YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3}
   transitions:
    b0(3) -> 3*
    a0(3) -> 3*
    b1(13) -> 14*
    b1(14) -> 15*
    b1(15) -> 16*
    b1(17) -> 18*
    a1(18) -> 19*
    a1(12) -> 13*
    a1(16) -> 17*
    19 -> 14,3
    3 -> 12*
  problem:
   
  Qed