YES

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

Proof:
 Bounds Processor:
  bound: 4
  enrichment: match
  automaton:
   final states: {6,1}
   transitions:
    b1(40) -> 41*
    b1(11) -> 12*
    b1(20) -> 21*
    b1(13) -> 14*
    b2(58) -> 59*
    b2(38) -> 39*
    b2(36) -> 37*
    b2(166) -> 167*
    b2(65) -> 66*
    b2(56) -> 57*
    a1(41) -> 42*
    a1(21) -> 22*
    a1(12) -> 13*
    a1(42) -> 43*
    a1(43) -> 44*
    a1(10) -> 11*
    a1(156) -> 157*
    a1(23) -> 24*
    a1(22) -> 23*
    f20() -> 2*
    a4(150) -> 151*
    a4(122) -> 123*
    a4(174) -> 175*
    a4(144) -> 145*
    a4(130) -> 131*
    a4(94) -> 95*
    a4(152) -> 153*
    a4(96) -> 97*
    a4(132) -> 133*
    b4(131) -> 132*
    b4(95) -> 96*
    b4(133) -> 134*
    b4(97) -> 98*
    a0(4) -> 5*
    a0(2) -> 3*
    a0(8) -> 9*
    a0(9) -> 6*
    a0(7) -> 8*
    b0(5) -> 1*
    b0(2) -> 7*
    b0(3) -> 4*
    a2(66) -> 67*
    a2(68) -> 69*
    a2(67) -> 68*
    a2(57) -> 58*
    a2(82) -> 83*
    a2(55) -> 56*
    a2(35) -> 36*
    a2(37) -> 38*
    a2(160) -> 161*
    a2(106) -> 107*
    b3(142) -> 143*
    b3(168) -> 169*
    b3(89) -> 90*
    b3(112) -> 113*
    b3(110) -> 111*
    b3(71) -> 72*
    b3(73) -> 74*
    a3(176) -> 177*
    a3(90) -> 91*
    a3(72) -> 73*
    a3(70) -> 71*
    a3(113) -> 114*
    a3(128) -> 129*
    a3(114) -> 115*
    a3(91) -> 92*
    a3(92) -> 93*
    a3(115) -> 116*
    151 -> 95*
    166 -> 176*
    24 -> 57,12,4
    74 -> 69,21
    142 -> 150*
    168 -> 174*
    160 -> 168,166
    83 -> 36*
    35 -> 89*
    69 -> 21*
    169 -> 113*
    112 -> 130*
    93 -> 113,66
    14 -> 6*
    106 -> 142*
    4 -> 20*
    2 -> 40,10
    143 -> 90*
    82 -> 110*
    153 -> 131*
    116 -> 90*
    6 -> 41,7
    177 -> 71*
    161 -> 38*
    58 -> 82*
    73 -> 106*
    44 -> 90,21
    13 -> 160,156
    123 -> 95*
    40 -> 55*
    1 -> 56,11,3
    107 -> 36*
    20 -> 35*
    175 -> 131*
    65 -> 70*
    110 -> 122*
    59 -> 44,21
    37 -> 112,65
    134 -> 116,90
    39 -> 24,4,20
    133 -> 144*
    145 -> 95*
    167 -> 66*
    129 -> 71*
    97 -> 152,128
    98 -> 93,66
    89 -> 94*
    111 -> 90*
    157 -> 11*
  problem:
   
  Qed