YES
Input TRS:
      1: f(X) -> if(X,c(),n__f(true()))
      2: if(true(),X,Y) -> X
      3: if(false(),X,Y) -> activate(Y)
      4: f(X) -> n__f(X)
      5: activate(n__f(X)) -> f(X)
      6: activate(X) -> X
Number of strict rules: 6
Direct POLO(bPol) ... removes: 4 1 3 5 6 2
      activate	w: 2 * x1 + 44923
      false	w: 21244
      c 	w: 1
      true	w: 1
      f 	w: 2 * x1 + 2447
      if	w: 2 * x1 + 2 * x2 + 2 * x3 + 2437
      n__f	w: 2 * x1 + 1
Number of strict rules: 0