LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__from(X) -> cons(mark(X), from(s(X)))
, a__head(cons(X, XS)) -> mark(X)
, a__2nd(cons(X, XS)) -> a__head(mark(XS))
, a__take(0(), XS) -> nil()
, a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
, a__sel(0(), cons(X, XS)) -> mark(X)
, a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
, mark(from(X)) -> a__from(mark(X))
, mark(head(X)) -> a__head(mark(X))
, mark(2nd(X)) -> a__2nd(mark(X))
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, mark(nil()) -> nil()
, a__from(X) -> from(X)
, a__head(X) -> head(X)
, a__2nd(X) -> 2nd(X)
, a__take(X1, X2) -> take(X1, X2)
, a__sel(X1, X2) -> sel(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__from(X) -> cons(mark(X), from(s(X)))
, a__head(cons(X, XS)) -> mark(X)
, a__2nd(cons(X, XS)) -> a__head(mark(XS))
, a__take(0(), XS) -> nil()
, a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
, a__sel(0(), cons(X, XS)) -> mark(X)
, a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
, mark(from(X)) -> a__from(mark(X))
, mark(head(X)) -> a__head(mark(X))
, mark(2nd(X)) -> a__2nd(mark(X))
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, mark(nil()) -> nil()
, a__from(X) -> from(X)
, a__head(X) -> head(X)
, a__2nd(X) -> 2nd(X)
, a__take(X1, X2) -> take(X1, X2)
, a__sel(X1, X2) -> sel(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__from(X) -> cons(mark(X), from(s(X)))
, a__head(cons(X, XS)) -> mark(X)
, a__2nd(cons(X, XS)) -> a__head(mark(XS))
, a__take(0(), XS) -> nil()
, a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
, a__sel(0(), cons(X, XS)) -> mark(X)
, a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
, mark(from(X)) -> a__from(mark(X))
, mark(head(X)) -> a__head(mark(X))
, mark(2nd(X)) -> a__2nd(mark(X))
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, mark(nil()) -> nil()
, a__from(X) -> from(X)
, a__head(X) -> head(X)
, a__2nd(X) -> 2nd(X)
, a__take(X1, X2) -> take(X1, X2)
, a__sel(X1, X2) -> sel(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__from(X) -> cons(mark(X), from(s(X)))
, a__head(cons(X, XS)) -> mark(X)
, a__2nd(cons(X, XS)) -> a__head(mark(XS))
, a__take(0(), XS) -> nil()
, a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
, a__sel(0(), cons(X, XS)) -> mark(X)
, a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
, mark(from(X)) -> a__from(mark(X))
, mark(head(X)) -> a__head(mark(X))
, mark(2nd(X)) -> a__2nd(mark(X))
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, mark(nil()) -> nil()
, a__from(X) -> from(X)
, a__head(X) -> head(X)
, a__2nd(X) -> 2nd(X)
, a__take(X1, X2) -> take(X1, X2)
, a__sel(X1, X2) -> sel(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__from(X) -> cons(mark(X), from(s(X)))
, a__head(cons(X, XS)) -> mark(X)
, a__2nd(cons(X, XS)) -> a__head(mark(XS))
, a__take(0(), XS) -> nil()
, a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
, a__sel(0(), cons(X, XS)) -> mark(X)
, a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
, mark(from(X)) -> a__from(mark(X))
, mark(head(X)) -> a__head(mark(X))
, mark(2nd(X)) -> a__2nd(mark(X))
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, mark(nil()) -> nil()
, a__from(X) -> from(X)
, a__head(X) -> head(X)
, a__2nd(X) -> 2nd(X)
, a__take(X1, X2) -> take(X1, X2)
, a__sel(X1, X2) -> sel(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__from(X) -> cons(mark(X), from(s(X)))
, a__head(cons(X, XS)) -> mark(X)
, a__2nd(cons(X, XS)) -> a__head(mark(XS))
, a__take(0(), XS) -> nil()
, a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
, a__sel(0(), cons(X, XS)) -> mark(X)
, a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
, mark(from(X)) -> a__from(mark(X))
, mark(head(X)) -> a__head(mark(X))
, mark(2nd(X)) -> a__2nd(mark(X))
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(s(X)) -> s(mark(X))
, mark(0()) -> 0()
, mark(nil()) -> nil()
, a__from(X) -> from(X)
, a__head(X) -> head(X)
, a__2nd(X) -> 2nd(X)
, a__take(X1, X2) -> take(X1, X2)
, a__sel(X1, X2) -> sel(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..