LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ qsort(nil()) -> nil()
, qsort(cons(x, xs)) ->
append(qsort(filterlow(last(cons(x, xs)), cons(x, xs))),
cons(last(cons(x, xs)),
qsort(filterhigh(last(cons(x, xs)), cons(x, xs)))))
, filterlow(n, nil()) -> nil()
, filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs)
, if1(true(), n, x, xs) -> filterlow(n, xs)
, if1(false(), n, x, xs) -> cons(x, filterlow(n, xs))
, filterhigh(n, nil()) -> nil()
, filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs)
, if2(true(), n, x, xs) -> filterhigh(n, xs)
, if2(false(), n, x, xs) -> cons(x, filterhigh(n, xs))
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, append(nil(), ys()) -> ys()
, append(cons(x, xs), ys()) -> cons(x, append(xs, ys()))
, last(nil()) -> 0()
, last(cons(x, nil())) -> x
, last(cons(x, cons(y, xs))) -> last(cons(y, xs))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ qsort(nil()) -> nil()
, qsort(cons(x, xs)) ->
append(qsort(filterlow(last(cons(x, xs)), cons(x, xs))),
cons(last(cons(x, xs)),
qsort(filterhigh(last(cons(x, xs)), cons(x, xs)))))
, filterlow(n, nil()) -> nil()
, filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs)
, if1(true(), n, x, xs) -> filterlow(n, xs)
, if1(false(), n, x, xs) -> cons(x, filterlow(n, xs))
, filterhigh(n, nil()) -> nil()
, filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs)
, if2(true(), n, x, xs) -> filterhigh(n, xs)
, if2(false(), n, x, xs) -> cons(x, filterhigh(n, xs))
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, append(nil(), ys()) -> ys()
, append(cons(x, xs), ys()) -> cons(x, append(xs, ys()))
, last(nil()) -> 0()
, last(cons(x, nil())) -> x
, last(cons(x, cons(y, xs))) -> last(cons(y, xs))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ qsort(nil()) -> nil()
, qsort(cons(x, xs)) ->
append(qsort(filterlow(last(cons(x, xs)), cons(x, xs))),
cons(last(cons(x, xs)),
qsort(filterhigh(last(cons(x, xs)), cons(x, xs)))))
, filterlow(n, nil()) -> nil()
, filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs)
, if1(true(), n, x, xs) -> filterlow(n, xs)
, if1(false(), n, x, xs) -> cons(x, filterlow(n, xs))
, filterhigh(n, nil()) -> nil()
, filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs)
, if2(true(), n, x, xs) -> filterhigh(n, xs)
, if2(false(), n, x, xs) -> cons(x, filterhigh(n, xs))
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, append(nil(), ys()) -> ys()
, append(cons(x, xs), ys()) -> cons(x, append(xs, ys()))
, last(nil()) -> 0()
, last(cons(x, nil())) -> x
, last(cons(x, cons(y, xs))) -> last(cons(y, xs))}
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:
{ qsort(nil()) -> nil()
, qsort(cons(x, xs)) ->
append(qsort(filterlow(last(cons(x, xs)), cons(x, xs))),
cons(last(cons(x, xs)),
qsort(filterhigh(last(cons(x, xs)), cons(x, xs)))))
, filterlow(n, nil()) -> nil()
, filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs)
, if1(true(), n, x, xs) -> filterlow(n, xs)
, if1(false(), n, x, xs) -> cons(x, filterlow(n, xs))
, filterhigh(n, nil()) -> nil()
, filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs)
, if2(true(), n, x, xs) -> filterhigh(n, xs)
, if2(false(), n, x, xs) -> cons(x, filterhigh(n, xs))
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, append(nil(), ys()) -> ys()
, append(cons(x, xs), ys()) -> cons(x, append(xs, ys()))
, last(nil()) -> 0()
, last(cons(x, nil())) -> x
, last(cons(x, cons(y, xs))) -> last(cons(y, xs))}
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:
{ qsort(nil()) -> nil()
, qsort(cons(x, xs)) ->
append(qsort(filterlow(last(cons(x, xs)), cons(x, xs))),
cons(last(cons(x, xs)),
qsort(filterhigh(last(cons(x, xs)), cons(x, xs)))))
, filterlow(n, nil()) -> nil()
, filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs)
, if1(true(), n, x, xs) -> filterlow(n, xs)
, if1(false(), n, x, xs) -> cons(x, filterlow(n, xs))
, filterhigh(n, nil()) -> nil()
, filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs)
, if2(true(), n, x, xs) -> filterhigh(n, xs)
, if2(false(), n, x, xs) -> cons(x, filterhigh(n, xs))
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, append(nil(), ys()) -> ys()
, append(cons(x, xs), ys()) -> cons(x, append(xs, ys()))
, last(nil()) -> 0()
, last(cons(x, nil())) -> x
, last(cons(x, cons(y, xs))) -> last(cons(y, xs))}
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:
{ qsort(nil()) -> nil()
, qsort(cons(x, xs)) ->
append(qsort(filterlow(last(cons(x, xs)), cons(x, xs))),
cons(last(cons(x, xs)),
qsort(filterhigh(last(cons(x, xs)), cons(x, xs)))))
, filterlow(n, nil()) -> nil()
, filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs)
, if1(true(), n, x, xs) -> filterlow(n, xs)
, if1(false(), n, x, xs) -> cons(x, filterlow(n, xs))
, filterhigh(n, nil()) -> nil()
, filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs)
, if2(true(), n, x, xs) -> filterhigh(n, xs)
, if2(false(), n, x, xs) -> cons(x, filterhigh(n, xs))
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, append(nil(), ys()) -> ys()
, append(cons(x, xs), ys()) -> cons(x, append(xs, ys()))
, last(nil()) -> 0()
, last(cons(x, nil())) -> x
, last(cons(x, cons(y, xs))) -> last(cons(y, xs))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..