Termination w.r.t. Q proof of /tmp/tmpC0dRlE/Ex23_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)) → c(n__f(n__g(n__f(n__a))))
f(X) → n__f(X)
g(X) → n__g(X)
a → n__a
activate(n__f(X)) → f(activate(X))
activate(n__g(X)) → g(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)) → c(n__f(n__g(n__f(n__a))))
f(X) → n__f(X)
g(X) → n__g(X)
a → n__a
activate(n__f(X)) → f(activate(X))
activate(n__g(X)) → g(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}
activate₁ > g₁ > n_{_g₁}

and weight map:

c_1=3
a=10
f_1=5
n__g_1=3
g_1=3
n__f_1=5
activate_1=10
n__a=1