YES

Problem:
 f(x,y) -> h(x,y)
 f(x,y) -> h(y,x)
 h(x,x) -> x

Proof:
 Bounds Processor:
  bound: 0
  enrichment: roof
  automaton:
   final states: {3,2,1}
   transitions:
    h0(3,3) -> 1*
    h0(2,3) -> 1*
    h0(3,2) -> 1*
    h0(2,2) -> 1*
    f20() -> 3*,1,2
    2 -> 1*
    3 -> 1*
  problem:
   
  Qed