YES

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

Proof:
 String Reversal Processor:
  b(b(a(a(x1)))) -> a(a(a(b(b(b(x1))))))
  Bounds Processor:
   bound: 5
   enrichment: match
   automaton:
    final states: {2,1}
    transitions:
     b3(212) -> 213*
     b3(177) -> 178*
     b3(167) -> 168*
     b3(152) -> 153*
     b3(214) -> 215*
     b3(154) -> 155*
     b3(144) -> 145*
     b3(114) -> 115*
     b3(176) -> 177*
     b3(166) -> 167*
     b3(141) -> 142*
     b3(121) -> 122*
     b3(116) -> 117*
     b3(213) -> 214*
     b3(168) -> 169*
     b3(153) -> 154*
     b3(143) -> 144*
     b3(175) -> 176*
     b3(150) -> 151*
     b3(145) -> 146*
     b3(115) -> 116*
     a4(252) -> 253*
     a4(237) -> 238*
     a4(274) -> 275*
     a4(259) -> 260*
     a4(254) -> 255*
     a4(194) -> 195*
     a4(281) -> 282*
     a4(261) -> 262*
     a4(236) -> 237*
     a4(196) -> 197*
     a4(273) -> 274*
     a4(253) -> 254*
     a4(238) -> 239*
     a4(280) -> 281*
     a4(275) -> 276*
     a4(260) -> 261*
     a4(195) -> 196*
     a4(282) -> 283*
     b4(277) -> 278*
     b4(272) -> 273*
     b4(257) -> 258*
     b4(192) -> 193*
     b4(279) -> 280*
     b4(249) -> 250*
     b4(234) -> 235*
     b4(271) -> 272*
     b4(256) -> 257*
     b4(251) -> 252*
     b4(191) -> 192*
     b4(278) -> 279*
     b4(258) -> 259*
     b4(233) -> 234*
     b4(193) -> 194*
     b4(270) -> 271*
     b4(250) -> 251*
     b4(240) -> 241*
     b4(235) -> 236*
     b0(2) -> 1*
     b0(1) -> 1*
     a5(299) -> 300*
     a5(291) -> 292*
     a5(298) -> 299*
     a5(293) -> 294*
     a5(300) -> 301*
     a5(292) -> 293*
     a0(2) -> 2*
     a0(1) -> 2*
     b5(289) -> 290*
     b5(296) -> 297*
     b5(288) -> 289*
     b5(295) -> 296*
     b5(290) -> 291*
     b5(297) -> 298*
     a1(30) -> 31*
     a1(32) -> 33*
     a1(7) -> 8*
     a1(9) -> 10*
     a1(31) -> 32*
     a1(8) -> 9*
     b1(25) -> 26*
     b1(5) -> 6*
     b1(27) -> 28*
     b1(29) -> 30*
     b1(4) -> 5*
     b1(61) -> 62*
     b1(36) -> 37*
     b1(6) -> 7*
     b1(63) -> 64*
     b1(28) -> 29*
     a2(70) -> 71*
     a2(137) -> 138*
     a2(77) -> 78*
     a2(72) -> 73*
     a2(42) -> 43*
     a2(94) -> 95*
     a2(79) -> 80*
     a2(136) -> 137*
     a2(71) -> 72*
     a2(41) -> 42*
     a2(93) -> 94*
     a2(78) -> 79*
     a2(43) -> 44*
     a2(135) -> 136*
     a2(95) -> 96*
     b2(75) -> 76*
     b2(40) -> 41*
     b2(132) -> 133*
     b2(97) -> 98*
     b2(92) -> 93*
     b2(67) -> 68*
     b2(134) -> 135*
     b2(74) -> 75*
     b2(69) -> 70*
     b2(39) -> 40*
     b2(101) -> 102*
     b2(91) -> 92*
     b2(76) -> 77*
     b2(133) -> 134*
     b2(103) -> 104*
     b2(68) -> 69*
     b2(38) -> 39*
     b2(105) -> 106*
     b2(90) -> 91*
     a3(217) -> 218*
     a3(157) -> 158*
     a3(147) -> 148*
     a3(117) -> 118*
     a3(179) -> 180*
     a3(169) -> 170*
     a3(119) -> 120*
     a3(216) -> 217*
     a3(171) -> 172*
     a3(156) -> 157*
     a3(146) -> 147*
     a3(178) -> 179*
     a3(148) -> 149*
     a3(118) -> 119*
     a3(215) -> 216*
     a3(180) -> 181*
     a3(170) -> 171*
     a3(155) -> 156*
     1 -> 25*
     2 -> 4*
     7 -> 74*
     8 -> 38,36
     9 -> 27*
     10 -> 26,6,5,1
     26 -> 5*
     30 -> 101*
     31 -> 67,63
     32 -> 61*
     33 -> 26,6,1,5
     37 -> 5*
     41 -> 150*
     42 -> 121,97
     43 -> 105*
     44 -> 40,75,7,6
     62 -> 5*
     64 -> 5*
     70 -> 143*
     71 -> 114,90
     72 -> 103*
     73 -> 75,6,7
     78 -> 132*
     80 -> 29*
     94 -> 141*
     96 -> 75*
     98 -> 91*
     102 -> 39*
     104 -> 39*
     106 -> 39*
     117 -> 191*
     118 -> 240*
     119 -> 175*
     120 -> 151,144,77,76
     122 -> 115*
     136 -> 166*
     138 -> 102*
     142 -> 115*
     147 -> 152*
     149 -> 40*
     151 -> 144*
     156 -> 233*
     158 -> 151,144
     169 -> 256*
     170 -> 249*
     171 -> 212*
     172 -> 41*
     181 -> 134*
     197 -> 177*
     216 -> 277*
     218 -> 92,116
     236 -> 295*
     238 -> 270*
     239 -> 146*
     241 -> 234*
     255 -> 145*
     262 -> 214*
     276 -> 154*
     281 -> 288*
     283 -> 192*
     294 -> 194*
     301 -> 272*
   problem:
    
   Qed