LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__zeros() -> cons(0(), zeros())
, a__U11(tt(), L) -> a__U12(tt(), L)
, a__U12(tt(), L) -> s(a__length(mark(L)))
, a__U21(tt(), IL, M, N) -> a__U22(tt(), IL, M, N)
, a__U22(tt(), IL, M, N) -> a__U23(tt(), IL, M, N)
, a__U23(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
, a__length(nil()) -> 0()
, a__length(cons(N, L)) -> a__U11(tt(), L)
, a__take(0(), IL) -> nil()
, a__take(s(M), cons(N, IL)) -> a__U21(tt(), IL, M, N)
, mark(zeros()) -> a__zeros()
, mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
, mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
, mark(length(X)) -> a__length(mark(X))
, mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4)
, mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4)
, mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4)
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, 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(X1, X2) -> U12(X1, X2)
, a__length(X) -> length(X)
, a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4)
, a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4)
, a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4)
, a__take(X1, X2) -> take(X1, X2)}
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(), L) -> a__U12(tt(), L)
, a__U12(tt(), L) -> s(a__length(mark(L)))
, a__U21(tt(), IL, M, N) -> a__U22(tt(), IL, M, N)
, a__U22(tt(), IL, M, N) -> a__U23(tt(), IL, M, N)
, a__U23(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
, a__length(nil()) -> 0()
, a__length(cons(N, L)) -> a__U11(tt(), L)
, a__take(0(), IL) -> nil()
, a__take(s(M), cons(N, IL)) -> a__U21(tt(), IL, M, N)
, mark(zeros()) -> a__zeros()
, mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
, mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
, mark(length(X)) -> a__length(mark(X))
, mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4)
, mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4)
, mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4)
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, 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(X1, X2) -> U12(X1, X2)
, a__length(X) -> length(X)
, a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4)
, a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4)
, a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4)
, a__take(X1, X2) -> take(X1, X2)}
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(), L) -> a__U12(tt(), L)
, a__U12(tt(), L) -> s(a__length(mark(L)))
, a__U21(tt(), IL, M, N) -> a__U22(tt(), IL, M, N)
, a__U22(tt(), IL, M, N) -> a__U23(tt(), IL, M, N)
, a__U23(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
, a__length(nil()) -> 0()
, a__length(cons(N, L)) -> a__U11(tt(), L)
, a__take(0(), IL) -> nil()
, a__take(s(M), cons(N, IL)) -> a__U21(tt(), IL, M, N)
, mark(zeros()) -> a__zeros()
, mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
, mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
, mark(length(X)) -> a__length(mark(X))
, mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4)
, mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4)
, mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4)
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, 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(X1, X2) -> U12(X1, X2)
, a__length(X) -> length(X)
, a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4)
, a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4)
, a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4)
, a__take(X1, X2) -> take(X1, X2)}
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(), L) -> a__U12(tt(), L)
, a__U12(tt(), L) -> s(a__length(mark(L)))
, a__U21(tt(), IL, M, N) -> a__U22(tt(), IL, M, N)
, a__U22(tt(), IL, M, N) -> a__U23(tt(), IL, M, N)
, a__U23(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
, a__length(nil()) -> 0()
, a__length(cons(N, L)) -> a__U11(tt(), L)
, a__take(0(), IL) -> nil()
, a__take(s(M), cons(N, IL)) -> a__U21(tt(), IL, M, N)
, mark(zeros()) -> a__zeros()
, mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
, mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
, mark(length(X)) -> a__length(mark(X))
, mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4)
, mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4)
, mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4)
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, 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(X1, X2) -> U12(X1, X2)
, a__length(X) -> length(X)
, a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4)
, a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4)
, a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4)
, a__take(X1, X2) -> take(X1, X2)}
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(), L) -> a__U12(tt(), L)
, a__U12(tt(), L) -> s(a__length(mark(L)))
, a__U21(tt(), IL, M, N) -> a__U22(tt(), IL, M, N)
, a__U22(tt(), IL, M, N) -> a__U23(tt(), IL, M, N)
, a__U23(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
, a__length(nil()) -> 0()
, a__length(cons(N, L)) -> a__U11(tt(), L)
, a__take(0(), IL) -> nil()
, a__take(s(M), cons(N, IL)) -> a__U21(tt(), IL, M, N)
, mark(zeros()) -> a__zeros()
, mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
, mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
, mark(length(X)) -> a__length(mark(X))
, mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4)
, mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4)
, mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4)
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, 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(X1, X2) -> U12(X1, X2)
, a__length(X) -> length(X)
, a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4)
, a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4)
, a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4)
, a__take(X1, X2) -> take(X1, X2)}
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(), L) -> a__U12(tt(), L)
, a__U12(tt(), L) -> s(a__length(mark(L)))
, a__U21(tt(), IL, M, N) -> a__U22(tt(), IL, M, N)
, a__U22(tt(), IL, M, N) -> a__U23(tt(), IL, M, N)
, a__U23(tt(), IL, M, N) -> cons(mark(N), take(M, IL))
, a__length(nil()) -> 0()
, a__length(cons(N, L)) -> a__U11(tt(), L)
, a__take(0(), IL) -> nil()
, a__take(s(M), cons(N, IL)) -> a__U21(tt(), IL, M, N)
, mark(zeros()) -> a__zeros()
, mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
, mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
, mark(length(X)) -> a__length(mark(X))
, mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4)
, mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4)
, mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4)
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, 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(X1, X2) -> U12(X1, X2)
, a__length(X) -> length(X)
, a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4)
, a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4)
, a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4)
, a__take(X1, X2) -> take(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..