YES(?,O(n^1))

Problem:
 b(b(x1)) -> b(a(b(a(a(b(x1))))))
 b(b(a(b(x1)))) -> b(a(b(b(x1))))
 b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(a(b(b(x1))))))
 b(b(a(a(b(x1))))) -> b(a(a(b(b(x1)))))

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