YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {1}
   transitions:
    a1(16) -> 17*
    a1(19) -> 20*
    a1(43) -> 44*
    a1(49) -> 50*
    a1(46) -> 47*
    a1(12) -> 13*
    a1(42) -> 43*
    a1(14) -> 15*
    a1(17) -> 18*
    a1(13) -> 14*
    a1(47) -> 48*
    a1(44) -> 45*
    f20() -> 2*
    a0(10) -> 1*
    a0(5) -> 6*
    a0(7) -> 8*
    a0(4) -> 5*
    a0(8) -> 9*
    a0(3) -> 4*
    b0(6) -> 7*
    b0(2) -> 3*
    b0(9) -> 10*
    b1(41) -> 42*
    b1(48) -> 49*
    b1(45) -> 46*
    b1(57) -> 58*
    b1(15) -> 16*
    b1(51) -> 52*
    b1(18) -> 19*
    b1(11) -> 12*
    19 -> 51*
    52 -> 12*
    58 -> 42*
    8 -> 11*
    1 -> 44,5
    49 -> 57*
    20 -> 48,9
    5 -> 41*
    50 -> 45,6
  problem:
   
  Qed