YES
O(n)
TRS:
 {
               f(X) -> n__f(X),
          f(f(a())) -> c(n__f(g(f(a())))),
        activate(X) -> X,
  activate(n__f(X)) -> f(X)
 }
 Natural interpretation:
  Strict:
   {
                 f(X) -> n__f(X),
            f(f(a())) -> c(n__f(g(f(a())))),
          activate(X) -> X,
    activate(n__f(X)) -> f(X)
   }
  Weak:
   {}
  Interpretation class: stronglylinear
  [activate](X0) = + 1*X0 + 3
  [a] = + 2
  [f](X0) = + 1*X0 + 2
  [g](X0) = + 1*X0 + 0
  [n__f](X0) = + 1*X0 + 0
  [c](X0) = + 1*X0 + 0
  
  Qed