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:

a__ca__f(g(c))
a__f(g(X)) → g(X)
mark(c) → a__c
mark(f(X)) → a__f(X)
mark(g(X)) → g(X)
a__cc
a__f(X) → f(X)

Q is empty.


QTRS
  ↳ DirectTerminationProof

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

a__ca__f(g(c))
a__f(g(X)) → g(X)
mark(c) → a__c
mark(f(X)) → a__f(X)
mark(g(X)) → g(X)
a__cc
a__f(X) → f(X)

Q is empty.

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

Recursive Path Order [2].
Precedence:
mark1 > ac > af1 > f1
mark1 > ac > g1 > f1
mark1 > ac > c > f1