YES
O(n)
TRS:
 {
           f(X, X) -> f(a(), n__b()),
               b() -> a(),
               b() -> n__b(),
       activate(X) -> X,
  activate(n__b()) -> b()
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
             f(X, X) -> f(a(), n__b()),
                 b() -> a(),
                 b() -> n__b(),
         activate(X) -> X,
    activate(n__b()) -> b()
   }
  BOUND:
   Automaton:
    {
     activate_0(9) -> 5,
     activate_0(8) -> 5,
     activate_0(5) -> 5,
             b_1() -> 5,
             b_0() -> 5,
          n__b_3() -> 9 | 7 | 5,
          n__b_2() -> 5,
          n__b_1() -> 5,
          n__b_0() -> 5,
             a_3() -> 8 | 6 | 5,
             a_2() -> 5,
             a_1() -> 5,
             a_0() -> 5,
         f_3(8, 9) -> 5,
         f_3(8, 7) -> 5,
         f_3(6, 9) -> 5,
         f_3(6, 7) -> 5,
         f_2(9, 9) -> 5,
         f_2(9, 8) -> 5,
         f_2(9, 5) -> 5,
         f_2(8, 9) -> 5,
         f_2(8, 8) -> 5,
         f_2(8, 5) -> 5,
         f_2(5, 9) -> 5,
         f_2(5, 8) -> 5,
         f_2(5, 5) -> 5,
         f_1(9, 9) -> 5,
         f_1(9, 8) -> 5,
         f_1(9, 5) -> 5,
         f_1(8, 9) -> 5,
         f_1(8, 8) -> 5,
         f_1(8, 5) -> 5,
         f_1(5, 9) -> 5,
         f_1(5, 8) -> 5,
         f_1(5, 5) -> 5,
         f_0(9, 9) -> 5,
         f_0(9, 8) -> 5,
         f_0(9, 5) -> 5,
         f_0(8, 9) -> 5,
         f_0(8, 8) -> 5,
         f_0(8, 5) -> 5,
         f_0(5, 9) -> 5,
         f_0(5, 8) -> 5,
         f_0(5, 5) -> 5,
                 9 -> 5,
                 8 -> 5
    }
   Strict:
    {}
   Qed