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