YES(?,O(n^1))

Problem:
 f(g(f(a()),h(a(),f(a())))) -> f(h(g(f(a()),a()),g(f(a()),f(a()))))

Proof:
 Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {4}
   transitions:
    f0(2) -> 4*
    f0(1) -> 4*
    f0(3) -> 4*
    g0(3,1) -> 1*
    g0(3,3) -> 1*
    g0(1,2) -> 1*
    g0(2,1) -> 1*
    g0(2,3) -> 1*
    g0(3,2) -> 1*
    g0(1,1) -> 1*
    g0(1,3) -> 1*
    g0(2,2) -> 1*
    a0() -> 2*
    h0(3,1) -> 3*
    h0(3,3) -> 3*
    h0(1,2) -> 3*
    h0(2,1) -> 3*
    h0(2,3) -> 3*
    h0(3,2) -> 3*
    h0(1,1) -> 3*
    h0(1,3) -> 3*
    h0(2,2) -> 3*
  problem:
   
  Qed