2) |
| isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) | U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| take#(0, IL) → isNatIList#(IL) | U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U121#(tt, IL) → isNatIListKind#(activate(IL)) | U136#(tt, IL, M, N) → activate#(M) |
| U12#(tt, V1) → activate#(V1) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U104#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → isNatKind#(activate(N)) | U45#(tt, V2) → activate#(V2) |
| U95#(tt, V2) → activate#(V2) | length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) |
| U135#(tt, IL, M, N) → activate#(M) | U45#(tt, V2) → isNatIList#(activate(V2)) |
| U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) → activate#(V1) | U91#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNat#(n__s(V1)) → activate#(V1) | U134#(tt, IL, M, N) → isNat#(activate(N)) |
| U41#(tt, V1, V2) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) | isNatList#(n__cons(V1, V2)) → activate#(V2) |
| isNatIList#(V) → isNatIListKind#(activate(V)) | isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → activate#(V2) | U112#(tt, L, N) → activate#(N) |
| U42#(tt, V1, V2) → activate#(V1) | U133#(tt, IL, M, N) → activate#(IL) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U112#(tt, L, N) → activate#(L) | U41#(tt, V1, V2) → activate#(V1) |
| U42#(tt, V1, V2) → activate#(V2) | U103#(tt, V1, V2) → activate#(V1) |
| U22#(tt, V1) → activate#(V1) | U12#(tt, V1) → isNatList#(activate(V1)) |
| U92#(tt, V1, V2) → activate#(V2) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U136#(tt, IL, M, N) → activate#(N) | U111#(tt, L, N) → activate#(N) |
| isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) | isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(M) | U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U22#(tt, V1) → isNat#(activate(V1)) | U111#(tt, L, N) → activate#(L) |
| U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(N) |
| U51#(tt, V2) → isNatIListKind#(activate(V2)) | U101#(tt, V1, V2) → activate#(V2) |
| U61#(tt, V2) → isNatIListKind#(activate(V2)) | U133#(tt, IL, M, N) → isNatKind#(activate(M)) |
| U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U132#(tt, IL, M, N) → activate#(N) |
| U135#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__take(V1, V2)) → activate#(V2) |
| U104#(tt, V1, V2) → activate#(V1) | U61#(tt, V2) → activate#(V2) |
| isNatIList#(V) → activate#(V) | U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) | U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) → isNat#(activate(V1)) | U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) → activate#(V1) | U104#(tt, V1, V2) → isNat#(activate(V1)) |
| activate#(n__length(X)) → length#(X) | U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U114#(tt, L) → s#(length(activate(L))) | U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → activate#(V1) |
| length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| length#(nil) → 0# | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → activate#(L) | U113#(tt, L, N) → isNatKind#(activate(N)) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| length#(cons(N, L)) → isNatList#(activate(L)) | U134#(tt, IL, M, N) → activate#(M) |
| U136#(tt, IL, M, N) → activate#(IL) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) → activate#(N) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | U132#(tt, IL, M, N) → activate#(M) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U102#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U131#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U102#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U11#(tt, V1) → activate#(V1) | U41#(tt, V1, V2) → activate#(V2) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) |
| isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(M) |
| U134#(tt, IL, M, N) → activate#(IL) | U113#(tt, L, N) → activate#(N) |
| U43#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V1) |
| U44#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| isNatList#(n__cons(V1, V2)) → activate#(V1) | activate#(n__take(X1, X2)) → take#(X1, X2) |
| isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) | take#(0, IL) → isNatIList#(IL) |
| U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U121#(tt, IL) → isNatIListKind#(activate(IL)) | U136#(tt, IL, M, N) → activate#(M) |
| U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U104#(tt, V1, V2) → activate#(V2) |
| U12#(tt, V1) → activate#(V1) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U45#(tt, V2) → activate#(V2) | U135#(tt, IL, M, N) → isNatKind#(activate(N)) |
| U95#(tt, V2) → activate#(V2) | length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U135#(tt, IL, M, N) → activate#(M) |
| U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) → activate#(V1) | U91#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U41#(tt, V1, V2) → isNatKind#(activate(V1)) | U105#(tt, V2) → U106#(isNatIList(activate(V2))) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | isNat#(n__s(V1)) → activate#(V1) |
| U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| isNatIList#(V) → isNatIListKind#(activate(V)) | isNatList#(n__cons(V1, V2)) → activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → activate#(V2) |
| U42#(tt, V1, V2) → activate#(V1) | U112#(tt, L, N) → activate#(N) |
| U133#(tt, IL, M, N) → activate#(IL) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → activate#(L) |
| U41#(tt, V1, V2) → activate#(V1) | U42#(tt, V1, V2) → activate#(V2) |
| U103#(tt, V1, V2) → activate#(V1) | U22#(tt, V1) → activate#(V1) |
| U12#(tt, V1) → isNatList#(activate(V1)) | U92#(tt, V1, V2) → activate#(V2) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U111#(tt, L, N) → activate#(N) |
| U136#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) |
| isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(M) |
| U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U22#(tt, V1) → isNat#(activate(V1)) |
| U111#(tt, L, N) → activate#(L) | U45#(tt, V2) → U46#(isNatIList(activate(V2))) |
| U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(N) |
| U51#(tt, V2) → isNatIListKind#(activate(V2)) | U101#(tt, V1, V2) → activate#(V2) |
| U61#(tt, V2) → isNatIListKind#(activate(V2)) | U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) → isNatKind#(activate(M)) | U135#(tt, IL, M, N) → activate#(N) |
| U132#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__take(V1, V2)) → activate#(V2) |
| U104#(tt, V1, V2) → activate#(V1) | U61#(tt, V2) → activate#(V2) |
| isNatIList#(V) → activate#(V) | U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) | U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) → isNat#(activate(V1)) | U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) → activate#(V1) | U104#(tt, V1, V2) → isNat#(activate(V1)) |
| activate#(n__length(X)) → length#(X) | U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U114#(tt, L) → s#(length(activate(L))) | U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → activate#(V1) |
| length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | U12#(tt, V1) → U13#(isNatList(activate(V1))) |
| isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) | U94#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → activate#(V1) | U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V1) | U121#(tt, IL) → activate#(IL) |
| U94#(tt, V1, V2) → activate#(V1) | U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) |
| U51#(tt, V2) → activate#(V2) | U31#(tt, V) → isNatIListKind#(activate(V)) |
| isNat#(n__length(V1)) → activate#(V1) | isNatIListKind#(n__cons(V1, V2)) → activate#(V2) |
| U111#(tt, L, N) → isNatIListKind#(activate(L)) | length#(nil) → 0# |
| U44#(tt, V1, V2) → isNat#(activate(V1)) | U105#(tt, V2) → isNatIList#(activate(V2)) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | U113#(tt, L, N) → activate#(L) |
| U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U134#(tt, IL, M, N) → activate#(M) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U136#(tt, IL, M, N) → activate#(IL) | U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U95#(tt, V2) → isNatList#(activate(V2)) | U134#(tt, IL, M, N) → activate#(N) |
| isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U132#(tt, IL, M, N) → activate#(M) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | take#(s(M), cons(N, IL)) → activate#(IL) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| U114#(tt, L) → activate#(L) | isNat#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V2) | U92#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) | isNatKind#(n__length(V1)) → activate#(V1) |
| isNatKind#(n__s(V1)) → activate#(V1) | U32#(tt, V) → isNatList#(activate(V)) |
| U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U102#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → activate#(V1) | U105#(tt, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U31#(tt, V) → activate#(V) | U132#(tt, IL, M, N) → activate#(IL) |
| U114#(tt, L) → length#(activate(L)) | U131#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V2) | U122#(tt) → nil# |
| U102#(tt, V1, V2) → activate#(V2) | U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U11#(tt, V1) → activate#(V1) |
| U32#(tt, V) → activate#(V) | U41#(tt, V1, V2) → activate#(V2) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) |
| isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(M) |
| U134#(tt, IL, M, N) → activate#(IL) | U113#(tt, L, N) → activate#(N) |
| U43#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V1) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → activate#(V1) | activate#(n__take(X1, X2)) → take#(X1, X2) |
| isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) | U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| take#(0, IL) → isNatIList#(IL) | U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U121#(tt, IL) → isNatIListKind#(activate(IL)) | U136#(tt, IL, M, N) → activate#(M) |
| U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U104#(tt, V1, V2) → activate#(V2) |
| U12#(tt, V1) → activate#(V1) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → isNatKind#(activate(N)) | U45#(tt, V2) → activate#(V2) |
| U95#(tt, V2) → activate#(V2) | length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) |
| U135#(tt, IL, M, N) → activate#(M) | U45#(tt, V2) → isNatIList#(activate(V2)) |
| U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) → activate#(V1) | U91#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNat#(n__s(V1)) → activate#(V1) | U134#(tt, IL, M, N) → isNat#(activate(N)) |
| U105#(tt, V2) → U106#(isNatIList(activate(V2))) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| isNatIList#(V) → isNatIListKind#(activate(V)) | isNatList#(n__cons(V1, V2)) → activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → activate#(N) | U42#(tt, V1, V2) → activate#(V1) |
| U133#(tt, IL, M, N) → activate#(IL) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → activate#(L) |
| U41#(tt, V1, V2) → activate#(V1) | U42#(tt, V1, V2) → activate#(V2) |
| U103#(tt, V1, V2) → activate#(V1) | U22#(tt, V1) → activate#(V1) |
| U12#(tt, V1) → isNatList#(activate(V1)) | U92#(tt, V1, V2) → activate#(V2) |
| U121#(tt, IL) → U122#(isNatIListKind(activate(IL))) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U111#(tt, L, N) → activate#(N) | U136#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) | isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(M) | U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U22#(tt, V1) → isNat#(activate(V1)) | U111#(tt, L, N) → activate#(L) |
| U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(N) |
| U51#(tt, V2) → isNatIListKind#(activate(V2)) | U101#(tt, V1, V2) → activate#(V2) |
| U61#(tt, V2) → isNatIListKind#(activate(V2)) | U133#(tt, IL, M, N) → isNatKind#(activate(M)) |
| U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U132#(tt, IL, M, N) → activate#(N) |
| U135#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__take(V1, V2)) → activate#(V2) |
| U104#(tt, V1, V2) → activate#(V1) | U61#(tt, V2) → activate#(V2) |
| isNatIList#(V) → activate#(V) | U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) | isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U94#(tt, V1, V2) → isNat#(activate(V1)) | U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) → activate#(V1) | U104#(tt, V1, V2) → isNat#(activate(V1)) |
| activate#(n__length(X)) → length#(X) | U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U114#(tt, L) → s#(length(activate(L))) | U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → activate#(V1) |
| length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | length#(nil) → 0# |
| U111#(tt, L, N) → isNatIListKind#(activate(L)) | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | U113#(tt, L, N) → activate#(L) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) → activate#(M) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U136#(tt, IL, M, N) → activate#(IL) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) → activate#(N) | U132#(tt, IL, M, N) → activate#(M) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U102#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U131#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U102#(tt, V1, V2) → activate#(V2) |
| U32#(tt, V) → U33#(isNatList(activate(V))) | U112#(tt, L, N) → isNat#(activate(N)) |
| U93#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → activate#(V1) |
| U32#(tt, V) → activate#(V) | U11#(tt, V1) → activate#(V1) |
| U41#(tt, V1, V2) → activate#(V2) | U11#(tt, V1) → isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) | isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(M) | U134#(tt, IL, M, N) → activate#(IL) |
| U113#(tt, L, N) → activate#(N) | U43#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U135#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V1) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → activate#(V1) |
| activate#(n__take(X1, X2)) → take#(X1, X2) | isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| take#(0, IL) → isNatIList#(IL) | U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U121#(tt, IL) → isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) → activate#(M) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U104#(tt, V1, V2) → activate#(V2) | U12#(tt, V1) → activate#(V1) |
| U21#(tt, V1) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → isNatKind#(activate(N)) |
| U45#(tt, V2) → activate#(V2) | U95#(tt, V2) → activate#(V2) |
| length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) | U135#(tt, IL, M, N) → activate#(M) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) | U44#(tt, V1, V2) → activate#(V1) |
| U91#(tt, V1, V2) → isNatKind#(activate(V1)) | U101#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | isNat#(n__s(V1)) → activate#(V1) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| isNatIList#(V) → isNatIListKind#(activate(V)) | isNatList#(n__cons(V1, V2)) → activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → activate#(N) | U42#(tt, V1, V2) → activate#(V1) |
| U133#(tt, IL, M, N) → activate#(IL) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → activate#(L) |
| U41#(tt, V1, V2) → activate#(V1) | U42#(tt, V1, V2) → activate#(V2) |
| U103#(tt, V1, V2) → activate#(V1) | U22#(tt, V1) → activate#(V1) |
| U12#(tt, V1) → isNatList#(activate(V1)) | U92#(tt, V1, V2) → activate#(V2) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U136#(tt, IL, M, N) → activate#(N) |
| U111#(tt, L, N) → activate#(N) | isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) |
| isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(M) |
| U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U22#(tt, V1) → isNat#(activate(V1)) |
| U111#(tt, L, N) → activate#(L) | U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(N) | U51#(tt, V2) → isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) → activate#(V2) | U61#(tt, V2) → isNatIListKind#(activate(V2)) |
| U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U133#(tt, IL, M, N) → isNatKind#(activate(M)) |
| U61#(tt, V2) → U62#(isNatIListKind(activate(V2))) | U132#(tt, IL, M, N) → activate#(N) |
| U135#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__take(V1, V2)) → activate#(V2) |
| U104#(tt, V1, V2) → activate#(V1) | U61#(tt, V2) → activate#(V2) |
| isNatIList#(V) → activate#(V) | U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) | U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) → isNat#(activate(V1)) | U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) → activate#(V1) | U104#(tt, V1, V2) → isNat#(activate(V1)) |
| activate#(n__length(X)) → length#(X) | U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U114#(tt, L) → s#(length(activate(L))) | U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → activate#(V1) |
| length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| length#(nil) → 0# | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → activate#(L) | U113#(tt, L, N) → isNatKind#(activate(N)) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) → activate#(M) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U136#(tt, IL, M, N) → activate#(IL) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) → activate#(N) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | U132#(tt, IL, M, N) → activate#(M) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U102#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U131#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U102#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U11#(tt, V1) → activate#(V1) | U41#(tt, V1, V2) → activate#(V2) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) |
| isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(M) |
| U134#(tt, IL, M, N) → activate#(IL) | U113#(tt, L, N) → activate#(N) |
| U43#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V1) |
| U44#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| isNatList#(n__cons(V1, V2)) → activate#(V1) | activate#(n__take(X1, X2)) → take#(X1, X2) |
| isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) | take#(0, IL) → isNatIList#(IL) |
| U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U121#(tt, IL) → isNatIListKind#(activate(IL)) | U136#(tt, IL, M, N) → activate#(M) |
| U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U104#(tt, V1, V2) → activate#(V2) |
| U12#(tt, V1) → activate#(V1) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U45#(tt, V2) → activate#(V2) | U135#(tt, IL, M, N) → isNatKind#(activate(N)) |
| U95#(tt, V2) → activate#(V2) | length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U135#(tt, IL, M, N) → activate#(M) |
| U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) → activate#(V1) | U91#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| isNat#(n__s(V1)) → activate#(V1) | U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) | isNatIList#(V) → isNatIListKind#(activate(V)) |
| isNatList#(n__cons(V1, V2)) → activate#(V2) | isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → activate#(V2) | U42#(tt, V1, V2) → activate#(V1) |
| U112#(tt, L, N) → activate#(N) | U133#(tt, IL, M, N) → activate#(IL) |
| U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) | U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) → activate#(L) | U41#(tt, V1, V2) → activate#(V1) |
| U42#(tt, V1, V2) → activate#(V2) | U103#(tt, V1, V2) → activate#(V1) |
| U22#(tt, V1) → activate#(V1) | U12#(tt, V1) → isNatList#(activate(V1)) |
| U92#(tt, V1, V2) → activate#(V2) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U111#(tt, L, N) → activate#(N) | U136#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) | isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(M) | U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U22#(tt, V1) → isNat#(activate(V1)) | U111#(tt, L, N) → activate#(L) |
| U45#(tt, V2) → U46#(isNatIList(activate(V2))) | U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(N) | U51#(tt, V2) → isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) → activate#(V2) | U61#(tt, V2) → isNatIListKind#(activate(V2)) |
| U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U133#(tt, IL, M, N) → isNatKind#(activate(M)) |
| U135#(tt, IL, M, N) → activate#(N) | U132#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V2) | U104#(tt, V1, V2) → activate#(V1) |
| U61#(tt, V2) → activate#(V2) | isNatIList#(V) → activate#(V) |
| U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(0, IL) → U121#(isNatIList(IL), IL) |
| U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) | isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) | U94#(tt, V1, V2) → isNat#(activate(V1)) |
| U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) | U43#(tt, V1, V2) → activate#(V1) |
| U104#(tt, V1, V2) → isNat#(activate(V1)) | activate#(n__length(X)) → length#(X) |
| U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | U114#(tt, L) → s#(length(activate(L))) |
| U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V1) | length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | length#(nil) → 0# |
| U111#(tt, L, N) → isNatIListKind#(activate(L)) | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | U113#(tt, L, N) → activate#(L) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) → activate#(M) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U136#(tt, IL, M, N) → activate#(IL) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) → activate#(N) | U132#(tt, IL, M, N) → activate#(M) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U102#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U131#(tt, IL, M, N) → activate#(IL) |
| U114#(tt, L) → length#(activate(L)) | U91#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U102#(tt, V1, V2) → activate#(V2) |
| U32#(tt, V) → U33#(isNatList(activate(V))) | U112#(tt, L, N) → isNat#(activate(N)) |
| U93#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → activate#(V1) |
| U32#(tt, V) → activate#(V) | U11#(tt, V1) → activate#(V1) |
| U41#(tt, V1, V2) → activate#(V2) | U11#(tt, V1) → isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) | isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(M) | U134#(tt, IL, M, N) → activate#(IL) |
| U113#(tt, L, N) → activate#(N) | U43#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U135#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V1) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → activate#(V1) |
| activate#(n__take(X1, X2)) → take#(X1, X2) | isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| take#(0, IL) → isNatIList#(IL) | U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U121#(tt, IL) → isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) → activate#(M) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U104#(tt, V1, V2) → activate#(V2) | U12#(tt, V1) → activate#(V1) |
| U21#(tt, V1) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → isNatKind#(activate(N)) |
| U45#(tt, V2) → activate#(V2) | U95#(tt, V2) → activate#(V2) |
| length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) | U135#(tt, IL, M, N) → activate#(M) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) | U44#(tt, V1, V2) → activate#(V1) |
| U91#(tt, V1, V2) → isNatKind#(activate(V1)) | U101#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | isNat#(n__s(V1)) → activate#(V1) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| isNatIList#(V) → isNatIListKind#(activate(V)) | isNatList#(n__cons(V1, V2)) → activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → activate#(N) | U42#(tt, V1, V2) → activate#(V1) |
| U133#(tt, IL, M, N) → activate#(IL) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → activate#(L) |
| U41#(tt, V1, V2) → activate#(V1) | U42#(tt, V1, V2) → activate#(V2) |
| U103#(tt, V1, V2) → activate#(V1) | U22#(tt, V1) → activate#(V1) |
| U12#(tt, V1) → isNatList#(activate(V1)) | U92#(tt, V1, V2) → activate#(V2) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U136#(tt, IL, M, N) → activate#(N) |
| U111#(tt, L, N) → activate#(N) | isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) |
| isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(M) |
| U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U22#(tt, V1) → isNat#(activate(V1)) |
| U111#(tt, L, N) → activate#(L) | U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(N) | U51#(tt, V2) → isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) → activate#(V2) | U61#(tt, V2) → isNatIListKind#(activate(V2)) |
| U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U133#(tt, IL, M, N) → isNatKind#(activate(M)) |
| U132#(tt, IL, M, N) → activate#(N) | U135#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V2) | U104#(tt, V1, V2) → activate#(V1) |
| U61#(tt, V2) → activate#(V2) | isNatIList#(V) → activate#(V) |
| U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(0, IL) → U121#(isNatIList(IL), IL) |
| U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) | isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) | U94#(tt, V1, V2) → isNat#(activate(V1)) |
| U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) | U43#(tt, V1, V2) → activate#(V1) |
| U104#(tt, V1, V2) → isNat#(activate(V1)) | activate#(n__length(X)) → length#(X) |
| U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | U114#(tt, L) → s#(length(activate(L))) |
| U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V1) | length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| length#(nil) → 0# | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → activate#(L) | U113#(tt, L, N) → isNatKind#(activate(N)) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| length#(cons(N, L)) → isNatList#(activate(L)) | U134#(tt, IL, M, N) → activate#(M) |
| isNatList#(n__take(V1, V2)) → activate#(V2) | U136#(tt, IL, M, N) → activate#(IL) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) → activate#(N) | U132#(tt, IL, M, N) → activate#(M) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V1) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U93#(tt, V1, V2) → activate#(V1) | U102#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(N) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U131#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V2) |
| U122#(tt) → nil# | U102#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U112#(tt, L, N) → isNat#(activate(N)) |
| U93#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → activate#(V1) |
| U11#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U41#(tt, V1, V2) → activate#(V2) | U95#(tt, V2) → U96#(isNatList(activate(V2))) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) |
| isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(M) |
| U134#(tt, IL, M, N) → activate#(IL) | U113#(tt, L, N) → activate#(N) |
| U43#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V1) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → activate#(V1) | activate#(n__take(X1, X2)) → take#(X1, X2) |
| isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) | take#(0, IL) → isNatIList#(IL) |
| U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U121#(tt, IL) → isNatIListKind#(activate(IL)) | U136#(tt, IL, M, N) → activate#(M) |
| U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U104#(tt, V1, V2) → activate#(V2) |
| U12#(tt, V1) → activate#(V1) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → isNatKind#(activate(N)) | U45#(tt, V2) → activate#(V2) |
| U95#(tt, V2) → activate#(V2) | length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) |
| U135#(tt, IL, M, N) → activate#(M) | U45#(tt, V2) → isNatIList#(activate(V2)) |
| U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) → activate#(V1) | U91#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| isNat#(n__s(V1)) → activate#(V1) | U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) | isNatIList#(V) → isNatIListKind#(activate(V)) |
| isNatList#(n__cons(V1, V2)) → activate#(V2) | isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → activate#(V2) | U112#(tt, L, N) → activate#(N) |
| U42#(tt, V1, V2) → activate#(V1) | U133#(tt, IL, M, N) → activate#(IL) |
| U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) | U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) → activate#(L) | U41#(tt, V1, V2) → activate#(V1) |
| U42#(tt, V1, V2) → activate#(V2) | U103#(tt, V1, V2) → activate#(V1) |
| U22#(tt, V1) → activate#(V1) | U12#(tt, V1) → isNatList#(activate(V1)) |
| U92#(tt, V1, V2) → activate#(V2) | U121#(tt, IL) → U122#(isNatIListKind(activate(IL))) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U111#(tt, L, N) → activate#(N) |
| U136#(tt, IL, M, N) → activate#(N) | U22#(tt, V1) → U23#(isNat(activate(V1))) |
| isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) | isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(M) | U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U22#(tt, V1) → isNat#(activate(V1)) | U111#(tt, L, N) → activate#(L) |
| U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(N) |
| U51#(tt, V2) → isNatIListKind#(activate(V2)) | U101#(tt, V1, V2) → activate#(V2) |
| U61#(tt, V2) → isNatIListKind#(activate(V2)) | U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) → isNatKind#(activate(M)) | U132#(tt, IL, M, N) → activate#(N) |
| U135#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__take(V1, V2)) → activate#(V2) |
| U104#(tt, V1, V2) → activate#(V1) | U61#(tt, V2) → activate#(V2) |
| isNatIList#(V) → activate#(V) | U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) | U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) → isNat#(activate(V1)) | U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) → activate#(V1) | U104#(tt, V1, V2) → isNat#(activate(V1)) |
| activate#(n__length(X)) → length#(X) | U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U114#(tt, L) → s#(length(activate(L))) | U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → activate#(V1) |
| length#(cons(N, L)) → activate#(L) |
| U132#(tt, IL, M, N) → isNat#(activate(M)) | take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| U44#(tt, V1, V2) → isNat#(activate(V1)) | U105#(tt, V2) → isNatIList#(activate(V2)) |
| U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U113#(tt, L, N) → activate#(L) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U134#(tt, IL, M, N) → activate#(M) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U136#(tt, IL, M, N) → activate#(IL) | U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U95#(tt, V2) → isNatList#(activate(V2)) | U134#(tt, IL, M, N) → activate#(N) |
| U132#(tt, IL, M, N) → activate#(M) | U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(s(M), cons(N, IL)) → activate#(IL) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| U114#(tt, L) → activate#(L) | isNat#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V2) | U92#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) | isNatKind#(n__length(V1)) → activate#(V1) |
| isNatKind#(n__s(V1)) → activate#(V1) | U32#(tt, V) → isNatList#(activate(V)) |
| U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U102#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → activate#(V1) | U105#(tt, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U31#(tt, V) → activate#(V) | U132#(tt, IL, M, N) → activate#(IL) |
| U114#(tt, L) → length#(activate(L)) | U131#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V2) | U102#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U112#(tt, L, N) → isNat#(activate(N)) |
| U93#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → activate#(V1) |
| U11#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U41#(tt, V1, V2) → activate#(V2) | U11#(tt, V1) → isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) | isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(M) | U134#(tt, IL, M, N) → activate#(IL) |
| U113#(tt, L, N) → activate#(N) | U43#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U135#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V1) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → activate#(V1) |
| activate#(n__take(X1, X2)) → take#(X1, X2) | isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| take#(0, IL) → isNatIList#(IL) | U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U121#(tt, IL) → isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) → activate#(M) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U12#(tt, V1) → activate#(V1) | U104#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → isNatKind#(activate(N)) |
| U45#(tt, V2) → activate#(V2) | U95#(tt, V2) → activate#(V2) |
| length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) | U135#(tt, IL, M, N) → activate#(M) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) | U44#(tt, V1, V2) → activate#(V1) |
| U91#(tt, V1, V2) → isNatKind#(activate(V1)) | U101#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | isNat#(n__s(V1)) → activate#(V1) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U105#(tt, V2) → U106#(isNatIList(activate(V2))) |
| U41#(tt, V1, V2) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) | isNatList#(n__cons(V1, V2)) → activate#(V2) |
| isNatIList#(V) → isNatIListKind#(activate(V)) | isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → activate#(V2) | U42#(tt, V1, V2) → activate#(V1) |
| U112#(tt, L, N) → activate#(N) | U133#(tt, IL, M, N) → activate#(IL) |
| U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) | U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) → activate#(L) | U41#(tt, V1, V2) → activate#(V1) |
| U42#(tt, V1, V2) → activate#(V2) | U103#(tt, V1, V2) → activate#(V1) |
| U22#(tt, V1) → activate#(V1) | U12#(tt, V1) → isNatList#(activate(V1)) |
| U92#(tt, V1, V2) → activate#(V2) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U111#(tt, L, N) → activate#(N) | U136#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) | isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(M) | U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U22#(tt, V1) → isNat#(activate(V1)) | U111#(tt, L, N) → activate#(L) |
| U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(N) |
| U51#(tt, V2) → isNatIListKind#(activate(V2)) | U101#(tt, V1, V2) → activate#(V2) |
| U61#(tt, V2) → isNatIListKind#(activate(V2)) | U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) → isNatKind#(activate(M)) | U132#(tt, IL, M, N) → activate#(N) |
| U135#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__take(V1, V2)) → activate#(V2) |
| U104#(tt, V1, V2) → activate#(V1) | U61#(tt, V2) → activate#(V2) |
| isNatIList#(V) → activate#(V) | U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) | U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) → isNat#(activate(V1)) | U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) → activate#(V1) | U104#(tt, V1, V2) → isNat#(activate(V1)) |
| activate#(n__length(X)) → length#(X) | U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V1) | length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | length#(nil) → 0# |
| U111#(tt, L, N) → isNatIListKind#(activate(L)) | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | U113#(tt, L, N) → activate#(L) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) → activate#(M) | length#(cons(N, L)) → isNatList#(activate(L)) |
| isNatList#(n__take(V1, V2)) → activate#(V2) | U136#(tt, IL, M, N) → activate#(IL) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) → activate#(N) | U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U132#(tt, IL, M, N) → activate#(M) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U102#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U131#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U102#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U11#(tt, V1) → activate#(V1) | U41#(tt, V1, V2) → activate#(V2) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) |
| isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(M) |
| U134#(tt, IL, M, N) → activate#(IL) | U113#(tt, L, N) → activate#(N) |
| U43#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V1) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → activate#(V1) | activate#(n__take(X1, X2)) → take#(X1, X2) |
| isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) | take#(0, IL) → isNatIList#(IL) |
| U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U121#(tt, IL) → isNatIListKind#(activate(IL)) | U136#(tt, IL, M, N) → activate#(M) |
| U104#(tt, V1, V2) → activate#(V2) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U12#(tt, V1) → activate#(V1) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → isNatKind#(activate(N)) | U45#(tt, V2) → activate#(V2) |
| U95#(tt, V2) → activate#(V2) | length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) |
| U135#(tt, IL, M, N) → activate#(M) | U45#(tt, V2) → isNatIList#(activate(V2)) |
| U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) → activate#(V1) | U91#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U105#(tt, V2) → U106#(isNatIList(activate(V2))) |
| U41#(tt, V1, V2) → isNatKind#(activate(V1)) | isNat#(n__s(V1)) → activate#(V1) |
| U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| isNatList#(n__cons(V1, V2)) → activate#(V2) | isNatIList#(V) → isNatIListKind#(activate(V)) |
| isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → activate#(N) | U42#(tt, V1, V2) → activate#(V1) |
| U133#(tt, IL, M, N) → activate#(IL) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → activate#(L) |
| U41#(tt, V1, V2) → activate#(V1) | U42#(tt, V1, V2) → activate#(V2) |
| U103#(tt, V1, V2) → activate#(V1) | U22#(tt, V1) → activate#(V1) |
| U92#(tt, V1, V2) → activate#(V2) | U12#(tt, V1) → isNatList#(activate(V1)) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U136#(tt, IL, M, N) → activate#(N) |
| U111#(tt, L, N) → activate#(N) | isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) |
| isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(M) |
| U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U22#(tt, V1) → isNat#(activate(V1)) |
| U111#(tt, L, N) → activate#(L) | U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(N) | U51#(tt, V2) → isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) → activate#(V2) | U61#(tt, V2) → isNatIListKind#(activate(V2)) |
| U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U133#(tt, IL, M, N) → isNatKind#(activate(M)) |
| U135#(tt, IL, M, N) → activate#(N) | U132#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V2) | U104#(tt, V1, V2) → activate#(V1) |
| U61#(tt, V2) → activate#(V2) | isNatIList#(V) → activate#(V) |
| U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(0, IL) → U121#(isNatIList(IL), IL) |
| U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) | isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) | U94#(tt, V1, V2) → isNat#(activate(V1)) |
| U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) | U43#(tt, V1, V2) → activate#(V1) |
| U104#(tt, V1, V2) → isNat#(activate(V1)) | activate#(n__length(X)) → length#(X) |
| U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | U114#(tt, L) → s#(length(activate(L))) |
| U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V1) | length#(cons(N, L)) → activate#(L) |
| U132#(tt, IL, M, N) → isNat#(activate(M)) | take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| length#(nil) → 0# | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | U113#(tt, L, N) → activate#(L) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| length#(cons(N, L)) → isNatList#(activate(L)) | U134#(tt, IL, M, N) → activate#(M) |
| isNatList#(n__take(V1, V2)) → activate#(V2) | U136#(tt, IL, M, N) → activate#(IL) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) → activate#(N) | U132#(tt, IL, M, N) → activate#(M) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V1) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U102#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(N) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U131#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V2) |
| U122#(tt) → nil# | U102#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U112#(tt, L, N) → isNat#(activate(N)) |
| U93#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → activate#(V1) |
| U11#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U41#(tt, V1, V2) → activate#(V2) | U11#(tt, V1) → isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) | isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(M) | U134#(tt, IL, M, N) → activate#(IL) |
| U113#(tt, L, N) → activate#(N) | U43#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U135#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V1) | U44#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | isNatList#(n__cons(V1, V2)) → activate#(V1) |
| activate#(n__take(X1, X2)) → take#(X1, X2) | isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| take#(0, IL) → isNatIList#(IL) | U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U121#(tt, IL) → isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) → activate#(M) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U104#(tt, V1, V2) → activate#(V2) | U12#(tt, V1) → activate#(V1) |
| U21#(tt, V1) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → isNatKind#(activate(N)) |
| U45#(tt, V2) → activate#(V2) | U95#(tt, V2) → activate#(V2) |
| length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) | U135#(tt, IL, M, N) → activate#(M) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) | U44#(tt, V1, V2) → activate#(V1) |
| U91#(tt, V1, V2) → isNatKind#(activate(V1)) | U101#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U105#(tt, V2) → U106#(isNatIList(activate(V2))) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| isNat#(n__s(V1)) → activate#(V1) | U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) | isNatIList#(V) → isNatIListKind#(activate(V)) |
| isNatList#(n__cons(V1, V2)) → activate#(V2) | isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → activate#(V2) | U112#(tt, L, N) → activate#(N) |
| U42#(tt, V1, V2) → activate#(V1) | U133#(tt, IL, M, N) → activate#(IL) |
| U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) | U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) → activate#(L) | U41#(tt, V1, V2) → activate#(V1) |
| U42#(tt, V1, V2) → activate#(V2) | U103#(tt, V1, V2) → activate#(V1) |
| U22#(tt, V1) → activate#(V1) | U12#(tt, V1) → isNatList#(activate(V1)) |
| U92#(tt, V1, V2) → activate#(V2) | U121#(tt, IL) → U122#(isNatIListKind(activate(IL))) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U111#(tt, L, N) → activate#(N) |
| U136#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) |
| isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(M) |
| U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U22#(tt, V1) → isNat#(activate(V1)) |
| U111#(tt, L, N) → activate#(L) | U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(N) | U51#(tt, V2) → isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) → activate#(V2) | U61#(tt, V2) → isNatIListKind#(activate(V2)) |
| U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U133#(tt, IL, M, N) → isNatKind#(activate(M)) |
| U132#(tt, IL, M, N) → activate#(N) | U135#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V2) | U104#(tt, V1, V2) → activate#(V1) |
| U61#(tt, V2) → activate#(V2) | isNatIList#(V) → activate#(V) |
| U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(0, IL) → U121#(isNatIList(IL), IL) |
| U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) | isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) | U94#(tt, V1, V2) → isNat#(activate(V1)) |
| U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) | U43#(tt, V1, V2) → activate#(V1) |
| U104#(tt, V1, V2) → isNat#(activate(V1)) | activate#(n__length(X)) → length#(X) |
| U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | U114#(tt, L) → s#(length(activate(L))) |
| U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V1) | length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | U12#(tt, V1) → U13#(isNatList(activate(V1))) |
| isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) | U94#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → activate#(V1) | U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V1) | U121#(tt, IL) → activate#(IL) |
| U94#(tt, V1, V2) → activate#(V1) | U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) |
| U51#(tt, V2) → activate#(V2) | U31#(tt, V) → isNatIListKind#(activate(V)) |
| isNat#(n__length(V1)) → activate#(V1) | isNatIListKind#(n__cons(V1, V2)) → activate#(V2) |
| U111#(tt, L, N) → isNatIListKind#(activate(L)) | length#(nil) → 0# |
| U44#(tt, V1, V2) → isNat#(activate(V1)) | U105#(tt, V2) → isNatIList#(activate(V2)) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | U113#(tt, L, N) → activate#(L) |
| U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U134#(tt, IL, M, N) → activate#(M) | U136#(tt, IL, M, N) → activate#(IL) |
| isNatList#(n__take(V1, V2)) → activate#(V2) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → activate#(N) |
| U132#(tt, IL, M, N) → activate#(M) | U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(s(M), cons(N, IL)) → activate#(IL) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| U114#(tt, L) → activate#(L) | isNat#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V2) | U92#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) | isNatKind#(n__length(V1)) → activate#(V1) |
| isNatKind#(n__s(V1)) → activate#(V1) | U32#(tt, V) → isNatList#(activate(V)) |
| U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U93#(tt, V1, V2) → activate#(V1) |
| U102#(tt, V1, V2) → activate#(V1) | U105#(tt, V2) → activate#(V2) |
| U131#(tt, IL, M, N) → activate#(N) | isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U31#(tt, V) → activate#(V) | U132#(tt, IL, M, N) → activate#(IL) |
| U131#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U91#(tt, V1, V2) → activate#(V2) | U122#(tt) → nil# |
| U102#(tt, V1, V2) → activate#(V2) | U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U11#(tt, V1) → activate#(V1) |
| U32#(tt, V) → activate#(V) | U41#(tt, V1, V2) → activate#(V2) |
| U95#(tt, V2) → U96#(isNatList(activate(V2))) | U11#(tt, V1) → isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) | isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(M) | U134#(tt, IL, M, N) → activate#(IL) |
| U113#(tt, L, N) → activate#(N) | U43#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U135#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V1) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → activate#(V1) |
| activate#(n__take(X1, X2)) → take#(X1, X2) | isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| take#(0, IL) → isNatIList#(IL) | U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U121#(tt, IL) → isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) → activate#(M) | U12#(tt, V1) → activate#(V1) |
| U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U104#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → isNatKind#(activate(N)) |
| U45#(tt, V2) → activate#(V2) | U95#(tt, V2) → activate#(V2) |
| length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) | U135#(tt, IL, M, N) → activate#(M) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) | U44#(tt, V1, V2) → activate#(V1) |
| U91#(tt, V1, V2) → isNatKind#(activate(V1)) | U101#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | isNat#(n__s(V1)) → activate#(V1) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U105#(tt, V2) → U106#(isNatIList(activate(V2))) |
| U41#(tt, V1, V2) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) | isNatIList#(V) → isNatIListKind#(activate(V)) |
| isNatList#(n__cons(V1, V2)) → activate#(V2) | isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → activate#(V2) | U112#(tt, L, N) → activate#(N) |
| U42#(tt, V1, V2) → activate#(V1) | U133#(tt, IL, M, N) → activate#(IL) |
| U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) | U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) → activate#(L) | U41#(tt, V1, V2) → activate#(V1) |
| U42#(tt, V1, V2) → activate#(V2) | U103#(tt, V1, V2) → activate#(V1) |
| U22#(tt, V1) → activate#(V1) | U12#(tt, V1) → isNatList#(activate(V1)) |
| U92#(tt, V1, V2) → activate#(V2) | U121#(tt, IL) → U122#(isNatIListKind(activate(IL))) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U111#(tt, L, N) → activate#(N) |
| U136#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) |
| isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(M) |
| U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U22#(tt, V1) → isNat#(activate(V1)) |
| U111#(tt, L, N) → activate#(L) | U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(N) | U51#(tt, V2) → isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) → activate#(V2) | U61#(tt, V2) → isNatIListKind#(activate(V2)) |
| U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U133#(tt, IL, M, N) → isNatKind#(activate(M)) |
| U132#(tt, IL, M, N) → activate#(N) | U135#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V2) | U104#(tt, V1, V2) → activate#(V1) |
| U61#(tt, V2) → activate#(V2) | isNatIList#(V) → activate#(V) |
| U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(0, IL) → U121#(isNatIList(IL), IL) |
| U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) | isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) | U94#(tt, V1, V2) → isNat#(activate(V1)) |
| U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) | U43#(tt, V1, V2) → activate#(V1) |
| U104#(tt, V1, V2) → isNat#(activate(V1)) | activate#(n__length(X)) → length#(X) |
| U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → activate#(V1) |
| length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| length#(nil) → 0# | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | U113#(tt, L, N) → activate#(L) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| length#(cons(N, L)) → isNatList#(activate(L)) | U134#(tt, IL, M, N) → activate#(M) |
| isNatList#(n__take(V1, V2)) → activate#(V2) | U136#(tt, IL, M, N) → activate#(IL) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) → activate#(N) | U132#(tt, IL, M, N) → activate#(M) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V1) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U102#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(N) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U131#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V2) |
| U122#(tt) → nil# | U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) |
| U102#(tt, V1, V2) → activate#(V2) | U32#(tt, V) → U33#(isNatList(activate(V))) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U11#(tt, V1) → activate#(V1) |
| U32#(tt, V) → activate#(V) | U41#(tt, V1, V2) → activate#(V2) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) |
| isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(M) |
| U134#(tt, IL, M, N) → activate#(IL) | U113#(tt, L, N) → activate#(N) |
| U43#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V1) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → activate#(V1) | activate#(n__take(X1, X2)) → take#(X1, X2) |
| isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) | take#(0, IL) → isNatIList#(IL) |
| U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U121#(tt, IL) → isNatIListKind#(activate(IL)) | U136#(tt, IL, M, N) → activate#(M) |
| U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U104#(tt, V1, V2) → activate#(V2) |
| U12#(tt, V1) → activate#(V1) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → isNatKind#(activate(N)) | U45#(tt, V2) → activate#(V2) |
| U95#(tt, V2) → activate#(V2) | length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) |
| U135#(tt, IL, M, N) → activate#(M) | U45#(tt, V2) → isNatIList#(activate(V2)) |
| U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) → activate#(V1) | U91#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U105#(tt, V2) → U106#(isNatIList(activate(V2))) |
| U41#(tt, V1, V2) → isNatKind#(activate(V1)) | isNat#(n__s(V1)) → activate#(V1) |
| U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| isNatIList#(V) → isNatIListKind#(activate(V)) | isNatList#(n__cons(V1, V2)) → activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → activate#(N) | U42#(tt, V1, V2) → activate#(V1) |
| U133#(tt, IL, M, N) → activate#(IL) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → activate#(L) |
| U41#(tt, V1, V2) → activate#(V1) | U42#(tt, V1, V2) → activate#(V2) |
| U103#(tt, V1, V2) → activate#(V1) | U22#(tt, V1) → activate#(V1) |
| U12#(tt, V1) → isNatList#(activate(V1)) | U92#(tt, V1, V2) → activate#(V2) |
| U121#(tt, IL) → U122#(isNatIListKind(activate(IL))) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U111#(tt, L, N) → activate#(N) | U136#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) | isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(M) | U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U22#(tt, V1) → isNat#(activate(V1)) | U111#(tt, L, N) → activate#(L) |
| U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(N) |
| U51#(tt, V2) → isNatIListKind#(activate(V2)) | U101#(tt, V1, V2) → activate#(V2) |
| U61#(tt, V2) → isNatIListKind#(activate(V2)) | U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) → isNatKind#(activate(M)) | U132#(tt, IL, M, N) → activate#(N) |
| U135#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__take(V1, V2)) → activate#(V2) |
| U104#(tt, V1, V2) → activate#(V1) | U61#(tt, V2) → activate#(V2) |
| isNatIList#(V) → activate#(V) | U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) | U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) → isNat#(activate(V1)) | U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) → activate#(V1) | U104#(tt, V1, V2) → isNat#(activate(V1)) |
| activate#(n__length(X)) → length#(X) | U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U114#(tt, L) → s#(length(activate(L))) | U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → activate#(V1) |
| length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U31#(tt, V) → isNatIListKind#(activate(V)) |
| U51#(tt, V2) → activate#(V2) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | length#(nil) → 0# |
| U111#(tt, L, N) → isNatIListKind#(activate(L)) | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | U113#(tt, L, N) → activate#(L) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) → activate#(M) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U136#(tt, IL, M, N) → activate#(IL) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) → activate#(N) | U132#(tt, IL, M, N) → activate#(M) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V1) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U102#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U131#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V2) |
| U122#(tt) → nil# | U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) |
| U102#(tt, V1, V2) → activate#(V2) | U32#(tt, V) → U33#(isNatList(activate(V))) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U11#(tt, V1) → activate#(V1) | U41#(tt, V1, V2) → activate#(V2) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) |
| isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(M) |
| U134#(tt, IL, M, N) → activate#(IL) | U113#(tt, L, N) → activate#(N) |
| U43#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V1) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → activate#(V1) | activate#(n__take(X1, X2)) → take#(X1, X2) |
| isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) | take#(0, IL) → isNatIList#(IL) |
| U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U121#(tt, IL) → isNatIListKind#(activate(IL)) | U136#(tt, IL, M, N) → activate#(M) |
| U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U104#(tt, V1, V2) → activate#(V2) |
| U12#(tt, V1) → activate#(V1) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → isNatKind#(activate(N)) | U45#(tt, V2) → activate#(V2) |
| U95#(tt, V2) → activate#(V2) | length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) |
| U135#(tt, IL, M, N) → activate#(M) | U45#(tt, V2) → isNatIList#(activate(V2)) |
| U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) → activate#(V1) | U91#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNat#(n__s(V1)) → activate#(V1) | U134#(tt, IL, M, N) → isNat#(activate(N)) |
| U41#(tt, V1, V2) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) | isNatIList#(V) → isNatIListKind#(activate(V)) |
| isNatList#(n__cons(V1, V2)) → activate#(V2) | isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → activate#(V2) | U112#(tt, L, N) → activate#(N) |
| U42#(tt, V1, V2) → activate#(V1) | U133#(tt, IL, M, N) → activate#(IL) |
| U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) | U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) → activate#(L) | U41#(tt, V1, V2) → activate#(V1) |
| U42#(tt, V1, V2) → activate#(V2) | U103#(tt, V1, V2) → activate#(V1) |
| U22#(tt, V1) → activate#(V1) | U12#(tt, V1) → isNatList#(activate(V1)) |
| U92#(tt, V1, V2) → activate#(V2) | U121#(tt, IL) → U122#(isNatIListKind(activate(IL))) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U136#(tt, IL, M, N) → activate#(N) |
| U111#(tt, L, N) → activate#(N) | isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) |
| isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(M) |
| U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U22#(tt, V1) → isNat#(activate(V1)) |
| U111#(tt, L, N) → activate#(L) | U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(N) | U51#(tt, V2) → isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) → activate#(V2) | U61#(tt, V2) → isNatIListKind#(activate(V2)) |
| U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U133#(tt, IL, M, N) → isNatKind#(activate(M)) |
| U132#(tt, IL, M, N) → activate#(N) | U135#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V2) | U104#(tt, V1, V2) → activate#(V1) |
| isNatIList#(V) → activate#(V) | U61#(tt, V2) → activate#(V2) |
| U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(0, IL) → U121#(isNatIList(IL), IL) |
| U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) | isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) | U94#(tt, V1, V2) → isNat#(activate(V1)) |
| U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) | U43#(tt, V1, V2) → activate#(V1) |
| U104#(tt, V1, V2) → isNat#(activate(V1)) | activate#(n__length(X)) → length#(X) |
| U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | U114#(tt, L) → s#(length(activate(L))) |
| U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V1) | length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| length#(nil) → 0# | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | U113#(tt, L, N) → activate#(L) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| length#(cons(N, L)) → isNatList#(activate(L)) | U134#(tt, IL, M, N) → activate#(M) |
| isNatList#(n__take(V1, V2)) → activate#(V2) | U136#(tt, IL, M, N) → activate#(IL) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) → activate#(N) | U132#(tt, IL, M, N) → activate#(M) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V1) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U102#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(N) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U131#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V2) |
| U122#(tt) → nil# | U102#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U112#(tt, L, N) → isNat#(activate(N)) |
| U93#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → activate#(V1) |
| U11#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U41#(tt, V1, V2) → activate#(V2) | U11#(tt, V1) → isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) | isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(M) | U134#(tt, IL, M, N) → activate#(IL) |
| U113#(tt, L, N) → activate#(N) | U43#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U135#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V1) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → activate#(V1) |
| activate#(n__take(X1, X2)) → take#(X1, X2) | isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| take#(0, IL) → isNatIList#(IL) | U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U121#(tt, IL) → isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) → activate#(M) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U104#(tt, V1, V2) → activate#(V2) | U12#(tt, V1) → activate#(V1) |
| U21#(tt, V1) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → isNatKind#(activate(N)) |
| U45#(tt, V2) → activate#(V2) | U95#(tt, V2) → activate#(V2) |
| length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) | U135#(tt, IL, M, N) → activate#(M) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) | U44#(tt, V1, V2) → activate#(V1) |
| U91#(tt, V1, V2) → isNatKind#(activate(V1)) | U101#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | isNat#(n__s(V1)) → activate#(V1) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U105#(tt, V2) → U106#(isNatIList(activate(V2))) |
| U41#(tt, V1, V2) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) | isNatIList#(V) → isNatIListKind#(activate(V)) |
| isNatList#(n__cons(V1, V2)) → activate#(V2) | isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → activate#(V2) | U112#(tt, L, N) → activate#(N) |
| U42#(tt, V1, V2) → activate#(V1) | U133#(tt, IL, M, N) → activate#(IL) |
| U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) | U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) → activate#(L) | U41#(tt, V1, V2) → activate#(V1) |
| U42#(tt, V1, V2) → activate#(V2) | U103#(tt, V1, V2) → activate#(V1) |
| U22#(tt, V1) → activate#(V1) | U12#(tt, V1) → isNatList#(activate(V1)) |
| U92#(tt, V1, V2) → activate#(V2) | U121#(tt, IL) → U122#(isNatIListKind(activate(IL))) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U111#(tt, L, N) → activate#(N) |
| U22#(tt, V1) → U23#(isNat(activate(V1))) | U136#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) | isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(M) | U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U22#(tt, V1) → isNat#(activate(V1)) | U111#(tt, L, N) → activate#(L) |
| U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(N) |
| U51#(tt, V2) → isNatIListKind#(activate(V2)) | U101#(tt, V1, V2) → activate#(V2) |
| U61#(tt, V2) → isNatIListKind#(activate(V2)) | U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) → isNatKind#(activate(M)) | U132#(tt, IL, M, N) → activate#(N) |
| U135#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__take(V1, V2)) → activate#(V2) |
| U104#(tt, V1, V2) → activate#(V1) | U61#(tt, V2) → activate#(V2) |
| isNatIList#(V) → activate#(V) | U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) | U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) → isNat#(activate(V1)) | U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) → activate#(V1) | U104#(tt, V1, V2) → isNat#(activate(V1)) |
| activate#(n__length(X)) → length#(X) | U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U114#(tt, L) → s#(length(activate(L))) | U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → activate#(V1) |
| length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | length#(nil) → 0# |
| U111#(tt, L, N) → isNatIListKind#(activate(L)) | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | U113#(tt, L, N) → activate#(L) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) → activate#(M) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U136#(tt, IL, M, N) → activate#(IL) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) → activate#(N) | U132#(tt, IL, M, N) → activate#(M) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U102#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U131#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U102#(tt, V1, V2) → activate#(V2) |
| U32#(tt, V) → U33#(isNatList(activate(V))) | U112#(tt, L, N) → isNat#(activate(N)) |
| U93#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → activate#(V1) |
| U32#(tt, V) → activate#(V) | U11#(tt, V1) → activate#(V1) |
| U41#(tt, V1, V2) → activate#(V2) | U11#(tt, V1) → isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) | isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(M) | U134#(tt, IL, M, N) → activate#(IL) |
| U113#(tt, L, N) → activate#(N) | U43#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U135#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V1) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → activate#(V1) |
| activate#(n__take(X1, X2)) → take#(X1, X2) | isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| take#(0, IL) → isNatIList#(IL) | U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U121#(tt, IL) → isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) → activate#(M) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U104#(tt, V1, V2) → activate#(V2) | U12#(tt, V1) → activate#(V1) |
| U21#(tt, V1) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → isNatKind#(activate(N)) |
| U45#(tt, V2) → activate#(V2) | U95#(tt, V2) → activate#(V2) |
| length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) | U135#(tt, IL, M, N) → activate#(M) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) | U44#(tt, V1, V2) → activate#(V1) |
| U91#(tt, V1, V2) → isNatKind#(activate(V1)) | U101#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | isNat#(n__s(V1)) → activate#(V1) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| isNatIList#(V) → isNatIListKind#(activate(V)) | isNatList#(n__cons(V1, V2)) → activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → activate#(N) | U42#(tt, V1, V2) → activate#(V1) |
| U133#(tt, IL, M, N) → activate#(IL) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → activate#(L) |
| U41#(tt, V1, V2) → activate#(V1) | U42#(tt, V1, V2) → activate#(V2) |
| U103#(tt, V1, V2) → activate#(V1) | U22#(tt, V1) → activate#(V1) |
| U12#(tt, V1) → isNatList#(activate(V1)) | U92#(tt, V1, V2) → activate#(V2) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U136#(tt, IL, M, N) → activate#(N) |
| U22#(tt, V1) → U23#(isNat(activate(V1))) | U111#(tt, L, N) → activate#(N) |
| isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) | isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(M) | U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U22#(tt, V1) → isNat#(activate(V1)) | U111#(tt, L, N) → activate#(L) |
| U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(N) |
| U51#(tt, V2) → isNatIListKind#(activate(V2)) | U101#(tt, V1, V2) → activate#(V2) |
| U61#(tt, V2) → isNatIListKind#(activate(V2)) | U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) → isNatKind#(activate(M)) | U132#(tt, IL, M, N) → activate#(N) |
| U135#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__take(V1, V2)) → activate#(V2) |
| U104#(tt, V1, V2) → activate#(V1) | U61#(tt, V2) → activate#(V2) |
| isNatIList#(V) → activate#(V) | U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) | U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) → isNat#(activate(V1)) | U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) → activate#(V1) | U104#(tt, V1, V2) → isNat#(activate(V1)) |
| activate#(n__length(X)) → length#(X) | U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U114#(tt, L) → s#(length(activate(L))) | U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → activate#(V1) |
| length#(cons(N, L)) → activate#(L) |
| U132#(tt, IL, M, N) → isNat#(activate(M)) | take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| U44#(tt, V1, V2) → isNat#(activate(V1)) | U105#(tt, V2) → isNatIList#(activate(V2)) |
| U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U113#(tt, L, N) → activate#(L) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U134#(tt, IL, M, N) → activate#(M) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U136#(tt, IL, M, N) → activate#(IL) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → activate#(N) |
| U132#(tt, IL, M, N) → activate#(M) | U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(s(M), cons(N, IL)) → activate#(IL) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| U114#(tt, L) → activate#(L) | isNat#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V2) | U92#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) | isNatKind#(n__length(V1)) → activate#(V1) |
| isNatKind#(n__s(V1)) → activate#(V1) | U32#(tt, V) → isNatList#(activate(V)) |
| U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U102#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → activate#(V1) | U105#(tt, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U31#(tt, V) → activate#(V) | U132#(tt, IL, M, N) → activate#(IL) |
| U114#(tt, L) → length#(activate(L)) | U131#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V2) | U102#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U112#(tt, L, N) → isNat#(activate(N)) |
| U93#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → activate#(V1) |
| U11#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U41#(tt, V1, V2) → activate#(V2) | U95#(tt, V2) → U96#(isNatList(activate(V2))) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) |
| isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(M) |
| U134#(tt, IL, M, N) → activate#(IL) | U113#(tt, L, N) → activate#(N) |
| U43#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V1) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → activate#(V1) | activate#(n__take(X1, X2)) → take#(X1, X2) |
| isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) | take#(0, IL) → isNatIList#(IL) |
| U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U121#(tt, IL) → isNatIListKind#(activate(IL)) | U136#(tt, IL, M, N) → activate#(M) |
| U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U12#(tt, V1) → activate#(V1) |
| U104#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → isNatKind#(activate(N)) | U45#(tt, V2) → activate#(V2) |
| U95#(tt, V2) → activate#(V2) | length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) |
| U135#(tt, IL, M, N) → activate#(M) | U45#(tt, V2) → isNatIList#(activate(V2)) |
| U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) → activate#(V1) | U91#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNat#(n__s(V1)) → activate#(V1) | U134#(tt, IL, M, N) → isNat#(activate(N)) |
| U105#(tt, V2) → U106#(isNatIList(activate(V2))) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| isNatList#(n__cons(V1, V2)) → activate#(V2) | isNatIList#(V) → isNatIListKind#(activate(V)) |
| isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → activate#(V2) |
| U42#(tt, V1, V2) → activate#(V1) | U112#(tt, L, N) → activate#(N) |
| U133#(tt, IL, M, N) → activate#(IL) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → activate#(L) |
| U41#(tt, V1, V2) → activate#(V1) | U42#(tt, V1, V2) → activate#(V2) |
| U103#(tt, V1, V2) → activate#(V1) | U22#(tt, V1) → activate#(V1) |
| U12#(tt, V1) → isNatList#(activate(V1)) | U92#(tt, V1, V2) → activate#(V2) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U111#(tt, L, N) → activate#(N) |
| U136#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) |
| isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(M) |
| U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U22#(tt, V1) → isNat#(activate(V1)) |
| U111#(tt, L, N) → activate#(L) | U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(N) | U51#(tt, V2) → isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) → activate#(V2) | U61#(tt, V2) → isNatIListKind#(activate(V2)) |
| U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U133#(tt, IL, M, N) → isNatKind#(activate(M)) |
| U132#(tt, IL, M, N) → activate#(N) | U135#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V2) | U104#(tt, V1, V2) → activate#(V1) |
| U61#(tt, V2) → activate#(V2) | isNatIList#(V) → activate#(V) |
| U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(0, IL) → U121#(isNatIList(IL), IL) |
| U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) | isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) | U94#(tt, V1, V2) → isNat#(activate(V1)) |
| U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) | U43#(tt, V1, V2) → activate#(V1) |
| U104#(tt, V1, V2) → isNat#(activate(V1)) | activate#(n__length(X)) → length#(X) |
| U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → activate#(V1) |
| length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| length#(nil) → 0# | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → activate#(L) | U113#(tt, L, N) → isNatKind#(activate(N)) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) → activate#(M) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U136#(tt, IL, M, N) → activate#(IL) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U95#(tt, V2) → isNatList#(activate(V2)) | U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) → activate#(N) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | U132#(tt, IL, M, N) → activate#(M) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U93#(tt, V1, V2) → activate#(V1) | U102#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U131#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U102#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U11#(tt, V1) → activate#(V1) | U41#(tt, V1, V2) → activate#(V2) |
| U95#(tt, V2) → U96#(isNatList(activate(V2))) | U11#(tt, V1) → isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) | isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(M) | U134#(tt, IL, M, N) → activate#(IL) |
| U113#(tt, L, N) → activate#(N) | U43#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U135#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V1) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → activate#(V1) |
| activate#(n__take(X1, X2)) → take#(X1, X2) | isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| take#(0, IL) → isNatIList#(IL) | U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U121#(tt, IL) → isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) → activate#(M) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U104#(tt, V1, V2) → activate#(V2) | U12#(tt, V1) → activate#(V1) |
| U21#(tt, V1) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → isNatKind#(activate(N)) |
| U45#(tt, V2) → activate#(V2) | U95#(tt, V2) → activate#(V2) |
| length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) | U135#(tt, IL, M, N) → activate#(M) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) | U44#(tt, V1, V2) → activate#(V1) |
| U91#(tt, V1, V2) → isNatKind#(activate(V1)) | U101#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | isNat#(n__s(V1)) → activate#(V1) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| isNatList#(n__cons(V1, V2)) → activate#(V2) | isNatIList#(V) → isNatIListKind#(activate(V)) |
| isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → activate#(N) | U42#(tt, V1, V2) → activate#(V1) |
| U133#(tt, IL, M, N) → activate#(IL) | U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) | U112#(tt, L, N) → activate#(L) |
| U41#(tt, V1, V2) → activate#(V1) | U42#(tt, V1, V2) → activate#(V2) |
| U103#(tt, V1, V2) → activate#(V1) | U22#(tt, V1) → activate#(V1) |
| U92#(tt, V1, V2) → activate#(V2) | U12#(tt, V1) → isNatList#(activate(V1)) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U111#(tt, L, N) → activate#(N) |
| U136#(tt, IL, M, N) → activate#(N) | isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) | U133#(tt, IL, M, N) → activate#(M) |
| U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U22#(tt, V1) → isNat#(activate(V1)) |
| U111#(tt, L, N) → activate#(L) | U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(N) | U51#(tt, V2) → isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) → activate#(V2) | U61#(tt, V2) → isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) → isNatKind#(activate(M)) | U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U135#(tt, IL, M, N) → activate#(N) | U132#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V2) | U104#(tt, V1, V2) → activate#(V1) |
| U61#(tt, V2) → activate#(V2) | isNatIList#(V) → activate#(V) |
| U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(0, IL) → U121#(isNatIList(IL), IL) |
| U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) | isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) | U94#(tt, V1, V2) → isNat#(activate(V1)) |
| U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) | U43#(tt, V1, V2) → activate#(V1) |
| U104#(tt, V1, V2) → isNat#(activate(V1)) | activate#(n__length(X)) → length#(X) |
| U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | U114#(tt, L) → s#(length(activate(L))) |
| U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V1) | length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| U44#(tt, V1, V2) → isNat#(activate(V1)) | U105#(tt, V2) → isNatIList#(activate(V2)) |
| U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U113#(tt, L, N) → activate#(L) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U134#(tt, IL, M, N) → activate#(M) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U136#(tt, IL, M, N) → activate#(IL) | U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U95#(tt, V2) → isNatList#(activate(V2)) | U134#(tt, IL, M, N) → activate#(N) |
| U132#(tt, IL, M, N) → activate#(M) | U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(s(M), cons(N, IL)) → activate#(IL) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| U114#(tt, L) → activate#(L) | isNat#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V2) | U92#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) | isNatKind#(n__length(V1)) → activate#(V1) |
| isNatKind#(n__s(V1)) → activate#(V1) | U32#(tt, V) → isNatList#(activate(V)) |
| U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U93#(tt, V1, V2) → activate#(V1) |
| U102#(tt, V1, V2) → activate#(V1) | U105#(tt, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U31#(tt, V) → activate#(V) | U132#(tt, IL, M, N) → activate#(IL) |
| U114#(tt, L) → length#(activate(L)) | U131#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V2) | U122#(tt) → nil# |
| U102#(tt, V1, V2) → activate#(V2) | U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U11#(tt, V1) → activate#(V1) |
| U32#(tt, V) → activate#(V) | U41#(tt, V1, V2) → activate#(V2) |
| U95#(tt, V2) → U96#(isNatList(activate(V2))) | U11#(tt, V1) → isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) | isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(M) | U134#(tt, IL, M, N) → activate#(IL) |
| U113#(tt, L, N) → activate#(N) | U43#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U135#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V1) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → activate#(V1) |
| activate#(n__take(X1, X2)) → take#(X1, X2) | isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| take#(0, IL) → isNatIList#(IL) | U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U121#(tt, IL) → isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) → activate#(M) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U104#(tt, V1, V2) → activate#(V2) | U12#(tt, V1) → activate#(V1) |
| U21#(tt, V1) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → isNatKind#(activate(N)) |
| U45#(tt, V2) → activate#(V2) | U95#(tt, V2) → activate#(V2) |
| length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) | U135#(tt, IL, M, N) → activate#(M) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) | U44#(tt, V1, V2) → activate#(V1) |
| U91#(tt, V1, V2) → isNatKind#(activate(V1)) | U101#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U134#(tt, IL, M, N) → isNat#(activate(N)) |
| U41#(tt, V1, V2) → isNatKind#(activate(V1)) | isNat#(n__s(V1)) → activate#(V1) |
| U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| isNatIList#(V) → isNatIListKind#(activate(V)) | isNatList#(n__cons(V1, V2)) → activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → activate#(N) | U42#(tt, V1, V2) → activate#(V1) |
| U133#(tt, IL, M, N) → activate#(IL) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → activate#(L) |
| U41#(tt, V1, V2) → activate#(V1) | U42#(tt, V1, V2) → activate#(V2) |
| U103#(tt, V1, V2) → activate#(V1) | U22#(tt, V1) → activate#(V1) |
| U12#(tt, V1) → isNatList#(activate(V1)) | U92#(tt, V1, V2) → activate#(V2) |
| U121#(tt, IL) → U122#(isNatIListKind(activate(IL))) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U111#(tt, L, N) → activate#(N) | U136#(tt, IL, M, N) → activate#(N) |
| U22#(tt, V1) → U23#(isNat(activate(V1))) | isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) |
| isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(M) |
| U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U22#(tt, V1) → isNat#(activate(V1)) |
| U111#(tt, L, N) → activate#(L) | U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(N) | U51#(tt, V2) → isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) → activate#(V2) | U61#(tt, V2) → isNatIListKind#(activate(V2)) |
| U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U133#(tt, IL, M, N) → isNatKind#(activate(M)) |
| U132#(tt, IL, M, N) → activate#(N) | U135#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V2) | U104#(tt, V1, V2) → activate#(V1) |
| U61#(tt, V2) → activate#(V2) | isNatIList#(V) → activate#(V) |
| U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(0, IL) → U121#(isNatIList(IL), IL) |
| U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) | isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) | U94#(tt, V1, V2) → isNat#(activate(V1)) |
| U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) | U43#(tt, V1, V2) → activate#(V1) |
| U104#(tt, V1, V2) → isNat#(activate(V1)) | activate#(n__length(X)) → length#(X) |
| U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → activate#(V1) |
| length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | U12#(tt, V1) → U13#(isNatList(activate(V1))) |
| isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) | U94#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → activate#(V1) | U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V1) | U121#(tt, IL) → activate#(IL) |
| U94#(tt, V1, V2) → activate#(V1) | U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) |
| U51#(tt, V2) → activate#(V2) | U31#(tt, V) → isNatIListKind#(activate(V)) |
| isNat#(n__length(V1)) → activate#(V1) | isNatIListKind#(n__cons(V1, V2)) → activate#(V2) |
| U111#(tt, L, N) → isNatIListKind#(activate(L)) | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U113#(tt, L, N) → isNatKind#(activate(N)) |
| U113#(tt, L, N) → activate#(L) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) → activate#(M) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U136#(tt, IL, M, N) → activate#(IL) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U95#(tt, V2) → isNatList#(activate(V2)) | U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) → activate#(N) | U132#(tt, IL, M, N) → activate#(M) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V1) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U93#(tt, V1, V2) → activate#(V1) | U102#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U131#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V2) |
| U122#(tt) → nil# | U102#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U112#(tt, L, N) → isNat#(activate(N)) |
| U93#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → activate#(V1) |
| U11#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U41#(tt, V1, V2) → activate#(V2) | U95#(tt, V2) → U96#(isNatList(activate(V2))) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) |
| isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(M) |
| U134#(tt, IL, M, N) → activate#(IL) | U113#(tt, L, N) → activate#(N) |
| U43#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V1) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → activate#(V1) | activate#(n__take(X1, X2)) → take#(X1, X2) |
| isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) | take#(0, IL) → isNatIList#(IL) |
| U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U121#(tt, IL) → isNatIListKind#(activate(IL)) | U136#(tt, IL, M, N) → activate#(M) |
| U12#(tt, V1) → activate#(V1) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U104#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → isNatKind#(activate(N)) | U45#(tt, V2) → activate#(V2) |
| U95#(tt, V2) → activate#(V2) | length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) |
| U135#(tt, IL, M, N) → activate#(M) | U45#(tt, V2) → isNatIList#(activate(V2)) |
| U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) → activate#(V1) | U91#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNat#(n__s(V1)) → activate#(V1) | U134#(tt, IL, M, N) → isNat#(activate(N)) |
| U105#(tt, V2) → U106#(isNatIList(activate(V2))) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| isNatIList#(V) → isNatIListKind#(activate(V)) | isNatList#(n__cons(V1, V2)) → activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → activate#(N) | U42#(tt, V1, V2) → activate#(V1) |
| U133#(tt, IL, M, N) → activate#(IL) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → activate#(L) |
| U41#(tt, V1, V2) → activate#(V1) | U42#(tt, V1, V2) → activate#(V2) |
| U103#(tt, V1, V2) → activate#(V1) | U22#(tt, V1) → activate#(V1) |
| U12#(tt, V1) → isNatList#(activate(V1)) | U92#(tt, V1, V2) → activate#(V2) |
| U121#(tt, IL) → U122#(isNatIListKind(activate(IL))) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U111#(tt, L, N) → activate#(N) | U136#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) | isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(M) | U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U22#(tt, V1) → isNat#(activate(V1)) | U111#(tt, L, N) → activate#(L) |
| U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(N) |
| U51#(tt, V2) → isNatIListKind#(activate(V2)) | U101#(tt, V1, V2) → activate#(V2) |
| U61#(tt, V2) → isNatIListKind#(activate(V2)) | U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) → isNatKind#(activate(M)) | U132#(tt, IL, M, N) → activate#(N) |
| U135#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__take(V1, V2)) → activate#(V2) |
| U104#(tt, V1, V2) → activate#(V1) | U61#(tt, V2) → activate#(V2) |
| isNatIList#(V) → activate#(V) | U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) | U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) → isNat#(activate(V1)) | U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) → activate#(V1) | U104#(tt, V1, V2) → isNat#(activate(V1)) |
| activate#(n__length(X)) → length#(X) | U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V1) | length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| length#(nil) → 0# | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → activate#(L) | U113#(tt, L, N) → isNatKind#(activate(N)) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) → activate#(M) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U136#(tt, IL, M, N) → activate#(IL) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) → activate#(N) | U132#(tt, IL, M, N) → activate#(M) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U102#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U131#(tt, IL, M, N) → activate#(IL) |
| U114#(tt, L) → length#(activate(L)) | U91#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U102#(tt, V1, V2) → activate#(V2) |
| U32#(tt, V) → U33#(isNatList(activate(V))) | U112#(tt, L, N) → isNat#(activate(N)) |
| U93#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → activate#(V1) |
| U32#(tt, V) → activate#(V) | U11#(tt, V1) → activate#(V1) |
| U41#(tt, V1, V2) → activate#(V2) | U11#(tt, V1) → isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) | isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(M) | U134#(tt, IL, M, N) → activate#(IL) |
| U113#(tt, L, N) → activate#(N) | U43#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U135#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V1) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → activate#(V1) |
| activate#(n__take(X1, X2)) → take#(X1, X2) | isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| take#(0, IL) → isNatIList#(IL) | U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U121#(tt, IL) → isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) → activate#(M) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U104#(tt, V1, V2) → activate#(V2) | U12#(tt, V1) → activate#(V1) |
| U21#(tt, V1) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → isNatKind#(activate(N)) |
| U45#(tt, V2) → activate#(V2) | U95#(tt, V2) → activate#(V2) |
| length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) | U135#(tt, IL, M, N) → activate#(M) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) | U44#(tt, V1, V2) → activate#(V1) |
| U91#(tt, V1, V2) → isNatKind#(activate(V1)) | U101#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U134#(tt, IL, M, N) → isNat#(activate(N)) |
| U105#(tt, V2) → U106#(isNatIList(activate(V2))) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| isNat#(n__s(V1)) → activate#(V1) | U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) | isNatIList#(V) → isNatIListKind#(activate(V)) |
| isNatList#(n__cons(V1, V2)) → activate#(V2) | isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → activate#(V2) | U112#(tt, L, N) → activate#(N) |
| U42#(tt, V1, V2) → activate#(V1) | U133#(tt, IL, M, N) → activate#(IL) |
| U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) | U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) → activate#(L) | U41#(tt, V1, V2) → activate#(V1) |
| U42#(tt, V1, V2) → activate#(V2) | U103#(tt, V1, V2) → activate#(V1) |
| U22#(tt, V1) → activate#(V1) | U12#(tt, V1) → isNatList#(activate(V1)) |
| U92#(tt, V1, V2) → activate#(V2) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U111#(tt, L, N) → activate#(N) | U136#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) | isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(M) | U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U22#(tt, V1) → isNat#(activate(V1)) | U111#(tt, L, N) → activate#(L) |
| U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(N) |
| U51#(tt, V2) → isNatIListKind#(activate(V2)) | U101#(tt, V1, V2) → activate#(V2) |
| U61#(tt, V2) → isNatIListKind#(activate(V2)) | U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) → isNatKind#(activate(M)) | U132#(tt, IL, M, N) → activate#(N) |
| U135#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__take(V1, V2)) → activate#(V2) |
| U104#(tt, V1, V2) → activate#(V1) | U61#(tt, V2) → activate#(V2) |
| isNatIList#(V) → activate#(V) | U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) | U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) → isNat#(activate(V1)) | U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) → activate#(V1) | U104#(tt, V1, V2) → isNat#(activate(V1)) |
| activate#(n__length(X)) → length#(X) | U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U114#(tt, L) → s#(length(activate(L))) | U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → activate#(V1) |
| length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | U51#(tt, V2) → U52#(isNatIListKind(activate(V2))) |
| isNatList#(n__take(V1, V2)) → activate#(V1) | U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V1) | U121#(tt, IL) → activate#(IL) |
| U94#(tt, V1, V2) → activate#(V1) | U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) |
| U51#(tt, V2) → activate#(V2) | U31#(tt, V) → isNatIListKind#(activate(V)) |
| isNat#(n__length(V1)) → activate#(V1) | isNatIListKind#(n__cons(V1, V2)) → activate#(V2) |
| U111#(tt, L, N) → isNatIListKind#(activate(L)) | length#(nil) → 0# |
| U44#(tt, V1, V2) → isNat#(activate(V1)) | U105#(tt, V2) → isNatIList#(activate(V2)) |
| U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U113#(tt, L, N) → isNatKind#(activate(N)) |
| U113#(tt, L, N) → activate#(L) | isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U134#(tt, IL, M, N) → activate#(M) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U136#(tt, IL, M, N) → activate#(IL) | U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U95#(tt, V2) → isNatList#(activate(V2)) | U134#(tt, IL, M, N) → activate#(N) |
| U132#(tt, IL, M, N) → activate#(M) | U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(s(M), cons(N, IL)) → activate#(IL) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| U114#(tt, L) → activate#(L) | isNat#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V2) | U92#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) | isNatKind#(n__length(V1)) → activate#(V1) |
| isNatKind#(n__s(V1)) → activate#(V1) | U32#(tt, V) → isNatList#(activate(V)) |
| U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U102#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → activate#(V1) | U105#(tt, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U31#(tt, V) → activate#(V) | U132#(tt, IL, M, N) → activate#(IL) |
| U114#(tt, L) → length#(activate(L)) | U131#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V2) | U122#(tt) → nil# |
| U102#(tt, V1, V2) → activate#(V2) | U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U11#(tt, V1) → activate#(V1) |
| U32#(tt, V) → activate#(V) | U41#(tt, V1, V2) → activate#(V2) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) |
| isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(M) |
| U134#(tt, IL, M, N) → activate#(IL) | U113#(tt, L, N) → activate#(N) |
| U43#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V1) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → activate#(V1) | activate#(n__take(X1, X2)) → take#(X1, X2) |
| isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) | take#(0, IL) → isNatIList#(IL) |
| U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U121#(tt, IL) → isNatIListKind#(activate(IL)) | U136#(tt, IL, M, N) → activate#(M) |
| U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U104#(tt, V1, V2) → activate#(V2) |
| U12#(tt, V1) → activate#(V1) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → isNatKind#(activate(N)) | U45#(tt, V2) → activate#(V2) |
| U95#(tt, V2) → activate#(V2) | length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) |
| U135#(tt, IL, M, N) → activate#(M) | U45#(tt, V2) → isNatIList#(activate(V2)) |
| U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) → activate#(V1) | U91#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U105#(tt, V2) → U106#(isNatIList(activate(V2))) |
| U41#(tt, V1, V2) → isNatKind#(activate(V1)) | isNat#(n__s(V1)) → activate#(V1) |
| U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| isNatIList#(V) → isNatIListKind#(activate(V)) | isNatList#(n__cons(V1, V2)) → activate#(V2) |
| isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → activate#(N) | U42#(tt, V1, V2) → activate#(V1) |
| U133#(tt, IL, M, N) → activate#(IL) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → activate#(L) |
| U41#(tt, V1, V2) → activate#(V1) | U42#(tt, V1, V2) → activate#(V2) |
| U103#(tt, V1, V2) → activate#(V1) | U22#(tt, V1) → activate#(V1) |
| U12#(tt, V1) → isNatList#(activate(V1)) | U92#(tt, V1, V2) → activate#(V2) |
| U121#(tt, IL) → U122#(isNatIListKind(activate(IL))) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U111#(tt, L, N) → activate#(N) | U136#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) | isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(M) | U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U22#(tt, V1) → isNat#(activate(V1)) | U111#(tt, L, N) → activate#(L) |
| U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(N) |
| U51#(tt, V2) → isNatIListKind#(activate(V2)) | U101#(tt, V1, V2) → activate#(V2) |
| U61#(tt, V2) → isNatIListKind#(activate(V2)) | U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) → isNatKind#(activate(M)) | U132#(tt, IL, M, N) → activate#(N) |
| U135#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__take(V1, V2)) → activate#(V2) |
| U104#(tt, V1, V2) → activate#(V1) | U61#(tt, V2) → activate#(V2) |
| isNatIList#(V) → activate#(V) | U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) | U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) → isNat#(activate(V1)) | U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) → activate#(V1) | U104#(tt, V1, V2) → isNat#(activate(V1)) |
| activate#(n__length(X)) → length#(X) | U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U114#(tt, L) → s#(length(activate(L))) | U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → activate#(V1) |
| length#(cons(N, L)) → activate#(L) |
Problem 2: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| take#(s(M), cons(N, IL)) | → | isNatIList#(activate(IL)) | | U132#(tt, IL, M, N) | → | isNat#(activate(M)) |
| U101#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | isNatIList#(V) | → | U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) | → | activate#(V2) | | isNatList#(n__take(V1, V2)) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | U105#(isNat(activate(V1)), activate(V2)) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V1) |
| U121#(tt, IL) | → | activate#(IL) | | U94#(tt, V1, V2) | → | activate#(V1) |
| U131#(tt, IL, M, N) | → | U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U134#(tt, IL, M, N) | → | U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) | → | U61#(isNatKind(activate(V1)), activate(V2)) | | U31#(tt, V) | → | isNatIListKind#(activate(V)) |
| U51#(tt, V2) | → | activate#(V2) | | isNat#(n__length(V1)) | → | activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V2) | | length#(nil) | → | 0# |
| U111#(tt, L, N) | → | isNatIListKind#(activate(L)) | | U44#(tt, V1, V2) | → | isNat#(activate(V1)) |
| U105#(tt, V2) | → | isNatIList#(activate(V2)) | | U113#(tt, L, N) | → | activate#(L) |
| U113#(tt, L, N) | → | isNatKind#(activate(N)) | | U92#(tt, V1, V2) | → | U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | take#(s(M), cons(N, IL)) | → | U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| length#(cons(N, L)) | → | isNatList#(activate(L)) | | U134#(tt, IL, M, N) | → | activate#(M) |
| isNatList#(n__take(V1, V2)) | → | activate#(V2) | | U136#(tt, IL, M, N) | → | activate#(IL) |
| U133#(tt, IL, M, N) | → | U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U95#(tt, V2) | → | isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) | → | activate#(N) | | U132#(tt, IL, M, N) | → | activate#(M) |
| U132#(tt, IL, M, N) | → | U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | | isNatIList#(n__cons(V1, V2)) | → | U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(s(M), cons(N, IL)) | → | activate#(IL) | | isNatKind#(n__s(V1)) | → | isNatKind#(activate(V1)) |
| isNatIListKind#(n__cons(V1, V2)) | → | activate#(V1) | | U114#(tt, L) | → | activate#(L) |
| isNat#(n__s(V1)) | → | isNatKind#(activate(V1)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V2) |
| U92#(tt, V1, V2) | → | activate#(V1) | | U93#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) | → | activate#(V1) | | isNatKind#(n__s(V1)) | → | activate#(V1) |
| U32#(tt, V) | → | isNatList#(activate(V)) | | U102#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | activate#(V1) | | U102#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U105#(tt, V2) | → | activate#(V2) | | U131#(tt, IL, M, N) | → | activate#(N) |
| isNatList#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) | | U103#(tt, V1, V2) | → | U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNatList#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U31#(tt, V) | → | activate#(V) |
| U132#(tt, IL, M, N) | → | activate#(IL) | | U131#(tt, IL, M, N) | → | activate#(IL) |
| U114#(tt, L) | → | length#(activate(L)) | | U91#(tt, V1, V2) | → | activate#(V2) |
| U122#(tt) | → | nil# | | U31#(tt, V) | → | U32#(isNatIListKind(activate(V)), activate(V)) |
| U102#(tt, V1, V2) | → | activate#(V2) | | U112#(tt, L, N) | → | isNat#(activate(N)) |
| U93#(tt, V1, V2) | → | activate#(V2) | | U21#(tt, V1) | → | activate#(V1) |
| U32#(tt, V) | → | activate#(V) | | U11#(tt, V1) | → | activate#(V1) |
| U41#(tt, V1, V2) | → | activate#(V2) | | U11#(tt, V1) | → | isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) | → | cons#(activate(N), n__take(activate(M), activate(IL))) | | U131#(tt, IL, M, N) | → | activate#(M) |
| isNatIListKind#(n__take(V1, V2)) | → | isNatKind#(activate(V1)) | | U134#(tt, IL, M, N) | → | activate#(IL) |
| U113#(tt, L, N) | → | activate#(N) | | U43#(tt, V1, V2) | → | activate#(V2) |
| isNatList#(n__take(V1, V2)) | → | U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U135#(tt, IL, M, N) | → | activate#(IL) |
| U91#(tt, V1, V2) | → | activate#(V1) | | U44#(tt, V1, V2) | → | activate#(V2) |
| U21#(tt, V1) | → | U22#(isNatKind(activate(V1)), activate(V1)) | | isNatList#(n__cons(V1, V2)) | → | activate#(V1) |
| activate#(n__take(X1, X2)) | → | take#(X1, X2) | | isNat#(n__length(V1)) | → | isNatIListKind#(activate(V1)) |
| U43#(tt, V1, V2) | → | U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U42#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| take#(0, IL) | → | isNatIList#(IL) | | U121#(tt, IL) | → | isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) | → | activate#(M) | | U12#(tt, V1) | → | activate#(V1) |
| U104#(tt, V1, V2) | → | activate#(V2) | | U101#(tt, V1, V2) | → | U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U21#(tt, V1) | → | isNatKind#(activate(V1)) | | U45#(tt, V2) | → | activate#(V2) |
| U135#(tt, IL, M, N) | → | isNatKind#(activate(N)) | | U95#(tt, V2) | → | activate#(V2) |
| length#(cons(N, L)) | → | U111#(isNatList(activate(L)), activate(L), N) | | U135#(tt, IL, M, N) | → | activate#(M) |
| U45#(tt, V2) | → | isNatIList#(activate(V2)) | | U11#(tt, V1) | → | U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) | → | U45#(isNat(activate(V1)), activate(V2)) | | U44#(tt, V1, V2) | → | activate#(V1) |
| U91#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U101#(tt, V1, V2) | → | activate#(V1) |
| U93#(tt, V1, V2) | → | U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | isNat#(n__s(V1)) | → | activate#(V1) |
| U134#(tt, IL, M, N) | → | isNat#(activate(N)) | | U105#(tt, V2) | → | U106#(isNatIList(activate(V2))) |
| U41#(tt, V1, V2) | → | isNatKind#(activate(V1)) | | U135#(tt, IL, M, N) | → | U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatKind#(n__length(V1)) | → | isNatIListKind#(activate(V1)) | | isNatIList#(V) | → | isNatIListKind#(activate(V)) |
| isNatList#(n__cons(V1, V2)) | → | activate#(V2) | | isNatIListKind#(n__cons(V1, V2)) | → | isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) | → | activate#(V2) | | U112#(tt, L, N) | → | activate#(N) |
| U42#(tt, V1, V2) | → | activate#(V1) | | U133#(tt, IL, M, N) | → | activate#(IL) |
| U112#(tt, L, N) | → | U113#(isNat(activate(N)), activate(L), activate(N)) | | U42#(tt, V1, V2) | → | U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) | → | activate#(L) | | U41#(tt, V1, V2) | → | activate#(V1) |
| U42#(tt, V1, V2) | → | activate#(V2) | | U103#(tt, V1, V2) | → | activate#(V1) |
| U22#(tt, V1) | → | activate#(V1) | | U12#(tt, V1) | → | isNatList#(activate(V1)) |
| U92#(tt, V1, V2) | → | activate#(V2) | | U121#(tt, IL) | → | U122#(isNatIListKind(activate(IL))) |
| isNat#(n__s(V1)) | → | U21#(isNatKind(activate(V1)), activate(V1)) | | U111#(tt, L, N) | → | activate#(N) |
| U22#(tt, V1) | → | U23#(isNat(activate(V1))) | | U136#(tt, IL, M, N) | → | activate#(N) |
| isNatIListKind#(n__cons(V1, V2)) | → | U51#(isNatKind(activate(V1)), activate(V2)) | | isNatList#(n__cons(V1, V2)) | → | U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) | → | activate#(M) | | U103#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U22#(tt, V1) | → | isNat#(activate(V1)) | | U111#(tt, L, N) | → | activate#(L) |
| U102#(tt, V1, V2) | → | U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U133#(tt, IL, M, N) | → | activate#(N) |
| U51#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U101#(tt, V1, V2) | → | activate#(V2) |
| U61#(tt, V2) | → | isNatIListKind#(activate(V2)) | | U92#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) | → | isNatKind#(activate(M)) | | U132#(tt, IL, M, N) | → | activate#(N) |
| U135#(tt, IL, M, N) | → | activate#(N) | | isNatIListKind#(n__take(V1, V2)) | → | activate#(V2) |
| U104#(tt, V1, V2) | → | activate#(V1) | | U61#(tt, V2) | → | activate#(V2) |
| isNatIList#(V) | → | activate#(V) | | U41#(tt, V1, V2) | → | U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) | → | U121#(isNatIList(IL), IL) | | U94#(tt, V1, V2) | → | U95#(isNat(activate(V1)), activate(V2)) |
| isNat#(n__length(V1)) | → | U11#(isNatIListKind(activate(V1)), activate(V1)) | | U131#(tt, IL, M, N) | → | isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) | → | isNat#(activate(V1)) | | U113#(tt, L, N) | → | U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) | → | activate#(V1) | | U104#(tt, V1, V2) | → | isNat#(activate(V1)) |
| activate#(n__length(X)) | → | length#(X) | | U111#(tt, L, N) | → | U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U114#(tt, L) | → | s#(length(activate(L))) | | U43#(tt, V1, V2) | → | isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) | → | U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatIList#(n__cons(V1, V2)) | → | activate#(V1) |
| length#(cons(N, L)) | → | activate#(L) |
Rewrite Rules
| zeros | → | cons(0, n__zeros) | | U101(tt, V1, V2) | → | U102(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U102(tt, V1, V2) | → | U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U103(tt, V1, V2) | → | U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U104(tt, V1, V2) | → | U105(isNat(activate(V1)), activate(V2)) | | U105(tt, V2) | → | U106(isNatIList(activate(V2))) |
| U106(tt) | → | tt | | U11(tt, V1) | → | U12(isNatIListKind(activate(V1)), activate(V1)) |
| U111(tt, L, N) | → | U112(isNatIListKind(activate(L)), activate(L), activate(N)) | | U112(tt, L, N) | → | U113(isNat(activate(N)), activate(L), activate(N)) |
| U113(tt, L, N) | → | U114(isNatKind(activate(N)), activate(L)) | | U114(tt, L) | → | s(length(activate(L))) |
| U12(tt, V1) | → | U13(isNatList(activate(V1))) | | U121(tt, IL) | → | U122(isNatIListKind(activate(IL))) |
| U122(tt) | → | nil | | U13(tt) | → | tt |
| U131(tt, IL, M, N) | → | U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | | U132(tt, IL, M, N) | → | U133(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U133(tt, IL, M, N) | → | U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | | U134(tt, IL, M, N) | → | U135(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| U135(tt, IL, M, N) | → | U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | | U136(tt, IL, M, N) | → | cons(activate(N), n__take(activate(M), activate(IL))) |
| U21(tt, V1) | → | U22(isNatKind(activate(V1)), activate(V1)) | | U22(tt, V1) | → | U23(isNat(activate(V1))) |
| U23(tt) | → | tt | | U31(tt, V) | → | U32(isNatIListKind(activate(V)), activate(V)) |
| U32(tt, V) | → | U33(isNatList(activate(V))) | | U33(tt) | → | tt |
| U41(tt, V1, V2) | → | U42(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U42(tt, V1, V2) | → | U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U43(tt, V1, V2) | → | U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U44(tt, V1, V2) | → | U45(isNat(activate(V1)), activate(V2)) |
| U45(tt, V2) | → | U46(isNatIList(activate(V2))) | | U46(tt) | → | tt |
| U51(tt, V2) | → | U52(isNatIListKind(activate(V2))) | | U52(tt) | → | tt |
| U61(tt, V2) | → | U62(isNatIListKind(activate(V2))) | | U62(tt) | → | tt |
| U71(tt) | → | tt | | U81(tt) | → | tt |
| U91(tt, V1, V2) | → | U92(isNatKind(activate(V1)), activate(V1), activate(V2)) | | U92(tt, V1, V2) | → | U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U93(tt, V1, V2) | → | U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | | U94(tt, V1, V2) | → | U95(isNat(activate(V1)), activate(V2)) |
| U95(tt, V2) | → | U96(isNatList(activate(V2))) | | U96(tt) | → | tt |
| isNat(n__0) | → | tt | | isNat(n__length(V1)) | → | U11(isNatIListKind(activate(V1)), activate(V1)) |
| isNat(n__s(V1)) | → | U21(isNatKind(activate(V1)), activate(V1)) | | isNatIList(V) | → | U31(isNatIListKind(activate(V)), activate(V)) |
| isNatIList(n__zeros) | → | tt | | isNatIList(n__cons(V1, V2)) | → | U41(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIListKind(n__nil) | → | tt | | isNatIListKind(n__zeros) | → | tt |
| isNatIListKind(n__cons(V1, V2)) | → | U51(isNatKind(activate(V1)), activate(V2)) | | isNatIListKind(n__take(V1, V2)) | → | U61(isNatKind(activate(V1)), activate(V2)) |
| isNatKind(n__0) | → | tt | | isNatKind(n__length(V1)) | → | U71(isNatIListKind(activate(V1))) |
| isNatKind(n__s(V1)) | → | U81(isNatKind(activate(V1))) | | isNatList(n__nil) | → | tt |
| isNatList(n__cons(V1, V2)) | → | U91(isNatKind(activate(V1)), activate(V1), activate(V2)) | | isNatList(n__take(V1, V2)) | → | U101(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| length(nil) | → | 0 | | length(cons(N, L)) | → | U111(isNatList(activate(L)), activate(L), N) |
| take(0, IL) | → | U121(isNatIList(IL), IL) | | take(s(M), cons(N, IL)) | → | U131(isNatIList(activate(IL)), activate(IL), M, N) |
| zeros | → | n__zeros | | take(X1, X2) | → | n__take(X1, X2) |
| 0 | → | n__0 | | length(X) | → | n__length(X) |
| s(X) | → | n__s(X) | | cons(X1, X2) | → | n__cons(X1, X2) |
| nil | → | n__nil | | activate(n__zeros) | → | zeros |
| activate(n__take(X1, X2)) | → | take(X1, X2) | | activate(n__0) | → | 0 |
| activate(n__length(X)) | → | length(X) | | activate(n__s(X)) | → | s(X) |
| activate(n__cons(X1, X2)) | → | cons(X1, X2) | | activate(n__nil) | → | nil |
| activate(X) | → | X |
Original Signature
Termination of terms over the following signature is verified: U104, U105, U106, n__s, U112, activate, U111, U62, U114, U61, U113, n__nil, U23, U21, U22, isNatIList, n__length, isNatKind, U71, n__cons, U122, 0, U121, zeros, U31, U32, U33, isNatIListKind, U96, U94, U95, isNat, U46, U45, U132, U44, n__0, U131, U43, U93, U134, U42, U92, U133, U41, U91, U136, U135, length, n__zeros, cons, n__take, U51, s, isNatList, tt, take, U52, U81, U11, U12, U13, U102, U103, nil, U101
Strategy
The following SCCs where found
| U132#(tt, IL, M, N) → isNat#(activate(M)) | take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | length#(nil) → 0# |
| U111#(tt, L, N) → isNatIListKind#(activate(L)) | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | U113#(tt, L, N) → activate#(L) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) → activate#(M) | length#(cons(N, L)) → isNatList#(activate(L)) |
| isNatList#(n__take(V1, V2)) → activate#(V2) | U136#(tt, IL, M, N) → activate#(IL) |
| U95#(tt, V2) → isNatList#(activate(V2)) | U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U134#(tt, IL, M, N) → activate#(N) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) → activate#(M) | U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U102#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(N) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U131#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U102#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U11#(tt, V1) → activate#(V1) | U41#(tt, V1, V2) → activate#(V2) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(M) | U134#(tt, IL, M, N) → activate#(IL) |
| U113#(tt, L, N) → activate#(N) | U43#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U135#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V1) | U44#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | isNatList#(n__cons(V1, V2)) → activate#(V1) |
| activate#(n__take(X1, X2)) → take#(X1, X2) | isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| take#(0, IL) → isNatIList#(IL) | U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U121#(tt, IL) → isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) → activate#(M) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U12#(tt, V1) → activate#(V1) | U104#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → isNatKind#(activate(N)) |
| U45#(tt, V2) → activate#(V2) | U95#(tt, V2) → activate#(V2) |
| length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) | U45#(tt, V2) → isNatIList#(activate(V2)) |
| U135#(tt, IL, M, N) → activate#(M) | U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) | U44#(tt, V1, V2) → activate#(V1) |
| U91#(tt, V1, V2) → isNatKind#(activate(V1)) | U101#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U134#(tt, IL, M, N) → isNat#(activate(N)) |
| U105#(tt, V2) → U106#(isNatIList(activate(V2))) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| isNat#(n__s(V1)) → activate#(V1) | U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) | isNatList#(n__cons(V1, V2)) → activate#(V2) |
| isNatIList#(V) → isNatIListKind#(activate(V)) | isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → activate#(V2) | U112#(tt, L, N) → activate#(N) |
| U42#(tt, V1, V2) → activate#(V1) | U133#(tt, IL, M, N) → activate#(IL) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U112#(tt, L, N) → activate#(L) | U41#(tt, V1, V2) → activate#(V1) |
| U42#(tt, V1, V2) → activate#(V2) | U103#(tt, V1, V2) → activate#(V1) |
| U22#(tt, V1) → activate#(V1) | U12#(tt, V1) → isNatList#(activate(V1)) |
| U92#(tt, V1, V2) → activate#(V2) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U136#(tt, IL, M, N) → activate#(N) | U111#(tt, L, N) → activate#(N) |
| isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) | isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(M) | U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U22#(tt, V1) → isNat#(activate(V1)) | U111#(tt, L, N) → activate#(L) |
| U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(N) |
| U51#(tt, V2) → isNatIListKind#(activate(V2)) | U101#(tt, V1, V2) → activate#(V2) |
| U61#(tt, V2) → isNatIListKind#(activate(V2)) | U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) → isNatKind#(activate(M)) | U135#(tt, IL, M, N) → activate#(N) |
| U132#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__take(V1, V2)) → activate#(V2) |
| U104#(tt, V1, V2) → activate#(V1) | U61#(tt, V2) → activate#(V2) |
| isNatIList#(V) → activate#(V) | U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) | U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) → isNat#(activate(V1)) | U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) → activate#(V1) | U104#(tt, V1, V2) → isNat#(activate(V1)) |
| activate#(n__length(X)) → length#(X) | U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U114#(tt, L) → s#(length(activate(L))) | U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → activate#(V1) |
| length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| U44#(tt, V1, V2) → isNat#(activate(V1)) | U105#(tt, V2) → isNatIList#(activate(V2)) |
| U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U113#(tt, L, N) → isNatKind#(activate(N)) |
| U113#(tt, L, N) → activate#(L) | isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U134#(tt, IL, M, N) → activate#(M) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U136#(tt, IL, M, N) → activate#(IL) | U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U95#(tt, V2) → isNatList#(activate(V2)) | U134#(tt, IL, M, N) → activate#(N) |
| isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U132#(tt, IL, M, N) → activate#(M) | take#(s(M), cons(N, IL)) → activate#(IL) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V1) | isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) |
| U114#(tt, L) → activate#(L) | isNat#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V2) | U92#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) | isNatKind#(n__length(V1)) → activate#(V1) |
| isNatKind#(n__s(V1)) → activate#(V1) | U32#(tt, V) → isNatList#(activate(V)) |
| U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U93#(tt, V1, V2) → activate#(V1) |
| U102#(tt, V1, V2) → activate#(V1) | U105#(tt, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U31#(tt, V) → activate#(V) | U132#(tt, IL, M, N) → activate#(IL) |
| U131#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U91#(tt, V1, V2) → activate#(V2) | U102#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U112#(tt, L, N) → isNat#(activate(N)) |
| U93#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → activate#(V1) |
| U11#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U41#(tt, V1, V2) → activate#(V2) | U11#(tt, V1) → isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) | isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(M) | U134#(tt, IL, M, N) → activate#(IL) |
| U113#(tt, L, N) → activate#(N) | U43#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U135#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V1) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → activate#(V1) |
| activate#(n__take(X1, X2)) → take#(X1, X2) | isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| take#(0, IL) → isNatIList#(IL) | U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U121#(tt, IL) → isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) → activate#(M) | U12#(tt, V1) → activate#(V1) |
| U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U104#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → isNatKind#(activate(N)) |
| U45#(tt, V2) → activate#(V2) | U95#(tt, V2) → activate#(V2) |
| length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) | U135#(tt, IL, M, N) → activate#(M) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) | U44#(tt, V1, V2) → activate#(V1) |
| U91#(tt, V1, V2) → isNatKind#(activate(V1)) | U101#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | isNat#(n__s(V1)) → activate#(V1) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| isNatList#(n__cons(V1, V2)) → activate#(V2) | isNatIList#(V) → isNatIListKind#(activate(V)) |
| isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → activate#(N) | U42#(tt, V1, V2) → activate#(V1) |
| U133#(tt, IL, M, N) → activate#(IL) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → activate#(L) |
| U41#(tt, V1, V2) → activate#(V1) | U42#(tt, V1, V2) → activate#(V2) |
| U103#(tt, V1, V2) → activate#(V1) | U22#(tt, V1) → activate#(V1) |
| U12#(tt, V1) → isNatList#(activate(V1)) | U92#(tt, V1, V2) → activate#(V2) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U136#(tt, IL, M, N) → activate#(N) |
| U111#(tt, L, N) → activate#(N) | isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) |
| isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(M) |
| U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U22#(tt, V1) → isNat#(activate(V1)) |
| U111#(tt, L, N) → activate#(L) | U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(N) | U51#(tt, V2) → isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) → activate#(V2) | U61#(tt, V2) → isNatIListKind#(activate(V2)) |
| U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U133#(tt, IL, M, N) → isNatKind#(activate(M)) |
| U132#(tt, IL, M, N) → activate#(N) | U135#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V2) | U104#(tt, V1, V2) → activate#(V1) |
| U61#(tt, V2) → activate#(V2) | isNatIList#(V) → activate#(V) |
| U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(0, IL) → U121#(isNatIList(IL), IL) |
| U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) | isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) | U94#(tt, V1, V2) → isNat#(activate(V1)) |
| U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) | U43#(tt, V1, V2) → activate#(V1) |
| U104#(tt, V1, V2) → isNat#(activate(V1)) | activate#(n__length(X)) → length#(X) |
| U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | U114#(tt, L) → s#(length(activate(L))) |
| U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V1) | length#(cons(N, L)) → activate#(L) |
| U132#(tt, IL, M, N) → isNat#(activate(M)) | take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U94#(tt, V1, V2) → activate#(V1) | U121#(tt, IL) → activate#(IL) |
| U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| length#(nil) → 0# | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → activate#(L) | U113#(tt, L, N) → isNatKind#(activate(N)) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) → activate#(M) | length#(cons(N, L)) → isNatList#(activate(L)) |
| isNatList#(n__take(V1, V2)) → activate#(V2) | U136#(tt, IL, M, N) → activate#(IL) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) → activate#(N) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) → activate#(M) | U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U93#(tt, V1, V2) → activate#(V1) | U102#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(N) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U131#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U102#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U11#(tt, V1) → activate#(V1) | U41#(tt, V1, V2) → activate#(V2) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(M) | U134#(tt, IL, M, N) → activate#(IL) |
| U113#(tt, L, N) → activate#(N) | U43#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U135#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V1) | U44#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | isNatList#(n__cons(V1, V2)) → activate#(V1) |
| activate#(n__take(X1, X2)) → take#(X1, X2) | isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| take#(0, IL) → isNatIList#(IL) | U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U121#(tt, IL) → isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) → activate#(M) | U12#(tt, V1) → activate#(V1) |
| U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U104#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → isNatKind#(activate(N)) |
| U45#(tt, V2) → activate#(V2) | U95#(tt, V2) → activate#(V2) |
| length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) | U45#(tt, V2) → isNatIList#(activate(V2)) |
| U135#(tt, IL, M, N) → activate#(M) | U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) | U44#(tt, V1, V2) → activate#(V1) |
| U91#(tt, V1, V2) → isNatKind#(activate(V1)) | U101#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U134#(tt, IL, M, N) → isNat#(activate(N)) |
| U41#(tt, V1, V2) → isNatKind#(activate(V1)) | isNat#(n__s(V1)) → activate#(V1) |
| U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| isNatList#(n__cons(V1, V2)) → activate#(V2) | isNatIList#(V) → isNatIListKind#(activate(V)) |
| isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → activate#(N) | U42#(tt, V1, V2) → activate#(V1) |
| U133#(tt, IL, M, N) → activate#(IL) | U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) | U112#(tt, L, N) → activate#(L) |
| U41#(tt, V1, V2) → activate#(V1) | U42#(tt, V1, V2) → activate#(V2) |
| U103#(tt, V1, V2) → activate#(V1) | U22#(tt, V1) → activate#(V1) |
| U92#(tt, V1, V2) → activate#(V2) | U12#(tt, V1) → isNatList#(activate(V1)) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U136#(tt, IL, M, N) → activate#(N) |
| U111#(tt, L, N) → activate#(N) | isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) |
| isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(M) |
| U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U22#(tt, V1) → isNat#(activate(V1)) |
| U111#(tt, L, N) → activate#(L) | U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(N) | U51#(tt, V2) → isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) → activate#(V2) | U61#(tt, V2) → isNatIListKind#(activate(V2)) |
| U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U133#(tt, IL, M, N) → isNatKind#(activate(M)) |
| U135#(tt, IL, M, N) → activate#(N) | U132#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V2) | U104#(tt, V1, V2) → activate#(V1) |
| U61#(tt, V2) → activate#(V2) | isNatIList#(V) → activate#(V) |
| U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) | U94#(tt, V1, V2) → isNat#(activate(V1)) |
| U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) | U43#(tt, V1, V2) → activate#(V1) |
| U104#(tt, V1, V2) → isNat#(activate(V1)) | activate#(n__length(X)) → length#(X) |
| U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | U114#(tt, L) → s#(length(activate(L))) |
| U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V1) | length#(cons(N, L)) → activate#(L) |
| U122#(tt) → nil# | U121#(tt, IL) → U122#(isNatIListKind(activate(IL))) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| U44#(tt, V1, V2) → isNat#(activate(V1)) | U105#(tt, V2) → isNatIList#(activate(V2)) |
| U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U113#(tt, L, N) → activate#(L) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U134#(tt, IL, M, N) → activate#(M) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U136#(tt, IL, M, N) → activate#(IL) | U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U95#(tt, V2) → isNatList#(activate(V2)) | U134#(tt, IL, M, N) → activate#(N) |
| isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U132#(tt, IL, M, N) → activate#(M) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | take#(s(M), cons(N, IL)) → activate#(IL) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V1) | isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) |
| U114#(tt, L) → activate#(L) | isNat#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V2) | U92#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) | isNatKind#(n__length(V1)) → activate#(V1) |
| isNatKind#(n__s(V1)) → activate#(V1) | U32#(tt, V) → isNatList#(activate(V)) |
| U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U93#(tt, V1, V2) → activate#(V1) |
| U102#(tt, V1, V2) → activate#(V1) | U105#(tt, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U31#(tt, V) → activate#(V) | U132#(tt, IL, M, N) → activate#(IL) |
| U131#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U91#(tt, V1, V2) → activate#(V2) | U122#(tt) → nil# |
| U102#(tt, V1, V2) → activate#(V2) | U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U11#(tt, V1) → activate#(V1) |
| U32#(tt, V) → activate#(V) | U41#(tt, V1, V2) → activate#(V2) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) |
| isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(M) |
| U134#(tt, IL, M, N) → activate#(IL) | U113#(tt, L, N) → activate#(N) |
| U43#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V1) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → activate#(V1) | activate#(n__take(X1, X2)) → take#(X1, X2) |
| isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) | take#(0, IL) → isNatIList#(IL) |
| U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U121#(tt, IL) → isNatIListKind#(activate(IL)) | U136#(tt, IL, M, N) → activate#(M) |
| U12#(tt, V1) → activate#(V1) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U104#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U45#(tt, V2) → activate#(V2) | U135#(tt, IL, M, N) → isNatKind#(activate(N)) |
| U95#(tt, V2) → activate#(V2) | length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U135#(tt, IL, M, N) → activate#(M) |
| U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) → activate#(V1) | U91#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNat#(n__s(V1)) → activate#(V1) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) | isNatList#(n__cons(V1, V2)) → activate#(V2) |
| isNatIList#(V) → isNatIListKind#(activate(V)) | isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → activate#(V2) | U42#(tt, V1, V2) → activate#(V1) |
| U112#(tt, L, N) → activate#(N) | U133#(tt, IL, M, N) → activate#(IL) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U112#(tt, L, N) → activate#(L) | U41#(tt, V1, V2) → activate#(V1) |
| U42#(tt, V1, V2) → activate#(V2) | U103#(tt, V1, V2) → activate#(V1) |
| U22#(tt, V1) → activate#(V1) | U12#(tt, V1) → isNatList#(activate(V1)) |
| U92#(tt, V1, V2) → activate#(V2) | U121#(tt, IL) → U122#(isNatIListKind(activate(IL))) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U136#(tt, IL, M, N) → activate#(N) |
| U111#(tt, L, N) → activate#(N) | isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) |
| isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(M) |
| U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U22#(tt, V1) → isNat#(activate(V1)) |
| U111#(tt, L, N) → activate#(L) | U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(N) | U51#(tt, V2) → isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) → activate#(V2) | U61#(tt, V2) → isNatIListKind#(activate(V2)) |
| U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U133#(tt, IL, M, N) → isNatKind#(activate(M)) |
| U135#(tt, IL, M, N) → activate#(N) | U132#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V2) | U104#(tt, V1, V2) → activate#(V1) |
| U61#(tt, V2) → activate#(V2) | isNatIList#(V) → activate#(V) |
| U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(0, IL) → U121#(isNatIList(IL), IL) |
| U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) | isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) | U94#(tt, V1, V2) → isNat#(activate(V1)) |
| U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) | U43#(tt, V1, V2) → activate#(V1) |
| U104#(tt, V1, V2) → isNat#(activate(V1)) | activate#(n__length(X)) → length#(X) |
| U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → activate#(V1) |
| length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| U44#(tt, V1, V2) → isNat#(activate(V1)) | U105#(tt, V2) → isNatIList#(activate(V2)) |
| U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U113#(tt, L, N) → activate#(L) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U134#(tt, IL, M, N) → activate#(M) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U136#(tt, IL, M, N) → activate#(IL) | U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U95#(tt, V2) → isNatList#(activate(V2)) | U134#(tt, IL, M, N) → activate#(N) |
| isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U132#(tt, IL, M, N) → activate#(M) | take#(s(M), cons(N, IL)) → activate#(IL) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V1) | isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) |
| U114#(tt, L) → activate#(L) | isNat#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V2) | U92#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) | isNatKind#(n__length(V1)) → activate#(V1) |
| isNatKind#(n__s(V1)) → activate#(V1) | U32#(tt, V) → isNatList#(activate(V)) |
| U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U93#(tt, V1, V2) → activate#(V1) |
| U102#(tt, V1, V2) → activate#(V1) | U105#(tt, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U31#(tt, V) → activate#(V) | U132#(tt, IL, M, N) → activate#(IL) |
| U131#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U91#(tt, V1, V2) → activate#(V2) | U122#(tt) → nil# |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U102#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U11#(tt, V1) → activate#(V1) | U41#(tt, V1, V2) → activate#(V2) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) |
| isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(M) |
| U134#(tt, IL, M, N) → activate#(IL) | U113#(tt, L, N) → activate#(N) |
| U43#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V1) |
| U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → activate#(V1) | activate#(n__take(X1, X2)) → take#(X1, X2) |
| isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) | take#(0, IL) → isNatIList#(IL) |
| U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U121#(tt, IL) → isNatIListKind#(activate(IL)) | U136#(tt, IL, M, N) → activate#(M) |
| U12#(tt, V1) → activate#(V1) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U104#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → isNatKind#(activate(N)) | U45#(tt, V2) → activate#(V2) |
| U95#(tt, V2) → activate#(V2) | length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) |
| U135#(tt, IL, M, N) → activate#(M) | U45#(tt, V2) → isNatIList#(activate(V2)) |
| U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) → activate#(V1) | U91#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNat#(n__s(V1)) → activate#(V1) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) | isNatList#(n__cons(V1, V2)) → activate#(V2) |
| isNatIList#(V) → isNatIListKind#(activate(V)) | isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → activate#(V2) | U42#(tt, V1, V2) → activate#(V1) |
| U112#(tt, L, N) → activate#(N) | U133#(tt, IL, M, N) → activate#(IL) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U112#(tt, L, N) → activate#(L) | U41#(tt, V1, V2) → activate#(V1) |
| U42#(tt, V1, V2) → activate#(V2) | U103#(tt, V1, V2) → activate#(V1) |
| U22#(tt, V1) → activate#(V1) | U12#(tt, V1) → isNatList#(activate(V1)) |
| U92#(tt, V1, V2) → activate#(V2) | U121#(tt, IL) → U122#(isNatIListKind(activate(IL))) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U22#(tt, V1) → U23#(isNat(activate(V1))) |
| U136#(tt, IL, M, N) → activate#(N) | U111#(tt, L, N) → activate#(N) |
| isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) | isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(M) | U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U22#(tt, V1) → isNat#(activate(V1)) | U111#(tt, L, N) → activate#(L) |
| U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(N) |
| U51#(tt, V2) → isNatIListKind#(activate(V2)) | U101#(tt, V1, V2) → activate#(V2) |
| U61#(tt, V2) → isNatIListKind#(activate(V2)) | U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) → isNatKind#(activate(M)) | U132#(tt, IL, M, N) → activate#(N) |
| U135#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__take(V1, V2)) → activate#(V2) |
| U104#(tt, V1, V2) → activate#(V1) | U61#(tt, V2) → activate#(V2) |
| isNatIList#(V) → activate#(V) | U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) | U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) → isNat#(activate(V1)) | U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) → activate#(V1) | U104#(tt, V1, V2) → isNat#(activate(V1)) |
| activate#(n__length(X)) → length#(X) | U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V1) | length#(cons(N, L)) → activate#(L) |
| U132#(tt, IL, M, N) → isNat#(activate(M)) | take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | length#(nil) → 0# |
| U111#(tt, L, N) → isNatIListKind#(activate(L)) | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | U113#(tt, L, N) → activate#(L) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) → activate#(M) | length#(cons(N, L)) → isNatList#(activate(L)) |
| isNatList#(n__take(V1, V2)) → activate#(V2) | U136#(tt, IL, M, N) → activate#(IL) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) → activate#(N) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | U132#(tt, IL, M, N) → activate#(M) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U93#(tt, V1, V2) → activate#(V1) | U102#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(N) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U131#(tt, IL, M, N) → activate#(IL) |
| U114#(tt, L) → length#(activate(L)) | U91#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U102#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U11#(tt, V1) → activate#(V1) | U41#(tt, V1, V2) → activate#(V2) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) |
| isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(M) |
| U134#(tt, IL, M, N) → activate#(IL) | U113#(tt, L, N) → activate#(N) |
| U43#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V1) |
| U44#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| isNatList#(n__cons(V1, V2)) → activate#(V1) | activate#(n__take(X1, X2)) → take#(X1, X2) |
| isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) | take#(0, IL) → isNatIList#(IL) |
| U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U121#(tt, IL) → isNatIListKind#(activate(IL)) | U136#(tt, IL, M, N) → activate#(M) |
| U12#(tt, V1) → activate#(V1) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U104#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → isNatKind#(activate(N)) | U45#(tt, V2) → activate#(V2) |
| U95#(tt, V2) → activate#(V2) | length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U135#(tt, IL, M, N) → activate#(M) |
| U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) → activate#(V1) | U91#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| isNat#(n__s(V1)) → activate#(V1) | U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) | isNatList#(n__cons(V1, V2)) → activate#(V2) |
| isNatIList#(V) → isNatIListKind#(activate(V)) | isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → activate#(V2) | U112#(tt, L, N) → activate#(N) |
| U42#(tt, V1, V2) → activate#(V1) | U133#(tt, IL, M, N) → activate#(IL) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U112#(tt, L, N) → activate#(L) | U41#(tt, V1, V2) → activate#(V1) |
| U42#(tt, V1, V2) → activate#(V2) | U103#(tt, V1, V2) → activate#(V1) |
| U22#(tt, V1) → activate#(V1) | U12#(tt, V1) → isNatList#(activate(V1)) |
| U92#(tt, V1, V2) → activate#(V2) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U136#(tt, IL, M, N) → activate#(N) | U111#(tt, L, N) → activate#(N) |
| U22#(tt, V1) → U23#(isNat(activate(V1))) | isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) |
| isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(M) |
| U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U22#(tt, V1) → isNat#(activate(V1)) |
| U111#(tt, L, N) → activate#(L) | U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(N) | U51#(tt, V2) → isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) → activate#(V2) | U61#(tt, V2) → isNatIListKind#(activate(V2)) |
| U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U133#(tt, IL, M, N) → isNatKind#(activate(M)) |
| U132#(tt, IL, M, N) → activate#(N) | U135#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V2) | U104#(tt, V1, V2) → activate#(V1) |
| U61#(tt, V2) → activate#(V2) | isNatIList#(V) → activate#(V) |
| U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(0, IL) → U121#(isNatIList(IL), IL) |
| U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) | isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) | U94#(tt, V1, V2) → isNat#(activate(V1)) |
| U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) | U43#(tt, V1, V2) → activate#(V1) |
| U104#(tt, V1, V2) → isNat#(activate(V1)) | activate#(n__length(X)) → length#(X) |
| U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | U114#(tt, L) → s#(length(activate(L))) |
| U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V1) | length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| U44#(tt, V1, V2) → isNat#(activate(V1)) | U105#(tt, V2) → isNatIList#(activate(V2)) |
| U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U113#(tt, L, N) → activate#(L) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U134#(tt, IL, M, N) → activate#(M) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U136#(tt, IL, M, N) → activate#(IL) | U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U95#(tt, V2) → isNatList#(activate(V2)) | U134#(tt, IL, M, N) → activate#(N) |
| isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) |
| U132#(tt, IL, M, N) → activate#(M) | take#(s(M), cons(N, IL)) → activate#(IL) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V1) | isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) |
| U114#(tt, L) → activate#(L) | isNat#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V2) | U92#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) | isNatKind#(n__length(V1)) → activate#(V1) |
| isNatKind#(n__s(V1)) → activate#(V1) | U32#(tt, V) → isNatList#(activate(V)) |
| U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U102#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → activate#(V1) | U105#(tt, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U31#(tt, V) → activate#(V) | U132#(tt, IL, M, N) → activate#(IL) |
| U131#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U91#(tt, V1, V2) → activate#(V2) | U102#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U112#(tt, L, N) → isNat#(activate(N)) |
| U93#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → activate#(V1) |
| U11#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U41#(tt, V1, V2) → activate#(V2) | U11#(tt, V1) → isNatIListKind#(activate(V1)) |
| U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) | isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(M) | U134#(tt, IL, M, N) → activate#(IL) |
| U113#(tt, L, N) → activate#(N) | U43#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U135#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V1) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → activate#(V1) |
| activate#(n__take(X1, X2)) → take#(X1, X2) | isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| take#(0, IL) → isNatIList#(IL) | U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U121#(tt, IL) → isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) → activate#(M) | U12#(tt, V1) → activate#(V1) |
| U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U104#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → isNatKind#(activate(V1)) | U135#(tt, IL, M, N) → isNatKind#(activate(N)) |
| U45#(tt, V2) → activate#(V2) | U95#(tt, V2) → activate#(V2) |
| length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) | U135#(tt, IL, M, N) → activate#(M) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) | U44#(tt, V1, V2) → activate#(V1) |
| U91#(tt, V1, V2) → isNatKind#(activate(V1)) | U101#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | isNat#(n__s(V1)) → activate#(V1) |
| U41#(tt, V1, V2) → isNatKind#(activate(V1)) | U105#(tt, V2) → U106#(isNatIList(activate(V2))) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) | isNatList#(n__cons(V1, V2)) → activate#(V2) |
| isNatIList#(V) → isNatIListKind#(activate(V)) | isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → activate#(V2) | U42#(tt, V1, V2) → activate#(V1) |
| U112#(tt, L, N) → activate#(N) | U133#(tt, IL, M, N) → activate#(IL) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U112#(tt, L, N) → activate#(L) | U41#(tt, V1, V2) → activate#(V1) |
| U42#(tt, V1, V2) → activate#(V2) | U103#(tt, V1, V2) → activate#(V1) |
| U22#(tt, V1) → activate#(V1) | U12#(tt, V1) → isNatList#(activate(V1)) |
| U92#(tt, V1, V2) → activate#(V2) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U136#(tt, IL, M, N) → activate#(N) | U111#(tt, L, N) → activate#(N) |
| isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) | isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(M) | U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U22#(tt, V1) → isNat#(activate(V1)) | U111#(tt, L, N) → activate#(L) |
| U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(N) |
| U51#(tt, V2) → isNatIListKind#(activate(V2)) | U101#(tt, V1, V2) → activate#(V2) |
| U61#(tt, V2) → isNatIListKind#(activate(V2)) | U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) → isNatKind#(activate(M)) | U132#(tt, IL, M, N) → activate#(N) |
| U135#(tt, IL, M, N) → activate#(N) | U104#(tt, V1, V2) → activate#(V1) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V2) | U61#(tt, V2) → activate#(V2) |
| isNatIList#(V) → activate#(V) | U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) | U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) → isNat#(activate(V1)) | U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) → activate#(V1) | U104#(tt, V1, V2) → isNat#(activate(V1)) |
| activate#(n__length(X)) → length#(X) | U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V1) | length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) | U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| U44#(tt, V1, V2) → isNat#(activate(V1)) | U105#(tt, V2) → isNatIList#(activate(V2)) |
| U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U113#(tt, L, N) → activate#(L) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) | length#(cons(N, L)) → isNatList#(activate(L)) |
| U134#(tt, IL, M, N) → activate#(M) | isNatList#(n__take(V1, V2)) → activate#(V2) |
| U136#(tt, IL, M, N) → activate#(IL) | U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) |
| U95#(tt, V2) → isNatList#(activate(V2)) | U134#(tt, IL, M, N) → activate#(N) |
| isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U132#(tt, IL, M, N) → activate#(M) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | take#(s(M), cons(N, IL)) → activate#(IL) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V1) | isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) |
| U114#(tt, L) → activate#(L) | isNat#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V2) | U92#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) | isNatKind#(n__length(V1)) → activate#(V1) |
| isNatKind#(n__s(V1)) → activate#(V1) | U32#(tt, V) → isNatList#(activate(V)) |
| U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U93#(tt, V1, V2) → activate#(V1) |
| U102#(tt, V1, V2) → activate#(V1) | U105#(tt, V2) → activate#(V2) |
| isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(N) |
| isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U31#(tt, V) → activate#(V) | U132#(tt, IL, M, N) → activate#(IL) |
| U131#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U91#(tt, V1, V2) → activate#(V2) | U122#(tt) → nil# |
| U102#(tt, V1, V2) → activate#(V2) | U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U11#(tt, V1) → activate#(V1) |
| U32#(tt, V) → activate#(V) | U41#(tt, V1, V2) → activate#(V2) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(M) | U134#(tt, IL, M, N) → activate#(IL) |
| U113#(tt, L, N) → activate#(N) | U43#(tt, V1, V2) → activate#(V2) |
| isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U135#(tt, IL, M, N) → activate#(IL) |
| U91#(tt, V1, V2) → activate#(V1) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → activate#(V1) |
| activate#(n__take(X1, X2)) → take#(X1, X2) | isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| take#(0, IL) → isNatIList#(IL) | U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U121#(tt, IL) → isNatIListKind#(activate(IL)) |
| U136#(tt, IL, M, N) → activate#(M) | U12#(tt, V1) → activate#(V1) |
| U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U104#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → isNatKind#(activate(V1)) | U45#(tt, V2) → activate#(V2) |
| U135#(tt, IL, M, N) → isNatKind#(activate(N)) | U95#(tt, V2) → activate#(V2) |
| length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) | U45#(tt, V2) → isNatIList#(activate(V2)) |
| U135#(tt, IL, M, N) → activate#(M) | U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) |
| U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) | U44#(tt, V1, V2) → activate#(V1) |
| U91#(tt, V1, V2) → isNatKind#(activate(V1)) | U101#(tt, V1, V2) → activate#(V1) |
| U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | isNat#(n__s(V1)) → activate#(V1) |
| U41#(tt, V1, V2) → isNatKind#(activate(V1)) | U134#(tt, IL, M, N) → isNat#(activate(N)) |
| U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| isNatList#(n__cons(V1, V2)) → activate#(V2) | isNatIList#(V) → isNatIListKind#(activate(V)) |
| isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → activate#(V2) |
| U42#(tt, V1, V2) → activate#(V1) | U112#(tt, L, N) → activate#(N) |
| U133#(tt, IL, M, N) → activate#(IL) | U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) | U112#(tt, L, N) → activate#(L) |
| U41#(tt, V1, V2) → activate#(V1) | U42#(tt, V1, V2) → activate#(V2) |
| U103#(tt, V1, V2) → activate#(V1) | U22#(tt, V1) → activate#(V1) |
| U12#(tt, V1) → isNatList#(activate(V1)) | U92#(tt, V1, V2) → activate#(V2) |
| U121#(tt, IL) → U122#(isNatIListKind(activate(IL))) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U136#(tt, IL, M, N) → activate#(N) | U111#(tt, L, N) → activate#(N) |
| isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) | isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(M) | U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U22#(tt, V1) → isNat#(activate(V1)) | U111#(tt, L, N) → activate#(L) |
| U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(N) |
| U51#(tt, V2) → isNatIListKind#(activate(V2)) | U101#(tt, V1, V2) → activate#(V2) |
| U61#(tt, V2) → isNatIListKind#(activate(V2)) | U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) → isNatKind#(activate(M)) | U135#(tt, IL, M, N) → activate#(N) |
| U132#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__take(V1, V2)) → activate#(V2) |
| U104#(tt, V1, V2) → activate#(V1) | U61#(tt, V2) → activate#(V2) |
| isNatIList#(V) → activate#(V) | U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) | U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) → isNat#(activate(V1)) | U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) → activate#(V1) | U104#(tt, V1, V2) → isNat#(activate(V1)) |
| activate#(n__length(X)) → length#(X) | U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V1) | length#(cons(N, L)) → activate#(L) |
| U132#(tt, IL, M, N) → isNat#(activate(M)) | take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | U111#(tt, L, N) → isNatIListKind#(activate(L)) |
| length#(nil) → 0# | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | U113#(tt, L, N) → activate#(L) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| U134#(tt, IL, M, N) → activate#(M) | length#(cons(N, L)) → isNatList#(activate(L)) |
| isNatList#(n__take(V1, V2)) → activate#(V2) | U136#(tt, IL, M, N) → activate#(IL) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) → activate#(N) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | U132#(tt, IL, M, N) → activate#(M) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V1) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U93#(tt, V1, V2) → activate#(V1) | U102#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(N) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U114#(tt, L) → length#(activate(L)) |
| U131#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U102#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U11#(tt, V1) → activate#(V1) | U41#(tt, V1, V2) → activate#(V2) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) |
| isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(M) |
| U134#(tt, IL, M, N) → activate#(IL) | U113#(tt, L, N) → activate#(N) |
| U43#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V1) |
| U44#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| isNatList#(n__cons(V1, V2)) → activate#(V1) | activate#(n__take(X1, X2)) → take#(X1, X2) |
| isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) | take#(0, IL) → isNatIList#(IL) |
| U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U121#(tt, IL) → isNatIListKind#(activate(IL)) | U136#(tt, IL, M, N) → activate#(M) |
| U12#(tt, V1) → activate#(V1) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U104#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → isNatKind#(activate(N)) | U45#(tt, V2) → activate#(V2) |
| U95#(tt, V2) → activate#(V2) | length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U135#(tt, IL, M, N) → activate#(M) |
| U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) → activate#(V1) | U91#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| isNat#(n__s(V1)) → activate#(V1) | U134#(tt, IL, M, N) → isNat#(activate(N)) |
| U105#(tt, V2) → U106#(isNatIList(activate(V2))) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) | isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) |
| isNatList#(n__cons(V1, V2)) → activate#(V2) | isNatIList#(V) → isNatIListKind#(activate(V)) |
| isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | U103#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → activate#(N) | U42#(tt, V1, V2) → activate#(V1) |
| U133#(tt, IL, M, N) → activate#(IL) | U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) | U112#(tt, L, N) → activate#(L) |
| U41#(tt, V1, V2) → activate#(V1) | U42#(tt, V1, V2) → activate#(V2) |
| U103#(tt, V1, V2) → activate#(V1) | U22#(tt, V1) → activate#(V1) |
| U12#(tt, V1) → isNatList#(activate(V1)) | U92#(tt, V1, V2) → activate#(V2) |
| isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) | U136#(tt, IL, M, N) → activate#(N) |
| U111#(tt, L, N) → activate#(N) | isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) |
| isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(M) |
| U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U22#(tt, V1) → isNat#(activate(V1)) |
| U111#(tt, L, N) → activate#(L) | U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(N) | U51#(tt, V2) → isNatIListKind#(activate(V2)) |
| U101#(tt, V1, V2) → activate#(V2) | U61#(tt, V2) → isNatIListKind#(activate(V2)) |
| U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U133#(tt, IL, M, N) → isNatKind#(activate(M)) |
| U132#(tt, IL, M, N) → activate#(N) | U135#(tt, IL, M, N) → activate#(N) |
| isNatIListKind#(n__take(V1, V2)) → activate#(V2) | U104#(tt, V1, V2) → activate#(V1) |
| U61#(tt, V2) → activate#(V2) | isNatIList#(V) → activate#(V) |
| U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) | take#(0, IL) → U121#(isNatIList(IL), IL) |
| U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) | isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) |
| U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) | U94#(tt, V1, V2) → isNat#(activate(V1)) |
| U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) | U43#(tt, V1, V2) → activate#(V1) |
| U104#(tt, V1, V2) → isNat#(activate(V1)) | activate#(n__length(X)) → length#(X) |
| U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) | U114#(tt, L) → s#(length(activate(L))) |
| U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| isNatIList#(n__cons(V1, V2)) → activate#(V1) | length#(cons(N, L)) → activate#(L) |
| take#(s(M), cons(N, IL)) → isNatIList#(activate(IL)) | U132#(tt, IL, M, N) → isNat#(activate(M)) |
| U101#(tt, V1, V2) → isNatKind#(activate(V1)) | isNatIList#(V) → U31#(isNatIListKind(activate(V)), activate(V)) |
| U94#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → activate#(V1) |
| U104#(tt, V1, V2) → U105#(isNat(activate(V1)), activate(V2)) | isNatIListKind#(n__take(V1, V2)) → activate#(V1) |
| U121#(tt, IL) → activate#(IL) | U94#(tt, V1, V2) → activate#(V1) |
| U131#(tt, IL, M, N) → U132#(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)) | U134#(tt, IL, M, N) → U135#(isNat(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatIListKind#(n__take(V1, V2)) → U61#(isNatKind(activate(V1)), activate(V2)) | U51#(tt, V2) → activate#(V2) |
| U31#(tt, V) → isNatIListKind#(activate(V)) | isNat#(n__length(V1)) → activate#(V1) |
| isNatIListKind#(n__cons(V1, V2)) → activate#(V2) | length#(nil) → 0# |
| U111#(tt, L, N) → isNatIListKind#(activate(L)) | U44#(tt, V1, V2) → isNat#(activate(V1)) |
| U105#(tt, V2) → isNatIList#(activate(V2)) | U92#(tt, V1, V2) → U93#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U113#(tt, L, N) → isNatKind#(activate(N)) | U113#(tt, L, N) → activate#(L) |
| isNatIList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) | take#(s(M), cons(N, IL)) → U131#(isNatIList(activate(IL)), activate(IL), M, N) |
| length#(cons(N, L)) → isNatList#(activate(L)) | U134#(tt, IL, M, N) → activate#(M) |
| isNatList#(n__take(V1, V2)) → activate#(V2) | U136#(tt, IL, M, N) → activate#(IL) |
| U133#(tt, IL, M, N) → U134#(isNatKind(activate(M)), activate(IL), activate(M), activate(N)) | U95#(tt, V2) → isNatList#(activate(V2)) |
| U134#(tt, IL, M, N) → activate#(N) | isNatIList#(n__cons(V1, V2)) → U41#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U132#(tt, IL, M, N) → U133#(isNat(activate(M)), activate(IL), activate(M), activate(N)) | U132#(tt, IL, M, N) → activate#(M) |
| take#(s(M), cons(N, IL)) → activate#(IL) | isNatIListKind#(n__cons(V1, V2)) → activate#(V1) |
| isNatKind#(n__s(V1)) → isNatKind#(activate(V1)) | U114#(tt, L) → activate#(L) |
| isNat#(n__s(V1)) → isNatKind#(activate(V1)) | isNatIList#(n__cons(V1, V2)) → activate#(V2) |
| U92#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| isNatKind#(n__length(V1)) → activate#(V1) | isNatKind#(n__s(V1)) → activate#(V1) |
| U32#(tt, V) → isNatList#(activate(V)) | U102#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U93#(tt, V1, V2) → activate#(V1) | U102#(tt, V1, V2) → activate#(V1) |
| U105#(tt, V2) → activate#(V2) | isNatList#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U131#(tt, IL, M, N) → activate#(N) | isNatList#(n__take(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → U104#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U31#(tt, V) → activate#(V) |
| U132#(tt, IL, M, N) → activate#(IL) | U131#(tt, IL, M, N) → activate#(IL) |
| U114#(tt, L) → length#(activate(L)) | U91#(tt, V1, V2) → activate#(V2) |
| U31#(tt, V) → U32#(isNatIListKind(activate(V)), activate(V)) | U102#(tt, V1, V2) → activate#(V2) |
| U112#(tt, L, N) → isNat#(activate(N)) | U93#(tt, V1, V2) → activate#(V2) |
| U21#(tt, V1) → activate#(V1) | U32#(tt, V) → activate#(V) |
| U11#(tt, V1) → activate#(V1) | U41#(tt, V1, V2) → activate#(V2) |
| U11#(tt, V1) → isNatIListKind#(activate(V1)) | U136#(tt, IL, M, N) → cons#(activate(N), n__take(activate(M), activate(IL))) |
| isNatIListKind#(n__take(V1, V2)) → isNatKind#(activate(V1)) | U131#(tt, IL, M, N) → activate#(M) |
| U134#(tt, IL, M, N) → activate#(IL) | U113#(tt, L, N) → activate#(N) |
| U43#(tt, V1, V2) → activate#(V2) | isNatList#(n__take(V1, V2)) → U101#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U135#(tt, IL, M, N) → activate#(IL) | U91#(tt, V1, V2) → activate#(V1) |
| U44#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → U22#(isNatKind(activate(V1)), activate(V1)) |
| isNatList#(n__cons(V1, V2)) → activate#(V1) | activate#(n__take(X1, X2)) → take#(X1, X2) |
| isNat#(n__length(V1)) → isNatIListKind#(activate(V1)) | take#(0, IL) → isNatIList#(IL) |
| U42#(tt, V1, V2) → isNatIListKind#(activate(V2)) | U43#(tt, V1, V2) → U44#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U121#(tt, IL) → isNatIListKind#(activate(IL)) | U136#(tt, IL, M, N) → activate#(M) |
| U12#(tt, V1) → activate#(V1) | U101#(tt, V1, V2) → U102#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U104#(tt, V1, V2) → activate#(V2) | U21#(tt, V1) → isNatKind#(activate(V1)) |
| U135#(tt, IL, M, N) → isNatKind#(activate(N)) | U45#(tt, V2) → activate#(V2) |
| U95#(tt, V2) → activate#(V2) | length#(cons(N, L)) → U111#(isNatList(activate(L)), activate(L), N) |
| U45#(tt, V2) → isNatIList#(activate(V2)) | U135#(tt, IL, M, N) → activate#(M) |
| U11#(tt, V1) → U12#(isNatIListKind(activate(V1)), activate(V1)) | U44#(tt, V1, V2) → U45#(isNat(activate(V1)), activate(V2)) |
| U44#(tt, V1, V2) → activate#(V1) | U91#(tt, V1, V2) → isNatKind#(activate(V1)) |
| U101#(tt, V1, V2) → activate#(V1) | U93#(tt, V1, V2) → U94#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) |
| U134#(tt, IL, M, N) → isNat#(activate(N)) | U41#(tt, V1, V2) → isNatKind#(activate(V1)) |
| isNat#(n__s(V1)) → activate#(V1) | U135#(tt, IL, M, N) → U136#(isNatKind(activate(N)), activate(IL), activate(M), activate(N)) |
| isNatKind#(n__length(V1)) → isNatIListKind#(activate(V1)) | isNatList#(n__cons(V1, V2)) → activate#(V2) |
| isNatIList#(V) → isNatIListKind#(activate(V)) | isNatIListKind#(n__cons(V1, V2)) → isNatKind#(activate(V1)) |
| U103#(tt, V1, V2) → activate#(V2) | U112#(tt, L, N) → activate#(N) |
| U42#(tt, V1, V2) → activate#(V1) | U133#(tt, IL, M, N) → activate#(IL) |
| U42#(tt, V1, V2) → U43#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U112#(tt, L, N) → U113#(isNat(activate(N)), activate(L), activate(N)) |
| U112#(tt, L, N) → activate#(L) | U41#(tt, V1, V2) → activate#(V1) |
| U42#(tt, V1, V2) → activate#(V2) | U103#(tt, V1, V2) → activate#(V1) |
| U22#(tt, V1) → activate#(V1) | U12#(tt, V1) → isNatList#(activate(V1)) |
| U92#(tt, V1, V2) → activate#(V2) | isNat#(n__s(V1)) → U21#(isNatKind(activate(V1)), activate(V1)) |
| U136#(tt, IL, M, N) → activate#(N) | U111#(tt, L, N) → activate#(N) |
| isNatIListKind#(n__cons(V1, V2)) → U51#(isNatKind(activate(V1)), activate(V2)) | isNatList#(n__cons(V1, V2)) → U91#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| U133#(tt, IL, M, N) → activate#(M) | U103#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U22#(tt, V1) → isNat#(activate(V1)) | U111#(tt, L, N) → activate#(L) |
| U102#(tt, V1, V2) → U103#(isNatIListKind(activate(V2)), activate(V1), activate(V2)) | U133#(tt, IL, M, N) → activate#(N) |
| U51#(tt, V2) → isNatIListKind#(activate(V2)) | U101#(tt, V1, V2) → activate#(V2) |
| U61#(tt, V2) → isNatIListKind#(activate(V2)) | U92#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U133#(tt, IL, M, N) → isNatKind#(activate(M)) | U132#(tt, IL, M, N) → activate#(N) |
| U135#(tt, IL, M, N) → activate#(N) | isNatIListKind#(n__take(V1, V2)) → activate#(V2) |
| U104#(tt, V1, V2) → activate#(V1) | U61#(tt, V2) → activate#(V2) |
| isNatIList#(V) → activate#(V) | U41#(tt, V1, V2) → U42#(isNatKind(activate(V1)), activate(V1), activate(V2)) |
| take#(0, IL) → U121#(isNatIList(IL), IL) | U94#(tt, V1, V2) → U95#(isNat(activate(V1)), activate(V2)) |
| isNat#(n__length(V1)) → U11#(isNatIListKind(activate(V1)), activate(V1)) | U131#(tt, IL, M, N) → isNatIListKind#(activate(IL)) |
| U94#(tt, V1, V2) → isNat#(activate(V1)) | U113#(tt, L, N) → U114#(isNatKind(activate(N)), activate(L)) |
| U43#(tt, V1, V2) → activate#(V1) | U104#(tt, V1, V2) → isNat#(activate(V1)) |
| activate#(n__length(X)) → length#(X) | U111#(tt, L, N) → U112#(isNatIListKind(activate(L)), activate(L), activate(N)) |
| U114#(tt, L) → s#(length(activate(L))) | U43#(tt, V1, V2) → isNatIListKind#(activate(V2)) |
| U91#(tt, V1, V2) → U92#(isNatKind(activate(V1)), activate(V1), activate(V2)) | isNatIList#(n__cons(V1, V2)) → activate#(V1) |
| length#(cons(N, L)) → activate#(L) |