YES

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

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