LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ eq(0(), 0()) -> true()
, eq(0(), s(m)) -> false()
, eq(s(n), 0()) -> false()
, eq(s(n), s(m)) -> eq(n, m)
, le(0(), m) -> true()
, le(s(n), 0()) -> false()
, le(s(n), s(m)) -> le(n, m)
, min(cons(0(), nil())) -> 0()
, min(cons(s(n), nil())) -> s(n)
, min(cons(n, cons(m, x))) -> if_min(le(n, m), cons(n, cons(m, x)))
, if_min(true(), cons(n, cons(m, x))) -> min(cons(n, x))
, if_min(false(), cons(n, cons(m, x))) -> min(cons(m, x))
, replace(n, m, nil()) -> nil()
, replace(n, m, cons(k, x)) ->
if_replace(eq(n, k), n, m, cons(k, x))
, if_replace(true(), n, m, cons(k, x)) -> cons(m, x)
, if_replace(false(), n, m, cons(k, x)) ->
cons(k, replace(n, m, x))
, sort(nil()) -> nil()
, sort(cons(n, x)) ->
cons(min(cons(n, x)), sort(replace(min(cons(n, x)), n, x)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ eq(0(), 0()) -> true()
, eq(0(), s(m)) -> false()
, eq(s(n), 0()) -> false()
, eq(s(n), s(m)) -> eq(n, m)
, le(0(), m) -> true()
, le(s(n), 0()) -> false()
, le(s(n), s(m)) -> le(n, m)
, min(cons(0(), nil())) -> 0()
, min(cons(s(n), nil())) -> s(n)
, min(cons(n, cons(m, x))) -> if_min(le(n, m), cons(n, cons(m, x)))
, if_min(true(), cons(n, cons(m, x))) -> min(cons(n, x))
, if_min(false(), cons(n, cons(m, x))) -> min(cons(m, x))
, replace(n, m, nil()) -> nil()
, replace(n, m, cons(k, x)) ->
if_replace(eq(n, k), n, m, cons(k, x))
, if_replace(true(), n, m, cons(k, x)) -> cons(m, x)
, if_replace(false(), n, m, cons(k, x)) ->
cons(k, replace(n, m, x))
, sort(nil()) -> nil()
, sort(cons(n, x)) ->
cons(min(cons(n, x)), sort(replace(min(cons(n, x)), n, x)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ eq(0(), 0()) -> true()
, eq(0(), s(m)) -> false()
, eq(s(n), 0()) -> false()
, eq(s(n), s(m)) -> eq(n, m)
, le(0(), m) -> true()
, le(s(n), 0()) -> false()
, le(s(n), s(m)) -> le(n, m)
, min(cons(0(), nil())) -> 0()
, min(cons(s(n), nil())) -> s(n)
, min(cons(n, cons(m, x))) -> if_min(le(n, m), cons(n, cons(m, x)))
, if_min(true(), cons(n, cons(m, x))) -> min(cons(n, x))
, if_min(false(), cons(n, cons(m, x))) -> min(cons(m, x))
, replace(n, m, nil()) -> nil()
, replace(n, m, cons(k, x)) ->
if_replace(eq(n, k), n, m, cons(k, x))
, if_replace(true(), n, m, cons(k, x)) -> cons(m, x)
, if_replace(false(), n, m, cons(k, x)) ->
cons(k, replace(n, m, x))
, sort(nil()) -> nil()
, sort(cons(n, x)) ->
cons(min(cons(n, x)), sort(replace(min(cons(n, x)), n, x)))}
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:
{ eq(0(), 0()) -> true()
, eq(0(), s(m)) -> false()
, eq(s(n), 0()) -> false()
, eq(s(n), s(m)) -> eq(n, m)
, le(0(), m) -> true()
, le(s(n), 0()) -> false()
, le(s(n), s(m)) -> le(n, m)
, min(cons(0(), nil())) -> 0()
, min(cons(s(n), nil())) -> s(n)
, min(cons(n, cons(m, x))) -> if_min(le(n, m), cons(n, cons(m, x)))
, if_min(true(), cons(n, cons(m, x))) -> min(cons(n, x))
, if_min(false(), cons(n, cons(m, x))) -> min(cons(m, x))
, replace(n, m, nil()) -> nil()
, replace(n, m, cons(k, x)) ->
if_replace(eq(n, k), n, m, cons(k, x))
, if_replace(true(), n, m, cons(k, x)) -> cons(m, x)
, if_replace(false(), n, m, cons(k, x)) ->
cons(k, replace(n, m, x))
, sort(nil()) -> nil()
, sort(cons(n, x)) ->
cons(min(cons(n, x)), sort(replace(min(cons(n, x)), n, x)))}
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:
{ eq(0(), 0()) -> true()
, eq(0(), s(m)) -> false()
, eq(s(n), 0()) -> false()
, eq(s(n), s(m)) -> eq(n, m)
, le(0(), m) -> true()
, le(s(n), 0()) -> false()
, le(s(n), s(m)) -> le(n, m)
, min(cons(0(), nil())) -> 0()
, min(cons(s(n), nil())) -> s(n)
, min(cons(n, cons(m, x))) -> if_min(le(n, m), cons(n, cons(m, x)))
, if_min(true(), cons(n, cons(m, x))) -> min(cons(n, x))
, if_min(false(), cons(n, cons(m, x))) -> min(cons(m, x))
, replace(n, m, nil()) -> nil()
, replace(n, m, cons(k, x)) ->
if_replace(eq(n, k), n, m, cons(k, x))
, if_replace(true(), n, m, cons(k, x)) -> cons(m, x)
, if_replace(false(), n, m, cons(k, x)) ->
cons(k, replace(n, m, x))
, sort(nil()) -> nil()
, sort(cons(n, x)) ->
cons(min(cons(n, x)), sort(replace(min(cons(n, x)), n, x)))}
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:
{ eq(0(), 0()) -> true()
, eq(0(), s(m)) -> false()
, eq(s(n), 0()) -> false()
, eq(s(n), s(m)) -> eq(n, m)
, le(0(), m) -> true()
, le(s(n), 0()) -> false()
, le(s(n), s(m)) -> le(n, m)
, min(cons(0(), nil())) -> 0()
, min(cons(s(n), nil())) -> s(n)
, min(cons(n, cons(m, x))) -> if_min(le(n, m), cons(n, cons(m, x)))
, if_min(true(), cons(n, cons(m, x))) -> min(cons(n, x))
, if_min(false(), cons(n, cons(m, x))) -> min(cons(m, x))
, replace(n, m, nil()) -> nil()
, replace(n, m, cons(k, x)) ->
if_replace(eq(n, k), n, m, cons(k, x))
, if_replace(true(), n, m, cons(k, x)) -> cons(m, x)
, if_replace(false(), n, m, cons(k, x)) ->
cons(k, replace(n, m, x))
, sort(nil()) -> nil()
, sort(cons(n, x)) ->
cons(min(cons(n, x)), sort(replace(min(cons(n, x)), n, x)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..