YES(?,O(n^1))

Problem:
 f(f(a(),b()),x) -> f(a(),f(a(),x))
 f(f(b(),a()),x) -> f(b(),f(b(),x))
 f(x,f(y,z)) -> f(f(x,y),z)

Proof:
 Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {3}
   transitions:
    f0(1,2) -> 3*
    f0(2,1) -> 3*
    f0(1,1) -> 3*
    f0(2,2) -> 3*
    a0() -> 1*
    b0() -> 2*
  problem:
   
  Qed