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(f(a, f(x, a)), a) → f(a, f(f(x, a), a))

Q is empty.


QTRS
  ↳ DirectTerminationProof

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

f(f(a, f(x, a)), a) → f(a, f(f(x, a), a))

Q is empty.

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

Recursive path order with status [2].
Quasi-Precedence:
[f2, a]

Status:
a: multiset
f2: [1,2]