Tool LMPO
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ f(x, 0(), 0()) -> s(x)
, f(0(), y, 0()) -> s(y)
, f(0(), 0(), z) -> s(z)
, f(s(0()), y, z) -> f(0(), s(y), s(z))
, f(s(x), s(y), 0()) -> f(x, y, s(0()))
, f(s(x), 0(), s(z)) -> f(x, s(0()), z)
, f(0(), s(0()), s(0())) -> s(s(0()))
, f(s(x), s(y), s(z)) -> f(x, y, f(s(x), s(y), z))
, f(0(), s(s(y)), s(0())) -> f(0(), y, s(0()))
, f(0(), s(0()), s(s(z))) -> f(0(), s(0()), z)
, f(0(), s(s(y)), s(s(z))) -> f(0(), y, f(0(), s(s(y)), s(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:
{ f(x, 0(), 0()) -> s(x)
, f(0(), y, 0()) -> s(y)
, f(0(), 0(), z) -> s(z)
, f(s(0()), y, z) -> f(0(), s(y), s(z))
, f(s(x), s(y), 0()) -> f(x, y, s(0()))
, f(s(x), 0(), s(z)) -> f(x, s(0()), z)
, f(0(), s(0()), s(0())) -> s(s(0()))
, f(s(x), s(y), s(z)) -> f(x, y, f(s(x), s(y), z))
, f(0(), s(s(y)), s(0())) -> f(0(), y, s(0()))
, f(0(), s(0()), s(s(z))) -> f(0(), s(0()), z)
, f(0(), s(s(y)), s(s(z))) -> f(0(), y, f(0(), s(s(y)), s(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:
{ f(x, 0(), 0()) -> s(x)
, f(0(), y, 0()) -> s(y)
, f(0(), 0(), z) -> s(z)
, f(s(0()), y, z) -> f(0(), s(y), s(z))
, f(s(x), s(y), 0()) -> f(x, y, s(0()))
, f(s(x), 0(), s(z)) -> f(x, s(0()), z)
, f(0(), s(0()), s(0())) -> s(s(0()))
, f(s(x), s(y), s(z)) -> f(x, y, f(s(x), s(y), z))
, f(0(), s(s(y)), s(0())) -> f(0(), y, s(0()))
, f(0(), s(0()), s(s(z))) -> f(0(), s(0()), z)
, f(0(), s(s(y)), s(s(z))) -> f(0(), y, f(0(), s(s(y)), s(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:
{ f(x, 0(), 0()) -> s(x)
, f(0(), y, 0()) -> s(y)
, f(0(), 0(), z) -> s(z)
, f(s(0()), y, z) -> f(0(), s(y), s(z))
, f(s(x), s(y), 0()) -> f(x, y, s(0()))
, f(s(x), 0(), s(z)) -> f(x, s(0()), z)
, f(0(), s(0()), s(0())) -> s(s(0()))
, f(s(x), s(y), s(z)) -> f(x, y, f(s(x), s(y), z))
, f(0(), s(s(y)), s(0())) -> f(0(), y, s(0()))
, f(0(), s(0()), s(s(z))) -> f(0(), s(0()), z)
, f(0(), s(s(y)), s(s(z))) -> f(0(), y, f(0(), s(s(y)), s(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:
{ f(x, 0(), 0()) -> s(x)
, f(0(), y, 0()) -> s(y)
, f(0(), 0(), z) -> s(z)
, f(s(0()), y, z) -> f(0(), s(y), s(z))
, f(s(x), s(y), 0()) -> f(x, y, s(0()))
, f(s(x), 0(), s(z)) -> f(x, s(0()), z)
, f(0(), s(0()), s(0())) -> s(s(0()))
, f(s(x), s(y), s(z)) -> f(x, y, f(s(x), s(y), z))
, f(0(), s(s(y)), s(0())) -> f(0(), y, s(0()))
, f(0(), s(0()), s(s(z))) -> f(0(), s(0()), z)
, f(0(), s(s(y)), s(s(z))) -> f(0(), y, f(0(), s(s(y)), s(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:
{ f(x, 0(), 0()) -> s(x)
, f(0(), y, 0()) -> s(y)
, f(0(), 0(), z) -> s(z)
, f(s(0()), y, z) -> f(0(), s(y), s(z))
, f(s(x), s(y), 0()) -> f(x, y, s(0()))
, f(s(x), 0(), s(z)) -> f(x, s(0()), z)
, f(0(), s(0()), s(0())) -> s(s(0()))
, f(s(x), s(y), s(z)) -> f(x, y, f(s(x), s(y), z))
, f(0(), s(s(y)), s(0())) -> f(0(), y, s(0()))
, f(0(), s(0()), s(s(z))) -> f(0(), s(0()), z)
, f(0(), s(s(y)), s(s(z))) -> f(0(), y, f(0(), s(s(y)), s(z)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..