Termination w.r.t. Q proof of TRS/TRCSREx6_GM04

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__c → a__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__c → c
a__f(X) → f(X)

Q is empty.

↳ QTRS

  ↳ DirectTerminationProof

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

a__c → a__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__c → c
a__f(X) → f(X)

Q is empty.

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

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

[a_{_c}, mark_1] > a_{_f₁} > f₁
[a_{_c}, mark_1] > g₁
[a_{_c}, mark_1] > c

Status:

mark₁: [1]
a_{_f₁}: multiset
c: multiset
f₁: [1]
a_{_c}: multiset
g₁: multiset