YES
O(n)
TRS:
 {f(x, x) -> f(a(), b()),
      b() -> c()}
 DUP: We consider a non-duplicating system.
  Trs:
   {f(x, x) -> f(a(), b()),
        b() -> c()}
  BOUND:
   Automaton:
    {
           c_2() -> 10 | 8 | 4,
           c_1() -> 4,
           c_0() -> 4,
           b_1() -> 8 | 6 | 4,
           b_0() -> 4,
           a_1() -> 7 | 5 | 4,
           a_0() -> 4,
      f_1(7, 10) -> 4,
       f_1(7, 8) -> 4,
       f_1(7, 6) -> 4,
      f_1(5, 10) -> 4,
       f_1(5, 8) -> 4,
       f_1(5, 6) -> 4,
     f_0(10, 10) -> 4,
      f_0(10, 8) -> 4,
      f_0(10, 7) -> 4,
      f_0(10, 4) -> 4,
      f_0(8, 10) -> 4,
       f_0(8, 8) -> 4,
       f_0(8, 7) -> 4,
       f_0(8, 4) -> 4,
      f_0(7, 10) -> 4,
       f_0(7, 8) -> 4,
       f_0(7, 7) -> 4,
       f_0(7, 4) -> 4,
      f_0(4, 10) -> 4,
       f_0(4, 8) -> 4,
       f_0(4, 7) -> 4,
       f_0(4, 4) -> 4
    }
   Strict:
    {}
   Qed