YES

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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {4}
   transitions:
    f1(13,13) -> 14*
    f1(19,14) -> 14*
    f1(14,14) -> 4*
    f1(4,14) -> 4*
    f1(11,10) -> 12*
    f1(13,14) -> 14*
    f1(14,13) -> 14*
    f1(4,13) -> 14*
    f1(10,12) -> 13*
    a1() -> 10*
    h1(10) -> 11*
    f2(12,18) -> 19*
    f2(13,19) -> 14*
    f2(15,17) -> 18*
    f2(19,19) -> 14*
    f2(14,19) -> 14*
    f2(16,15) -> 17*
    f0(4,4) -> 4*
    a2() -> 15*
    a0() -> 4*
    h2(15) -> 16*
    h0(4) -> 4*
  problem:
   
  Qed