YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {450,442,433,425,419,411,403,394,385,376,367,358,350,
                  342,336,328,320,311,302,293,286,277,269,262,253,244,
                  235,228,220,212,203,194,185,177,169,163,153,144,135,
                  125,118,111,103,94,85,77,69,60,51,42,32,22,12,1}
   transitions:
    10(213) -> 214*
    10(272) -> 273*
    10(2) -> 13*
    10(245) -> 329*
    10(337) -> 338*
    10(359) -> 360*
    10(426) -> 427*
    10(264) -> 265*
    10(322) -> 323*
    10(398) -> 399*
    10(291) -> 292*
    10(377) -> 378*
    10(366) -> 358*
    10(23) -> 254*
    10(410) -> 403*
    10(33) -> 61*
    10(405) -> 406*
    10(300) -> 301*
    10(126) -> 377*
    10(210) -> 211*
    10(131) -> 132*
    10(310) -> 302*
    10(292) -> 286*
    10(195) -> 196*
    10(34) -> 35*
    10(380) -> 381*
    10(354) -> 355*
    10(329) -> 330*
    10(217) -> 218*
    10(3) -> 359*
    10(189) -> 190*
    10(48) -> 49*
    10(443) -> 444*
    10(416) -> 417*
    10(119) -> 120*
    10(154) -> 245*
    10(251) -> 252*
    10(83) -> 84*
    10(452) -> 453*
    10(181) -> 182*
    10(285) -> 277*
    10(166) -> 167*
    10(288) -> 289*
    10(93) -> 85*
    10(429) -> 430*
    10(6) -> 420*
    10(343) -> 344*
    10(43) -> 321*
    10(295) -> 296*
    10(184) -> 177*
    10(373) -> 374*
    10(351) -> 352*
    10(59) -> 51*
    10(407) -> 408*
    10(230) -> 231*
    10(330) -> 331*
    10(349) -> 342*
    10(362) -> 363*
    10(192) -> 193*
    10(58) -> 59*
    10(318) -> 319*
    10(406) -> 407*
    10(132) -> 133*
    10(106) -> 107*
    10(341) -> 336*
    10(238) -> 239*
    10(301) -> 293*
    10(19) -> 20*
    21(470) -> 471*
    21(476) -> 477*
    21(475) -> 476*
    21(492) -> 493*
    21(498) -> 499*
    21(497) -> 498*
    51(477) -> 478*
    51(499) -> 500*
    00(297) -> 298*
    00(171) -> 172*
    00(47) -> 48*
    00(432) -> 425*
    00(427) -> 428*
    00(417) -> 418*
    00(399) -> 400*
    00(207) -> 208*
    00(445) -> 446*
    00(273) -> 274*
    00(446) -> 447*
    00(88) -> 89*
    00(296) -> 297*
    00(13) -> 386*
    00(370) -> 371*
    00(392) -> 393*
    00(360) -> 361*
    00(242) -> 243*
    00(187) -> 188*
    00(16) -> 17*
    00(44) -> 112*
    00(78) -> 79*
    00(34) -> 404*
    00(422) -> 423*
    00(186) -> 187*
    00(447) -> 448*
    00(97) -> 98*
    00(174) -> 175*
    00(57) -> 58*
    00(372) -> 373*
    00(126) -> 312*
    00(381) -> 382*
    00(183) -> 184*
    00(382) -> 383*
    00(455) -> 456*
    00(45) -> 46*
    00(101) -> 102*
    00(267) -> 268*
    00(340) -> 341*
    00(439) -> 440*
    00(15) -> 16*
    00(33) -> 95*
    00(312) -> 426*
    00(345) -> 346*
    00(307) -> 308*
    00(280) -> 281*
    00(137) -> 138*
    00(112) -> 113*
    00(324) -> 325*
    00(81) -> 82*
    00(221) -> 222*
    00(347) -> 348*
    00(23) -> 368*
    00(70) -> 71*
    00(66) -> 67*
    00(86) -> 87*
    00(11) -> 1*
    00(249) -> 250*
    00(17) -> 18*
    00(282) -> 283*
    00(214) -> 215*
    00(3) -> 4*
    00(206) -> 207*
    00(383) -> 384*
    00(89) -> 90*
    00(38) -> 39*
    00(178) -> 179*
    00(150) -> 151*
    00(104) -> 105*
    00(234) -> 228*
    00(37) -> 38*
    00(334) -> 335*
    00(8) -> 9*
    00(159) -> 160*
    00(43) -> 44*
    00(239) -> 240*
    00(247) -> 248*
    00(113) -> 114*
    00(79) -> 80*
    00(378) -> 379*
    00(246) -> 247*
    00(67) -> 68*
    00(95) -> 270*
    00(49) -> 50*
    00(257) -> 258*
    00(346) -> 347*
    00(224) -> 225*
    00(91) -> 92*
    00(457) -> 450*
    00(46) -> 47*
    00(250) -> 251*
    00(298) -> 299*
    00(420) -> 421*
    00(440) -> 441*
    00(114) -> 115*
    00(167) -> 168*
    00(2) -> 3*
    30(65) -> 66*
    30(208) -> 209*
    30(368) -> 369*
    30(127) -> 128*
    30(43) -> 70*
    30(252) -> 244*
    30(52) -> 78*
    30(414) -> 415*
    30(3) -> 186*
    30(86) -> 178*
    30(237) -> 238*
    30(145) -> 146*
    30(449) -> 442*
    30(355) -> 356*
    30(180) -> 181*
    30(204) -> 213*
    30(365) -> 366*
    30(138) -> 139*
    30(197) -> 198*
    30(236) -> 237*
    30(107) -> 108*
    30(13) -> 294*
    30(265) -> 266*
    30(139) -> 140*
    30(134) -> 125*
    30(154) -> 236*
    30(23) -> 395*
    30(281) -> 282*
    30(143) -> 135*
    30(356) -> 357*
    30(36) -> 37*
    30(390) -> 391*
    30(172) -> 173*
    30(108) -> 109*
    30(400) -> 401*
    30(126) -> 195*
    30(397) -> 398*
    30(270) -> 271*
    30(421) -> 422*
    30(387) -> 388*
    30(374) -> 375*
    30(332) -> 333*
    30(308) -> 309*
    30(260) -> 261*
    30(198) -> 199*
    30(164) -> 165*
    30(245) -> 246*
    30(140) -> 141*
    30(254) -> 255*
    30(100) -> 101*
    30(283) -> 284*
    30(353) -> 354*
    30(115) -> 116*
    30(24) -> 25*
    30(4) -> 5*
    30(423) -> 424*
    30(395) -> 396*
    30(348) -> 349*
    30(202) -> 194*
    30(147) -> 148*
    30(44) -> 119*
    30(110) -> 103*
    30(201) -> 202*
    30(71) -> 72*
    30(124) -> 118*
    30(434) -> 451*
    30(155) -> 351*
    30(175) -> 176*
    30(21) -> 12*
    30(2) -> 126*
    30(357) -> 350*
    30(331) -> 332*
    30(72) -> 73*
    31(472) -> 473*
    31(500) -> 501*
    31(494) -> 495*
    31(478) -> 479*
    20(219) -> 212*
    20(393) -> 385*
    20(226) -> 227*
    20(54) -> 55*
    20(152) -> 144*
    20(104) -> 263*
    20(306) -> 307*
    20(156) -> 157*
    20(168) -> 163*
    20(325) -> 326*
    20(241) -> 242*
    20(154) -> 434*
    20(266) -> 267*
    20(176) -> 169*
    20(23) -> 136*
    20(2) -> 23*
    20(122) -> 123*
    20(40) -> 41*
    20(259) -> 260*
    20(160) -> 161*
    20(391) -> 392*
    20(441) -> 433*
    20(225) -> 226*
    20(438) -> 439*
    20(191) -> 192*
    20(4) -> 170*
    20(338) -> 339*
    20(63) -> 64*
    20(90) -> 91*
    20(13) -> 14*
    20(196) -> 197*
    20(233) -> 234*
    20(126) -> 127*
    20(39) -> 40*
    20(148) -> 149*
    20(431) -> 432*
    20(401) -> 402*
    20(274) -> 275*
    20(287) -> 288*
    20(6) -> 7*
    20(248) -> 249*
    20(27) -> 28*
    20(179) -> 180*
    20(151) -> 152*
    20(314) -> 315*
    20(384) -> 376*
    20(82) -> 83*
    20(9) -> 10*
    20(68) -> 60*
    20(64) -> 65*
    20(18) -> 19*
    20(56) -> 57*
    20(29) -> 30*
    20(339) -> 340*
    20(409) -> 410*
    20(165) -> 166*
    20(52) -> 53*
    20(80) -> 81*
    20(268) -> 262*
    20(276) -> 269*
    20(323) -> 324*
    20(61) -> 62*
    20(121) -> 122*
    20(312) -> 313*
    20(231) -> 232*
    20(319) -> 311*
    20(98) -> 99*
    20(222) -> 223*
    20(129) -> 130*
    20(33) -> 34*
    20(240) -> 241*
    20(44) -> 45*
    20(3) -> 43*
    20(193) -> 185*
    20(95) -> 96*
    20(41) -> 32*
    20(162) -> 153*
    20(316) -> 317*
    20(200) -> 201*
    20(278) -> 279*
    20(92) -> 93*
    20(53) -> 54*
    20(413) -> 414*
    20(130) -> 131*
    20(371) -> 372*
    20(190) -> 191*
    20(456) -> 457*
    20(31) -> 22*
    11(473) -> 474*
    11(495) -> 496*
    40(333) -> 334*
    40(186) -> 221*
    40(364) -> 365*
    40(44) -> 229*
    40(229) -> 230*
    40(188) -> 189*
    40(24) -> 412*
    40(290) -> 291*
    40(141) -> 142*
    40(256) -> 257*
    40(2) -> 33*
    40(321) -> 322*
    40(10) -> 11*
    40(5) -> 6*
    40(317) -> 318*
    40(62) -> 63*
    40(74) -> 75*
    40(13) -> 52*
    40(20) -> 21*
    40(215) -> 216*
    40(305) -> 306*
    40(453) -> 454*
    40(437) -> 438*
    40(261) -> 253*
    40(128) -> 129*
    40(388) -> 389*
    40(96) -> 97*
    40(54) -> 337*
    40(204) -> 205*
    40(430) -> 431*
    40(232) -> 233*
    40(363) -> 364*
    40(25) -> 26*
    40(154) -> 155*
    40(396) -> 397*
    40(255) -> 256*
    40(284) -> 285*
    40(271) -> 272*
    40(435) -> 436*
    40(299) -> 300*
    40(3) -> 145*
    40(379) -> 380*
    40(87) -> 88*
    40(404) -> 405*
    40(436) -> 437*
    40(451) -> 452*
    40(361) -> 362*
    40(209) -> 210*
    40(55) -> 56*
    40(294) -> 295*
    40(258) -> 259*
    40(158) -> 159*
    40(155) -> 156*
    40(120) -> 121*
    40(149) -> 150*
    40(428) -> 429*
    40(335) -> 328*
    40(105) -> 106*
    40(386) -> 443*
    40(454) -> 455*
    40(434) -> 435*
    40(34) -> 104*
    40(309) -> 310*
    40(84) -> 77*
    40(45) -> 164*
    40(444) -> 445*
    40(35) -> 36*
    40(205) -> 206*
    40(136) -> 137*
    40(408) -> 409*
    40(173) -> 174*
    40(7) -> 8*
    40(199) -> 200*
    40(402) -> 394*
    40(289) -> 290*
    40(30) -> 31*
    40(14) -> 15*
    40(279) -> 280*
    40(216) -> 217*
    40(76) -> 69*
    40(327) -> 320*
    40(218) -> 219*
    40(412) -> 413*
    40(26) -> 27*
    40(170) -> 171*
    40(245) -> 343*
    40(315) -> 316*
    40(23) -> 86*
    40(126) -> 204*
    40(227) -> 220*
    40(33) -> 303*
    40(369) -> 370*
    40(182) -> 183*
    40(303) -> 304*
    01(471) -> 472*
    01(469) -> 470*
    01(491) -> 492*
    01(493) -> 494*
    41(474) -> 475*
    41(496) -> 497*
    50(415) -> 416*
    50(223) -> 224*
    50(313) -> 314*
    50(102) -> 94*
    50(33) -> 278*
    50(424) -> 419*
    50(161) -> 162*
    50(326) -> 327*
    50(375) -> 367*
    50(116) -> 117*
    50(28) -> 29*
    50(304) -> 305*
    50(170) -> 287*
    50(142) -> 143*
    50(75) -> 76*
    50(2) -> 154*
    50(344) -> 345*
    50(386) -> 387*
    50(117) -> 111*
    50(389) -> 390*
    50(109) -> 110*
    50(133) -> 134*
    50(50) -> 42*
    50(23) -> 24*
    50(243) -> 235*
    50(211) -> 203*
    50(73) -> 74*
    50(157) -> 158*
    50(448) -> 449*
    50(352) -> 353*
    50(99) -> 100*
    50(275) -> 276*
    50(418) -> 411*
    50(263) -> 264*
    50(123) -> 124*
    50(146) -> 147*
    f60() -> 2*
    307 -> 491*
    228 -> 154,387
    94 -> 154*
    262 -> 3*
    163 -> 23,14
    442 -> 154*
    403 -> 154*
    194 -> 126,395,128
    144 -> 13,359
    367 -> 126,236
    328 -> 23,434
    358 -> 126,195,396
    203 -> 126,236
    320 -> 23,127
    42 -> 154,278
    69 -> 23,434
    77 -> 33,155
    450 -> 154*
    169 -> 23,127
    85 -> 154*
    12 -> 23,14
    425 -> 154*
    479 -> 203*
    419 -> 154*
    501 -> 24*
    212 -> 33,52
    244 -> 154,278
    118 -> 154*
    350 -> 126,395,451
    433 -> 154*
    336 -> 23,434
    394 -> 33,86,435
    22 -> 23,434
    220 -> 33,52
    153 -> 13,245
    302 -> 23,127
    277 -> 13,254
    311 -> 23,127
    207 -> 469*
    177 -> 23,127
    385 -> 33,52
    269 -> 13,329
    253 -> 3,312
    235 -> 154,278
    125 -> 154*
    135 -> 154*
    342 -> 23,434
    60 -> 23,127
    1 -> 3,368
    293 -> 23,14
    185 -> 23,434
    411 -> 154*
    51 -> 13,245
    286 -> 13,377
    103 -> 154*
    32 -> 23,434
    376 -> 33,145,443
    111 -> 154*
  problem:
   
  Qed