YES
O(n^2)
TRS:
 {
   if(true(), X, Y) -> X,
  if(false(), X, Y) -> activate(Y),
               f(X) -> if(X, c(), n__f(true())),
               f(X) -> n__f(X),
        activate(X) -> X,
  activate(n__f(X)) -> f(X)
 }
 Natural interpretation:
  Strict:
   {
     if(true(), X, Y) -> X,
    if(false(), X, Y) -> activate(Y),
                 f(X) -> if(X, c(), n__f(true())),
                 f(X) -> n__f(X),
          activate(X) -> X,
    activate(n__f(X)) -> f(X)
   }
  Weak:
   {}
  Interpretation class: deltarestricted
  [false](delta) = + 0 + 3*delta
  [activate](delta, X0) = + 1*X0 + 0 + 0*X0*delta + 3*delta
  [f](delta, X0) = + 1*X0 + 0 + 0*X0*delta + 2*delta
  [true](delta) = + 0 + 0*delta
  [n__f](delta, X0) = + 1*X0 + 0 + 0*X0*delta + 0*delta
  [c](delta) = + 0 + 0*delta
  [if](delta, X2, X1, X0) = + 1*X0 + 1*X1 + 1*X2 + 0 + 0*X0*delta + 0*X1*delta + 0*X2*delta + 1*delta
  
  activate_tau_1(delta) = delta/(1 + 0 * delta)
  f_tau_1(delta) = delta/(1 + 0 * delta)
  
  n__f_tau_1(delta) = delta/(1 + 0 * delta)
  
  if_tau_1(delta) = delta/(1 + 0 * delta)if_tau_2(delta) = delta/(1 + 0 * delta)if_tau_3(delta) = delta/(1 + 0 * delta)
  
  Qed