YES

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

Proof:
 Bounds Processor:
  bound: 4
  enrichment: match
  automaton:
   final states: {13,8,1}
   transitions:
    b0(4) -> 5*
    b0(3) -> 4*
    b0(11) -> 12*
    b0(9) -> 10*
    b0(2) -> 3*
    b0(12) -> 8*
    b0(5) -> 9*
    b0(10) -> 11*
    a2(501) -> 502*
    a2(187) -> 188*
    a2(188) -> 189*
    a2(134) -> 135*
    a2(210) -> 211*
    a2(133) -> 134*
    a2(189) -> 190*
    a2(347) -> 348*
    a2(289) -> 290*
    a2(290) -> 291*
    a2(350) -> 351*
    a2(149) -> 150*
    a2(817) -> 818*
    a2(209) -> 210*
    a2(348) -> 349*
    a2(147) -> 148*
    a2(148) -> 149*
    a2(288) -> 289*
    a2(282) -> 283*
    a2(211) -> 212*
    a2(349) -> 350*
    a2(281) -> 282*
    a2(135) -> 136*
    a2(825) -> 826*
    a2(283) -> 284*
    f30() -> 2*
    b4(669) -> 670*
    b4(666) -> 667*
    b4(673) -> 674*
    b4(671) -> 672*
    b4(667) -> 668*
    b4(668) -> 669*
    b4(670) -> 671*
    b4(672) -> 673*
    a3(380) -> 381*
    a3(399) -> 400*
    a3(379) -> 380*
    a3(378) -> 379*
    a3(401) -> 402*
    a3(400) -> 401*
    a1(122) -> 123*
    a1(179) -> 180*
    a1(31) -> 32*
    a1(39) -> 40*
    a1(259) -> 260*
    a1(32) -> 33*
    a1(125) -> 126*
    a1(256) -> 257*
    a1(176) -> 177*
    a1(38) -> 39*
    a1(178) -> 179*
    a1(37) -> 38*
    a1(124) -> 125*
    a1(30) -> 31*
    a1(258) -> 259*
    a1(257) -> 258*
    a1(123) -> 124*
    a1(177) -> 178*
    b2(589) -> 590*
    b2(151) -> 152*
    b2(343) -> 344*
    b2(585) -> 586*
    b2(153) -> 154*
    b2(158) -> 159*
    b2(215) -> 216*
    b2(208) -> 209*
    b2(821) -> 822*
    b2(815) -> 816*
    b2(239) -> 240*
    b2(425) -> 426*
    b2(493) -> 494*
    b2(278) -> 279*
    b2(497) -> 498*
    b2(301) -> 302*
    b2(341) -> 342*
    b2(404) -> 405*
    b2(627) -> 628*
    b2(626) -> 627*
    b2(513) -> 514*
    b2(312) -> 313*
    b2(130) -> 131*
    b2(430) -> 431*
    b2(237) -> 238*
    b2(146) -> 147*
    b2(145) -> 146*
    b2(632) -> 633*
    b2(512) -> 513*
    b2(206) -> 207*
    b2(307) -> 308*
    b2(344) -> 345*
    b2(498) -> 499*
    b2(437) -> 438*
    b2(306) -> 307*
    b2(184) -> 185*
    b2(285) -> 286*
    b2(424) -> 425*
    b2(540) -> 541*
    b2(216) -> 217*
    b2(299) -> 300*
    b2(131) -> 132*
    b2(491) -> 492*
    b2(541) -> 542*
    b2(503) -> 504*
    b2(428) -> 429*
    b2(236) -> 237*
    b2(156) -> 157*
    b2(300) -> 301*
    b2(439) -> 440*
    b2(438) -> 439*
    b2(507) -> 508*
    b2(217) -> 218*
    b2(154) -> 155*
    b2(586) -> 587*
    b2(542) -> 543*
    b2(499) -> 500*
    b2(305) -> 306*
    b2(635) -> 636*
    b2(342) -> 343*
    b2(511) -> 512*
    b2(630) -> 631*
    b2(238) -> 239*
    b2(679) -> 680*
    b2(302) -> 303*
    b2(405) -> 406*
    b2(545) -> 546*
    b2(403) -> 404*
    b2(279) -> 280*
    b2(504) -> 505*
    b2(406) -> 407*
    b2(287) -> 288*
    b2(634) -> 635*
    b2(675) -> 676*
    b2(505) -> 506*
    b2(547) -> 548*
    b2(490) -> 491*
    b2(214) -> 215*
    b2(407) -> 408*
    b2(492) -> 493*
    b2(303) -> 304*
    b2(207) -> 208*
    b2(308) -> 309*
    b2(793) -> 794*
    b2(628) -> 629*
    b2(185) -> 186*
    b2(426) -> 427*
    b2(636) -> 637*
    b2(676) -> 677*
    b2(280) -> 281*
    b2(427) -> 428*
    b2(345) -> 346*
    b2(633) -> 634*
    b2(495) -> 496*
    b2(286) -> 287*
    b2(510) -> 511*
    b2(431) -> 432*
    b2(489) -> 490*
    b2(144) -> 145*
    b2(309) -> 310*
    b2(433) -> 434*
    b2(509) -> 510*
    b2(436) -> 437*
    b2(587) -> 588*
    b2(678) -> 679*
    b2(629) -> 630*
    b2(544) -> 545*
    b2(677) -> 678*
    b2(310) -> 311*
    b2(429) -> 430*
    b2(435) -> 436*
    b2(157) -> 158*
    b2(186) -> 187*
    b2(496) -> 497*
    b2(152) -> 153*
    b2(311) -> 312*
    b2(434) -> 435*
    b2(588) -> 589*
    b2(155) -> 156*
    b2(543) -> 544*
    b2(440) -> 441*
    b2(546) -> 547*
    b2(235) -> 236*
    b2(132) -> 133*
    b2(506) -> 507*
    b2(213) -> 214*
    b3(377) -> 378*
    b3(595) -> 596*
    b3(644) -> 645*
    b3(531) -> 532*
    b3(481) -> 482*
    b3(487) -> 488*
    b3(376) -> 377*
    b3(483) -> 484*
    b3(654) -> 655*
    b3(396) -> 397*
    b3(823) -> 824*
    b3(621) -> 622*
    b3(593) -> 594*
    b3(655) -> 656*
    b3(522) -> 523*
    b3(660) -> 661*
    b3(375) -> 376*
    b3(702) -> 703*
    b3(515) -> 516*
    b3(520) -> 521*
    b3(530) -> 531*
    b3(624) -> 625*
    b3(527) -> 528*
    b3(661) -> 662*
    b3(639) -> 640*
    b3(656) -> 657*
    b3(658) -> 659*
    b3(642) -> 643*
    b3(663) -> 664*
    b3(480) -> 481*
    b3(594) -> 595*
    b3(518) -> 519*
    b3(705) -> 706*
    b3(526) -> 527*
    b3(482) -> 483*
    b3(829) -> 830*
    b3(706) -> 707*
    b3(620) -> 621*
    b3(485) -> 486*
    b3(525) -> 526*
    b3(521) -> 522*
    b3(657) -> 658*
    b3(623) -> 624*
    b3(640) -> 641*
    b3(622) -> 623*
    b3(664) -> 665*
    b3(638) -> 639*
    b3(524) -> 525*
    b3(528) -> 529*
    b3(641) -> 642*
    b3(827) -> 828*
    b3(529) -> 530*
    b3(486) -> 487*
    b3(591) -> 592*
    b3(703) -> 704*
    b3(397) -> 398*
    b3(517) -> 518*
    b3(708) -> 709*
    b3(484) -> 485*
    b3(819) -> 820*
    b3(519) -> 520*
    b3(704) -> 705*
    b3(398) -> 399*
    b3(662) -> 663*
    b3(643) -> 644*
    b3(592) -> 593*
    b3(645) -> 646*
    b3(516) -> 517*
    c1(182) -> 183*
    c1(181) -> 182*
    c1(261) -> 262*
    c1(126) -> 127*
    c1(262) -> 263*
    c1(128) -> 129*
    c1(127) -> 128*
    c1(180) -> 181*
    c1(260) -> 261*
    b1(229) -> 230*
    b1(233) -> 234*
    b1(330) -> 331*
    b1(103) -> 104*
    b1(62) -> 63*
    b1(328) -> 329*
    b1(27) -> 28*
    b1(102) -> 103*
    b1(61) -> 62*
    b1(80) -> 81*
    b1(101) -> 102*
    b1(96) -> 97*
    b1(54) -> 55*
    b1(232) -> 233*
    b1(57) -> 58*
    b1(64) -> 65*
    b1(97) -> 98*
    b1(28) -> 29*
    b1(82) -> 83*
    b1(87) -> 88*
    b1(29) -> 30*
    b1(329) -> 330*
    b1(36) -> 37*
    b1(88) -> 89*
    b1(56) -> 57*
    b1(228) -> 229*
    b1(55) -> 56*
    b1(79) -> 80*
    b1(231) -> 232*
    b1(60) -> 61*
    b1(99) -> 100*
    b1(34) -> 35*
    b1(84) -> 85*
    b1(35) -> 36*
    b1(58) -> 59*
    b1(85) -> 86*
    b1(86) -> 87*
    b1(230) -> 231*
    b1(63) -> 64*
    b1(78) -> 79*
    b1(327) -> 328*
    b1(81) -> 82*
    b1(100) -> 101*
    b1(227) -> 228*
    b1(98) -> 99*
    b1(226) -> 227*
    b1(326) -> 327*
    a0(14) -> 15*
    a0(6) -> 7*
    a0(16) -> 17*
    a0(15) -> 16*
    a0(2) -> 14*
    a0(7) -> 1*
    a0(5) -> 6*
    c2(351) -> 352*
    c2(352) -> 353*
    c2(353) -> 354*
    c0(17) -> 18*
    c0(18) -> 19*
    c0(19) -> 13*
    408 -> 278*
    291 -> 263,8,5,86
    822 -> 157*
    354 -> 36,37,35,59,57,58,55,56,65,64,54,63,62,61,83,81,8,82,80,12,11,79,87,10,89
    680 -> 626*
    351 -> 396*
    378 -> 666*
    259 -> 403*
    523 -> 527,427
    159 -> 436,99
    190 -> 183*
    17 -> 34*
    83 -> 60*
    707 -> 660*
    256 -> 675*
    828 -> 703*
    240 -> 151*
    825 -> 827*
    709 -> 703*
    637 -> 503*
    189 -> 821,326
    30 -> 235*
    126 -> 144*
    290 -> 433*
    234 -> 60,12
    514 -> 489*
    104 -> 60,10
    596 -> 396*
    348 -> 660*
    14 -> 78*
    16 -> 54*
    379 -> 638*
    508 -> 495*
    820 -> 703*
    188 -> 829,424
    501 -> 702*
    284 -> 262*
    258 -> 585*
    212 -> 182*
    313 -> 229*
    180 -> 206*
    2 -> 84*
    665 -> 654*
    350 -> 591*
    124 -> 299*
    288 -> 620*
    257 -> 626*
    824 -> 525*
    346 -> 206*
    532 -> 159,99,436
    441 -> 37,36,35,59,34,58,57,56,55,65,64,63,62,61,83,60,82,81,8,89,80,79,12,11,10,87,78
    178 -> 495*
    150 -> 128*
    177 -> 503*
    349 -> 654*
    816 -> 434*
    125 -> 213*
    261 -> 347,285
    179 -> 341*
    488 -> 527,308
    402 -> 353*
    135 -> 815,226
    590 -> 403*
    548 -> 37,35,36,59,58,57,56,55,65,63,64,61,62,81,80,82,12,11,8,79,83
    183 -> 60,11
    13 -> 85,3,86,4
    127 -> 817,176,130
    8 -> 85,3,86,4,87,5
    826 -> 348*
    123 -> 489*
    40 -> 19*
    631 -> 585*
    380 -> 540*
    31 -> 151*
    304 -> 213*
    674 -> 641*
    381 -> 354,87,88,4,9,5,86,89
    65 -> 54*
    59 -> 34*
    331 -> 84*
    134 -> 823,305
    347 -> 708*
    646 -> 543*
    187 -> 515*
    500 -> 341*
    817 -> 819*
    218 -> 144*
    18 -> 122,27
    625 -> 524*
    260 -> 278*
    133 -> 480*
    122 -> 509*
    659 -> 591*
    502 -> 348*
    136 -> 129*
    352 -> 501,375
    129 -> 87,86,85,89,12,81,83,62,64,65,56,58,59,36,60,9
    432 -> 329*
    181 -> 825,256,184
    15 -> 60*
    289 -> 524*
    794 -> 434*
    87 -> 37,36,35,59,34,58,57,56,55,65,54,64,63,62,61,83,82,8,81,80,12,11,79,89,10,78,88,86,4,9,5
    263 -> 8,3,4,5,87,86,85
    830 -> 525*
    89 -> 78*
    818 -> 348*
    32 -> 793,96
    494 -> 299*
    176 -> 632*
    33 -> 13*
  problem:
   
  Qed