YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4,2,1}
   transitions:
    f30() -> 3*
    a0() -> 4*,2,1
    f0(3,3) -> 2*
    a1() -> 1,4*,2
  problem:
   
  Qed