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(g(x)) → g(g(f(x)))
f(g(x)) → g(g(g(x)))

Q is empty.


QTRS
  ↳ DirectTerminationProof

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

f(g(x)) → g(g(f(x)))
f(g(x)) → g(g(g(x)))

Q is empty.

We use [23] with the following order to prove termination.

Lexicographic path order with status [19].
Quasi-Precedence:
f1 > g1

Status:
f1: [1]
g1: [1]