YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {1}
   transitions:
    f1(15,13) -> 16*
    f1(14,3) -> 15*
    f1(16,7) -> 6*
    f1(12,12) -> 14*
    a1() -> 12*
    h1(12) -> 13*
    f30() -> 2*
    f0(3,3) -> 5*
    f0(5,3) -> 8*
    f0(6,4) -> 7*
    f0(7,5) -> 6*
    f0(7,7) -> 1*
    f0(8,4) -> 9*
    f0(9,7) -> 6*
    f0(5,2) -> 6*
    f0(7,2) -> 1*
    a0() -> 3*
    h0(3) -> 4*
  problem:
   
  Qed