LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ 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(), V1, V2) -> a__U62(a__isNat(V1), V2)
, a__U62(tt(), V2) -> a__U63(a__isNatIList(V2))
, a__U63(tt()) -> tt()
, a__U71(tt(), L) -> s(a__length(mark(L)))
, a__U81(tt()) -> nil()
, a__U91(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
, 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__isNatIListKind(take(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__isNatList(take(V1, V2)) ->
a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
, a__length(nil()) -> 0()
, a__length(cons(N, L)) ->
a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)),
and(isNat(N), isNatKind(N))),
L)
, a__take(0(), IL) ->
a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL)))
, a__take(s(M), cons(N, IL)) ->
a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)),
and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))),
IL,
M,
N)
, 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, X3)) -> a__U61(mark(X1), X2, X3)
, mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
, mark(U63(X)) -> a__U63(mark(X))
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(length(X)) -> a__length(mark(X))
, mark(U81(X)) -> a__U81(mark(X))
, mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4)
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, 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, X3) -> U61(X1, X2, X3)
, a__U62(X1, X2) -> U62(X1, X2)
, a__U63(X) -> U63(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__length(X) -> length(X)
, a__U81(X) -> U81(X)
, a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
, a__take(X1, X2) -> take(X1, X2)
, a__and(X1, X2) -> and(X1, X2)
, a__isNatIListKind(X) -> isNatIListKind(X)
, a__isNatKind(X) -> isNatKind(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ 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(), V1, V2) -> a__U62(a__isNat(V1), V2)
, a__U62(tt(), V2) -> a__U63(a__isNatIList(V2))
, a__U63(tt()) -> tt()
, a__U71(tt(), L) -> s(a__length(mark(L)))
, a__U81(tt()) -> nil()
, a__U91(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
, 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__isNatIListKind(take(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__isNatList(take(V1, V2)) ->
a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
, a__length(nil()) -> 0()
, a__length(cons(N, L)) ->
a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)),
and(isNat(N), isNatKind(N))),
L)
, a__take(0(), IL) ->
a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL)))
, a__take(s(M), cons(N, IL)) ->
a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)),
and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))),
IL,
M,
N)
, 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, X3)) -> a__U61(mark(X1), X2, X3)
, mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
, mark(U63(X)) -> a__U63(mark(X))
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(length(X)) -> a__length(mark(X))
, mark(U81(X)) -> a__U81(mark(X))
, mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4)
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, 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, X3) -> U61(X1, X2, X3)
, a__U62(X1, X2) -> U62(X1, X2)
, a__U63(X) -> U63(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__length(X) -> length(X)
, a__U81(X) -> U81(X)
, a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
, a__take(X1, X2) -> take(X1, X2)
, a__and(X1, X2) -> and(X1, X2)
, a__isNatIListKind(X) -> isNatIListKind(X)
, a__isNatKind(X) -> isNatKind(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__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(), V1, V2) -> a__U62(a__isNat(V1), V2)
, a__U62(tt(), V2) -> a__U63(a__isNatIList(V2))
, a__U63(tt()) -> tt()
, a__U71(tt(), L) -> s(a__length(mark(L)))
, a__U81(tt()) -> nil()
, a__U91(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
, 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__isNatIListKind(take(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__isNatList(take(V1, V2)) ->
a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
, a__length(nil()) -> 0()
, a__length(cons(N, L)) ->
a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)),
and(isNat(N), isNatKind(N))),
L)
, a__take(0(), IL) ->
a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL)))
, a__take(s(M), cons(N, IL)) ->
a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)),
and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))),
IL,
M,
N)
, 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, X3)) -> a__U61(mark(X1), X2, X3)
, mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
, mark(U63(X)) -> a__U63(mark(X))
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(length(X)) -> a__length(mark(X))
, mark(U81(X)) -> a__U81(mark(X))
, mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4)
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, 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, X3) -> U61(X1, X2, X3)
, a__U62(X1, X2) -> U62(X1, X2)
, a__U63(X) -> U63(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__length(X) -> length(X)
, a__U81(X) -> U81(X)
, a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
, a__take(X1, X2) -> take(X1, X2)
, a__and(X1, X2) -> and(X1, X2)
, a__isNatIListKind(X) -> isNatIListKind(X)
, a__isNatKind(X) -> isNatKind(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__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(), V1, V2) -> a__U62(a__isNat(V1), V2)
, a__U62(tt(), V2) -> a__U63(a__isNatIList(V2))
, a__U63(tt()) -> tt()
, a__U71(tt(), L) -> s(a__length(mark(L)))
, a__U81(tt()) -> nil()
, a__U91(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
, 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__isNatIListKind(take(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__isNatList(take(V1, V2)) ->
a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
, a__length(nil()) -> 0()
, a__length(cons(N, L)) ->
a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)),
and(isNat(N), isNatKind(N))),
L)
, a__take(0(), IL) ->
a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL)))
, a__take(s(M), cons(N, IL)) ->
a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)),
and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))),
IL,
M,
N)
, 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, X3)) -> a__U61(mark(X1), X2, X3)
, mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
, mark(U63(X)) -> a__U63(mark(X))
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(length(X)) -> a__length(mark(X))
, mark(U81(X)) -> a__U81(mark(X))
, mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4)
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, 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, X3) -> U61(X1, X2, X3)
, a__U62(X1, X2) -> U62(X1, X2)
, a__U63(X) -> U63(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__length(X) -> length(X)
, a__U81(X) -> U81(X)
, a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
, a__take(X1, X2) -> take(X1, X2)
, a__and(X1, X2) -> and(X1, X2)
, a__isNatIListKind(X) -> isNatIListKind(X)
, a__isNatKind(X) -> isNatKind(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__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(), V1, V2) -> a__U62(a__isNat(V1), V2)
, a__U62(tt(), V2) -> a__U63(a__isNatIList(V2))
, a__U63(tt()) -> tt()
, a__U71(tt(), L) -> s(a__length(mark(L)))
, a__U81(tt()) -> nil()
, a__U91(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
, 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__isNatIListKind(take(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__isNatList(take(V1, V2)) ->
a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
, a__length(nil()) -> 0()
, a__length(cons(N, L)) ->
a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)),
and(isNat(N), isNatKind(N))),
L)
, a__take(0(), IL) ->
a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL)))
, a__take(s(M), cons(N, IL)) ->
a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)),
and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))),
IL,
M,
N)
, 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, X3)) -> a__U61(mark(X1), X2, X3)
, mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
, mark(U63(X)) -> a__U63(mark(X))
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(length(X)) -> a__length(mark(X))
, mark(U81(X)) -> a__U81(mark(X))
, mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4)
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, 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, X3) -> U61(X1, X2, X3)
, a__U62(X1, X2) -> U62(X1, X2)
, a__U63(X) -> U63(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__length(X) -> length(X)
, a__U81(X) -> U81(X)
, a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
, a__take(X1, X2) -> take(X1, X2)
, a__and(X1, X2) -> and(X1, X2)
, a__isNatIListKind(X) -> isNatIListKind(X)
, a__isNatKind(X) -> isNatKind(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__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(), V1, V2) -> a__U62(a__isNat(V1), V2)
, a__U62(tt(), V2) -> a__U63(a__isNatIList(V2))
, a__U63(tt()) -> tt()
, a__U71(tt(), L) -> s(a__length(mark(L)))
, a__U81(tt()) -> nil()
, a__U91(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
, 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__isNatIListKind(take(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__isNatList(take(V1, V2)) ->
a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
, a__length(nil()) -> 0()
, a__length(cons(N, L)) ->
a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)),
and(isNat(N), isNatKind(N))),
L)
, a__take(0(), IL) ->
a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL)))
, a__take(s(M), cons(N, IL)) ->
a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)),
and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))),
IL,
M,
N)
, 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, X3)) -> a__U61(mark(X1), X2, X3)
, mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
, mark(U63(X)) -> a__U63(mark(X))
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(length(X)) -> a__length(mark(X))
, mark(U81(X)) -> a__U81(mark(X))
, mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4)
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, 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, X3) -> U61(X1, X2, X3)
, a__U62(X1, X2) -> U62(X1, X2)
, a__U63(X) -> U63(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__length(X) -> length(X)
, a__U81(X) -> U81(X)
, a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
, a__take(X1, X2) -> take(X1, X2)
, a__and(X1, X2) -> and(X1, X2)
, a__isNatIListKind(X) -> isNatIListKind(X)
, a__isNatKind(X) -> isNatKind(X)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..