YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {2,1}
   transitions:
    f1(4,4) -> 6*
    f1(1,4) -> 5*
    f1(6,1) -> 7*
    f1(6,5) -> 7*
    f1(7,4) -> 5,1
    f1(2,4) -> 5*
    a1() -> 4*
    f2(7,16) -> 17*
    f2(18,17) -> 19*
    f2(19,16) -> 5*
    f2(16,16) -> 18*
    f0(1,2) -> 1*
    f0(2,1) -> 1*
    f0(1,1) -> 1*
    f0(2,2) -> 1*
    a2() -> 16*
    a0() -> 2*
  problem:
   
  Qed