YES
Trs:
 {f(g(x), y) -> f(x, y),
     f(x, x) -> a()}
 Comment:
  We consider a non-duplicating trs.
  BOUND:
   Automaton:
    {      a_2() -> q2,
           a_1() -> q2,
           a_0() -> q2,
         g_0(q3) -> q3,
         g_0(q2) -> q3,
     f_1(q3, q3) -> q2,
     f_1(q3, q2) -> q2,
     f_1(q2, q3) -> q2,
     f_1(q2, q2) -> q2,
     f_0(q3, q3) -> q2,
     f_0(q3, q2) -> q2,
     f_0(q2, q3) -> q2,
     f_0(q2, q2) -> q2}
   Strict:
   {}
   Qed