YES
O(n^2)
TRS:
 {
               f(X) -> n__f(X),
    f(n__f(n__a())) -> f(n__g(f(n__a()))),
                a() -> n__a(),
               g(X) -> n__g(X),
        activate(X) -> X,
  activate(n__g(X)) -> g(X),
   activate(n__a()) -> a(),
  activate(n__f(X)) -> f(X)
 }
 Natural interpretation:
  Strict:
   {
                 f(X) -> n__f(X),
      f(n__f(n__a())) -> f(n__g(f(n__a()))),
                  a() -> n__a(),
                 g(X) -> n__g(X),
          activate(X) -> X,
    activate(n__g(X)) -> g(X),
     activate(n__a()) -> a(),
    activate(n__f(X)) -> f(X)
   }
  Weak:
   {}
  Interpretation class: deltarestricted
  [activate](delta, X0) = + 1*X0 + 0 + 0*X0*delta + 2*delta
  [g](delta, X0) = + 0*X0 + 0 + 1*X0*delta + 1*delta
  [a](delta) = + 0 + 1*delta
  [n__f](delta, X0) = + 0*X0 + 2 + 2*X0*delta + 0*delta
  [n__a](delta) = + 0 + 0*delta
  [n__g](delta, X0) = + 0*X0 + 0 + 1*X0*delta + 0*delta
  [f](delta, X0) = + 0*X0 + 2 + 2*X0*delta + 1*delta
  activate_tau_1(delta) = delta/(1 + 0 * delta)
  g_tau_1(delta) = delta/(0 + 1 * delta)
  
  n__f_tau_1(delta) = delta/(0 + 2 * delta)
  
  n__g_tau_1(delta) = delta/(0 + 1 * delta)
  f_tau_1(delta) = delta/(0 + 2 * delta)
  
  Qed