YES

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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {8,7,4,1}
   transitions:
    l0(3) -> 1*
    l0(9) -> 8*
    a2(39) -> 40*
    a2(40) -> 41*
    r0(2) -> 5*
    a0(6) -> 4*
    a0(2) -> 3*
    a0(5) -> 6*
    r1(26) -> 27*
    b1(28) -> 29*
    f40() -> 2*
    b0(2) -> 9*
    b0(6) -> 7*
    a1(30) -> 31*
    a1(10) -> 11*
    a1(27) -> 28*
    a1(19) -> 20*
    l1(20) -> 21*
    l1(11) -> 12*
    r2(38) -> 39*
    19 -> 38*
    7 -> 9*
    12 -> 6*
    4 -> 5*
    11 -> 26,19
    21 -> 4,5
    8 -> 5*
    1 -> 3*
    31 -> 11*
    20 -> 30*
    9 -> 10*
    41 -> 39,27
    29 -> 7,9,10
  problem:
   
  Qed