YES

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

Proof:
 String Reversal Processor:
  a(a(c(b(c(b(x1)))))) -> c(b(c(b(c(b(a(a(a(x1)))))))))
  Bounds Processor:
   bound: 5
   enrichment: match
   automaton:
    final states: {4}
    transitions:
     b3(172) -> 173*
     b3(112) -> 113*
     b3(102) -> 103*
     b3(114) -> 115*
     b3(104) -> 105*
     b3(146) -> 147*
     b3(168) -> 169*
     b3(148) -> 149*
     b3(170) -> 171*
     b3(150) -> 151*
     b3(110) -> 111*
     b3(100) -> 101*
     a3(167) -> 168*
     a3(137) -> 138*
     a3(107) -> 108*
     a3(97) -> 98*
     a3(144) -> 145*
     a3(109) -> 110*
     a3(99) -> 100*
     a3(251) -> 252*
     a3(166) -> 167*
     a3(143) -> 144*
     a3(108) -> 109*
     a3(98) -> 99*
     a3(205) -> 206*
     a3(165) -> 166*
     a3(145) -> 146*
     c4(277) -> 278*
     c4(299) -> 300*
     c4(279) -> 280*
     c4(189) -> 190*
     c4(179) -> 180*
     c4(301) -> 302*
     c4(281) -> 282*
     c4(231) -> 232*
     c4(191) -> 192*
     c4(181) -> 182*
     c4(303) -> 304*
     c4(233) -> 234*
     c4(193) -> 194*
     c4(183) -> 184*
     c4(235) -> 236*
     b4(232) -> 233*
     b4(192) -> 193*
     b4(182) -> 183*
     b4(234) -> 235*
     b4(276) -> 277*
     b4(298) -> 299*
     b4(278) -> 279*
     b4(188) -> 189*
     b4(178) -> 179*
     b4(300) -> 301*
     b4(280) -> 281*
     b4(230) -> 231*
     b4(190) -> 191*
     b4(180) -> 181*
     b4(302) -> 303*
     a0(4) -> 4*
     a4(227) -> 228*
     a4(187) -> 188*
     a4(177) -> 178*
     a4(274) -> 275*
     a4(229) -> 230*
     a4(296) -> 297*
     a4(186) -> 187*
     a4(176) -> 177*
     a4(273) -> 274*
     a4(228) -> 229*
     a4(295) -> 296*
     a4(275) -> 276*
     a4(185) -> 186*
     a4(175) -> 176*
     a4(297) -> 298*
     c0(4) -> 4*
     c5(247) -> 248*
     c5(309) -> 310*
     c5(249) -> 250*
     c5(311) -> 312*
     c5(313) -> 314*
     c5(245) -> 246*
     b0(4) -> 4*
     b5(244) -> 245*
     b5(246) -> 247*
     b5(308) -> 309*
     b5(248) -> 249*
     b5(310) -> 311*
     b5(312) -> 313*
     c1(19) -> 20*
     c1(21) -> 22*
     c1(23) -> 24*
     a5(242) -> 243*
     a5(306) -> 307*
     a5(241) -> 242*
     a5(243) -> 244*
     a5(305) -> 306*
     a5(307) -> 308*
     b1(20) -> 21*
     b1(22) -> 23*
     b1(18) -> 19*
     a1(65) -> 66*
     a1(15) -> 16*
     a1(17) -> 18*
     a1(39) -> 40*
     a1(16) -> 17*
     a1(63) -> 64*
     c2(75) -> 76*
     c2(77) -> 78*
     c2(79) -> 80*
     c2(29) -> 30*
     c2(31) -> 32*
     c2(33) -> 34*
     b2(30) -> 31*
     b2(32) -> 33*
     b2(74) -> 75*
     b2(76) -> 77*
     b2(78) -> 79*
     b2(28) -> 29*
     a2(25) -> 26*
     a2(72) -> 73*
     a2(67) -> 68*
     a2(27) -> 28*
     a2(71) -> 72*
     a2(26) -> 27*
     a2(93) -> 94*
     a2(73) -> 74*
     a2(95) -> 96*
     c3(147) -> 148*
     c3(169) -> 170*
     c3(149) -> 150*
     c3(171) -> 172*
     c3(151) -> 152*
     c3(111) -> 112*
     c3(101) -> 102*
     c3(173) -> 174*
     c3(113) -> 114*
     c3(103) -> 104*
     c3(115) -> 116*
     c3(105) -> 106*
     4 -> 15*
     18 -> 71*
     20 -> 25*
     22 -> 39*
     24 -> 16,17,4
     28 -> 137,93
     30 -> 97,67,63
     32 -> 95,65
     34 -> 72,18,16,4,15,17
     40 -> 26*
     64 -> 16*
     66 -> 16*
     68 -> 26*
     76 -> 107*
     80 -> 27*
     94 -> 26*
     96 -> 72*
     100 -> 175*
     104 -> 165*
     106 -> 74,73
     112 -> 227,143
     116 -> 72,138,98,94
     138 -> 98*
     146 -> 295*
     148 -> 185*
     150 -> 205*
     152 -> 74,28,93,137
     174 -> 109*
     184 -> 167*
     190 -> 273,251
     194 -> 109,17,27,99
     206 -> 186*
     232 -> 241*
     236 -> 100*
     250 -> 177*
     252 -> 108*
     278 -> 305*
     282 -> 176*
     304 -> 187*
     314 -> 178*
   problem:
    
   Qed