YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {5,4,3}
   transitions:
    f0(2) -> 3*
    f0(1) -> 3*
    a0() -> 1*
    g0(2) -> 2*
    g0(1) -> 2*
    h0(2) -> 4*
    h0(1) -> 4*
    k0(1,1,1) -> 5*
    k0(2,2,1) -> 5*
    k0(1,1,2) -> 5*
    k0(2,2,2) -> 5*
    k0(1,2,1) -> 5*
    k0(2,1,1) -> 5*
    k0(1,2,2) -> 5*
    k0(2,1,2) -> 5*
    g1(10) -> 4*
    g1(4) -> 3*
    h1(1) -> 4*
    h1(3) -> 10*
    f1(2) -> 3*
    f1(1) -> 3*
    a1() -> 1*
    g2(15) -> 10*
    g2(4) -> 3*
    h2(14) -> 15*
    h2(1) -> 4*
    a2() -> 1*
    f2(4) -> 14*
  problem:
   
  Qed