LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ leq(0(), x) -> tt()
, leq(s(x), 0()) -> ff()
, leq(s(x), s(y)) -> leq(x, y)
, split(nil()) -> app(nil(), nil())
, split(cons(x, nil())) -> app(cons(x, nil()), nil())
, split(cons(x, cons(y, xs))) -> split1(x, y, split(xs))
, split1(x, y, app(xs, ys)) -> app(cons(x, xs), cons(y, ys))
, merge([](), xs) -> xs
, merge(xs, []()) -> xs
, merge(cons(x, xs), cons(y, ys)) ->
ifmerge(leq(x, y), x, y, xs, ys)
, ifmerge(tt(), x, y, xs, ys) -> cons(x, merge(xs, cons(y, ys)))
, ifmerge(ff(), x, y, xs, ys) -> cons(y, merge(cons(x, xs), ys))
, mergesort(xs) -> mergesort1(split(xs))
, mergesort1(app(xs, ys)) -> merge(mergesort(xs), mergesort(ys))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ leq(0(), x) -> tt()
, leq(s(x), 0()) -> ff()
, leq(s(x), s(y)) -> leq(x, y)
, split(nil()) -> app(nil(), nil())
, split(cons(x, nil())) -> app(cons(x, nil()), nil())
, split(cons(x, cons(y, xs))) -> split1(x, y, split(xs))
, split1(x, y, app(xs, ys)) -> app(cons(x, xs), cons(y, ys))
, merge([](), xs) -> xs
, merge(xs, []()) -> xs
, merge(cons(x, xs), cons(y, ys)) ->
ifmerge(leq(x, y), x, y, xs, ys)
, ifmerge(tt(), x, y, xs, ys) -> cons(x, merge(xs, cons(y, ys)))
, ifmerge(ff(), x, y, xs, ys) -> cons(y, merge(cons(x, xs), ys))
, mergesort(xs) -> mergesort1(split(xs))
, mergesort1(app(xs, ys)) -> merge(mergesort(xs), mergesort(ys))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ leq(0(), x) -> tt()
, leq(s(x), 0()) -> ff()
, leq(s(x), s(y)) -> leq(x, y)
, split(nil()) -> app(nil(), nil())
, split(cons(x, nil())) -> app(cons(x, nil()), nil())
, split(cons(x, cons(y, xs))) -> split1(x, y, split(xs))
, split1(x, y, app(xs, ys)) -> app(cons(x, xs), cons(y, ys))
, merge([](), xs) -> xs
, merge(xs, []()) -> xs
, merge(cons(x, xs), cons(y, ys)) ->
ifmerge(leq(x, y), x, y, xs, ys)
, ifmerge(tt(), x, y, xs, ys) -> cons(x, merge(xs, cons(y, ys)))
, ifmerge(ff(), x, y, xs, ys) -> cons(y, merge(cons(x, xs), ys))
, mergesort(xs) -> mergesort1(split(xs))
, mergesort1(app(xs, ys)) -> merge(mergesort(xs), mergesort(ys))}
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:
{ leq(0(), x) -> tt()
, leq(s(x), 0()) -> ff()
, leq(s(x), s(y)) -> leq(x, y)
, split(nil()) -> app(nil(), nil())
, split(cons(x, nil())) -> app(cons(x, nil()), nil())
, split(cons(x, cons(y, xs))) -> split1(x, y, split(xs))
, split1(x, y, app(xs, ys)) -> app(cons(x, xs), cons(y, ys))
, merge([](), xs) -> xs
, merge(xs, []()) -> xs
, merge(cons(x, xs), cons(y, ys)) ->
ifmerge(leq(x, y), x, y, xs, ys)
, ifmerge(tt(), x, y, xs, ys) -> cons(x, merge(xs, cons(y, ys)))
, ifmerge(ff(), x, y, xs, ys) -> cons(y, merge(cons(x, xs), ys))
, mergesort(xs) -> mergesort1(split(xs))
, mergesort1(app(xs, ys)) -> merge(mergesort(xs), mergesort(ys))}
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:
{ leq(0(), x) -> tt()
, leq(s(x), 0()) -> ff()
, leq(s(x), s(y)) -> leq(x, y)
, split(nil()) -> app(nil(), nil())
, split(cons(x, nil())) -> app(cons(x, nil()), nil())
, split(cons(x, cons(y, xs))) -> split1(x, y, split(xs))
, split1(x, y, app(xs, ys)) -> app(cons(x, xs), cons(y, ys))
, merge([](), xs) -> xs
, merge(xs, []()) -> xs
, merge(cons(x, xs), cons(y, ys)) ->
ifmerge(leq(x, y), x, y, xs, ys)
, ifmerge(tt(), x, y, xs, ys) -> cons(x, merge(xs, cons(y, ys)))
, ifmerge(ff(), x, y, xs, ys) -> cons(y, merge(cons(x, xs), ys))
, mergesort(xs) -> mergesort1(split(xs))
, mergesort1(app(xs, ys)) -> merge(mergesort(xs), mergesort(ys))}
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:
{ leq(0(), x) -> tt()
, leq(s(x), 0()) -> ff()
, leq(s(x), s(y)) -> leq(x, y)
, split(nil()) -> app(nil(), nil())
, split(cons(x, nil())) -> app(cons(x, nil()), nil())
, split(cons(x, cons(y, xs))) -> split1(x, y, split(xs))
, split1(x, y, app(xs, ys)) -> app(cons(x, xs), cons(y, ys))
, merge([](), xs) -> xs
, merge(xs, []()) -> xs
, merge(cons(x, xs), cons(y, ys)) ->
ifmerge(leq(x, y), x, y, xs, ys)
, ifmerge(tt(), x, y, xs, ys) -> cons(x, merge(xs, cons(y, ys)))
, ifmerge(ff(), x, y, xs, ys) -> cons(y, merge(cons(x, xs), ys))
, mergesort(xs) -> mergesort1(split(xs))
, mergesort1(app(xs, ys)) -> merge(mergesort(xs), mergesort(ys))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..