The TRS could not be proven terminating. The proof attempt took 60010 ms.
Problem 1 was processed with processor DependencyGraph (6315ms). | – Problem 2 remains open; application of the following processors failed [SubtermCriterion (1ms), DependencyGraph (3600ms), PolynomialLinearRange4iUR (timeout), DependencyGraph (3715ms), PolynomialLinearRange8NegiUR (30032ms), DependencyGraph (timeout), ReductionPairSAT (timeout)].
| a__U51#(tt, V1, V2) | → | a__isNat#(V1) | mark#(U11(X1, X2)) | → | mark#(X1) | |
| a__length#(cons(N, L)) | → | a__and#(a__isNatList(L), isNatIListKind(L)) | mark#(isNatIListKind(X)) | → | a__isNatIListKind#(X) | |
| mark#(isNatIList(X)) | → | a__isNatIList#(X) | a__isNatKind#(length(V1)) | → | a__isNatIListKind#(V1) | |
| a__and#(tt, X) | → | mark#(X) | a__U52#(tt, V2) | → | a__isNatList#(V2) | |
| mark#(U31(X1, X2)) | → | mark#(X1) | mark#(s(X)) | → | mark#(X) | |
| a__U21#(tt, V1) | → | a__isNat#(V1) | mark#(U53(X)) | → | mark#(X) | |
| a__isNatList#(cons(V1, V2)) | → | a__isNatKind#(V1) | mark#(U42(X1, X2)) | → | a__U42#(mark(X1), X2) | |
| a__isNatIList#(V) | → | a__U31#(a__isNatIListKind(V), V) | mark#(cons(X1, X2)) | → | mark#(X1) | |
| a__isNat#(s(V1)) | → | a__isNatKind#(V1) | a__isNatIList#(cons(V1, V2)) | → | a__and#(a__isNatKind(V1), isNatIListKind(V2)) | |
| mark#(isNatList(X)) | → | a__isNatList#(X) | mark#(U61(X1, X2)) | → | a__U61#(mark(X1), X2) | |
| mark#(and(X1, X2)) | → | mark#(X1) | mark#(and(X1, X2)) | → | a__and#(mark(X1), X2) | |
| mark#(U41(X1, X2, X3)) | → | mark#(X1) | a__isNatIListKind#(cons(V1, V2)) | → | a__and#(a__isNatKind(V1), isNatIListKind(V2)) | |
| a__isNatIList#(cons(V1, V2)) | → | a__U41#(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) | a__U51#(tt, V1, V2) | → | a__U52#(a__isNat(V1), V2) | |
| a__length#(cons(N, L)) | → | a__U61#(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) | mark#(U61(X1, X2)) | → | mark#(X1) | |
| mark#(isNat(X)) | → | a__isNat#(X) | a__isNat#(length(V1)) | → | a__isNatIListKind#(V1) | |
| a__U41#(tt, V1, V2) | → | a__isNat#(V1) | a__isNatIList#(V) | → | a__isNatIListKind#(V) | |
| a__isNatIListKind#(cons(V1, V2)) | → | a__isNatKind#(V1) | mark#(U32(X)) | → | mark#(X) | |
| mark#(U21(X1, X2)) | → | mark#(X1) | mark#(U41(X1, X2, X3)) | → | a__U41#(mark(X1), X2, X3) | |
| mark#(U31(X1, X2)) | → | a__U31#(mark(X1), X2) | a__isNatKind#(s(V1)) | → | a__isNatKind#(V1) | |
| mark#(length(X)) | → | a__length#(mark(X)) | mark#(U51(X1, X2, X3)) | → | mark#(X1) | |
| a__U61#(tt, L) | → | a__length#(mark(L)) | a__isNatIList#(cons(V1, V2)) | → | a__isNatKind#(V1) | |
| mark#(U52(X1, X2)) | → | a__U52#(mark(X1), X2) | mark#(length(X)) | → | mark#(X) | |
| a__length#(cons(N, L)) | → | a__isNatList#(L) | a__U11#(tt, V1) | → | a__isNatList#(V1) | |
| mark#(U12(X)) | → | mark#(X) | mark#(U42(X1, X2)) | → | mark#(X1) | |
| a__U61#(tt, L) | → | mark#(L) | mark#(U52(X1, X2)) | → | mark#(X1) | |
| a__isNat#(length(V1)) | → | a__U11#(a__isNatIListKind(V1), V1) | a__U42#(tt, V2) | → | a__isNatIList#(V2) | |
| a__isNatList#(cons(V1, V2)) | → | a__and#(a__isNatKind(V1), isNatIListKind(V2)) | mark#(U51(X1, X2, X3)) | → | a__U51#(mark(X1), X2, X3) | |
| mark#(U22(X)) | → | mark#(X) | a__length#(cons(N, L)) | → | a__and#(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))) | |
| mark#(U43(X)) | → | mark#(X) | a__isNat#(s(V1)) | → | a__U21#(a__isNatKind(V1), V1) | |
| mark#(U21(X1, X2)) | → | a__U21#(mark(X1), X2) | a__U31#(tt, V) | → | a__isNatList#(V) | |
| a__U41#(tt, V1, V2) | → | a__U42#(a__isNat(V1), V2) | mark#(isNatKind(X)) | → | a__isNatKind#(X) | |
| a__isNatList#(cons(V1, V2)) | → | a__U51#(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) | mark#(U11(X1, X2)) | → | a__U11#(mark(X1), X2) |
| a__zeros | → | cons(0, zeros) | a__U11(tt, V1) | → | a__U12(a__isNatList(V1)) | |
| a__U12(tt) | → | tt | a__U21(tt, V1) | → | a__U22(a__isNat(V1)) | |
| a__U22(tt) | → | tt | a__U31(tt, V) | → | a__U32(a__isNatList(V)) | |
| a__U32(tt) | → | tt | a__U41(tt, V1, V2) | → | a__U42(a__isNat(V1), V2) | |
| a__U42(tt, V2) | → | a__U43(a__isNatIList(V2)) | a__U43(tt) | → | tt | |
| a__U51(tt, V1, V2) | → | a__U52(a__isNat(V1), V2) | a__U52(tt, V2) | → | a__U53(a__isNatList(V2)) | |
| a__U53(tt) | → | tt | a__U61(tt, L) | → | s(a__length(mark(L))) | |
| a__and(tt, X) | → | mark(X) | a__isNat(0) | → | tt | |
| a__isNat(length(V1)) | → | a__U11(a__isNatIListKind(V1), V1) | a__isNat(s(V1)) | → | a__U21(a__isNatKind(V1), V1) | |
| a__isNatIList(V) | → | a__U31(a__isNatIListKind(V), V) | a__isNatIList(zeros) | → | tt | |
| a__isNatIList(cons(V1, V2)) | → | a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) | a__isNatIListKind(nil) | → | tt | |
| a__isNatIListKind(zeros) | → | tt | a__isNatIListKind(cons(V1, V2)) | → | a__and(a__isNatKind(V1), isNatIListKind(V2)) | |
| a__isNatKind(0) | → | tt | a__isNatKind(length(V1)) | → | a__isNatIListKind(V1) | |
| a__isNatKind(s(V1)) | → | a__isNatKind(V1) | a__isNatList(nil) | → | tt | |
| a__isNatList(cons(V1, V2)) | → | a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) | a__length(nil) | → | 0 | |
| a__length(cons(N, L)) | → | a__U61(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) | mark(zeros) | → | a__zeros | |
| mark(U11(X1, X2)) | → | a__U11(mark(X1), X2) | mark(U12(X)) | → | a__U12(mark(X)) | |
| mark(isNatList(X)) | → | a__isNatList(X) | mark(U21(X1, X2)) | → | a__U21(mark(X1), X2) | |
| mark(U22(X)) | → | a__U22(mark(X)) | mark(isNat(X)) | → | a__isNat(X) | |
| mark(U31(X1, X2)) | → | a__U31(mark(X1), X2) | mark(U32(X)) | → | a__U32(mark(X)) | |
| mark(U41(X1, X2, X3)) | → | a__U41(mark(X1), X2, X3) | mark(U42(X1, X2)) | → | a__U42(mark(X1), X2) | |
| mark(U43(X)) | → | a__U43(mark(X)) | mark(isNatIList(X)) | → | a__isNatIList(X) | |
| mark(U51(X1, X2, X3)) | → | a__U51(mark(X1), X2, X3) | mark(U52(X1, X2)) | → | a__U52(mark(X1), X2) | |
| mark(U53(X)) | → | a__U53(mark(X)) | mark(U61(X1, X2)) | → | a__U61(mark(X1), X2) | |
| mark(length(X)) | → | a__length(mark(X)) | mark(and(X1, X2)) | → | a__and(mark(X1), X2) | |
| mark(isNatIListKind(X)) | → | a__isNatIListKind(X) | mark(isNatKind(X)) | → | a__isNatKind(X) | |
| mark(cons(X1, X2)) | → | cons(mark(X1), X2) | mark(0) | → | 0 | |
| mark(tt) | → | tt | mark(s(X)) | → | s(mark(X)) | |
| mark(nil) | → | nil | a__zeros | → | zeros | |
| a__U11(X1, X2) | → | U11(X1, X2) | a__U12(X) | → | U12(X) | |
| a__isNatList(X) | → | isNatList(X) | a__U21(X1, X2) | → | U21(X1, X2) | |
| a__U22(X) | → | U22(X) | a__isNat(X) | → | isNat(X) | |
| a__U31(X1, X2) | → | U31(X1, X2) | a__U32(X) | → | U32(X) | |
| a__U41(X1, X2, X3) | → | U41(X1, X2, X3) | a__U42(X1, X2) | → | U42(X1, X2) | |
| a__U43(X) | → | U43(X) | a__isNatIList(X) | → | isNatIList(X) | |
| a__U51(X1, X2, X3) | → | U51(X1, X2, X3) | a__U52(X1, X2) | → | U52(X1, X2) | |
| a__U53(X) | → | U53(X) | a__U61(X1, X2) | → | U61(X1, X2) | |
| a__length(X) | → | length(X) | a__and(X1, X2) | → | and(X1, X2) | |
| a__isNatIListKind(X) | → | isNatIListKind(X) | a__isNatKind(X) | → | isNatKind(X) |
Termination of terms over the following signature is verified: a__U51, a__U52, a__U53, isNatIListKind, a__isNatIListKind, a__and, isNat, a__isNatList, U61, U43, U42, U41, length, a__U41, a__U22, a__U43, a__U42, U21, a__U21, U22, cons, a__zeros, isNatIList, isNatKind, a__length, mark, and, 0, U51, isNatList, a__isNatIList, s, tt, zeros, U53, a__isNat, U52, a__U32, U11, a__U31, U12, a__U12, U31, a__U11, U32, a__U61, nil, a__isNatKind
| a__U51#(tt, V1, V2) | → | a__isNat#(V1) | mark#(U11(X1, X2)) | → | mark#(X1) | |
| mark#(isNatIListKind(X)) | → | a__isNatIListKind#(X) | a__length#(cons(N, L)) | → | a__and#(a__isNatList(L), isNatIListKind(L)) | |
| mark#(isNatIList(X)) | → | a__isNatIList#(X) | a__isNatKind#(length(V1)) | → | a__isNatIListKind#(V1) | |
| mark#(U53(X)) | → | a__U53#(mark(X)) | a__and#(tt, X) | → | mark#(X) | |
| a__U52#(tt, V2) | → | a__isNatList#(V2) | mark#(U31(X1, X2)) | → | mark#(X1) | |
| mark#(s(X)) | → | mark#(X) | a__U31#(tt, V) | → | a__U32#(a__isNatList(V)) | |
| a__U21#(tt, V1) | → | a__isNat#(V1) | mark#(U53(X)) | → | mark#(X) | |
| a__isNatList#(cons(V1, V2)) | → | a__isNatKind#(V1) | a__isNatIList#(V) | → | a__U31#(a__isNatIListKind(V), V) | |
| mark#(U42(X1, X2)) | → | a__U42#(mark(X1), X2) | mark#(cons(X1, X2)) | → | mark#(X1) | |
| a__isNat#(s(V1)) | → | a__isNatKind#(V1) | mark#(isNatList(X)) | → | a__isNatList#(X) | |
| a__isNatIList#(cons(V1, V2)) | → | a__and#(a__isNatKind(V1), isNatIListKind(V2)) | mark#(U61(X1, X2)) | → | a__U61#(mark(X1), X2) | |
| mark#(and(X1, X2)) | → | mark#(X1) | mark#(U41(X1, X2, X3)) | → | mark#(X1) | |
| mark#(and(X1, X2)) | → | a__and#(mark(X1), X2) | a__isNatIListKind#(cons(V1, V2)) | → | a__and#(a__isNatKind(V1), isNatIListKind(V2)) | |
| a__isNatIList#(cons(V1, V2)) | → | a__U41#(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) | a__U51#(tt, V1, V2) | → | a__U52#(a__isNat(V1), V2) | |
| a__length#(cons(N, L)) | → | a__U61#(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) | mark#(U61(X1, X2)) | → | mark#(X1) | |
| mark#(U43(X)) | → | a__U43#(mark(X)) | mark#(isNat(X)) | → | a__isNat#(X) | |
| a__isNat#(length(V1)) | → | a__isNatIListKind#(V1) | a__U41#(tt, V1, V2) | → | a__isNat#(V1) | |
| a__U42#(tt, V2) | → | a__U43#(a__isNatIList(V2)) | mark#(U32(X)) | → | a__U32#(mark(X)) | |
| mark#(zeros) | → | a__zeros# | a__isNatIList#(V) | → | a__isNatIListKind#(V) | |
| a__isNatIListKind#(cons(V1, V2)) | → | a__isNatKind#(V1) | mark#(U32(X)) | → | mark#(X) | |
| mark#(U21(X1, X2)) | → | mark#(X1) | mark#(U41(X1, X2, X3)) | → | a__U41#(mark(X1), X2, X3) | |
| mark#(U31(X1, X2)) | → | a__U31#(mark(X1), X2) | a__isNatKind#(s(V1)) | → | a__isNatKind#(V1) | |
| mark#(length(X)) | → | a__length#(mark(X)) | a__U21#(tt, V1) | → | a__U22#(a__isNat(V1)) | |
| mark#(U51(X1, X2, X3)) | → | mark#(X1) | a__U61#(tt, L) | → | a__length#(mark(L)) | |
| a__U11#(tt, V1) | → | a__U12#(a__isNatList(V1)) | mark#(U22(X)) | → | a__U22#(mark(X)) | |
| a__isNatIList#(cons(V1, V2)) | → | a__isNatKind#(V1) | mark#(U52(X1, X2)) | → | a__U52#(mark(X1), X2) | |
| mark#(length(X)) | → | mark#(X) | a__length#(cons(N, L)) | → | a__isNatList#(L) | |
| a__U11#(tt, V1) | → | a__isNatList#(V1) | mark#(U12(X)) | → | mark#(X) | |
| mark#(U42(X1, X2)) | → | mark#(X1) | a__U61#(tt, L) | → | mark#(L) | |
| mark#(U52(X1, X2)) | → | mark#(X1) | a__isNat#(length(V1)) | → | a__U11#(a__isNatIListKind(V1), V1) | |
| mark#(U12(X)) | → | a__U12#(mark(X)) | a__U42#(tt, V2) | → | a__isNatIList#(V2) | |
| a__isNatList#(cons(V1, V2)) | → | a__and#(a__isNatKind(V1), isNatIListKind(V2)) | a__U52#(tt, V2) | → | a__U53#(a__isNatList(V2)) | |
| mark#(U51(X1, X2, X3)) | → | a__U51#(mark(X1), X2, X3) | mark#(U22(X)) | → | mark#(X) | |
| a__length#(cons(N, L)) | → | a__and#(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))) | mark#(U43(X)) | → | mark#(X) | |
| a__isNat#(s(V1)) | → | a__U21#(a__isNatKind(V1), V1) | mark#(U21(X1, X2)) | → | a__U21#(mark(X1), X2) | |
| a__U31#(tt, V) | → | a__isNatList#(V) | a__isNatList#(cons(V1, V2)) | → | a__U51#(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) | |
| a__U41#(tt, V1, V2) | → | a__U42#(a__isNat(V1), V2) | mark#(isNatKind(X)) | → | a__isNatKind#(X) | |
| mark#(U11(X1, X2)) | → | a__U11#(mark(X1), X2) |
| a__zeros | → | cons(0, zeros) | a__U11(tt, V1) | → | a__U12(a__isNatList(V1)) | |
| a__U12(tt) | → | tt | a__U21(tt, V1) | → | a__U22(a__isNat(V1)) | |
| a__U22(tt) | → | tt | a__U31(tt, V) | → | a__U32(a__isNatList(V)) | |
| a__U32(tt) | → | tt | a__U41(tt, V1, V2) | → | a__U42(a__isNat(V1), V2) | |
| a__U42(tt, V2) | → | a__U43(a__isNatIList(V2)) | a__U43(tt) | → | tt | |
| a__U51(tt, V1, V2) | → | a__U52(a__isNat(V1), V2) | a__U52(tt, V2) | → | a__U53(a__isNatList(V2)) | |
| a__U53(tt) | → | tt | a__U61(tt, L) | → | s(a__length(mark(L))) | |
| a__and(tt, X) | → | mark(X) | a__isNat(0) | → | tt | |
| a__isNat(length(V1)) | → | a__U11(a__isNatIListKind(V1), V1) | a__isNat(s(V1)) | → | a__U21(a__isNatKind(V1), V1) | |
| a__isNatIList(V) | → | a__U31(a__isNatIListKind(V), V) | a__isNatIList(zeros) | → | tt | |
| a__isNatIList(cons(V1, V2)) | → | a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) | a__isNatIListKind(nil) | → | tt | |
| a__isNatIListKind(zeros) | → | tt | a__isNatIListKind(cons(V1, V2)) | → | a__and(a__isNatKind(V1), isNatIListKind(V2)) | |
| a__isNatKind(0) | → | tt | a__isNatKind(length(V1)) | → | a__isNatIListKind(V1) | |
| a__isNatKind(s(V1)) | → | a__isNatKind(V1) | a__isNatList(nil) | → | tt | |
| a__isNatList(cons(V1, V2)) | → | a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) | a__length(nil) | → | 0 | |
| a__length(cons(N, L)) | → | a__U61(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) | mark(zeros) | → | a__zeros | |
| mark(U11(X1, X2)) | → | a__U11(mark(X1), X2) | mark(U12(X)) | → | a__U12(mark(X)) | |
| mark(isNatList(X)) | → | a__isNatList(X) | mark(U21(X1, X2)) | → | a__U21(mark(X1), X2) | |
| mark(U22(X)) | → | a__U22(mark(X)) | mark(isNat(X)) | → | a__isNat(X) | |
| mark(U31(X1, X2)) | → | a__U31(mark(X1), X2) | mark(U32(X)) | → | a__U32(mark(X)) | |
| mark(U41(X1, X2, X3)) | → | a__U41(mark(X1), X2, X3) | mark(U42(X1, X2)) | → | a__U42(mark(X1), X2) | |
| mark(U43(X)) | → | a__U43(mark(X)) | mark(isNatIList(X)) | → | a__isNatIList(X) | |
| mark(U51(X1, X2, X3)) | → | a__U51(mark(X1), X2, X3) | mark(U52(X1, X2)) | → | a__U52(mark(X1), X2) | |
| mark(U53(X)) | → | a__U53(mark(X)) | mark(U61(X1, X2)) | → | a__U61(mark(X1), X2) | |
| mark(length(X)) | → | a__length(mark(X)) | mark(and(X1, X2)) | → | a__and(mark(X1), X2) | |
| mark(isNatIListKind(X)) | → | a__isNatIListKind(X) | mark(isNatKind(X)) | → | a__isNatKind(X) | |
| mark(cons(X1, X2)) | → | cons(mark(X1), X2) | mark(0) | → | 0 | |
| mark(tt) | → | tt | mark(s(X)) | → | s(mark(X)) | |
| mark(nil) | → | nil | a__zeros | → | zeros | |
| a__U11(X1, X2) | → | U11(X1, X2) | a__U12(X) | → | U12(X) | |
| a__isNatList(X) | → | isNatList(X) | a__U21(X1, X2) | → | U21(X1, X2) | |
| a__U22(X) | → | U22(X) | a__isNat(X) | → | isNat(X) | |
| a__U31(X1, X2) | → | U31(X1, X2) | a__U32(X) | → | U32(X) | |
| a__U41(X1, X2, X3) | → | U41(X1, X2, X3) | a__U42(X1, X2) | → | U42(X1, X2) | |
| a__U43(X) | → | U43(X) | a__isNatIList(X) | → | isNatIList(X) | |
| a__U51(X1, X2, X3) | → | U51(X1, X2, X3) | a__U52(X1, X2) | → | U52(X1, X2) | |
| a__U53(X) | → | U53(X) | a__U61(X1, X2) | → | U61(X1, X2) | |
| a__length(X) | → | length(X) | a__and(X1, X2) | → | and(X1, X2) | |
| a__isNatIListKind(X) | → | isNatIListKind(X) | a__isNatKind(X) | → | isNatKind(X) |
Termination of terms over the following signature is verified: a__U51, a__U52, a__U53, isNatIListKind, a__isNatIListKind, a__and, isNat, a__isNatList, U43, U61, U42, U41, length, a__U41, a__U22, a__U43, a__U42, U21, a__U21, U22, cons, a__zeros, isNatIList, isNatKind, a__length, mark, and, 0, s, a__isNatIList, isNatList, U51, zeros, tt, a__isNat, U53, U52, a__U32, a__U31, U11, a__U12, U12, a__U11, U31, a__U61, U32, a__isNatKind, nil
| a__U51#(tt, V1, V2) → a__isNat#(V1) | mark#(U11(X1, X2)) → mark#(X1) |
| mark#(isNatIListKind(X)) → a__isNatIListKind#(X) | a__length#(cons(N, L)) → a__and#(a__isNatList(L), isNatIListKind(L)) |
| mark#(isNatIList(X)) → a__isNatIList#(X) | a__isNatKind#(length(V1)) → a__isNatIListKind#(V1) |
| a__and#(tt, X) → mark#(X) | a__U52#(tt, V2) → a__isNatList#(V2) |
| mark#(U31(X1, X2)) → mark#(X1) | mark#(s(X)) → mark#(X) |
| a__U21#(tt, V1) → a__isNat#(V1) | mark#(U53(X)) → mark#(X) |
| a__isNatList#(cons(V1, V2)) → a__isNatKind#(V1) | a__isNatIList#(V) → a__U31#(a__isNatIListKind(V), V) |
| mark#(U42(X1, X2)) → a__U42#(mark(X1), X2) | mark#(cons(X1, X2)) → mark#(X1) |
| a__isNat#(s(V1)) → a__isNatKind#(V1) | mark#(isNatList(X)) → a__isNatList#(X) |
| a__isNatIList#(cons(V1, V2)) → a__and#(a__isNatKind(V1), isNatIListKind(V2)) | mark#(and(X1, X2)) → mark#(X1) |
| mark#(U61(X1, X2)) → a__U61#(mark(X1), X2) | a__isNatIListKind#(cons(V1, V2)) → a__and#(a__isNatKind(V1), isNatIListKind(V2)) |
| mark#(U41(X1, X2, X3)) → mark#(X1) | mark#(and(X1, X2)) → a__and#(mark(X1), X2) |
| a__isNatIList#(cons(V1, V2)) → a__U41#(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) | a__U51#(tt, V1, V2) → a__U52#(a__isNat(V1), V2) |
| a__length#(cons(N, L)) → a__U61#(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) | mark#(U61(X1, X2)) → mark#(X1) |
| mark#(isNat(X)) → a__isNat#(X) | a__isNat#(length(V1)) → a__isNatIListKind#(V1) |
| a__U41#(tt, V1, V2) → a__isNat#(V1) | a__isNatIListKind#(cons(V1, V2)) → a__isNatKind#(V1) |
| a__isNatIList#(V) → a__isNatIListKind#(V) | mark#(U32(X)) → mark#(X) |
| mark#(U21(X1, X2)) → mark#(X1) | mark#(U31(X1, X2)) → a__U31#(mark(X1), X2) |
| mark#(U41(X1, X2, X3)) → a__U41#(mark(X1), X2, X3) | a__isNatKind#(s(V1)) → a__isNatKind#(V1) |
| mark#(length(X)) → a__length#(mark(X)) | mark#(U51(X1, X2, X3)) → mark#(X1) |
| a__U61#(tt, L) → a__length#(mark(L)) | a__isNatIList#(cons(V1, V2)) → a__isNatKind#(V1) |
| mark#(U52(X1, X2)) → a__U52#(mark(X1), X2) | mark#(length(X)) → mark#(X) |
| a__length#(cons(N, L)) → a__isNatList#(L) | a__U11#(tt, V1) → a__isNatList#(V1) |
| mark#(U12(X)) → mark#(X) | mark#(U42(X1, X2)) → mark#(X1) |
| a__U61#(tt, L) → mark#(L) | mark#(U52(X1, X2)) → mark#(X1) |
| a__isNat#(length(V1)) → a__U11#(a__isNatIListKind(V1), V1) | a__U42#(tt, V2) → a__isNatIList#(V2) |
| a__isNatList#(cons(V1, V2)) → a__and#(a__isNatKind(V1), isNatIListKind(V2)) | mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3) |
| mark#(U43(X)) → mark#(X) | a__length#(cons(N, L)) → a__and#(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))) |
| mark#(U22(X)) → mark#(X) | a__isNat#(s(V1)) → a__U21#(a__isNatKind(V1), V1) |
| mark#(U21(X1, X2)) → a__U21#(mark(X1), X2) | a__U31#(tt, V) → a__isNatList#(V) |
| a__isNatList#(cons(V1, V2)) → a__U51#(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) | mark#(isNatKind(X)) → a__isNatKind#(X) |
| a__U41#(tt, V1, V2) → a__U42#(a__isNat(V1), V2) | mark#(U11(X1, X2)) → a__U11#(mark(X1), X2) |