(0) Obligation:

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

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

Q is empty.