YES(?,O(n^1))

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

Proof:
 RT Transformation Processor:
  strict:
   b(c(b(c(a(a(x1)))))) -> a(a(a(b(c(b(c(b(c(x1)))))))))
  weak:
   
  Bounds Processor:
   bound: 5
   enrichment: match-rt
   automaton:
    final states: {4}
    transitions:
     b3(242) -> 243*
     b3(314) -> 315*
     b3(164) -> 165*
     b3(154) -> 155*
     b3(206) -> 207*
     b3(196) -> 197*
     b3(166) -> 167*
     b3(156) -> 157*
     b3(106) -> 107*
     b3(238) -> 239*
     b3(208) -> 209*
     b3(198) -> 199*
     b3(168) -> 169*
     b3(158) -> 159*
     b3(310) -> 311*
     b3(108) -> 109*
     b3(240) -> 241*
     b3(210) -> 211*
     b3(200) -> 201*
     b3(312) -> 313*
     b3(110) -> 111*
     c3(237) -> 238*
     c3(207) -> 208*
     c3(197) -> 198*
     c3(167) -> 168*
     c3(157) -> 158*
     c3(309) -> 310*
     c3(107) -> 108*
     c3(239) -> 240*
     c3(209) -> 210*
     c3(199) -> 200*
     c3(311) -> 312*
     c3(109) -> 110*
     c3(241) -> 242*
     c3(313) -> 314*
     c3(163) -> 164*
     c3(153) -> 154*
     c3(235) -> 236*
     c3(205) -> 206*
     c3(195) -> 196*
     c3(165) -> 166*
     c3(155) -> 156*
     c3(105) -> 106*
     a4(399) -> 400*
     a4(369) -> 370*
     a4(359) -> 360*
     a4(284) -> 285*
     a4(264) -> 265*
     a4(401) -> 402*
     a4(371) -> 372*
     a4(361) -> 362*
     a4(336) -> 337*
     a4(283) -> 284*
     a4(263) -> 264*
     a4(400) -> 401*
     a4(370) -> 371*
     a4(360) -> 361*
     a4(335) -> 336*
     a4(285) -> 286*
     a4(265) -> 266*
     a4(337) -> 338*
     b4(282) -> 283*
     b4(262) -> 263*
     b4(394) -> 395*
     b4(364) -> 365*
     b4(354) -> 355*
     b4(334) -> 335*
     b4(396) -> 397*
     b4(366) -> 367*
     b4(356) -> 357*
     b4(398) -> 399*
     b4(368) -> 369*
     b4(358) -> 359*
     b4(278) -> 279*
     b4(258) -> 259*
     b4(330) -> 331*
     b4(280) -> 281*
     b4(260) -> 261*
     b4(332) -> 333*
     b0(4) -> 4*
     c4(277) -> 278*
     c4(257) -> 258*
     c4(339) -> 340*
     c4(329) -> 330*
     c4(279) -> 280*
     c4(259) -> 260*
     c4(331) -> 332*
     c4(281) -> 282*
     c4(261) -> 262*
     c4(393) -> 394*
     c4(363) -> 364*
     c4(353) -> 354*
     c4(333) -> 334*
     c4(395) -> 396*
     c4(365) -> 366*
     c4(355) -> 356*
     c4(397) -> 398*
     c4(367) -> 368*
     c4(357) -> 358*
     c4(287) -> 288*
     c0(4) -> 4*
     a5(439) -> 440*
     a5(409) -> 410*
     a5(441) -> 442*
     a5(411) -> 412*
     a5(440) -> 441*
     a5(410) -> 411*
     a0(4) -> 4*
     b5(434) -> 435*
     b5(404) -> 405*
     b5(436) -> 437*
     b5(406) -> 407*
     b5(438) -> 439*
     b5(408) -> 409*
     a1(45) -> 46*
     a1(47) -> 48*
     a1(22) -> 23*
     a1(46) -> 47*
     a1(21) -> 22*
     a1(23) -> 24*
     c5(433) -> 434*
     c5(403) -> 404*
     c5(435) -> 436*
     c5(405) -> 406*
     c5(437) -> 438*
     c5(407) -> 408*
     b1(40) -> 41*
     b1(20) -> 21*
     b1(42) -> 43*
     b1(44) -> 45*
     b1(16) -> 17*
     b1(18) -> 19*
     c1(15) -> 16*
     c1(17) -> 18*
     c1(99) -> 100*
     c1(69) -> 70*
     c1(39) -> 40*
     c1(19) -> 20*
     c1(41) -> 42*
     c1(43) -> 44*
     c1(85) -> 86*
     a2(137) -> 138*
     a2(32) -> 33*
     a2(179) -> 180*
     a2(139) -> 140*
     a2(79) -> 80*
     a2(181) -> 182*
     a2(81) -> 82*
     a2(31) -> 32*
     a2(138) -> 139*
     a2(33) -> 34*
     a2(180) -> 181*
     a2(80) -> 81*
     b2(30) -> 31*
     b2(132) -> 133*
     b2(174) -> 175*
     b2(134) -> 135*
     b2(74) -> 75*
     b2(176) -> 177*
     b2(136) -> 137*
     b2(76) -> 77*
     b2(26) -> 27*
     b2(178) -> 179*
     b2(78) -> 79*
     b2(28) -> 29*
     c2(75) -> 76*
     c2(25) -> 26*
     c2(177) -> 178*
     c2(127) -> 128*
     c2(77) -> 78*
     c2(27) -> 28*
     c2(29) -> 30*
     c2(131) -> 132*
     c2(173) -> 174*
     c2(133) -> 134*
     c2(83) -> 84*
     c2(73) -> 74*
     c2(175) -> 176*
     c2(135) -> 136*
     c2(115) -> 116*
     a3(212) -> 213*
     a3(202) -> 203*
     a3(112) -> 113*
     a3(244) -> 245*
     a3(169) -> 170*
     a3(159) -> 160*
     a3(316) -> 317*
     a3(211) -> 212*
     a3(201) -> 202*
     a3(171) -> 172*
     a3(161) -> 162*
     a3(111) -> 112*
     a3(243) -> 244*
     a3(213) -> 214*
     a3(203) -> 204*
     a3(315) -> 316*
     a3(113) -> 114*
     a3(245) -> 246*
     a3(170) -> 171*
     a3(160) -> 161*
     a3(317) -> 318*
     4 -> 15*
     21 -> 73*
     22 -> 69,25
     23 -> 39*
     24 -> 17,19,4
     31 -> 163*
     32 -> 131,105
     33 -> 115*
     34 -> 75,29,21,19
     45 -> 127*
     46 -> 99,83
     47 -> 85*
     48 -> 17,4,15,19
     70 -> 16*
     80 -> 173*
     82 -> 43*
     84 -> 26*
     86 -> 16*
     100 -> 16*
     111 -> 329*
     112 -> 277*
     113 -> 235*
     114 -> 165,79,77
     116 -> 26*
     128 -> 26*
     138 -> 153*
     140 -> 75*
     159 -> 339*
     161 -> 205*
     162 -> 79*
     170 -> 237*
     172 -> 29*
     180 -> 195*
     182 -> 27*
     201 -> 353*
     202 -> 257*
     203 -> 309*
     204 -> 31*
     214 -> 177*
     236 -> 206*
     244 -> 287*
     246 -> 165*
     266 -> 167*
     283 -> 403*
     285 -> 363*
     286 -> 169*
     288 -> 278*
     316 -> 393*
     318 -> 109,135
     338 -> 209*
     340 -> 330*
     362 -> 313*
     372 -> 241*
     400 -> 433*
     402 -> 331*
     412 -> 367*
     442 -> 335*
   problem:
    strict:
     
    weak:
     b(c(b(c(a(a(x1)))))) -> a(a(a(b(c(b(c(b(c(x1)))))))))
   Qed