LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__from(X) -> cons(mark(X), from(s(X)))
, a__sel(0(), cons(X, XS)) -> mark(X)
, a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
, a__minus(X, 0()) -> 0()
, a__minus(s(X), s(Y)) -> a__minus(mark(X), mark(Y))
, a__quot(0(), s(Y)) -> 0()
, a__quot(s(X), s(Y)) ->
s(a__quot(a__minus(mark(X), mark(Y)), s(mark(Y))))
, a__zWquot(XS, nil()) -> nil()
, a__zWquot(nil(), XS) -> nil()
, a__zWquot(cons(X, XS), cons(Y, YS)) ->
cons(a__quot(mark(X), mark(Y)), zWquot(XS, YS))
, mark(from(X)) -> a__from(mark(X))
, mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
, mark(minus(X1, X2)) -> a__minus(mark(X1), mark(X2))
, mark(quot(X1, X2)) -> a__quot(mark(X1), mark(X2))
, mark(zWquot(X1, X2)) -> a__zWquot(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__sel(X1, X2) -> sel(X1, X2)
, a__minus(X1, X2) -> minus(X1, X2)
, a__quot(X1, X2) -> quot(X1, X2)
, a__zWquot(X1, X2) -> zWquot(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__sel(0(), cons(X, XS)) -> mark(X)
, a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
, a__minus(X, 0()) -> 0()
, a__minus(s(X), s(Y)) -> a__minus(mark(X), mark(Y))
, a__quot(0(), s(Y)) -> 0()
, a__quot(s(X), s(Y)) ->
s(a__quot(a__minus(mark(X), mark(Y)), s(mark(Y))))
, a__zWquot(XS, nil()) -> nil()
, a__zWquot(nil(), XS) -> nil()
, a__zWquot(cons(X, XS), cons(Y, YS)) ->
cons(a__quot(mark(X), mark(Y)), zWquot(XS, YS))
, mark(from(X)) -> a__from(mark(X))
, mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
, mark(minus(X1, X2)) -> a__minus(mark(X1), mark(X2))
, mark(quot(X1, X2)) -> a__quot(mark(X1), mark(X2))
, mark(zWquot(X1, X2)) -> a__zWquot(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__sel(X1, X2) -> sel(X1, X2)
, a__minus(X1, X2) -> minus(X1, X2)
, a__quot(X1, X2) -> quot(X1, X2)
, a__zWquot(X1, X2) -> zWquot(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__sel(0(), cons(X, XS)) -> mark(X)
, a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
, a__minus(X, 0()) -> 0()
, a__minus(s(X), s(Y)) -> a__minus(mark(X), mark(Y))
, a__quot(0(), s(Y)) -> 0()
, a__quot(s(X), s(Y)) ->
s(a__quot(a__minus(mark(X), mark(Y)), s(mark(Y))))
, a__zWquot(XS, nil()) -> nil()
, a__zWquot(nil(), XS) -> nil()
, a__zWquot(cons(X, XS), cons(Y, YS)) ->
cons(a__quot(mark(X), mark(Y)), zWquot(XS, YS))
, mark(from(X)) -> a__from(mark(X))
, mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
, mark(minus(X1, X2)) -> a__minus(mark(X1), mark(X2))
, mark(quot(X1, X2)) -> a__quot(mark(X1), mark(X2))
, mark(zWquot(X1, X2)) -> a__zWquot(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__sel(X1, X2) -> sel(X1, X2)
, a__minus(X1, X2) -> minus(X1, X2)
, a__quot(X1, X2) -> quot(X1, X2)
, a__zWquot(X1, X2) -> zWquot(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__sel(0(), cons(X, XS)) -> mark(X)
, a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
, a__minus(X, 0()) -> 0()
, a__minus(s(X), s(Y)) -> a__minus(mark(X), mark(Y))
, a__quot(0(), s(Y)) -> 0()
, a__quot(s(X), s(Y)) ->
s(a__quot(a__minus(mark(X), mark(Y)), s(mark(Y))))
, a__zWquot(XS, nil()) -> nil()
, a__zWquot(nil(), XS) -> nil()
, a__zWquot(cons(X, XS), cons(Y, YS)) ->
cons(a__quot(mark(X), mark(Y)), zWquot(XS, YS))
, mark(from(X)) -> a__from(mark(X))
, mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
, mark(minus(X1, X2)) -> a__minus(mark(X1), mark(X2))
, mark(quot(X1, X2)) -> a__quot(mark(X1), mark(X2))
, mark(zWquot(X1, X2)) -> a__zWquot(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__sel(X1, X2) -> sel(X1, X2)
, a__minus(X1, X2) -> minus(X1, X2)
, a__quot(X1, X2) -> quot(X1, X2)
, a__zWquot(X1, X2) -> zWquot(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__sel(0(), cons(X, XS)) -> mark(X)
, a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
, a__minus(X, 0()) -> 0()
, a__minus(s(X), s(Y)) -> a__minus(mark(X), mark(Y))
, a__quot(0(), s(Y)) -> 0()
, a__quot(s(X), s(Y)) ->
s(a__quot(a__minus(mark(X), mark(Y)), s(mark(Y))))
, a__zWquot(XS, nil()) -> nil()
, a__zWquot(nil(), XS) -> nil()
, a__zWquot(cons(X, XS), cons(Y, YS)) ->
cons(a__quot(mark(X), mark(Y)), zWquot(XS, YS))
, mark(from(X)) -> a__from(mark(X))
, mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
, mark(minus(X1, X2)) -> a__minus(mark(X1), mark(X2))
, mark(quot(X1, X2)) -> a__quot(mark(X1), mark(X2))
, mark(zWquot(X1, X2)) -> a__zWquot(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__sel(X1, X2) -> sel(X1, X2)
, a__minus(X1, X2) -> minus(X1, X2)
, a__quot(X1, X2) -> quot(X1, X2)
, a__zWquot(X1, X2) -> zWquot(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__sel(0(), cons(X, XS)) -> mark(X)
, a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
, a__minus(X, 0()) -> 0()
, a__minus(s(X), s(Y)) -> a__minus(mark(X), mark(Y))
, a__quot(0(), s(Y)) -> 0()
, a__quot(s(X), s(Y)) ->
s(a__quot(a__minus(mark(X), mark(Y)), s(mark(Y))))
, a__zWquot(XS, nil()) -> nil()
, a__zWquot(nil(), XS) -> nil()
, a__zWquot(cons(X, XS), cons(Y, YS)) ->
cons(a__quot(mark(X), mark(Y)), zWquot(XS, YS))
, mark(from(X)) -> a__from(mark(X))
, mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
, mark(minus(X1, X2)) -> a__minus(mark(X1), mark(X2))
, mark(quot(X1, X2)) -> a__quot(mark(X1), mark(X2))
, mark(zWquot(X1, X2)) -> a__zWquot(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__sel(X1, X2) -> sel(X1, X2)
, a__minus(X1, X2) -> minus(X1, X2)
, a__quot(X1, X2) -> quot(X1, X2)
, a__zWquot(X1, X2) -> zWquot(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..