YES
O(n)
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)
 }
 DUP: We consider a non-duplicating system.
  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)
   }
  BOUND:
   Automaton:
    {
            false_0() -> 8,
       activate_1(20) -> 7,
       activate_1(14) -> 7,
       activate_1(11) -> 7,
        activate_1(7) -> 7,
        activate_0(8) -> 7,
        activate_0(7) -> 7,
              f_2(19) -> 7,
              f_2(13) -> 7,
              f_2(10) -> 7,
               f_2(7) -> 7,
              f_1(19) -> 7,
              f_1(13) -> 7,
              f_1(10) -> 7,
               f_1(7) -> 7,
               f_0(8) -> 7,
               f_0(7) -> 7,
             true_3() -> 19,
             true_2() -> 13,
             true_1() -> 10,
             true_0() -> 7,
           n__f_3(19) -> 20,
           n__f_3(13) -> 7,
           n__f_3(10) -> 7,
            n__f_3(7) -> 7,
           n__f_2(19) -> 7,
           n__f_2(13) -> 14,
           n__f_2(10) -> 7,
            n__f_2(7) -> 7,
           n__f_1(10) -> 11,
            n__f_1(7) -> 7,
            n__f_0(8) -> 7,
            n__f_0(7) -> 7,
                c_3() -> 18,
                c_2() -> 12,
                c_1() -> 9,
                c_0() -> 7,
     if_3(19, 18, 20) -> 7,
     if_3(13, 18, 20) -> 7,
     if_3(10, 18, 20) -> 7,
      if_3(7, 18, 20) -> 7,
     if_2(19, 12, 14) -> 7,
     if_2(13, 12, 14) -> 7,
     if_2(10, 12, 14) -> 7,
      if_2(7, 12, 14) -> 7,
       if_1(7, 9, 11) -> 7,
        if_0(8, 8, 8) -> 7,
        if_0(8, 8, 7) -> 7,
        if_0(8, 7, 8) -> 7,
        if_0(8, 7, 7) -> 7,
        if_0(7, 8, 8) -> 7,
        if_0(7, 8, 7) -> 7,
        if_0(7, 7, 8) -> 7,
        if_0(7, 7, 7) -> 7,
                   20 -> 7,
                   18 -> 7,
                   14 -> 7,
                   12 -> 7,
                   11 -> 7,
                    9 -> 7,
                    8 -> 7
    }
   Strict:
    {}
   Qed