Termination w.r.t. Q proof of /tmp/tmpagrtUY/#3.35.trs

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:

g(s(x)) → f(x)
f(0) → s(0)
f(s(x)) → s(s(g(x)))
g(0) → 0

Q is empty.

↳ QTRS

  ↳ DirectTerminationProof

Q restricted rewrite system:
The TRS R consists of the following rules:

g(s(x)) → f(x)
f(0) → s(0)
f(s(x)) → s(s(g(x)))
g(0) → 0

Q is empty.

We use [27] with the following order to prove termination.

Knuth-Bendix order [24] with precedence:

g₁ > f₁ > s₁

and weight map:

f_1=2
s_1=1
g_1=1
0=1