Tool LMPO
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ f(0()) -> 0()
, f(s(0())) -> s(0())
, f(s(s(x))) -> p(h(g(x)))
, g(0()) -> pair(s(0()), s(0()))
, g(s(x)) -> h(g(x))
, h(x) -> pair(+(p(x), q(x)), p(x))
, p(pair(x, y)) -> x
, q(pair(x, y)) -> y
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))
, f(s(s(x))) -> +(p(g(x)), q(g(x)))
, g(s(x)) -> pair(+(p(g(x)), q(g(x))), p(g(x)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Tool MPO
Execution Time | 0.084 |
---|
Answer | YES(?,PRIMREC) |
---|
Input | SK90 2.26 |
---|
stdout:
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ f(0()) -> 0()
, f(s(0())) -> s(0())
, f(s(s(x))) -> p(h(g(x)))
, g(0()) -> pair(s(0()), s(0()))
, g(s(x)) -> h(g(x))
, h(x) -> pair(+(p(x), q(x)), p(x))
, p(pair(x, y)) -> x
, q(pair(x, y)) -> y
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))
, f(s(s(x))) -> +(p(g(x)), q(g(x)))
, g(s(x)) -> pair(+(p(g(x)), q(g(x))), p(g(x)))}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,PRIMREC)
Proof:
The input was oriented with the instance of
'multiset path orders' as induced by the precedence
f > p, f > h, f > g, f > +, f > q, h > p, h > pair, h > +, h > q,
g > s, g > p, g > h, g > pair, g > +, g > q, + > s .
Hurray, we answered YES(?,PRIMREC)
Tool POP*
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ f(0()) -> 0()
, f(s(0())) -> s(0())
, f(s(s(x))) -> p(h(g(x)))
, g(0()) -> pair(s(0()), s(0()))
, g(s(x)) -> h(g(x))
, h(x) -> pair(+(p(x), q(x)), p(x))
, p(pair(x, y)) -> x
, q(pair(x, y)) -> y
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))
, f(s(s(x))) -> +(p(g(x)), q(g(x)))
, g(s(x)) -> pair(+(p(g(x)), q(g(x))), p(g(x)))}
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(0()) -> 0()
, f(s(0())) -> s(0())
, f(s(s(x))) -> p(h(g(x)))
, g(0()) -> pair(s(0()), s(0()))
, g(s(x)) -> h(g(x))
, h(x) -> pair(+(p(x), q(x)), p(x))
, p(pair(x, y)) -> x
, q(pair(x, y)) -> y
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))
, f(s(s(x))) -> +(p(g(x)), q(g(x)))
, g(s(x)) -> pair(+(p(g(x)), q(g(x))), p(g(x)))}
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(0()) -> 0()
, f(s(0())) -> s(0())
, f(s(s(x))) -> p(h(g(x)))
, g(0()) -> pair(s(0()), s(0()))
, g(s(x)) -> h(g(x))
, h(x) -> pair(+(p(x), q(x)), p(x))
, p(pair(x, y)) -> x
, q(pair(x, y)) -> y
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))
, f(s(s(x))) -> +(p(g(x)), q(g(x)))
, g(s(x)) -> pair(+(p(g(x)), q(g(x))), p(g(x)))}
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(0()) -> 0()
, f(s(0())) -> s(0())
, f(s(s(x))) -> p(h(g(x)))
, g(0()) -> pair(s(0()), s(0()))
, g(s(x)) -> h(g(x))
, h(x) -> pair(+(p(x), q(x)), p(x))
, p(pair(x, y)) -> x
, q(pair(x, y)) -> y
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))
, f(s(s(x))) -> +(p(g(x)), q(g(x)))
, g(s(x)) -> pair(+(p(g(x)), q(g(x))), p(g(x)))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..