YES(?,O(n^1))

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

Proof:
 RT Transformation Processor:
  strict:
   f(f(x,a()),a()) -> f(f(f(x,a()),f(a(),a())),a())
  weak:
   
  Bounds Processor:
   bound: 2
   enrichment: match-rt
   automaton:
    final states: {3}
    transitions:
     f1(3,9) -> 11*
     f1(10,9) -> 11*
     f1(11,8) -> 10,3
     f1(8,8) -> 9*
     f1(3,8) -> 10*
     a1() -> 8*
     f2(11,12) -> 14*
     f2(14,13) -> 15*
     f2(15,12) -> 10*
     f2(12,12) -> 13*
     f0(3,3) -> 3*
     a2() -> 12*
     a0() -> 3*
   problem:
    strict:
     
    weak:
     f(f(x,a()),a()) -> f(f(f(x,a()),f(a(),a())),a())
   Qed