Tool LMPO
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ fib(0()) -> 0()
, fib(s(0())) -> s(0())
, fib(s(s(0()))) -> s(0())
, fib(s(s(x))) -> sp(g(x))
, g(0()) -> pair(s(0()), 0())
, g(s(0())) -> pair(s(0()), s(0()))
, g(s(x)) -> np(g(x))
, sp(pair(x, y)) -> +(x, y)
, np(pair(x, y)) -> pair(+(x, y), x)
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Tool MPO
Execution Time | 0.118 |
---|
Answer | YES(?,PRIMREC) |
---|
Input | SK90 2.27 |
---|
stdout:
YES(?,PRIMREC)
We consider the following Problem:
Strict Trs:
{ fib(0()) -> 0()
, fib(s(0())) -> s(0())
, fib(s(s(0()))) -> s(0())
, fib(s(s(x))) -> sp(g(x))
, g(0()) -> pair(s(0()), 0())
, g(s(0())) -> pair(s(0()), s(0()))
, g(s(x)) -> np(g(x))
, sp(pair(x, y)) -> +(x, y)
, np(pair(x, y)) -> pair(+(x, y), x)
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
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
fib > sp, fib > g, sp > +, g > s, g > pair, g > np, np > pair,
np > +, + > s .
Hurray, we answered YES(?,PRIMREC)
Tool POP*
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ fib(0()) -> 0()
, fib(s(0())) -> s(0())
, fib(s(s(0()))) -> s(0())
, fib(s(s(x))) -> sp(g(x))
, g(0()) -> pair(s(0()), 0())
, g(s(0())) -> pair(s(0()), s(0()))
, g(s(x)) -> np(g(x))
, sp(pair(x, y)) -> +(x, y)
, np(pair(x, y)) -> pair(+(x, y), x)
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
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:
{ fib(0()) -> 0()
, fib(s(0())) -> s(0())
, fib(s(s(0()))) -> s(0())
, fib(s(s(x))) -> sp(g(x))
, g(0()) -> pair(s(0()), 0())
, g(s(0())) -> pair(s(0()), s(0()))
, g(s(x)) -> np(g(x))
, sp(pair(x, y)) -> +(x, y)
, np(pair(x, y)) -> pair(+(x, y), x)
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
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:
{ fib(0()) -> 0()
, fib(s(0())) -> s(0())
, fib(s(s(0()))) -> s(0())
, fib(s(s(x))) -> sp(g(x))
, g(0()) -> pair(s(0()), 0())
, g(s(0())) -> pair(s(0()), s(0()))
, g(s(x)) -> np(g(x))
, sp(pair(x, y)) -> +(x, y)
, np(pair(x, y)) -> pair(+(x, y), x)
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
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:
{ fib(0()) -> 0()
, fib(s(0())) -> s(0())
, fib(s(s(0()))) -> s(0())
, fib(s(s(x))) -> sp(g(x))
, g(0()) -> pair(s(0()), 0())
, g(s(0())) -> pair(s(0()), s(0()))
, g(s(x)) -> np(g(x))
, sp(pair(x, y)) -> +(x, y)
, np(pair(x, y)) -> pair(+(x, y), x)
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..