YES

Problem:
 f(f(a())) -> c(n__f(g(f(a()))))
 f(X) -> n__f(X)
 activate(n__f(X)) -> f(X)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   activate#(n__f(X)) -> f#(X)
  TRS:
   f(f(a())) -> c(n__f(g(f(a()))))
   f(X) -> n__f(X)
   activate(n__f(X)) -> f(X)
   activate(X) -> X
  TDG Processor:
   DPs:
    activate#(n__f(X)) -> f#(X)
   TRS:
    f(f(a())) -> c(n__f(g(f(a()))))
    f(X) -> n__f(X)
    activate(n__f(X)) -> f(X)
    activate(X) -> X
   graph:
    
   Qed