YES

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

Proof:
 Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {1}
   transitions:
    f20() -> 2*
    b0(3) -> 4*
    b0(4) -> 5*
    b0(7) -> 8*
    a0(5) -> 6*
    a0(6) -> 7*
    a0(2) -> 3*
    a0(8) -> 1*
    1 -> 4*
  problem:
   
  Qed