YES

Problem:
 0(0(x1)) -> 0(4(4(5(1(1(3(1(2(1(x1))))))))))
 4(0(x1)) -> 4(4(2(3(0(2(4(2(3(4(x1))))))))))
 0(0(1(x1))) -> 0(4(1(3(0(2(1(5(0(1(x1))))))))))
 4(0(0(x1))) -> 2(2(2(3(0(0(4(4(2(1(x1))))))))))
 0(0(5(2(x1)))) -> 2(3(4(3(0(2(3(0(5(3(x1))))))))))
 1(1(0(0(x1)))) -> 1(3(3(3(4(4(3(2(5(0(x1))))))))))
 4(0(0(1(x1)))) -> 2(2(2(3(3(0(2(3(5(1(x1))))))))))
 5(0(0(4(x1)))) -> 2(5(4(5(2(1(2(3(0(4(x1))))))))))
 5(0(1(5(x1)))) -> 3(5(3(4(4(3(2(2(1(5(x1))))))))))
 0(3(3(5(4(x1))))) -> 0(3(3(2(4(3(3(0(3(4(x1))))))))))
 1(0(0(0(0(x1))))) -> 1(2(0(1(0(2(3(2(1(0(x1))))))))))
 1(0(1(0(1(x1))))) -> 3(5(5(4(4(1(3(1(3(2(x1))))))))))
 3(0(0(3(5(x1))))) -> 3(3(3(4(5(2(3(3(2(4(x1))))))))))
 3(0(0(4(0(x1))))) -> 3(3(0(5(5(3(2(2(5(0(x1))))))))))
 4(0(3(4(0(x1))))) -> 2(3(0(3(2(3(5(5(4(0(x1))))))))))
 5(0(0(0(3(x1))))) -> 5(1(4(2(3(0(0(2(1(3(x1))))))))))
 1(2(0(0(1(3(x1)))))) -> 0(4(2(5(2(2(3(4(4(3(x1))))))))))
 2(0(0(1(0(0(x1)))))) -> 2(4(4(1(0(5(5(2(1(1(x1))))))))))
 2(0(5(5(0(1(x1)))))) -> 2(3(1(4(3(1(3(3(5(1(x1))))))))))
 2(4(1(5(1(0(x1)))))) -> 1(0(3(1(4(5(0(5(4(4(x1))))))))))
 2(5(5(4(1(0(x1)))))) -> 2(5(5(1(1(1(4(2(3(0(x1))))))))))
 3(5(2(5(5(1(x1)))))) -> 2(1(3(4(5(1(4(0(4(1(x1))))))))))
 4(1(0(3(4(3(x1)))))) -> 4(1(4(5(4(1(2(0(1(3(x1))))))))))
 5(0(0(0(0(0(x1)))))) -> 4(5(3(4(0(4(1(4(0(0(x1))))))))))
 0(0(0(0(5(1(0(x1))))))) -> 3(0(5(0(5(5(0(4(0(2(x1))))))))))
 0(3(5(0(0(5(2(x1))))))) -> 2(1(4(4(3(2(5(1(4(3(x1))))))))))
 0(4(5(2(5(5(5(x1))))))) -> 0(4(1(4(0(1(3(2(2(3(x1))))))))))
 1(0(1(4(3(5(5(x1))))))) -> 3(3(0(3(5(4(3(4(0(1(x1))))))))))
 1(5(1(0(0(4(3(x1))))))) -> 4(4(1(1(4(0(4(3(0(3(x1))))))))))
 2(0(0(4(5(1(3(x1))))))) -> 1(0(2(1(4(3(0(4(4(2(x1))))))))))
 3(0(0(5(5(1(3(x1))))))) -> 2(4(5(2(4(4(2(0(0(3(x1))))))))))
 4(0(0(4(0(3(4(x1))))))) -> 3(3(3(3(0(1(5(4(0(4(x1))))))))))
 4(2(4(0(0(1(5(x1))))))) -> 2(3(4(1(3(0(1(2(3(2(x1))))))))))
 4(3(0(4(0(3(4(x1))))))) -> 4(2(4(2(4(4(0(3(0(4(x1))))))))))

Proof:
 String Reversal Processor:
  0(0(x1)) -> 1(2(1(3(1(1(5(4(4(0(x1))))))))))
  0(4(x1)) -> 4(3(2(4(2(0(3(2(4(4(x1))))))))))
  1(0(0(x1))) -> 1(0(5(1(2(0(3(1(4(0(x1))))))))))
  0(0(4(x1))) -> 1(2(4(4(0(0(3(2(2(2(x1))))))))))
  2(5(0(0(x1)))) -> 3(5(0(3(2(0(3(4(3(2(x1))))))))))
  0(0(1(1(x1)))) -> 0(5(2(3(4(4(3(3(3(1(x1))))))))))
  1(0(0(4(x1)))) -> 1(5(3(2(0(3(3(2(2(2(x1))))))))))
  4(0(0(5(x1)))) -> 4(0(3(2(1(2(5(4(5(2(x1))))))))))
  5(1(0(5(x1)))) -> 5(1(2(2(3(4(4(3(5(3(x1))))))))))
  4(5(3(3(0(x1))))) -> 4(3(0(3(3(4(2(3(3(0(x1))))))))))
  0(0(0(0(1(x1))))) -> 0(1(2(3(2(0(1(0(2(1(x1))))))))))
  1(0(1(0(1(x1))))) -> 2(3(1(3(1(4(4(5(5(3(x1))))))))))
  5(3(0(0(3(x1))))) -> 4(2(3(3(2(5(4(3(3(3(x1))))))))))
  0(4(0(0(3(x1))))) -> 0(5(2(2(3(5(5(0(3(3(x1))))))))))
  0(4(3(0(4(x1))))) -> 0(4(5(5(3(2(3(0(3(2(x1))))))))))
  3(0(0(0(5(x1))))) -> 3(1(2(0(0(3(2(4(1(5(x1))))))))))
  3(1(0(0(2(1(x1)))))) -> 3(4(4(3(2(2(5(2(4(0(x1))))))))))
  0(0(1(0(0(2(x1)))))) -> 1(1(2(5(5(0(1(4(4(2(x1))))))))))
  1(0(5(5(0(2(x1)))))) -> 1(5(3(3(1(3(4(1(3(2(x1))))))))))
  0(1(5(1(4(2(x1)))))) -> 4(4(5(0(5(4(1(3(0(1(x1))))))))))
  0(1(4(5(5(2(x1)))))) -> 0(3(2(4(1(1(1(5(5(2(x1))))))))))
  1(5(5(2(5(3(x1)))))) -> 1(4(0(4(1(5(4(3(1(2(x1))))))))))
  3(4(3(0(1(4(x1)))))) -> 3(1(0(2(1(4(5(4(1(4(x1))))))))))
  0(0(0(0(0(5(x1)))))) -> 0(0(4(1(4(0(4(3(5(4(x1))))))))))
  0(1(5(0(0(0(0(x1))))))) -> 2(0(4(0(5(5(0(5(0(3(x1))))))))))
  2(5(0(0(5(3(0(x1))))))) -> 3(4(1(5(2(3(4(4(1(2(x1))))))))))
  5(5(5(2(5(4(0(x1))))))) -> 3(2(2(3(1(0(4(1(4(0(x1))))))))))
  5(5(3(4(1(0(1(x1))))))) -> 1(0(4(3(4(5(3(0(3(3(x1))))))))))
  3(4(0(0(1(5(1(x1))))))) -> 3(0(3(4(0(4(1(1(4(4(x1))))))))))
  3(1(5(4(0(0(2(x1))))))) -> 2(4(4(0(3(4(1(2(0(1(x1))))))))))
  3(1(5(5(0(0(3(x1))))))) -> 3(0(0(2(4(4(2(5(4(2(x1))))))))))
  4(3(0(4(0(0(4(x1))))))) -> 4(0(4(5(1(0(3(3(3(3(x1))))))))))
  5(1(0(0(4(2(4(x1))))))) -> 2(3(2(1(0(3(1(4(3(2(x1))))))))))
  4(3(0(4(0(3(4(x1))))))) -> 4(0(3(0(4(4(2(4(2(4(x1))))))))))
  Bounds Processor:
   bound: 2
   enrichment: match
   automaton:
    final states: {283,276,269,261,253,245,238,231,223,214,205,196,187,
                   179,170,162,153,145,135,127,119,110,102,93,84,74,65,
                   59,49,40,30,22,12,1}
    transitions:
     12(622) -> 623*
     12(627) -> 628*
     12(623) -> 624*
     12(625) -> 626*
     40(258) -> 259*
     40(73) -> 65*
     40(2) -> 13*
     40(178) -> 170*
     40(264) -> 265*
     40(188) -> 224*
     40(104) -> 105*
     40(291) -> 283*
     40(259) -> 260*
     40(23) -> 232*
     40(199) -> 200*
     40(37) -> 38*
     40(77) -> 78*
     40(247) -> 248*
     40(183) -> 184*
     40(18) -> 19*
     40(173) -> 174*
     40(163) -> 164*
     40(150) -> 151*
     40(229) -> 230*
     40(197) -> 198*
     40(224) -> 225*
     40(137) -> 138*
     40(133) -> 134*
     40(240) -> 241*
     40(31) -> 154*
     40(3) -> 4*
     40(189) -> 190*
     40(103) -> 104*
     40(273) -> 274*
     40(154) -> 155*
     40(249) -> 250*
     40(194) -> 195*
     40(209) -> 210*
     40(92) -> 84*
     40(41) -> 42*
     40(220) -> 221*
     40(118) -> 110*
     40(207) -> 208*
     40(275) -> 269*
     40(284) -> 285*
     40(13) -> 14*
     40(4) -> 5*
     40(54) -> 55*
     40(36) -> 37*
     40(242) -> 243*
     40(66) -> 67*
     40(211) -> 212*
     40(53) -> 54*
     40(263) -> 264*
     40(177) -> 178*
     40(151) -> 152*
     40(255) -> 256*
     40(192) -> 193*
     40(78) -> 79*
     40(287) -> 288*
     40(112) -> 113*
     40(21) -> 12*
     40(286) -> 287*
     40(87) -> 88*
     22(626) -> 627*
     42(619) -> 620*
     42(620) -> 621*
     41(579) -> 580*
     41(496) -> 497*
     41(452) -> 453*
     41(658) -> 659*
     41(479) -> 480*
     41(397) -> 398*
     41(441) -> 442*
     41(444) -> 445*
     41(524) -> 525*
     41(455) -> 456*
     41(573) -> 574*
     41(535) -> 536*
     41(576) -> 577*
     41(447) -> 448*
     41(402) -> 403*
     41(446) -> 447*
     41(435) -> 436*
     41(485) -> 486*
     41(315) -> 316*
     41(391) -> 392*
     41(488) -> 489*
     41(304) -> 305*
     41(359) -> 360*
     41(540) -> 541*
     41(567) -> 568*
     41(616) -> 617*
     41(316) -> 317*
     41(403) -> 404*
     41(349) -> 350*
     41(499) -> 500*
     41(529) -> 530*
     41(655) -> 656*
     41(436) -> 437*
     41(578) -> 579*
     41(360) -> 361*
     41(480) -> 481*
     41(392) -> 393*
     41(587) -> 588*
     41(491) -> 492*
     41(400) -> 401*
     41(490) -> 491*
     41(305) -> 306*
     41(532) -> 533*
     41(650) -> 651*
     41(543) -> 544*
     41(348) -> 349*
     41(408) -> 409*
     41(568) -> 569*
     41(523) -> 524*
     41(615) -> 616*
     41(411) -> 412*
     41(584) -> 585*
     41(534) -> 535*
     21(393) -> 394*
     21(396) -> 397*
     21(492) -> 493*
     21(486) -> 487*
     21(440) -> 441*
     21(651) -> 652*
     21(572) -> 573*
     21(437) -> 438*
     21(442) -> 443*
     21(481) -> 482*
     21(453) -> 454*
     21(574) -> 575*
     21(366) -> 367*
     21(583) -> 584*
     21(484) -> 485*
     21(536) -> 537*
     21(541) -> 542*
     21(495) -> 496*
     21(311) -> 312*
     21(609) -> 610*
     21(525) -> 526*
     21(610) -> 611*
     21(497) -> 498*
     21(530) -> 531*
     21(407) -> 408*
     21(409) -> 410*
     21(404) -> 405*
     21(585) -> 586*
     21(451) -> 452*
     21(580) -> 581*
     21(322) -> 323*
     21(654) -> 655*
     21(398) -> 399*
     21(448) -> 449*
     21(656) -> 657*
     21(528) -> 529*
     21(611) -> 612*
     21(569) -> 570*
     21(539) -> 540*
     21(355) -> 356*
     10(69) -> 70*
     10(182) -> 183*
     10(160) -> 161*
     10(169) -> 162*
     10(200) -> 201*
     10(279) -> 280*
     10(13) -> 197*
     10(210) -> 211*
     10(31) -> 188*
     10(41) -> 163*
     10(143) -> 144*
     10(39) -> 30*
     10(82) -> 83*
     10(42) -> 277*
     10(172) -> 173*
     10(195) -> 187*
     10(165) -> 166*
     10(180) -> 181*
     10(7) -> 8*
     10(228) -> 229*
     10(29) -> 22*
     10(161) -> 153*
     10(136) -> 137*
     10(203) -> 204*
     10(100) -> 101*
     10(14) -> 246*
     10(6) -> 7*
     10(11) -> 1*
     10(181) -> 182*
     10(254) -> 255*
     10(244) -> 238*
     10(155) -> 156*
     10(26) -> 27*
     10(233) -> 234*
     10(4) -> 23*
     10(107) -> 108*
     10(246) -> 247*
     10(64) -> 59*
     10(191) -> 192*
     10(95) -> 96*
     10(105) -> 106*
     10(271) -> 272*
     10(9) -> 10*
     10(2) -> 50*
     50(272) -> 273*
     50(5) -> 6*
     50(158) -> 159*
     50(215) -> 216*
     50(239) -> 240*
     50(75) -> 76*
     50(146) -> 147*
     50(121) -> 122*
     50(168) -> 169*
     50(67) -> 68*
     50(66) -> 180*
     50(131) -> 132*
     50(63) -> 64*
     50(57) -> 58*
     50(13) -> 206*
     50(217) -> 218*
     50(154) -> 262*
     50(27) -> 28*
     50(125) -> 126*
     50(176) -> 177*
     50(190) -> 191*
     50(198) -> 199*
     50(47) -> 48*
     50(218) -> 219*
     50(83) -> 74*
     50(76) -> 103*
     50(174) -> 175*
     50(157) -> 158*
     50(227) -> 228*
     50(113) -> 114*
     50(120) -> 121*
     50(31) -> 66*
     50(132) -> 133*
     50(2) -> 136*
     11(352) -> 353*
     11(323) -> 324*
     11(351) -> 352*
     11(312) -> 313*
     11(310) -> 311*
     11(365) -> 366*
     11(354) -> 355*
     11(356) -> 357*
     11(307) -> 308*
     11(319) -> 320*
     11(363) -> 364*
     11(321) -> 322*
     11(367) -> 368*
     11(362) -> 363*
     11(318) -> 319*
     11(308) -> 309*
     30(188) -> 189*
     30(152) -> 145*
     30(20) -> 21*
     30(34) -> 60*
     30(241) -> 242*
     30(277) -> 278*
     30(85) -> 86*
     30(164) -> 165*
     30(185) -> 186*
     30(23) -> 24*
     30(2) -> 75*
     30(122) -> 123*
     30(139) -> 140*
     30(116) -> 117*
     30(250) -> 251*
     30(225) -> 226*
     30(88) -> 89*
     30(281) -> 282*
     30(76) -> 77*
     30(55) -> 56*
     30(171) -> 172*
     30(149) -> 150*
     30(42) -> 43*
     30(15) -> 16*
     30(71) -> 72*
     30(230) -> 223*
     30(62) -> 63*
     30(204) -> 196*
     30(75) -> 111*
     30(79) -> 80*
     30(289) -> 290*
     30(237) -> 231*
     30(128) -> 129*
     30(108) -> 109*
     30(111) -> 112*
     30(106) -> 107*
     30(89) -> 90*
     30(206) -> 207*
     30(52) -> 53*
     30(256) -> 257*
     30(167) -> 168*
     30(8) -> 9*
     30(268) -> 261*
     30(50) -> 51*
     30(48) -> 40*
     30(91) -> 92*
     30(98) -> 99*
     30(45) -> 46*
     30(33) -> 34*
     30(3) -> 85*
     30(112) -> 270*
     30(252) -> 245*
     30(144) -> 135*
     30(120) -> 239*
     30(234) -> 235*
     30(166) -> 167*
     30(130) -> 131*
     30(115) -> 116*
     30(31) -> 41*
     30(51) -> 52*
     02(618) -> 619*
     31(353) -> 354*
     31(575) -> 576*
     31(657) -> 658*
     31(364) -> 365*
     31(487) -> 488*
     31(449) -> 450*
     31(526) -> 527*
     31(493) -> 494*
     31(399) -> 400*
     31(320) -> 321*
     31(542) -> 543*
     31(570) -> 571*
     31(612) -> 613*
     31(410) -> 411*
     31(531) -> 532*
     31(498) -> 499*
     31(405) -> 406*
     31(586) -> 587*
     31(438) -> 439*
     31(394) -> 395*
     31(482) -> 483*
     31(581) -> 582*
     31(309) -> 310*
     31(454) -> 455*
     31(443) -> 444*
     31(652) -> 653*
     31(537) -> 538*
     20(171) -> 254*
     20(138) -> 139*
     20(44) -> 45*
     20(68) -> 69*
     20(4) -> 146*
     20(2) -> 31*
     20(10) -> 11*
     20(17) -> 18*
     20(31) -> 32*
     20(117) -> 118*
     20(13) -> 284*
     20(61) -> 62*
     20(80) -> 81*
     20(50) -> 94*
     20(236) -> 237*
     20(184) -> 185*
     20(285) -> 286*
     20(25) -> 26*
     20(235) -> 236*
     20(97) -> 98*
     20(222) -> 214*
     20(282) -> 276*
     20(56) -> 57*
     20(109) -> 102*
     20(129) -> 130*
     20(201) -> 202*
     20(38) -> 39*
     20(265) -> 266*
     20(99) -> 100*
     20(32) -> 33*
     20(262) -> 263*
     20(142) -> 143*
     20(86) -> 87*
     20(19) -> 20*
     20(147) -> 148*
     20(159) -> 160*
     20(14) -> 15*
     20(123) -> 124*
     20(81) -> 82*
     20(260) -> 253*
     20(70) -> 71*
     20(148) -> 149*
     20(124) -> 125*
     20(280) -> 281*
     20(226) -> 227*
     20(114) -> 115*
     51(306) -> 307*
     51(361) -> 362*
     51(317) -> 318*
     51(350) -> 351*
     01(571) -> 572*
     01(582) -> 583*
     01(538) -> 539*
     01(527) -> 528*
     01(395) -> 396*
     01(614) -> 615*
     01(450) -> 451*
     01(358) -> 359*
     01(347) -> 348*
     01(653) -> 654*
     01(314) -> 315*
     01(613) -> 614*
     01(439) -> 440*
     01(483) -> 484*
     01(494) -> 495*
     01(406) -> 407*
     01(303) -> 304*
     00(141) -> 142*
     00(248) -> 249*
     00(257) -> 258*
     00(219) -> 220*
     00(134) -> 127*
     00(288) -> 289*
     00(101) -> 93*
     00(208) -> 209*
     00(58) -> 49*
     00(35) -> 36*
     00(28) -> 29*
     00(75) -> 215*
     00(41) -> 128*
     00(221) -> 222*
     00(2) -> 3*
     00(43) -> 44*
     00(111) -> 120*
     00(216) -> 217*
     00(212) -> 213*
     00(213) -> 205*
     00(126) -> 119*
     00(186) -> 179*
     00(251) -> 252*
     00(140) -> 141*
     00(50) -> 171*
     00(243) -> 244*
     00(46) -> 47*
     00(202) -> 203*
     00(270) -> 271*
     00(94) -> 95*
     00(34) -> 35*
     00(175) -> 176*
     00(232) -> 233*
     00(278) -> 279*
     00(24) -> 25*
     00(193) -> 194*
     00(72) -> 73*
     00(266) -> 267*
     00(96) -> 97*
     00(156) -> 157*
     00(60) -> 61*
     00(16) -> 17*
     00(290) -> 291*
     00(274) -> 275*
     00(90) -> 91*
     00(267) -> 268*
     32(624) -> 625*
     52(621) -> 622*
     f60() -> 2*
     196 -> 75*
     247 -> 578*
     238 -> 136,103
     192 -> 490*
     544 -> 222*
     266 -> 314*
     412 -> 209*
     74 -> 136*
     489 -> 275*
     324 -> 268*
     242 -> 523*
     245 -> 75*
     231 -> 136*
     162 -> 50*
     30 -> 3*
     140 -> 358*
     12 -> 3*
     357 -> 205*
     93 -> 3*
     212 -> 347*
     313 -> 36*
     368 -> 142*
     283 -> 13*
     613 -> 618*
     22 -> 50*
     577 -> 289*
     153 -> 3*
     220 -> 534*
     207 -> 402*
     170 -> 3,171
     269 -> 13*
     253 -> 75,51
     261 -> 75,51
     179 -> 3,171
     135 -> 75,85
     127 -> 3*
     287 -> 567*
     40 -> 31*
     1 -> 3*
     49 -> 3*
     445 -> 348,650,213
     456 -> 233*
     65 -> 13,4
     34 -> 303*
     110 -> 136,76
     59 -> 50*
     187 -> 50,137,181
     617 -> 355*
     500 -> 194*
     133 -> 391*
     276 -> 136*
     145 -> 75,51
     659 -> 205*
     119 -> 3*
     211 -> 609,435
     84 -> 13*
     628 -> 615*
     401 -> 127*
     273 -> 479*
     214 -> 3,171
     533 -> 244*
     205 -> 3*
     102 -> 50*
     23 -> 446*
     588 -> 249*
     223 -> 31*
   problem:
    
   Qed