(0) Obligation:

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

f(X) → if(X, c, n__f(n__true))
if(true, X, Y) → X
if(false, X, Y) → activate(Y)
f(X) → n__f(X)
truen__true
activate(n__f(X)) → f(activate(X))
activate(n__true) → true
activate(X) → X

Q is empty.