YES
Input TRS:
      1: f(X) -> if(X,c(),n__f(n__true()))
      2: if(true(),X,Y) -> X
      3: if(false(),X,Y) -> activate(Y)
      4: f(X) -> n__f(X)
      5: true() -> n__true()
      6: activate(n__f(X)) -> f(activate(X))
      7: activate(n__true()) -> true()
      8: activate(X) -> X
Number of strict rules: 8
Direct POLO(bPol) ... removes: 8 3 7
      activate	w: x1 + 20538
      n__true	w: 0
      false	w: 20539
      c 	w: 0
      true	w: 0
      f 	w: x1 + 1
      if	w: x1 + x2 + x3
      n__f	w: x1 + 1
Number of strict rules: 5
Direct POLO(bPol) ... removes: 5 2
      activate	w: x1 + 20538
      n__true	w: 0
      false	w: 20538
      c 	w: 0
      true	w: 1
      f 	w: x1 + 8946
      if	w: x1 + x2 + x3
      n__f	w: x1 + 8946
Number of strict rules: 3
Direct POLO(bPol) ... removes: 4
      activate	w: 2 * x1 + 1
      n__true	w: 0
      false	w: 20538
      c 	w: 0
      true	w: 1
      f 	w: x1 + 57764
      if	w: x1 + x2 + 2 * x3
      n__f	w: x1 + 28882
Number of strict rules: 2
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #activate(n__f(X)) -> #f(activate(X))
     #2: #activate(n__f(X)) -> #activate(X)
Number of SCCs: 1, DPs: 1
  SCC { #2 }
POLO(Sum)... succeeded.
      activate	w: 0
      n__true	w: 0
      #activate	w: x1
      false	w: 0
      c 	w: 0
      true	w: 0
      f 	w: 0
      if	w: 0
      n__f	w: x1 + 1
      #f 	w: 0
    USABLE RULES: { }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0