Tool LMPO
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, quot(0(), s(y)) -> 0()
, quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
, app(nil(), y) -> y
, app(add(n, x), y) -> add(n, app(x, y))
, reverse(nil()) -> nil()
, reverse(add(n, x)) -> app(reverse(x), add(n, nil()))
, shuffle(nil()) -> nil()
, shuffle(add(n, x)) -> add(n, shuffle(reverse(x)))
, concat(leaf(), y) -> y
, concat(cons(u, v), y) -> cons(u, concat(v, y))
, less_leaves(x, leaf()) -> false()
, less_leaves(leaf(), cons(w, z)) -> true()
, less_leaves(cons(u, v), cons(w, z)) ->
less_leaves(concat(u, v), concat(w, z))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Tool MPO
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, quot(0(), s(y)) -> 0()
, quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
, app(nil(), y) -> y
, app(add(n, x), y) -> add(n, app(x, y))
, reverse(nil()) -> nil()
, reverse(add(n, x)) -> app(reverse(x), add(n, nil()))
, shuffle(nil()) -> nil()
, shuffle(add(n, x)) -> add(n, shuffle(reverse(x)))
, concat(leaf(), y) -> y
, concat(cons(u, v), y) -> cons(u, concat(v, y))
, less_leaves(x, leaf()) -> false()
, less_leaves(leaf(), cons(w, z)) -> true()
, less_leaves(cons(u, v), cons(w, z)) ->
less_leaves(concat(u, v), concat(w, z))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Tool POP*
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, quot(0(), s(y)) -> 0()
, quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
, app(nil(), y) -> y
, app(add(n, x), y) -> add(n, app(x, y))
, reverse(nil()) -> nil()
, reverse(add(n, x)) -> app(reverse(x), add(n, nil()))
, shuffle(nil()) -> nil()
, shuffle(add(n, x)) -> add(n, shuffle(reverse(x)))
, concat(leaf(), y) -> y
, concat(cons(u, v), y) -> cons(u, concat(v, y))
, less_leaves(x, leaf()) -> false()
, less_leaves(leaf(), cons(w, z)) -> true()
, less_leaves(cons(u, v), cons(w, z)) ->
less_leaves(concat(u, v), concat(w, z))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Tool POP* (PS)
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, quot(0(), s(y)) -> 0()
, quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
, app(nil(), y) -> y
, app(add(n, x), y) -> add(n, app(x, y))
, reverse(nil()) -> nil()
, reverse(add(n, x)) -> app(reverse(x), add(n, nil()))
, shuffle(nil()) -> nil()
, shuffle(add(n, x)) -> add(n, shuffle(reverse(x)))
, concat(leaf(), y) -> y
, concat(cons(u, v), y) -> cons(u, concat(v, y))
, less_leaves(x, leaf()) -> false()
, less_leaves(leaf(), cons(w, z)) -> true()
, less_leaves(cons(u, v), cons(w, z)) ->
less_leaves(concat(u, v), concat(w, z))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Tool Small POP*
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, quot(0(), s(y)) -> 0()
, quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
, app(nil(), y) -> y
, app(add(n, x), y) -> add(n, app(x, y))
, reverse(nil()) -> nil()
, reverse(add(n, x)) -> app(reverse(x), add(n, nil()))
, shuffle(nil()) -> nil()
, shuffle(add(n, x)) -> add(n, shuffle(reverse(x)))
, concat(leaf(), y) -> y
, concat(cons(u, v), y) -> cons(u, concat(v, y))
, less_leaves(x, leaf()) -> false()
, less_leaves(leaf(), cons(w, z)) -> true()
, less_leaves(cons(u, v), cons(w, z)) ->
less_leaves(concat(u, v), concat(w, z))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Tool Small POP* (PS)
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, quot(0(), s(y)) -> 0()
, quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
, app(nil(), y) -> y
, app(add(n, x), y) -> add(n, app(x, y))
, reverse(nil()) -> nil()
, reverse(add(n, x)) -> app(reverse(x), add(n, nil()))
, shuffle(nil()) -> nil()
, shuffle(add(n, x)) -> add(n, shuffle(reverse(x)))
, concat(leaf(), y) -> y
, concat(cons(u, v), y) -> cons(u, concat(v, y))
, less_leaves(x, leaf()) -> false()
, less_leaves(leaf(), cons(w, z)) -> true()
, less_leaves(cons(u, v), cons(w, z)) ->
less_leaves(concat(u, v), concat(w, z))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..