YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3}
   transitions:
    f1(4,2) -> 3*
    f1(4,1) -> 3*
    g1(2) -> 4*
    g1(4) -> 4*
    g1(1) -> 4*
    f0(1,2) -> 3*
    f0(2,1) -> 3*
    f0(1,1) -> 3*
    f0(2,2) -> 3*
    a0() -> 1*
    g0(2) -> 2*
    g0(1) -> 2*
    1 -> 3*
    2 -> 3*
    4 -> 3*
  problem:
   
  Qed