YES

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

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {1}
   transitions:
    b1(34) -> 35*
    b1(11) -> 12*
    b1(32) -> 33*
    b1(12) -> 13*
    b1(33) -> 34*
    b1(13) -> 14*
    b2(41) -> 42*
    b2(60) -> 61*
    b2(40) -> 41*
    b2(39) -> 40*
    b2(62) -> 63*
    b2(61) -> 62*
    a1(30) -> 31*
    a1(31) -> 32*
    a1(10) -> 11*
    a1(29) -> 30*
    a1(8) -> 9*
    a1(9) -> 10*
    f20() -> 2*
    a0(3) -> 4*
    a0(4) -> 5*
    a0(2) -> 3*
    b0(5) -> 6*
    b0(6) -> 7*
    b0(7) -> 1*
    a2(57) -> 58*
    a2(36) -> 37*
    a2(38) -> 39*
    a2(58) -> 59*
    a2(37) -> 38*
    a2(59) -> 60*
    a3(65) -> 66*
    a3(66) -> 67*
    a3(64) -> 65*
    b3(69) -> 70*
    b3(68) -> 69*
    b3(67) -> 68*
    70 -> 39*
    35 -> 10*
    42 -> 31*
    63 -> 37*
    14 -> 5*
    11 -> 36*
    6 -> 8*
    13 -> 29*
    1 -> 3,4
    61 -> 64*
    33 -> 57*
  problem:
   
  Qed