YES
O(n)
TRS:
 {
               c(X) -> d(activate(X)),
               f(X) -> n__f(X),
            f(f(X)) -> c(n__f(g(n__f(X)))),
               d(X) -> n__d(X),
        activate(X) -> X,
  activate(n__f(X)) -> f(X),
  activate(n__d(X)) -> d(X),
               h(X) -> c(n__d(X))
 }
 Natural interpretation:
  Strict:
   {
                 c(X) -> d(activate(X)),
                 f(X) -> n__f(X),
              f(f(X)) -> c(n__f(g(n__f(X)))),
                 d(X) -> n__d(X),
          activate(X) -> X,
    activate(n__f(X)) -> f(X),
    activate(n__d(X)) -> d(X),
                 h(X) -> c(n__d(X))
   }
  Weak:
   {}
  Interpretation class: stronglylinear
  [h](X0) = + 1*X0 + 14
  [n__d](X0) = + 1*X0 + 0
  [activate](X0) = + 1*X0 + 9
  [d](X0) = + 1*X0 + 1
  [f](X0) = + 1*X0 + 11
  [g](X0) = + 1*X0 + 0
  [n__f](X0) = + 1*X0 + 5
  [c](X0) = + 1*X0 + 11
  
  Qed