YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {4}
   transitions:
    f0(3,1) -> 4*
    f0(3,3) -> 4*
    f0(1,2) -> 4*
    f0(2,1) -> 4*
    f0(2,3) -> 4*
    f0(3,2) -> 4*
    f0(1,1) -> 4*
    f0(1,3) -> 4*
    f0(2,2) -> 4*
    a0() -> 1*
    c0() -> 2*
    b0() -> 3*
  problem:
   
  Qed