Termination w.r.t. Q proof of TRS/TRCSREx1_Zan97

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__g(X) → a__h(X)
a__c → d
a__h(d) → a__g(c)
mark(g(X)) → a__g(X)
mark(h(X)) → a__h(X)
mark(c) → a__c
mark(d) → d
a__g(X) → g(X)
a__h(X) → h(X)
a__c → c

Q is empty.

↳ QTRS

  ↳ DirectTerminationProof

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

a__g(X) → a__h(X)
a__c → d
a__h(d) → a__g(c)
mark(g(X)) → a__g(X)
mark(h(X)) → a__h(X)
mark(c) → a__c
mark(d) → d
a__g(X) → g(X)
a__h(X) → h(X)
a__c → c

Q is empty.

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

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

[a_{_c}, mark_1] > d > a_{_g₁} > a_{_h₁} > c > h₁
[a_{_c}, mark_1] > d > a_{_g₁} > g₁ > h₁

Status:

d: multiset
h₁: [1]
a_{_g₁}: [1]
mark₁: [1]
c: multiset
a_{_h₁}: [1]
a_{_c}: multiset
g₁: [1]