LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ -(x, 0()) -> x
, -(s(x), s(y)) -> -(x, y)
, <=(0(), y) -> true()
, <=(s(x), 0()) -> false()
, <=(s(x), s(y)) -> <=(x, y)
, if(true(), x, y) -> x
, if(false(), x, y) -> y
, perfectp(0()) -> false()
, perfectp(s(x)) -> f(x, s(0()), s(x), s(x))
, f(0(), y, 0(), u) -> true()
, f(0(), y, s(z), u) -> false()
, f(s(x), 0(), z, u) -> f(x, u, -(z, s(x)), u)
, f(s(x), s(y), z, u) ->
if(<=(x, y), f(s(x), -(y, x), z, u), f(x, u, z, u))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ -(x, 0()) -> x
, -(s(x), s(y)) -> -(x, y)
, <=(0(), y) -> true()
, <=(s(x), 0()) -> false()
, <=(s(x), s(y)) -> <=(x, y)
, if(true(), x, y) -> x
, if(false(), x, y) -> y
, perfectp(0()) -> false()
, perfectp(s(x)) -> f(x, s(0()), s(x), s(x))
, f(0(), y, 0(), u) -> true()
, f(0(), y, s(z), u) -> false()
, f(s(x), 0(), z, u) -> f(x, u, -(z, s(x)), u)
, f(s(x), s(y), z, u) ->
if(<=(x, y), f(s(x), -(y, x), z, u), f(x, u, z, u))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ -(x, 0()) -> x
, -(s(x), s(y)) -> -(x, y)
, <=(0(), y) -> true()
, <=(s(x), 0()) -> false()
, <=(s(x), s(y)) -> <=(x, y)
, if(true(), x, y) -> x
, if(false(), x, y) -> y
, perfectp(0()) -> false()
, perfectp(s(x)) -> f(x, s(0()), s(x), s(x))
, f(0(), y, 0(), u) -> true()
, f(0(), y, s(z), u) -> false()
, f(s(x), 0(), z, u) -> f(x, u, -(z, s(x)), u)
, f(s(x), s(y), z, u) ->
if(<=(x, y), f(s(x), -(y, x), z, u), f(x, u, z, u))}
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:
{ -(x, 0()) -> x
, -(s(x), s(y)) -> -(x, y)
, <=(0(), y) -> true()
, <=(s(x), 0()) -> false()
, <=(s(x), s(y)) -> <=(x, y)
, if(true(), x, y) -> x
, if(false(), x, y) -> y
, perfectp(0()) -> false()
, perfectp(s(x)) -> f(x, s(0()), s(x), s(x))
, f(0(), y, 0(), u) -> true()
, f(0(), y, s(z), u) -> false()
, f(s(x), 0(), z, u) -> f(x, u, -(z, s(x)), u)
, f(s(x), s(y), z, u) ->
if(<=(x, y), f(s(x), -(y, x), z, u), f(x, u, z, u))}
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:
{ -(x, 0()) -> x
, -(s(x), s(y)) -> -(x, y)
, <=(0(), y) -> true()
, <=(s(x), 0()) -> false()
, <=(s(x), s(y)) -> <=(x, y)
, if(true(), x, y) -> x
, if(false(), x, y) -> y
, perfectp(0()) -> false()
, perfectp(s(x)) -> f(x, s(0()), s(x), s(x))
, f(0(), y, 0(), u) -> true()
, f(0(), y, s(z), u) -> false()
, f(s(x), 0(), z, u) -> f(x, u, -(z, s(x)), u)
, f(s(x), s(y), z, u) ->
if(<=(x, y), f(s(x), -(y, x), z, u), f(x, u, z, u))}
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:
{ -(x, 0()) -> x
, -(s(x), s(y)) -> -(x, y)
, <=(0(), y) -> true()
, <=(s(x), 0()) -> false()
, <=(s(x), s(y)) -> <=(x, y)
, if(true(), x, y) -> x
, if(false(), x, y) -> y
, perfectp(0()) -> false()
, perfectp(s(x)) -> f(x, s(0()), s(x), s(x))
, f(0(), y, 0(), u) -> true()
, f(0(), y, s(z), u) -> false()
, f(s(x), 0(), z, u) -> f(x, u, -(z, s(x)), u)
, f(s(x), s(y), z, u) ->
if(<=(x, y), f(s(x), -(y, x), z, u), f(x, u, z, u))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..