YES
TRS:
 {             f(X) -> n__f(X),
          f(f(a())) -> f(g(n__f(n__a()))),
                a() -> n__a(),
        activate(X) -> X,
  activate(n__f(X)) -> f(activate(X)),
   activate(n__a()) -> a()}
 DP:
  Strict:
   {        f#(f(a())) -> f#(g(n__f(n__a()))),
    activate#(n__f(X)) -> f#(activate(X)),
    activate#(n__f(X)) -> activate#(X),
     activate#(n__a()) -> a#()}
  Weak:
  {             f(X) -> n__f(X),
           f(f(a())) -> f(g(n__f(n__a()))),
                 a() -> n__a(),
         activate(X) -> X,
   activate(n__f(X)) -> f(activate(X)),
    activate(n__a()) -> a()}
  EDG:
   {(activate#(n__f(X)) -> activate#(X), activate#(n__a()) -> a#())
    (activate#(n__f(X)) -> activate#(X), activate#(n__f(X)) -> activate#(X))
    (activate#(n__f(X)) -> activate#(X), activate#(n__f(X)) -> f#(activate(X)))
    (activate#(n__f(X)) -> f#(activate(X)), f#(f(a())) -> f#(g(n__f(n__a()))))}
   SCCS:
    Scc:
     {activate#(n__f(X)) -> activate#(X)}
    SCC:
     Strict:
      {activate#(n__f(X)) -> activate#(X)}
     Weak:
     {             f(X) -> n__f(X),
              f(f(a())) -> f(g(n__f(n__a()))),
                    a() -> n__a(),
            activate(X) -> X,
      activate(n__f(X)) -> f(activate(X)),
       activate(n__a()) -> a()}
     SPSC:
      Simple Projection:
       pi(activate#) = 0
      Strict:
       {}
      Qed