YES
Time: 0.002015
TRS:
 {f(x, x) -> f(a(), b()),
      b() -> c()}
 BOUND:
  Bound: top(-raise)-bounded by 2
  Automaton:
   {    c_2() -> 6* | 4 | 1
        b_1() -> 4* | 3 | 1
        a_1() -> 5* | 2 | 1
    f_1(5, 6) -> 1*
    f_1(5, 4) -> 1*
    f_1(5, 3) -> 1*
    f_1(2, 6) -> 1*
    f_1(2, 4) -> 1*
    f_1(2, 3) -> 1*
    f_0(6, 6) -> 1*
    f_0(6, 5) -> 1*
    f_0(6, 4) -> 1*
    f_0(6, 1) -> 1*
    f_0(5, 5) -> 1*
    f_0(5, 1) -> 1*
    f_0(4, 6) -> 1*
    f_0(4, 5) -> 1*
    f_0(4, 4) -> 1*
    f_0(4, 1) -> 1*
    f_0(1, 6) -> 1*
    f_0(1, 5) -> 1*
    f_0(1, 4) -> 1*
    f_0(1, 1) -> 1*}
  Strict:
   {}
  Qed