YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {1}
   transitions:
    f1(18,17) -> 19*
    f1(4,20) -> 21*
    f1(5,21) -> 10*
    f1(17,19) -> 20*
    f1(7,21) -> 7*
    f1(9,21) -> 10*
    f1(21,21) -> 10*
    a1() -> 17*
    h1(17) -> 18*
    f30() -> 6*
    f0(9,10) -> 7*
    f0(5,5) -> 10*
    f0(5,7) -> 7*
    f0(5,9) -> 10*
    f0(7,7) -> 1*
    f0(7,9) -> 7*
    f0(3,2) -> 4*
    f0(4,5) -> 9*
    f0(9,9) -> 10*
    f0(10,10) -> 1*
    f0(6,5) -> 7*
    f0(6,7) -> 1*
    f0(2,4) -> 5*
    f0(7,10) -> 1*
    a0() -> 2*
    h0(2) -> 3*
  problem:
   
  Qed