YES(?,O(n^1))
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:
   Bound: match(-raise)-bounded by 3
   Automaton:
    {
        activate_0(5) -> 1*
        activate_0(4) -> 1*
        activate_0(1) -> 1*
         b_1() -> 1*
         b_0() -> 1*
         n__b_3() -> 4* | 3 | 1
         n__b_2() -> 1*
         n__b_1() -> 1*
         n__b_0() -> 1*
         a_3() -> 5* | 2 | 1
         a_2() -> 1*
         a_1() -> 1*
         a_0() -> 1*
     f_3(5, 4) -> 1*
     f_3(5, 3) -> 1*
     f_3(2, 4) -> 1*
     f_3(2, 3) -> 1*
     f_2(5, 5) -> 1*
     f_2(5, 4) -> 1*
     f_2(5, 1) -> 1*
     f_2(4, 5) -> 1*
     f_2(4, 4) -> 1*
     f_2(4, 1) -> 1*
     f_2(1, 5) -> 1*
     f_2(1, 4) -> 1*
     f_2(1, 1) -> 1*
     f_1(5, 5) -> 1*
     f_1(5, 4) -> 1*
     f_1(5, 1) -> 1*
     f_1(4, 5) -> 1*
     f_1(4, 4) -> 1*
     f_1(4, 1) -> 1*
     f_1(1, 5) -> 1*
     f_1(1, 4) -> 1*
     f_1(1, 1) -> 1*
     f_0(5, 5) -> 1*
     f_0(5, 4) -> 1*
     f_0(5, 1) -> 1*
     f_0(4, 5) -> 1*
     f_0(4, 4) -> 1*
     f_0(4, 1) -> 1*
     f_0(1, 5) -> 1*
     f_0(1, 4) -> 1*
     f_0(1, 1) -> 1*
           5 -> 1*
           4 -> 1*
    }
   Strict:
    {}
   Qed