YES
O(n^2)
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: deltarestricted
  [h](delta, X0) = + 1*X0 + 4 + 0*X0*delta + 7*delta
  [n__d](delta, X0) = + 1*X0 + 0 + 0*X0*delta + 0*delta
  [activate](delta, X0) = + 1*X0 + 4 + 0*X0*delta + 4*delta
  [d](delta, X0) = + 1*X0 + 0 + 0*X0*delta + 1*delta
  [f](delta, X0) = + 1*X0 + 3 + 2*X0*delta + 1*delta
  [g](delta, X0) = + 1*X0 + 0 + 0*X0*delta + 0*delta
  [n__f](delta, X0) = + 1*X0 + 0 + 2*X0*delta + 0*delta
  [c](delta, X0) = + 1*X0 + 4 + 0*X0*delta + 6*delta
  h_tau_1(delta) = delta/(1 + 0 * delta)
  n__d_tau_1(delta) = delta/(1 + 0 * delta)
  activate_tau_1(delta) = delta/(1 + 0 * delta)
  d_tau_1(delta) = delta/(1 + 0 * delta)
  f_tau_1(delta) = delta/(1 + 2 * delta)
  g_tau_1(delta) = delta/(1 + 0 * delta)
  n__f_tau_1(delta) = delta/(1 + 2 * delta)
  c_tau_1(delta) = delta/(1 + 0 * delta)
  
  Qed