YES

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

Proof:
 String Reversal Processor:
  b(b(b(a(a(a(x1)))))) -> a(a(a(a(b(b(b(b(x1))))))))
  Bounds Processor:
   bound: 5
   enrichment: match
   automaton:
    final states: {2,1}
    transitions:
     b3(167) -> 168*
     b3(157) -> 158*
     b3(169) -> 170*
     b3(159) -> 160*
     b3(149) -> 150*
     b3(119) -> 120*
     b3(166) -> 167*
     b3(151) -> 152*
     b3(121) -> 122*
     b3(168) -> 169*
     b3(158) -> 159*
     b3(148) -> 149*
     b3(118) -> 119*
     b3(160) -> 161*
     b3(150) -> 151*
     b3(135) -> 136*
     b3(120) -> 121*
     a4(192) -> 193*
     a4(182) -> 183*
     a4(179) -> 180*
     a4(191) -> 192*
     a4(181) -> 182*
     a4(193) -> 194*
     a4(190) -> 191*
     a4(180) -> 181*
     b4(187) -> 188*
     b4(177) -> 178*
     b4(189) -> 190*
     b4(186) -> 187*
     b4(176) -> 177*
     b4(188) -> 189*
     b4(178) -> 179*
     b4(175) -> 176*
     b0(2) -> 1*
     b0(1) -> 1*
     a5(202) -> 203*
     a5(199) -> 200*
     a5(201) -> 202*
     a5(200) -> 201*
     a0(2) -> 2*
     a0(1) -> 2*
     b5(197) -> 198*
     b5(196) -> 197*
     b5(198) -> 199*
     b5(195) -> 196*
     a1(40) -> 41*
     a1(10) -> 11*
     a1(37) -> 38*
     a1(39) -> 40*
     a1(9) -> 10*
     a1(11) -> 12*
     a1(38) -> 39*
     a1(8) -> 9*
     b1(35) -> 36*
     b1(5) -> 6*
     b1(7) -> 8*
     b1(79) -> 80*
     b1(34) -> 35*
     b1(4) -> 5*
     b1(81) -> 82*
     b1(46) -> 47*
     b1(36) -> 37*
     b1(31) -> 32*
     b1(6) -> 7*
     b1(48) -> 49*
     b1(33) -> 34*
     b1(85) -> 86*
     a2(55) -> 56*
     a2(142) -> 143*
     a2(97) -> 98*
     a2(57) -> 58*
     a2(144) -> 145*
     a2(114) -> 115*
     a2(54) -> 55*
     a2(141) -> 142*
     a2(116) -> 117*
     a2(96) -> 97*
     a2(56) -> 57*
     a2(143) -> 144*
     a2(113) -> 114*
     a2(98) -> 99*
     a2(115) -> 116*
     a2(95) -> 96*
     b2(50) -> 51*
     b2(137) -> 138*
     b2(127) -> 128*
     b2(112) -> 113*
     b2(92) -> 93*
     b2(87) -> 88*
     b2(52) -> 53*
     b2(139) -> 140*
     b2(129) -> 130*
     b2(109) -> 110*
     b2(94) -> 95*
     b2(146) -> 147*
     b2(111) -> 112*
     b2(91) -> 92*
     b2(51) -> 52*
     b2(138) -> 139*
     b2(93) -> 94*
     b2(53) -> 54*
     b2(140) -> 141*
     b2(110) -> 111*
     a3(172) -> 173*
     a3(162) -> 163*
     a3(152) -> 153*
     a3(122) -> 123*
     a3(164) -> 165*
     a3(154) -> 155*
     a3(124) -> 125*
     a3(171) -> 172*
     a3(161) -> 162*
     a3(173) -> 174*
     a3(163) -> 164*
     a3(153) -> 154*
     a3(123) -> 124*
     a3(170) -> 171*
     a3(155) -> 156*
     a3(125) -> 126*
     1 -> 31*
     2 -> 4*
     8 -> 91*
     9 -> 50,48
     10 -> 46*
     11 -> 33*
     12 -> 6,7,32,1
     32 -> 5*
     37 -> 127*
     38 -> 87,85
     39 -> 81*
     40 -> 79*
     41 -> 6,1,31,7,32
     47 -> 34*
     49 -> 34*
     54 -> 135*
     55 -> 118*
     56 -> 109*
     57 -> 129*
     58 -> 93,92,8,7
     80 -> 5*
     82 -> 5*
     86 -> 5*
     88 -> 51*
     96 -> 146*
     99 -> 36*
     114 -> 166,137
     117 -> 36,53
     124 -> 157*
     126 -> 95,93,94
     128 -> 51*
     130 -> 92*
     136 -> 119*
     142 -> 148*
     145 -> 52*
     147 -> 138*
     153 -> 175*
     156 -> 136*
     165 -> 140*
     174 -> 120*
     179 -> 195*
     182 -> 186*
     183 -> 122*
     194 -> 160*
     203 -> 189*
   problem:
    
   Qed