LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__zeros() -> cons(0(), zeros())
, a__U101(tt(), V1, V2) -> a__U102(a__isNatKind(V1), V1, V2)
, a__U102(tt(), V1, V2) -> a__U103(a__isNatIListKind(V2), V1, V2)
, a__U103(tt(), V1, V2) -> a__U104(a__isNatIListKind(V2), V1, V2)
, a__U104(tt(), V1, V2) -> a__U105(a__isNat(V1), V2)
, a__U105(tt(), V2) -> a__U106(a__isNatIList(V2))
, a__U106(tt()) -> tt()
, a__U11(tt(), V1) -> a__U12(a__isNatIListKind(V1), V1)
, a__U111(tt(), L, N) -> a__U112(a__isNatIListKind(L), L, N)
, a__U112(tt(), L, N) -> a__U113(a__isNat(N), L, N)
, a__U113(tt(), L, N) -> a__U114(a__isNatKind(N), L)
, a__U114(tt(), L) -> s(a__length(mark(L)))
, a__U12(tt(), V1) -> a__U13(a__isNatList(V1))
, a__U121(tt(), IL) -> a__U122(a__isNatIListKind(IL))
, a__U122(tt()) -> nil()
, a__U13(tt()) -> tt()
, a__U131(tt(), IL, M, N) ->
a__U132(a__isNatIListKind(IL), IL, M, N)
, a__U132(tt(), IL, M, N) -> a__U133(a__isNat(M), IL, M, N)
, a__U133(tt(), IL, M, N) -> a__U134(a__isNatKind(M), IL, M, N)
, a__U134(tt(), IL, M, N) -> a__U135(a__isNat(N), IL, M, N)
, a__U135(tt(), IL, M, N) -> a__U136(a__isNatKind(N), IL, M, N)
, a__U136(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
, a__U21(tt(), V1) -> a__U22(a__isNatKind(V1), V1)
, a__U22(tt(), V1) -> a__U23(a__isNat(V1))
, a__U23(tt()) -> tt()
, a__U31(tt(), V) -> a__U32(a__isNatIListKind(V), V)
, a__U32(tt(), V) -> a__U33(a__isNatList(V))
, a__U33(tt()) -> tt()
, a__U41(tt(), V1, V2) -> a__U42(a__isNatKind(V1), V1, V2)
, a__U42(tt(), V1, V2) -> a__U43(a__isNatIListKind(V2), V1, V2)
, a__U43(tt(), V1, V2) -> a__U44(a__isNatIListKind(V2), V1, V2)
, a__U44(tt(), V1, V2) -> a__U45(a__isNat(V1), V2)
, a__U45(tt(), V2) -> a__U46(a__isNatIList(V2))
, a__U46(tt()) -> tt()
, a__U51(tt(), V2) -> a__U52(a__isNatIListKind(V2))
, a__U52(tt()) -> tt()
, a__U61(tt(), V2) -> a__U62(a__isNatIListKind(V2))
, a__U62(tt()) -> tt()
, a__U71(tt()) -> tt()
, a__U81(tt()) -> tt()
, a__U91(tt(), V1, V2) -> a__U92(a__isNatKind(V1), V1, V2)
, a__U92(tt(), V1, V2) -> a__U93(a__isNatIListKind(V2), V1, V2)
, a__U93(tt(), V1, V2) -> a__U94(a__isNatIListKind(V2), V1, V2)
, a__U94(tt(), V1, V2) -> a__U95(a__isNat(V1), V2)
, a__U95(tt(), V2) -> a__U96(a__isNatList(V2))
, a__U96(tt()) -> tt()
, 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__isNatKind(V1), V1, V2)
, a__isNatIListKind(nil()) -> tt()
, a__isNatIListKind(zeros()) -> tt()
, a__isNatIListKind(cons(V1, V2)) -> a__U51(a__isNatKind(V1), V2)
, a__isNatIListKind(take(V1, V2)) -> a__U61(a__isNatKind(V1), V2)
, a__isNatKind(0()) -> tt()
, a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1))
, a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1))
, a__isNatList(nil()) -> tt()
, a__isNatList(cons(V1, V2)) -> a__U91(a__isNatKind(V1), V1, V2)
, a__isNatList(take(V1, V2)) -> a__U101(a__isNatKind(V1), V1, V2)
, a__length(nil()) -> 0()
, a__length(cons(N, L)) -> a__U111(a__isNatList(L), L, N)
, a__take(0(), IL) -> a__U121(a__isNatIList(IL), IL)
, a__take(s(M), cons(N, IL)) ->
a__U131(a__isNatIList(IL), IL, M, N)
, mark(zeros()) -> a__zeros()
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
, mark(isNatKind(X)) -> a__isNatKind(X)
, mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
, mark(isNatIListKind(X)) -> a__isNatIListKind(X)
, mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
, mark(U105(X1, X2)) -> a__U105(mark(X1), X2)
, mark(isNat(X)) -> a__isNat(X)
, mark(U106(X)) -> a__U106(mark(X))
, mark(isNatIList(X)) -> a__isNatIList(X)
, mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
, mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
, mark(U111(X1, X2, X3)) -> a__U111(mark(X1), X2, X3)
, mark(U112(X1, X2, X3)) -> a__U112(mark(X1), X2, X3)
, mark(U113(X1, X2, X3)) -> a__U113(mark(X1), X2, X3)
, mark(U114(X1, X2)) -> a__U114(mark(X1), X2)
, mark(length(X)) -> a__length(mark(X))
, mark(U13(X)) -> a__U13(mark(X))
, mark(isNatList(X)) -> a__isNatList(X)
, mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
, mark(U122(X)) -> a__U122(mark(X))
, mark(U131(X1, X2, X3, X4)) -> a__U131(mark(X1), X2, X3, X4)
, mark(U132(X1, X2, X3, X4)) -> a__U132(mark(X1), X2, X3, X4)
, mark(U133(X1, X2, X3, X4)) -> a__U133(mark(X1), X2, X3, X4)
, mark(U134(X1, X2, X3, X4)) -> a__U134(mark(X1), X2, X3, X4)
, mark(U135(X1, X2, X3, X4)) -> a__U135(mark(X1), X2, X3, X4)
, mark(U136(X1, X2, X3, X4)) -> a__U136(mark(X1), X2, X3, X4)
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
, mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
, mark(U23(X)) -> a__U23(mark(X))
, mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
, mark(U32(X1, X2)) -> a__U32(mark(X1), X2)
, mark(U33(X)) -> a__U33(mark(X))
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
, mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3)
, mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3)
, mark(U45(X1, X2)) -> a__U45(mark(X1), X2)
, mark(U46(X)) -> a__U46(mark(X))
, mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
, mark(U52(X)) -> a__U52(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X)) -> a__U62(mark(X))
, mark(U71(X)) -> a__U71(mark(X))
, mark(U81(X)) -> a__U81(mark(X))
, mark(U91(X1, X2, X3)) -> a__U91(mark(X1), X2, X3)
, mark(U92(X1, X2, X3)) -> a__U92(mark(X1), X2, X3)
, mark(U93(X1, X2, X3)) -> a__U93(mark(X1), X2, X3)
, mark(U94(X1, X2, X3)) -> a__U94(mark(X1), X2, X3)
, mark(U95(X1, X2)) -> a__U95(mark(X1), X2)
, mark(U96(X)) -> a__U96(mark(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__U101(X1, X2, X3) -> U101(X1, X2, X3)
, a__U102(X1, X2, X3) -> U102(X1, X2, X3)
, a__isNatKind(X) -> isNatKind(X)
, a__U103(X1, X2, X3) -> U103(X1, X2, X3)
, a__isNatIListKind(X) -> isNatIListKind(X)
, a__U104(X1, X2, X3) -> U104(X1, X2, X3)
, a__U105(X1, X2) -> U105(X1, X2)
, a__isNat(X) -> isNat(X)
, a__U106(X) -> U106(X)
, a__isNatIList(X) -> isNatIList(X)
, a__U11(X1, X2) -> U11(X1, X2)
, a__U12(X1, X2) -> U12(X1, X2)
, a__U111(X1, X2, X3) -> U111(X1, X2, X3)
, a__U112(X1, X2, X3) -> U112(X1, X2, X3)
, a__U113(X1, X2, X3) -> U113(X1, X2, X3)
, a__U114(X1, X2) -> U114(X1, X2)
, a__length(X) -> length(X)
, a__U13(X) -> U13(X)
, a__isNatList(X) -> isNatList(X)
, a__U121(X1, X2) -> U121(X1, X2)
, a__U122(X) -> U122(X)
, a__U131(X1, X2, X3, X4) -> U131(X1, X2, X3, X4)
, a__U132(X1, X2, X3, X4) -> U132(X1, X2, X3, X4)
, a__U133(X1, X2, X3, X4) -> U133(X1, X2, X3, X4)
, a__U134(X1, X2, X3, X4) -> U134(X1, X2, X3, X4)
, a__U135(X1, X2, X3, X4) -> U135(X1, X2, X3, X4)
, a__U136(X1, X2, X3, X4) -> U136(X1, X2, X3, X4)
, a__take(X1, X2) -> take(X1, X2)
, a__U21(X1, X2) -> U21(X1, X2)
, a__U22(X1, X2) -> U22(X1, X2)
, a__U23(X) -> U23(X)
, a__U31(X1, X2) -> U31(X1, X2)
, a__U32(X1, X2) -> U32(X1, X2)
, a__U33(X) -> U33(X)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__U42(X1, X2, X3) -> U42(X1, X2, X3)
, a__U43(X1, X2, X3) -> U43(X1, X2, X3)
, a__U44(X1, X2, X3) -> U44(X1, X2, X3)
, a__U45(X1, X2) -> U45(X1, X2)
, a__U46(X) -> U46(X)
, a__U51(X1, X2) -> U51(X1, X2)
, a__U52(X) -> U52(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X) -> U62(X)
, a__U71(X) -> U71(X)
, a__U81(X) -> U81(X)
, a__U91(X1, X2, X3) -> U91(X1, X2, X3)
, a__U92(X1, X2, X3) -> U92(X1, X2, X3)
, a__U93(X1, X2, X3) -> U93(X1, X2, X3)
, a__U94(X1, X2, X3) -> U94(X1, X2, X3)
, a__U95(X1, X2) -> U95(X1, X2)
, a__U96(X) -> U96(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ a__zeros() -> cons(0(), zeros())
, a__U101(tt(), V1, V2) -> a__U102(a__isNatKind(V1), V1, V2)
, a__U102(tt(), V1, V2) -> a__U103(a__isNatIListKind(V2), V1, V2)
, a__U103(tt(), V1, V2) -> a__U104(a__isNatIListKind(V2), V1, V2)
, a__U104(tt(), V1, V2) -> a__U105(a__isNat(V1), V2)
, a__U105(tt(), V2) -> a__U106(a__isNatIList(V2))
, a__U106(tt()) -> tt()
, a__U11(tt(), V1) -> a__U12(a__isNatIListKind(V1), V1)
, a__U111(tt(), L, N) -> a__U112(a__isNatIListKind(L), L, N)
, a__U112(tt(), L, N) -> a__U113(a__isNat(N), L, N)
, a__U113(tt(), L, N) -> a__U114(a__isNatKind(N), L)
, a__U114(tt(), L) -> s(a__length(mark(L)))
, a__U12(tt(), V1) -> a__U13(a__isNatList(V1))
, a__U121(tt(), IL) -> a__U122(a__isNatIListKind(IL))
, a__U122(tt()) -> nil()
, a__U13(tt()) -> tt()
, a__U131(tt(), IL, M, N) ->
a__U132(a__isNatIListKind(IL), IL, M, N)
, a__U132(tt(), IL, M, N) -> a__U133(a__isNat(M), IL, M, N)
, a__U133(tt(), IL, M, N) -> a__U134(a__isNatKind(M), IL, M, N)
, a__U134(tt(), IL, M, N) -> a__U135(a__isNat(N), IL, M, N)
, a__U135(tt(), IL, M, N) -> a__U136(a__isNatKind(N), IL, M, N)
, a__U136(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
, a__U21(tt(), V1) -> a__U22(a__isNatKind(V1), V1)
, a__U22(tt(), V1) -> a__U23(a__isNat(V1))
, a__U23(tt()) -> tt()
, a__U31(tt(), V) -> a__U32(a__isNatIListKind(V), V)
, a__U32(tt(), V) -> a__U33(a__isNatList(V))
, a__U33(tt()) -> tt()
, a__U41(tt(), V1, V2) -> a__U42(a__isNatKind(V1), V1, V2)
, a__U42(tt(), V1, V2) -> a__U43(a__isNatIListKind(V2), V1, V2)
, a__U43(tt(), V1, V2) -> a__U44(a__isNatIListKind(V2), V1, V2)
, a__U44(tt(), V1, V2) -> a__U45(a__isNat(V1), V2)
, a__U45(tt(), V2) -> a__U46(a__isNatIList(V2))
, a__U46(tt()) -> tt()
, a__U51(tt(), V2) -> a__U52(a__isNatIListKind(V2))
, a__U52(tt()) -> tt()
, a__U61(tt(), V2) -> a__U62(a__isNatIListKind(V2))
, a__U62(tt()) -> tt()
, a__U71(tt()) -> tt()
, a__U81(tt()) -> tt()
, a__U91(tt(), V1, V2) -> a__U92(a__isNatKind(V1), V1, V2)
, a__U92(tt(), V1, V2) -> a__U93(a__isNatIListKind(V2), V1, V2)
, a__U93(tt(), V1, V2) -> a__U94(a__isNatIListKind(V2), V1, V2)
, a__U94(tt(), V1, V2) -> a__U95(a__isNat(V1), V2)
, a__U95(tt(), V2) -> a__U96(a__isNatList(V2))
, a__U96(tt()) -> tt()
, 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__isNatKind(V1), V1, V2)
, a__isNatIListKind(nil()) -> tt()
, a__isNatIListKind(zeros()) -> tt()
, a__isNatIListKind(cons(V1, V2)) -> a__U51(a__isNatKind(V1), V2)
, a__isNatIListKind(take(V1, V2)) -> a__U61(a__isNatKind(V1), V2)
, a__isNatKind(0()) -> tt()
, a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1))
, a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1))
, a__isNatList(nil()) -> tt()
, a__isNatList(cons(V1, V2)) -> a__U91(a__isNatKind(V1), V1, V2)
, a__isNatList(take(V1, V2)) -> a__U101(a__isNatKind(V1), V1, V2)
, a__length(nil()) -> 0()
, a__length(cons(N, L)) -> a__U111(a__isNatList(L), L, N)
, a__take(0(), IL) -> a__U121(a__isNatIList(IL), IL)
, a__take(s(M), cons(N, IL)) ->
a__U131(a__isNatIList(IL), IL, M, N)
, mark(zeros()) -> a__zeros()
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
, mark(isNatKind(X)) -> a__isNatKind(X)
, mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
, mark(isNatIListKind(X)) -> a__isNatIListKind(X)
, mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
, mark(U105(X1, X2)) -> a__U105(mark(X1), X2)
, mark(isNat(X)) -> a__isNat(X)
, mark(U106(X)) -> a__U106(mark(X))
, mark(isNatIList(X)) -> a__isNatIList(X)
, mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
, mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
, mark(U111(X1, X2, X3)) -> a__U111(mark(X1), X2, X3)
, mark(U112(X1, X2, X3)) -> a__U112(mark(X1), X2, X3)
, mark(U113(X1, X2, X3)) -> a__U113(mark(X1), X2, X3)
, mark(U114(X1, X2)) -> a__U114(mark(X1), X2)
, mark(length(X)) -> a__length(mark(X))
, mark(U13(X)) -> a__U13(mark(X))
, mark(isNatList(X)) -> a__isNatList(X)
, mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
, mark(U122(X)) -> a__U122(mark(X))
, mark(U131(X1, X2, X3, X4)) -> a__U131(mark(X1), X2, X3, X4)
, mark(U132(X1, X2, X3, X4)) -> a__U132(mark(X1), X2, X3, X4)
, mark(U133(X1, X2, X3, X4)) -> a__U133(mark(X1), X2, X3, X4)
, mark(U134(X1, X2, X3, X4)) -> a__U134(mark(X1), X2, X3, X4)
, mark(U135(X1, X2, X3, X4)) -> a__U135(mark(X1), X2, X3, X4)
, mark(U136(X1, X2, X3, X4)) -> a__U136(mark(X1), X2, X3, X4)
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
, mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
, mark(U23(X)) -> a__U23(mark(X))
, mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
, mark(U32(X1, X2)) -> a__U32(mark(X1), X2)
, mark(U33(X)) -> a__U33(mark(X))
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
, mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3)
, mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3)
, mark(U45(X1, X2)) -> a__U45(mark(X1), X2)
, mark(U46(X)) -> a__U46(mark(X))
, mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
, mark(U52(X)) -> a__U52(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X)) -> a__U62(mark(X))
, mark(U71(X)) -> a__U71(mark(X))
, mark(U81(X)) -> a__U81(mark(X))
, mark(U91(X1, X2, X3)) -> a__U91(mark(X1), X2, X3)
, mark(U92(X1, X2, X3)) -> a__U92(mark(X1), X2, X3)
, mark(U93(X1, X2, X3)) -> a__U93(mark(X1), X2, X3)
, mark(U94(X1, X2, X3)) -> a__U94(mark(X1), X2, X3)
, mark(U95(X1, X2)) -> a__U95(mark(X1), X2)
, mark(U96(X)) -> a__U96(mark(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__U101(X1, X2, X3) -> U101(X1, X2, X3)
, a__U102(X1, X2, X3) -> U102(X1, X2, X3)
, a__isNatKind(X) -> isNatKind(X)
, a__U103(X1, X2, X3) -> U103(X1, X2, X3)
, a__isNatIListKind(X) -> isNatIListKind(X)
, a__U104(X1, X2, X3) -> U104(X1, X2, X3)
, a__U105(X1, X2) -> U105(X1, X2)
, a__isNat(X) -> isNat(X)
, a__U106(X) -> U106(X)
, a__isNatIList(X) -> isNatIList(X)
, a__U11(X1, X2) -> U11(X1, X2)
, a__U12(X1, X2) -> U12(X1, X2)
, a__U111(X1, X2, X3) -> U111(X1, X2, X3)
, a__U112(X1, X2, X3) -> U112(X1, X2, X3)
, a__U113(X1, X2, X3) -> U113(X1, X2, X3)
, a__U114(X1, X2) -> U114(X1, X2)
, a__length(X) -> length(X)
, a__U13(X) -> U13(X)
, a__isNatList(X) -> isNatList(X)
, a__U121(X1, X2) -> U121(X1, X2)
, a__U122(X) -> U122(X)
, a__U131(X1, X2, X3, X4) -> U131(X1, X2, X3, X4)
, a__U132(X1, X2, X3, X4) -> U132(X1, X2, X3, X4)
, a__U133(X1, X2, X3, X4) -> U133(X1, X2, X3, X4)
, a__U134(X1, X2, X3, X4) -> U134(X1, X2, X3, X4)
, a__U135(X1, X2, X3, X4) -> U135(X1, X2, X3, X4)
, a__U136(X1, X2, X3, X4) -> U136(X1, X2, X3, X4)
, a__take(X1, X2) -> take(X1, X2)
, a__U21(X1, X2) -> U21(X1, X2)
, a__U22(X1, X2) -> U22(X1, X2)
, a__U23(X) -> U23(X)
, a__U31(X1, X2) -> U31(X1, X2)
, a__U32(X1, X2) -> U32(X1, X2)
, a__U33(X) -> U33(X)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__U42(X1, X2, X3) -> U42(X1, X2, X3)
, a__U43(X1, X2, X3) -> U43(X1, X2, X3)
, a__U44(X1, X2, X3) -> U44(X1, X2, X3)
, a__U45(X1, X2) -> U45(X1, X2)
, a__U46(X) -> U46(X)
, a__U51(X1, X2) -> U51(X1, X2)
, a__U52(X) -> U52(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X) -> U62(X)
, a__U71(X) -> U71(X)
, a__U81(X) -> U81(X)
, a__U91(X1, X2, X3) -> U91(X1, X2, X3)
, a__U92(X1, X2, X3) -> U92(X1, X2, X3)
, a__U93(X1, X2, X3) -> U93(X1, X2, X3)
, a__U94(X1, X2, X3) -> U94(X1, X2, X3)
, a__U95(X1, X2) -> U95(X1, X2)
, a__U96(X) -> U96(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ a__zeros() -> cons(0(), zeros())
, a__U101(tt(), V1, V2) -> a__U102(a__isNatKind(V1), V1, V2)
, a__U102(tt(), V1, V2) -> a__U103(a__isNatIListKind(V2), V1, V2)
, a__U103(tt(), V1, V2) -> a__U104(a__isNatIListKind(V2), V1, V2)
, a__U104(tt(), V1, V2) -> a__U105(a__isNat(V1), V2)
, a__U105(tt(), V2) -> a__U106(a__isNatIList(V2))
, a__U106(tt()) -> tt()
, a__U11(tt(), V1) -> a__U12(a__isNatIListKind(V1), V1)
, a__U111(tt(), L, N) -> a__U112(a__isNatIListKind(L), L, N)
, a__U112(tt(), L, N) -> a__U113(a__isNat(N), L, N)
, a__U113(tt(), L, N) -> a__U114(a__isNatKind(N), L)
, a__U114(tt(), L) -> s(a__length(mark(L)))
, a__U12(tt(), V1) -> a__U13(a__isNatList(V1))
, a__U121(tt(), IL) -> a__U122(a__isNatIListKind(IL))
, a__U122(tt()) -> nil()
, a__U13(tt()) -> tt()
, a__U131(tt(), IL, M, N) ->
a__U132(a__isNatIListKind(IL), IL, M, N)
, a__U132(tt(), IL, M, N) -> a__U133(a__isNat(M), IL, M, N)
, a__U133(tt(), IL, M, N) -> a__U134(a__isNatKind(M), IL, M, N)
, a__U134(tt(), IL, M, N) -> a__U135(a__isNat(N), IL, M, N)
, a__U135(tt(), IL, M, N) -> a__U136(a__isNatKind(N), IL, M, N)
, a__U136(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
, a__U21(tt(), V1) -> a__U22(a__isNatKind(V1), V1)
, a__U22(tt(), V1) -> a__U23(a__isNat(V1))
, a__U23(tt()) -> tt()
, a__U31(tt(), V) -> a__U32(a__isNatIListKind(V), V)
, a__U32(tt(), V) -> a__U33(a__isNatList(V))
, a__U33(tt()) -> tt()
, a__U41(tt(), V1, V2) -> a__U42(a__isNatKind(V1), V1, V2)
, a__U42(tt(), V1, V2) -> a__U43(a__isNatIListKind(V2), V1, V2)
, a__U43(tt(), V1, V2) -> a__U44(a__isNatIListKind(V2), V1, V2)
, a__U44(tt(), V1, V2) -> a__U45(a__isNat(V1), V2)
, a__U45(tt(), V2) -> a__U46(a__isNatIList(V2))
, a__U46(tt()) -> tt()
, a__U51(tt(), V2) -> a__U52(a__isNatIListKind(V2))
, a__U52(tt()) -> tt()
, a__U61(tt(), V2) -> a__U62(a__isNatIListKind(V2))
, a__U62(tt()) -> tt()
, a__U71(tt()) -> tt()
, a__U81(tt()) -> tt()
, a__U91(tt(), V1, V2) -> a__U92(a__isNatKind(V1), V1, V2)
, a__U92(tt(), V1, V2) -> a__U93(a__isNatIListKind(V2), V1, V2)
, a__U93(tt(), V1, V2) -> a__U94(a__isNatIListKind(V2), V1, V2)
, a__U94(tt(), V1, V2) -> a__U95(a__isNat(V1), V2)
, a__U95(tt(), V2) -> a__U96(a__isNatList(V2))
, a__U96(tt()) -> tt()
, 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__isNatKind(V1), V1, V2)
, a__isNatIListKind(nil()) -> tt()
, a__isNatIListKind(zeros()) -> tt()
, a__isNatIListKind(cons(V1, V2)) -> a__U51(a__isNatKind(V1), V2)
, a__isNatIListKind(take(V1, V2)) -> a__U61(a__isNatKind(V1), V2)
, a__isNatKind(0()) -> tt()
, a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1))
, a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1))
, a__isNatList(nil()) -> tt()
, a__isNatList(cons(V1, V2)) -> a__U91(a__isNatKind(V1), V1, V2)
, a__isNatList(take(V1, V2)) -> a__U101(a__isNatKind(V1), V1, V2)
, a__length(nil()) -> 0()
, a__length(cons(N, L)) -> a__U111(a__isNatList(L), L, N)
, a__take(0(), IL) -> a__U121(a__isNatIList(IL), IL)
, a__take(s(M), cons(N, IL)) ->
a__U131(a__isNatIList(IL), IL, M, N)
, mark(zeros()) -> a__zeros()
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
, mark(isNatKind(X)) -> a__isNatKind(X)
, mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
, mark(isNatIListKind(X)) -> a__isNatIListKind(X)
, mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
, mark(U105(X1, X2)) -> a__U105(mark(X1), X2)
, mark(isNat(X)) -> a__isNat(X)
, mark(U106(X)) -> a__U106(mark(X))
, mark(isNatIList(X)) -> a__isNatIList(X)
, mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
, mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
, mark(U111(X1, X2, X3)) -> a__U111(mark(X1), X2, X3)
, mark(U112(X1, X2, X3)) -> a__U112(mark(X1), X2, X3)
, mark(U113(X1, X2, X3)) -> a__U113(mark(X1), X2, X3)
, mark(U114(X1, X2)) -> a__U114(mark(X1), X2)
, mark(length(X)) -> a__length(mark(X))
, mark(U13(X)) -> a__U13(mark(X))
, mark(isNatList(X)) -> a__isNatList(X)
, mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
, mark(U122(X)) -> a__U122(mark(X))
, mark(U131(X1, X2, X3, X4)) -> a__U131(mark(X1), X2, X3, X4)
, mark(U132(X1, X2, X3, X4)) -> a__U132(mark(X1), X2, X3, X4)
, mark(U133(X1, X2, X3, X4)) -> a__U133(mark(X1), X2, X3, X4)
, mark(U134(X1, X2, X3, X4)) -> a__U134(mark(X1), X2, X3, X4)
, mark(U135(X1, X2, X3, X4)) -> a__U135(mark(X1), X2, X3, X4)
, mark(U136(X1, X2, X3, X4)) -> a__U136(mark(X1), X2, X3, X4)
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
, mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
, mark(U23(X)) -> a__U23(mark(X))
, mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
, mark(U32(X1, X2)) -> a__U32(mark(X1), X2)
, mark(U33(X)) -> a__U33(mark(X))
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
, mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3)
, mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3)
, mark(U45(X1, X2)) -> a__U45(mark(X1), X2)
, mark(U46(X)) -> a__U46(mark(X))
, mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
, mark(U52(X)) -> a__U52(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X)) -> a__U62(mark(X))
, mark(U71(X)) -> a__U71(mark(X))
, mark(U81(X)) -> a__U81(mark(X))
, mark(U91(X1, X2, X3)) -> a__U91(mark(X1), X2, X3)
, mark(U92(X1, X2, X3)) -> a__U92(mark(X1), X2, X3)
, mark(U93(X1, X2, X3)) -> a__U93(mark(X1), X2, X3)
, mark(U94(X1, X2, X3)) -> a__U94(mark(X1), X2, X3)
, mark(U95(X1, X2)) -> a__U95(mark(X1), X2)
, mark(U96(X)) -> a__U96(mark(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__U101(X1, X2, X3) -> U101(X1, X2, X3)
, a__U102(X1, X2, X3) -> U102(X1, X2, X3)
, a__isNatKind(X) -> isNatKind(X)
, a__U103(X1, X2, X3) -> U103(X1, X2, X3)
, a__isNatIListKind(X) -> isNatIListKind(X)
, a__U104(X1, X2, X3) -> U104(X1, X2, X3)
, a__U105(X1, X2) -> U105(X1, X2)
, a__isNat(X) -> isNat(X)
, a__U106(X) -> U106(X)
, a__isNatIList(X) -> isNatIList(X)
, a__U11(X1, X2) -> U11(X1, X2)
, a__U12(X1, X2) -> U12(X1, X2)
, a__U111(X1, X2, X3) -> U111(X1, X2, X3)
, a__U112(X1, X2, X3) -> U112(X1, X2, X3)
, a__U113(X1, X2, X3) -> U113(X1, X2, X3)
, a__U114(X1, X2) -> U114(X1, X2)
, a__length(X) -> length(X)
, a__U13(X) -> U13(X)
, a__isNatList(X) -> isNatList(X)
, a__U121(X1, X2) -> U121(X1, X2)
, a__U122(X) -> U122(X)
, a__U131(X1, X2, X3, X4) -> U131(X1, X2, X3, X4)
, a__U132(X1, X2, X3, X4) -> U132(X1, X2, X3, X4)
, a__U133(X1, X2, X3, X4) -> U133(X1, X2, X3, X4)
, a__U134(X1, X2, X3, X4) -> U134(X1, X2, X3, X4)
, a__U135(X1, X2, X3, X4) -> U135(X1, X2, X3, X4)
, a__U136(X1, X2, X3, X4) -> U136(X1, X2, X3, X4)
, a__take(X1, X2) -> take(X1, X2)
, a__U21(X1, X2) -> U21(X1, X2)
, a__U22(X1, X2) -> U22(X1, X2)
, a__U23(X) -> U23(X)
, a__U31(X1, X2) -> U31(X1, X2)
, a__U32(X1, X2) -> U32(X1, X2)
, a__U33(X) -> U33(X)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__U42(X1, X2, X3) -> U42(X1, X2, X3)
, a__U43(X1, X2, X3) -> U43(X1, X2, X3)
, a__U44(X1, X2, X3) -> U44(X1, X2, X3)
, a__U45(X1, X2) -> U45(X1, X2)
, a__U46(X) -> U46(X)
, a__U51(X1, X2) -> U51(X1, X2)
, a__U52(X) -> U52(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X) -> U62(X)
, a__U71(X) -> U71(X)
, a__U81(X) -> U81(X)
, a__U91(X1, X2, X3) -> U91(X1, X2, X3)
, a__U92(X1, X2, X3) -> U92(X1, X2, X3)
, a__U93(X1, X2, X3) -> U93(X1, X2, X3)
, a__U94(X1, X2, X3) -> U94(X1, X2, X3)
, a__U95(X1, X2) -> U95(X1, X2)
, a__U96(X) -> U96(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ a__zeros() -> cons(0(), zeros())
, a__U101(tt(), V1, V2) -> a__U102(a__isNatKind(V1), V1, V2)
, a__U102(tt(), V1, V2) -> a__U103(a__isNatIListKind(V2), V1, V2)
, a__U103(tt(), V1, V2) -> a__U104(a__isNatIListKind(V2), V1, V2)
, a__U104(tt(), V1, V2) -> a__U105(a__isNat(V1), V2)
, a__U105(tt(), V2) -> a__U106(a__isNatIList(V2))
, a__U106(tt()) -> tt()
, a__U11(tt(), V1) -> a__U12(a__isNatIListKind(V1), V1)
, a__U111(tt(), L, N) -> a__U112(a__isNatIListKind(L), L, N)
, a__U112(tt(), L, N) -> a__U113(a__isNat(N), L, N)
, a__U113(tt(), L, N) -> a__U114(a__isNatKind(N), L)
, a__U114(tt(), L) -> s(a__length(mark(L)))
, a__U12(tt(), V1) -> a__U13(a__isNatList(V1))
, a__U121(tt(), IL) -> a__U122(a__isNatIListKind(IL))
, a__U122(tt()) -> nil()
, a__U13(tt()) -> tt()
, a__U131(tt(), IL, M, N) ->
a__U132(a__isNatIListKind(IL), IL, M, N)
, a__U132(tt(), IL, M, N) -> a__U133(a__isNat(M), IL, M, N)
, a__U133(tt(), IL, M, N) -> a__U134(a__isNatKind(M), IL, M, N)
, a__U134(tt(), IL, M, N) -> a__U135(a__isNat(N), IL, M, N)
, a__U135(tt(), IL, M, N) -> a__U136(a__isNatKind(N), IL, M, N)
, a__U136(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
, a__U21(tt(), V1) -> a__U22(a__isNatKind(V1), V1)
, a__U22(tt(), V1) -> a__U23(a__isNat(V1))
, a__U23(tt()) -> tt()
, a__U31(tt(), V) -> a__U32(a__isNatIListKind(V), V)
, a__U32(tt(), V) -> a__U33(a__isNatList(V))
, a__U33(tt()) -> tt()
, a__U41(tt(), V1, V2) -> a__U42(a__isNatKind(V1), V1, V2)
, a__U42(tt(), V1, V2) -> a__U43(a__isNatIListKind(V2), V1, V2)
, a__U43(tt(), V1, V2) -> a__U44(a__isNatIListKind(V2), V1, V2)
, a__U44(tt(), V1, V2) -> a__U45(a__isNat(V1), V2)
, a__U45(tt(), V2) -> a__U46(a__isNatIList(V2))
, a__U46(tt()) -> tt()
, a__U51(tt(), V2) -> a__U52(a__isNatIListKind(V2))
, a__U52(tt()) -> tt()
, a__U61(tt(), V2) -> a__U62(a__isNatIListKind(V2))
, a__U62(tt()) -> tt()
, a__U71(tt()) -> tt()
, a__U81(tt()) -> tt()
, a__U91(tt(), V1, V2) -> a__U92(a__isNatKind(V1), V1, V2)
, a__U92(tt(), V1, V2) -> a__U93(a__isNatIListKind(V2), V1, V2)
, a__U93(tt(), V1, V2) -> a__U94(a__isNatIListKind(V2), V1, V2)
, a__U94(tt(), V1, V2) -> a__U95(a__isNat(V1), V2)
, a__U95(tt(), V2) -> a__U96(a__isNatList(V2))
, a__U96(tt()) -> tt()
, 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__isNatKind(V1), V1, V2)
, a__isNatIListKind(nil()) -> tt()
, a__isNatIListKind(zeros()) -> tt()
, a__isNatIListKind(cons(V1, V2)) -> a__U51(a__isNatKind(V1), V2)
, a__isNatIListKind(take(V1, V2)) -> a__U61(a__isNatKind(V1), V2)
, a__isNatKind(0()) -> tt()
, a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1))
, a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1))
, a__isNatList(nil()) -> tt()
, a__isNatList(cons(V1, V2)) -> a__U91(a__isNatKind(V1), V1, V2)
, a__isNatList(take(V1, V2)) -> a__U101(a__isNatKind(V1), V1, V2)
, a__length(nil()) -> 0()
, a__length(cons(N, L)) -> a__U111(a__isNatList(L), L, N)
, a__take(0(), IL) -> a__U121(a__isNatIList(IL), IL)
, a__take(s(M), cons(N, IL)) ->
a__U131(a__isNatIList(IL), IL, M, N)
, mark(zeros()) -> a__zeros()
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
, mark(isNatKind(X)) -> a__isNatKind(X)
, mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
, mark(isNatIListKind(X)) -> a__isNatIListKind(X)
, mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
, mark(U105(X1, X2)) -> a__U105(mark(X1), X2)
, mark(isNat(X)) -> a__isNat(X)
, mark(U106(X)) -> a__U106(mark(X))
, mark(isNatIList(X)) -> a__isNatIList(X)
, mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
, mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
, mark(U111(X1, X2, X3)) -> a__U111(mark(X1), X2, X3)
, mark(U112(X1, X2, X3)) -> a__U112(mark(X1), X2, X3)
, mark(U113(X1, X2, X3)) -> a__U113(mark(X1), X2, X3)
, mark(U114(X1, X2)) -> a__U114(mark(X1), X2)
, mark(length(X)) -> a__length(mark(X))
, mark(U13(X)) -> a__U13(mark(X))
, mark(isNatList(X)) -> a__isNatList(X)
, mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
, mark(U122(X)) -> a__U122(mark(X))
, mark(U131(X1, X2, X3, X4)) -> a__U131(mark(X1), X2, X3, X4)
, mark(U132(X1, X2, X3, X4)) -> a__U132(mark(X1), X2, X3, X4)
, mark(U133(X1, X2, X3, X4)) -> a__U133(mark(X1), X2, X3, X4)
, mark(U134(X1, X2, X3, X4)) -> a__U134(mark(X1), X2, X3, X4)
, mark(U135(X1, X2, X3, X4)) -> a__U135(mark(X1), X2, X3, X4)
, mark(U136(X1, X2, X3, X4)) -> a__U136(mark(X1), X2, X3, X4)
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
, mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
, mark(U23(X)) -> a__U23(mark(X))
, mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
, mark(U32(X1, X2)) -> a__U32(mark(X1), X2)
, mark(U33(X)) -> a__U33(mark(X))
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
, mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3)
, mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3)
, mark(U45(X1, X2)) -> a__U45(mark(X1), X2)
, mark(U46(X)) -> a__U46(mark(X))
, mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
, mark(U52(X)) -> a__U52(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X)) -> a__U62(mark(X))
, mark(U71(X)) -> a__U71(mark(X))
, mark(U81(X)) -> a__U81(mark(X))
, mark(U91(X1, X2, X3)) -> a__U91(mark(X1), X2, X3)
, mark(U92(X1, X2, X3)) -> a__U92(mark(X1), X2, X3)
, mark(U93(X1, X2, X3)) -> a__U93(mark(X1), X2, X3)
, mark(U94(X1, X2, X3)) -> a__U94(mark(X1), X2, X3)
, mark(U95(X1, X2)) -> a__U95(mark(X1), X2)
, mark(U96(X)) -> a__U96(mark(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__U101(X1, X2, X3) -> U101(X1, X2, X3)
, a__U102(X1, X2, X3) -> U102(X1, X2, X3)
, a__isNatKind(X) -> isNatKind(X)
, a__U103(X1, X2, X3) -> U103(X1, X2, X3)
, a__isNatIListKind(X) -> isNatIListKind(X)
, a__U104(X1, X2, X3) -> U104(X1, X2, X3)
, a__U105(X1, X2) -> U105(X1, X2)
, a__isNat(X) -> isNat(X)
, a__U106(X) -> U106(X)
, a__isNatIList(X) -> isNatIList(X)
, a__U11(X1, X2) -> U11(X1, X2)
, a__U12(X1, X2) -> U12(X1, X2)
, a__U111(X1, X2, X3) -> U111(X1, X2, X3)
, a__U112(X1, X2, X3) -> U112(X1, X2, X3)
, a__U113(X1, X2, X3) -> U113(X1, X2, X3)
, a__U114(X1, X2) -> U114(X1, X2)
, a__length(X) -> length(X)
, a__U13(X) -> U13(X)
, a__isNatList(X) -> isNatList(X)
, a__U121(X1, X2) -> U121(X1, X2)
, a__U122(X) -> U122(X)
, a__U131(X1, X2, X3, X4) -> U131(X1, X2, X3, X4)
, a__U132(X1, X2, X3, X4) -> U132(X1, X2, X3, X4)
, a__U133(X1, X2, X3, X4) -> U133(X1, X2, X3, X4)
, a__U134(X1, X2, X3, X4) -> U134(X1, X2, X3, X4)
, a__U135(X1, X2, X3, X4) -> U135(X1, X2, X3, X4)
, a__U136(X1, X2, X3, X4) -> U136(X1, X2, X3, X4)
, a__take(X1, X2) -> take(X1, X2)
, a__U21(X1, X2) -> U21(X1, X2)
, a__U22(X1, X2) -> U22(X1, X2)
, a__U23(X) -> U23(X)
, a__U31(X1, X2) -> U31(X1, X2)
, a__U32(X1, X2) -> U32(X1, X2)
, a__U33(X) -> U33(X)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__U42(X1, X2, X3) -> U42(X1, X2, X3)
, a__U43(X1, X2, X3) -> U43(X1, X2, X3)
, a__U44(X1, X2, X3) -> U44(X1, X2, X3)
, a__U45(X1, X2) -> U45(X1, X2)
, a__U46(X) -> U46(X)
, a__U51(X1, X2) -> U51(X1, X2)
, a__U52(X) -> U52(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X) -> U62(X)
, a__U71(X) -> U71(X)
, a__U81(X) -> U81(X)
, a__U91(X1, X2, X3) -> U91(X1, X2, X3)
, a__U92(X1, X2, X3) -> U92(X1, X2, X3)
, a__U93(X1, X2, X3) -> U93(X1, X2, X3)
, a__U94(X1, X2, X3) -> U94(X1, X2, X3)
, a__U95(X1, X2) -> U95(X1, X2)
, a__U96(X) -> U96(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ a__zeros() -> cons(0(), zeros())
, a__U101(tt(), V1, V2) -> a__U102(a__isNatKind(V1), V1, V2)
, a__U102(tt(), V1, V2) -> a__U103(a__isNatIListKind(V2), V1, V2)
, a__U103(tt(), V1, V2) -> a__U104(a__isNatIListKind(V2), V1, V2)
, a__U104(tt(), V1, V2) -> a__U105(a__isNat(V1), V2)
, a__U105(tt(), V2) -> a__U106(a__isNatIList(V2))
, a__U106(tt()) -> tt()
, a__U11(tt(), V1) -> a__U12(a__isNatIListKind(V1), V1)
, a__U111(tt(), L, N) -> a__U112(a__isNatIListKind(L), L, N)
, a__U112(tt(), L, N) -> a__U113(a__isNat(N), L, N)
, a__U113(tt(), L, N) -> a__U114(a__isNatKind(N), L)
, a__U114(tt(), L) -> s(a__length(mark(L)))
, a__U12(tt(), V1) -> a__U13(a__isNatList(V1))
, a__U121(tt(), IL) -> a__U122(a__isNatIListKind(IL))
, a__U122(tt()) -> nil()
, a__U13(tt()) -> tt()
, a__U131(tt(), IL, M, N) ->
a__U132(a__isNatIListKind(IL), IL, M, N)
, a__U132(tt(), IL, M, N) -> a__U133(a__isNat(M), IL, M, N)
, a__U133(tt(), IL, M, N) -> a__U134(a__isNatKind(M), IL, M, N)
, a__U134(tt(), IL, M, N) -> a__U135(a__isNat(N), IL, M, N)
, a__U135(tt(), IL, M, N) -> a__U136(a__isNatKind(N), IL, M, N)
, a__U136(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
, a__U21(tt(), V1) -> a__U22(a__isNatKind(V1), V1)
, a__U22(tt(), V1) -> a__U23(a__isNat(V1))
, a__U23(tt()) -> tt()
, a__U31(tt(), V) -> a__U32(a__isNatIListKind(V), V)
, a__U32(tt(), V) -> a__U33(a__isNatList(V))
, a__U33(tt()) -> tt()
, a__U41(tt(), V1, V2) -> a__U42(a__isNatKind(V1), V1, V2)
, a__U42(tt(), V1, V2) -> a__U43(a__isNatIListKind(V2), V1, V2)
, a__U43(tt(), V1, V2) -> a__U44(a__isNatIListKind(V2), V1, V2)
, a__U44(tt(), V1, V2) -> a__U45(a__isNat(V1), V2)
, a__U45(tt(), V2) -> a__U46(a__isNatIList(V2))
, a__U46(tt()) -> tt()
, a__U51(tt(), V2) -> a__U52(a__isNatIListKind(V2))
, a__U52(tt()) -> tt()
, a__U61(tt(), V2) -> a__U62(a__isNatIListKind(V2))
, a__U62(tt()) -> tt()
, a__U71(tt()) -> tt()
, a__U81(tt()) -> tt()
, a__U91(tt(), V1, V2) -> a__U92(a__isNatKind(V1), V1, V2)
, a__U92(tt(), V1, V2) -> a__U93(a__isNatIListKind(V2), V1, V2)
, a__U93(tt(), V1, V2) -> a__U94(a__isNatIListKind(V2), V1, V2)
, a__U94(tt(), V1, V2) -> a__U95(a__isNat(V1), V2)
, a__U95(tt(), V2) -> a__U96(a__isNatList(V2))
, a__U96(tt()) -> tt()
, 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__isNatKind(V1), V1, V2)
, a__isNatIListKind(nil()) -> tt()
, a__isNatIListKind(zeros()) -> tt()
, a__isNatIListKind(cons(V1, V2)) -> a__U51(a__isNatKind(V1), V2)
, a__isNatIListKind(take(V1, V2)) -> a__U61(a__isNatKind(V1), V2)
, a__isNatKind(0()) -> tt()
, a__isNatKind(length(V1)) -> a__U71(a__isNatIListKind(V1))
, a__isNatKind(s(V1)) -> a__U81(a__isNatKind(V1))
, a__isNatList(nil()) -> tt()
, a__isNatList(cons(V1, V2)) -> a__U91(a__isNatKind(V1), V1, V2)
, a__isNatList(take(V1, V2)) -> a__U101(a__isNatKind(V1), V1, V2)
, a__length(nil()) -> 0()
, a__length(cons(N, L)) -> a__U111(a__isNatList(L), L, N)
, a__take(0(), IL) -> a__U121(a__isNatIList(IL), IL)
, a__take(s(M), cons(N, IL)) ->
a__U131(a__isNatIList(IL), IL, M, N)
, mark(zeros()) -> a__zeros()
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
, mark(isNatKind(X)) -> a__isNatKind(X)
, mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
, mark(isNatIListKind(X)) -> a__isNatIListKind(X)
, mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
, mark(U105(X1, X2)) -> a__U105(mark(X1), X2)
, mark(isNat(X)) -> a__isNat(X)
, mark(U106(X)) -> a__U106(mark(X))
, mark(isNatIList(X)) -> a__isNatIList(X)
, mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
, mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
, mark(U111(X1, X2, X3)) -> a__U111(mark(X1), X2, X3)
, mark(U112(X1, X2, X3)) -> a__U112(mark(X1), X2, X3)
, mark(U113(X1, X2, X3)) -> a__U113(mark(X1), X2, X3)
, mark(U114(X1, X2)) -> a__U114(mark(X1), X2)
, mark(length(X)) -> a__length(mark(X))
, mark(U13(X)) -> a__U13(mark(X))
, mark(isNatList(X)) -> a__isNatList(X)
, mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
, mark(U122(X)) -> a__U122(mark(X))
, mark(U131(X1, X2, X3, X4)) -> a__U131(mark(X1), X2, X3, X4)
, mark(U132(X1, X2, X3, X4)) -> a__U132(mark(X1), X2, X3, X4)
, mark(U133(X1, X2, X3, X4)) -> a__U133(mark(X1), X2, X3, X4)
, mark(U134(X1, X2, X3, X4)) -> a__U134(mark(X1), X2, X3, X4)
, mark(U135(X1, X2, X3, X4)) -> a__U135(mark(X1), X2, X3, X4)
, mark(U136(X1, X2, X3, X4)) -> a__U136(mark(X1), X2, X3, X4)
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
, mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
, mark(U23(X)) -> a__U23(mark(X))
, mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
, mark(U32(X1, X2)) -> a__U32(mark(X1), X2)
, mark(U33(X)) -> a__U33(mark(X))
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
, mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3)
, mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3)
, mark(U45(X1, X2)) -> a__U45(mark(X1), X2)
, mark(U46(X)) -> a__U46(mark(X))
, mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
, mark(U52(X)) -> a__U52(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X)) -> a__U62(mark(X))
, mark(U71(X)) -> a__U71(mark(X))
, mark(U81(X)) -> a__U81(mark(X))
, mark(U91(X1, X2, X3)) -> a__U91(mark(X1), X2, X3)
, mark(U92(X1, X2, X3)) -> a__U92(mark(X1), X2, X3)
, mark(U93(X1, X2, X3)) -> a__U93(mark(X1), X2, X3)
, mark(U94(X1, X2, X3)) -> a__U94(mark(X1), X2, X3)
, mark(U95(X1, X2)) -> a__U95(mark(X1), X2)
, mark(U96(X)) -> a__U96(mark(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__U101(X1, X2, X3) -> U101(X1, X2, X3)
, a__U102(X1, X2, X3) -> U102(X1, X2, X3)
, a__isNatKind(X) -> isNatKind(X)
, a__U103(X1, X2, X3) -> U103(X1, X2, X3)
, a__isNatIListKind(X) -> isNatIListKind(X)
, a__U104(X1, X2, X3) -> U104(X1, X2, X3)
, a__U105(X1, X2) -> U105(X1, X2)
, a__isNat(X) -> isNat(X)
, a__U106(X) -> U106(X)
, a__isNatIList(X) -> isNatIList(X)
, a__U11(X1, X2) -> U11(X1, X2)
, a__U12(X1, X2) -> U12(X1, X2)
, a__U111(X1, X2, X3) -> U111(X1, X2, X3)
, a__U112(X1, X2, X3) -> U112(X1, X2, X3)
, a__U113(X1, X2, X3) -> U113(X1, X2, X3)
, a__U114(X1, X2) -> U114(X1, X2)
, a__length(X) -> length(X)
, a__U13(X) -> U13(X)
, a__isNatList(X) -> isNatList(X)
, a__U121(X1, X2) -> U121(X1, X2)
, a__U122(X) -> U122(X)
, a__U131(X1, X2, X3, X4) -> U131(X1, X2, X3, X4)
, a__U132(X1, X2, X3, X4) -> U132(X1, X2, X3, X4)
, a__U133(X1, X2, X3, X4) -> U133(X1, X2, X3, X4)
, a__U134(X1, X2, X3, X4) -> U134(X1, X2, X3, X4)
, a__U135(X1, X2, X3, X4) -> U135(X1, X2, X3, X4)
, a__U136(X1, X2, X3, X4) -> U136(X1, X2, X3, X4)
, a__take(X1, X2) -> take(X1, X2)
, a__U21(X1, X2) -> U21(X1, X2)
, a__U22(X1, X2) -> U22(X1, X2)
, a__U23(X) -> U23(X)
, a__U31(X1, X2) -> U31(X1, X2)
, a__U32(X1, X2) -> U32(X1, X2)
, a__U33(X) -> U33(X)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__U42(X1, X2, X3) -> U42(X1, X2, X3)
, a__U43(X1, X2, X3) -> U43(X1, X2, X3)
, a__U44(X1, X2, X3) -> U44(X1, X2, X3)
, a__U45(X1, X2) -> U45(X1, X2)
, a__U46(X) -> U46(X)
, a__U51(X1, X2) -> U51(X1, X2)
, a__U52(X) -> U52(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X) -> U62(X)
, a__U71(X) -> U71(X)
, a__U81(X) -> U81(X)
, a__U91(X1, X2, X3) -> U91(X1, X2, X3)
, a__U92(X1, X2, X3) -> U92(X1, X2, X3)
, a__U93(X1, X2, X3) -> U93(X1, X2, X3)
, a__U94(X1, X2, X3) -> U94(X1, X2, X3)
, a__U95(X1, X2) -> U95(X1, X2)
, a__U96(X) -> U96(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..