YES

Problem:
 f(x,x) -> a()
 f(g(x),y) -> f(x,y)

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {5,4}
   transitions:
    f0(4,4) -> 4*
    f0(5,5) -> 4*
    f0(4,5) -> 4*
    f0(5,4) -> 4*
    a0() -> 4*
    g0(5) -> 5*
    g0(4) -> 5*
    f1(4,4) -> 4*
    f1(5,5) -> 4*
    f1(4,5) -> 4*
    f1(5,4) -> 4*
    a1() -> 4*
    a2() -> 4*
  problem:
   
  Qed