Termination w.r.t. Q of the following Term Rewriting System could be proven:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(0) → 1
f(s(x)) → g(f(x))
g(x) → +(x, s(x))
f(s(x)) → +(f(x), s(f(x)))
Q is empty.
↳ QTRS
↳ DirectTerminationProof
Q restricted rewrite system:
The TRS R consists of the following rules:
f(0) → 1
f(s(x)) → g(f(x))
g(x) → +(x, s(x))
f(s(x)) → +(f(x), s(f(x)))
Q is empty.
We use [23] with the following order to prove termination.
Recursive path order with status [2].
Precedence:
f1 > 1 > +2
f1 > g1 > s1 > +2
0 > +2
Status:
+2: multiset
f1: multiset
1: multiset
0: multiset
s1: multiset
g1: multiset