YES
O(n)
TRS:
 {
               f(X) -> n__f(X),
             f(0()) -> cons(0(), n__f(s(0()))),
          f(s(0())) -> f(p(s(0()))),
            p(s(X)) -> X,
        activate(X) -> X,
  activate(n__f(X)) -> f(X)
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
                 f(X) -> n__f(X),
               f(0()) -> cons(0(), n__f(s(0()))),
            f(s(0())) -> f(p(s(0()))),
              p(s(X)) -> X,
          activate(X) -> X,
    activate(n__f(X)) -> f(X)
   }
  BOUND:
   Automaton:
    {
      activate_0(7) -> 7,
             p_1(9) -> 7,
             p_0(7) -> 7,
             f_1(7) -> 7,
             f_0(7) -> 7,
            s_2(11) -> 12,
             s_1(8) -> 9,
             s_0(7) -> 7,
         n__f_2(12) -> 13,
          n__f_2(7) -> 7,
          n__f_1(9) -> 10,
          n__f_1(7) -> 7,
          n__f_0(7) -> 7,
              0_2() -> 11,
              0_1() -> 8,
              0_0() -> 7,
     cons_2(11, 13) -> 7,
      cons_1(8, 10) -> 7,
       cons_0(7, 7) -> 7,
                  8 -> 7
    }
   Strict:
    {}
   Qed