YES

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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {1}
   transitions:
    b1(34) -> 35*
    b1(25) -> 26*
    b1(62) -> 63*
    b1(61) -> 62*
    b1(35) -> 36*
    b1(33) -> 34*
    b1(60) -> 61*
    b1(26) -> 27*
    b1(24) -> 25*
    b2(69) -> 70*
    b2(106) -> 107*
    b2(97) -> 98*
    b2(70) -> 71*
    b2(96) -> 97*
    b2(107) -> 108*
    b2(71) -> 72*
    b2(98) -> 99*
    b2(105) -> 106*
    a1(21) -> 22*
    a1(30) -> 31*
    a1(32) -> 33*
    a1(56) -> 57*
    a1(20) -> 21*
    a1(31) -> 32*
    a1(55) -> 56*
    a1(59) -> 60*
    a1(57) -> 58*
    a1(58) -> 59*
    a1(29) -> 30*
    a1(23) -> 24*
    a1(22) -> 23*
    a1(28) -> 29*
    a1(19) -> 20*
    f20() -> 2*
    a0(3) -> 4*
    a0(4) -> 5*
    a0(6) -> 7*
    a0(2) -> 3*
    a0(5) -> 6*
    b0(7) -> 8*
    b0(9) -> 1*
    b0(8) -> 9*
    a2(66) -> 67*
    a2(68) -> 69*
    a2(93) -> 94*
    a2(67) -> 68*
    a2(103) -> 104*
    a2(102) -> 103*
    a2(94) -> 95*
    a2(101) -> 102*
    a2(104) -> 105*
    a2(64) -> 65*
    a2(92) -> 93*
    a2(95) -> 96*
    a2(91) -> 92*
    a2(100) -> 101*
    a2(65) -> 66*
    27 -> 5,6
    35 -> 55*
    63 -> 21*
    72 -> 23*
    36 -> 7*
    8 -> 19*
    1 -> 3,4
    99 -> 57*
    108 -> 59*
    97 -> 100*
    61 -> 64*
    25 -> 28*
    33 -> 91*
  problem:
   
  Qed