Termination w.r.t. Q proof of TRS/TRCSRExConc_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__f(X) → g(h(f(X)))
mark(f(X)) → a__f(mark(X))
mark(g(X)) → g(X)
mark(h(X)) → h(mark(X))
a__f(X) → f(X)

Q is empty.

↳ QTRS

  ↳ DirectTerminationProof

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

a__f(X) → g(h(f(X)))
mark(f(X)) → a__f(mark(X))
mark(g(X)) → g(X)
mark(h(X)) → h(mark(X))
a__f(X) → f(X)

Q is empty.

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

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

mark₁ > a_{_f₁} > g₁ > h₁
mark₁ > a_{_f₁} > f₁ > h₁

Status:

h₁: [1]
mark₁: [1]
a_{_f₁}: [1]
f₁: [1]
g₁: [1]