YES

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

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {16,10,1}
   transitions:
    b0(7) -> 8*
    b0(4) -> 5*
    b0(3) -> 4*
    b0(2) -> 3*
    b0(12) -> 13*
    b0(14) -> 15*
    b0(5) -> 6*
    b0(13) -> 14*
    b0(6) -> 7*
    b0(15) -> 10*
    b3(352) -> 353*
    b3(373) -> 374*
    b3(350) -> 351*
    b3(375) -> 376*
    b3(351) -> 352*
    b3(414) -> 415*
    b3(384) -> 385*
    b3(412) -> 413*
    b3(385) -> 386*
    b3(353) -> 354*
    b3(413) -> 414*
    b3(386) -> 387*
    b3(415) -> 416*
    b3(374) -> 375*
    b3(372) -> 373*
    b3(383) -> 384*
    a1(102) -> 103*
    a1(97) -> 98*
    a1(101) -> 102*
    a1(29) -> 30*
    a1(100) -> 101*
    a1(155) -> 156*
    a1(55) -> 56*
    a1(99) -> 100*
    a1(64) -> 65*
    a1(98) -> 99*
    a1(65) -> 66*
    a1(156) -> 157*
    a1(56) -> 57*
    a1(28) -> 29*
    c0(2) -> 11*
    c0(11) -> 12*
    a2(129) -> 130*
    a2(334) -> 335*
    a2(119) -> 120*
    a2(173) -> 174*
    a2(120) -> 121*
    a2(172) -> 173*
    a2(128) -> 129*
    a2(333) -> 334*
    c2(252) -> 253*
    c2(253) -> 254*
    c2(268) -> 269*
    c2(233) -> 234*
    c2(250) -> 251*
    c2(185) -> 186*
    c2(346) -> 347*
    c2(232) -> 233*
    c2(239) -> 240*
    c2(275) -> 276*
    c2(295) -> 296*
    c2(184) -> 185*
    c2(269) -> 270*
    c2(281) -> 282*
    c2(344) -> 345*
    c2(397) -> 398*
    c2(406) -> 407*
    c2(296) -> 297*
    c2(283) -> 284*
    a0(4) -> 17*
    a0(18) -> 19*
    a0(21) -> 16*
    a0(19) -> 20*
    a0(8) -> 9*
    a0(9) -> 1*
    a0(17) -> 18*
    a0(20) -> 21*
    f30() -> 2*
    b1(52) -> 53*
    b1(22) -> 23*
    b1(24) -> 25*
    b1(153) -> 154*
    b1(62) -> 63*
    b1(53) -> 54*
    b1(49) -> 50*
    b1(27) -> 28*
    b1(224) -> 225*
    b1(61) -> 62*
    b1(208) -> 209*
    b1(50) -> 51*
    b1(96) -> 97*
    b1(54) -> 55*
    b1(25) -> 26*
    b1(154) -> 155*
    b1(164) -> 165*
    b1(202) -> 203*
    b1(158) -> 159*
    b1(149) -> 150*
    b1(152) -> 153*
    b1(60) -> 61*
    b1(95) -> 96*
    b1(210) -> 211*
    b1(51) -> 52*
    b1(58) -> 59*
    b1(59) -> 60*
    b1(63) -> 64*
    b1(216) -> 217*
    b1(78) -> 79*
    b1(218) -> 219*
    b1(26) -> 27*
    b1(150) -> 151*
    b1(23) -> 24*
    b1(151) -> 152*
    b1(226) -> 227*
    b2(272) -> 273*
    b2(122) -> 123*
    b2(171) -> 172*
    b2(368) -> 369*
    b2(127) -> 128*
    b2(237) -> 238*
    b2(189) -> 190*
    b2(271) -> 272*
    b2(327) -> 328*
    b2(328) -> 329*
    b2(166) -> 167*
    b2(256) -> 257*
    b2(330) -> 331*
    b2(168) -> 169*
    b2(306) -> 307*
    b2(170) -> 171*
    b2(304) -> 305*
    b2(116) -> 117*
    b2(236) -> 237*
    b2(257) -> 258*
    b2(118) -> 119*
    b2(169) -> 170*
    b2(273) -> 274*
    b2(200) -> 201*
    b2(359) -> 360*
    b2(342) -> 343*
    b2(125) -> 126*
    b2(298) -> 299*
    b2(126) -> 127*
    b2(321) -> 322*
    b2(270) -> 271*
    b2(329) -> 330*
    b2(187) -> 188*
    b2(332) -> 333*
    b2(123) -> 124*
    b2(114) -> 115*
    b2(336) -> 337*
    b2(254) -> 255*
    b2(115) -> 116*
    b2(234) -> 235*
    b2(319) -> 320*
    b2(186) -> 187*
    b2(167) -> 168*
    b2(113) -> 114*
    b2(124) -> 125*
    b2(188) -> 189*
    b2(117) -> 118*
    b2(235) -> 236*
    b2(255) -> 256*
    b2(331) -> 332*
    c1(81) -> 82*
    c1(80) -> 81*
    c3(382) -> 383*
    c3(348) -> 349*
    c3(349) -> 350*
    c3(370) -> 371*
    c3(381) -> 382*
    c3(410) -> 411*
    c3(411) -> 412*
    c3(371) -> 372*
    307 -> 167*
    238 -> 124,51
    156 -> 202*
    155 -> 208*
    354 -> 115*
    203 -> 59*
    320 -> 167*
    159 -> 23*
    398 -> 382*
    360 -> 114*
    190 -> 115,60
    17 -> 49*
    240 -> 233*
    30 -> 20*
    217 -> 23*
    282 -> 185*
    335 -> 100*
    100 -> 342,250,149
    66 -> 16*
    369 -> 123*
    284 -> 185*
    258 -> 329,151
    28 -> 78*
    4 -> 80,22
    2 -> 95*
    82 -> 26*
    174 -> 101*
    345 -> 253*
    337 -> 328*
    121 -> 103,18
    173 -> 336,239,226
    172 -> 381,268,200
    407 -> 253*
    251 -> 233*
    201 -> 114*
    79 -> 59*
    343 -> 328*
    297 -> 170*
    416 -> 329*
    334 -> 397,359
    101 -> 321,184,158
    165 -> 50*
    305 -> 123*
    99 -> 275,113
    130 -> 102*
    209 -> 50*
    219 -> 23*
    347 -> 253*
    225 -> 150*
    333 -> 410,406,368
    57 -> 21*
    120 -> 344,298,210
    227 -> 150*
    18 -> 58*
    299 -> 123*
    276 -> 269*
    119 -> 348,306,281,216
    211 -> 50*
    129 -> 319,283,218
    97 -> 295,166
    387 -> 24,168
    274 -> 168,24
    10 -> 96,97,295,3,4,80
    98 -> 252,122
    103 -> 99,113,275,18,58
    128 -> 370,327,232,224
    102 -> 346,304,164
    376 -> 124*
    322 -> 167*
    157 -> 19*
  problem:
   
  Qed