YES(?,O(n^1))

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

Proof:
 RT Transformation Processor:
  strict:
   f(f(a(),x),a()) -> f(f(a(),f(a(),f(a(),a()))),x)
  weak:
   
  Bounds Processor:
   bound: 1
   enrichment: match-rt
   automaton:
    final states: {3}
    transitions:
     f1(8,9) -> 10*
     f1(11,10) -> 3*
     f1(8,8) -> 9*
     f1(8,10) -> 11*
     f1(11,3) -> 3*
     a1() -> 8*
     f0(3,3) -> 3*
     a0() -> 3*
   problem:
    strict:
     
    weak:
     f(f(a(),x),a()) -> f(f(a(),f(a(),f(a(),a()))),x)
   Qed