Termination w.r.t. Q proof of /tmp/tmpcT78Nx/Ex18_Luc06

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(g(n__f(n__a)))
f(X) → n__f(X)
a → n__a
activate(n__f(X)) → f(activate(X))
activate(n__a) → a
activate(X) → X

Q is empty.

↳ QTRS

  ↳ DirectTerminationProof

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

f(f(a)) → f(g(n__f(n__a)))
f(X) → n__f(X)
a → n__a
activate(n__f(X)) → f(activate(X))
activate(n__a) → a
activate(X) → X

Q is empty.

We use [27] with the following order to prove termination.

Knuth-Bendix order [24] with precedence:

activate₁ > f₁ > n_{_f₁}

and weight map:

activate_1=5
f_1=3
a=5
g_1=2
n__a=1
n__f_1=3