YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {378,370,362,354,345,336,327,320,312,303,296,288,280,
                  271,263,254,245,236,228,220,212,203,196,187,179,171,
                  163,153,145,136,128,121,112,104,95,87,78,68,58,49,41,
                  31,21,12,1}
   transitions:
    10(200) -> 201*
    10(225) -> 226*
    10(317) -> 318*
    10(243) -> 244*
    10(258) -> 259*
    10(73) -> 74*
    10(113) -> 289*
    10(2) -> 69*
    10(178) -> 171*
    10(188) -> 189*
    10(291) -> 292*
    10(328) -> 329*
    10(23) -> 180*
    10(199) -> 200*
    10(313) -> 314*
    10(37) -> 38*
    10(331) -> 332*
    10(79) -> 80*
    10(114) -> 115*
    10(85) -> 86*
    10(131) -> 132*
    10(138) -> 139*
    10(57) -> 49*
    10(274) -> 275*
    10(197) -> 198*
    10(381) -> 382*
    10(137) -> 138*
    10(70) -> 146*
    10(338) -> 339*
    10(3) -> 4*
    10(256) -> 257*
    10(321) -> 322*
    10(35) -> 36*
    10(159) -> 160*
    10(251) -> 252*
    10(350) -> 351*
    10(72) -> 73*
    10(357) -> 358*
    10(209) -> 210*
    10(155) -> 156*
    10(276) -> 277*
    10(67) -> 58*
    10(22) -> 23*
    10(376) -> 377*
    10(162) -> 153*
    10(360) -> 361*
    10(284) -> 285*
    10(13) -> 14*
    10(6) -> 7*
    10(373) -> 374*
    10(198) -> 199*
    10(96) -> 164*
    10(60) -> 229*
    10(333) -> 334*
    10(59) -> 337*
    10(26) -> 27*
    10(69) -> 204*
    10(358) -> 359*
    10(50) -> 129*
    10(349) -> 350*
    10(86) -> 78*
    10(122) -> 123*
    10(5) -> 6*
    10(342) -> 343*
    10(255) -> 256*
    10(227) -> 220*
    10(82) -> 83*
    10(287) -> 280*
    10(132) -> 133*
    31(853) -> 854*
    31(486) -> 487*
    31(893) -> 894*
    31(886) -> 887*
    31(693) -> 694*
    31(889) -> 890*
    31(405) -> 406*
    31(449) -> 450*
    31(664) -> 665*
    31(571) -> 572*
    31(738) -> 739*
    31(614) -> 615*
    31(573) -> 574*
    31(535) -> 536*
    31(583) -> 584*
    31(925) -> 926*
    31(398) -> 399*
    31(884) -> 885*
    31(702) -> 703*
    31(661) -> 662*
    31(847) -> 848*
    31(447) -> 448*
    31(581) -> 582*
    31(621) -> 622*
    31(453) -> 454*
    31(613) -> 614*
    31(842) -> 843*
    31(651) -> 652*
    31(544) -> 545*
    31(844) -> 845*
    31(460) -> 461*
    31(663) -> 664*
    31(611) -> 612*
    31(654) -> 655*
    31(537) -> 538*
    31(403) -> 404*
    31(502) -> 503*
    31(416) -> 417*
    31(409) -> 410*
    31(653) -> 654*
    31(493) -> 494*
    31(491) -> 492*
    31(729) -> 730*
    31(624) -> 625*
    31(902) -> 903*
    31(899) -> 900*
    31(765) -> 766*
    31(855) -> 856*
    31(543) -> 544*
    31(504) -> 505*
    31(541) -> 542*
    31(442) -> 443*
    31(623) -> 624*
    31(917) -> 918*
    31(458) -> 459*
    31(530) -> 531*
    31(858) -> 859*
    31(774) -> 775*
    31(801) -> 802*
    31(497) -> 498*
    31(574) -> 575*
    31(584) -> 585*
    31(414) -> 415*
    31(810) -> 811*
    51(816) -> 817*
    51(890) -> 891*
    51(859) -> 860*
    51(848) -> 849*
    20(102) -> 103*
    20(119) -> 120*
    20(301) -> 302*
    20(116) -> 117*
    20(160) -> 161*
    20(115) -> 116*
    20(169) -> 170*
    20(385) -> 386*
    20(231) -> 232*
    20(210) -> 211*
    20(190) -> 191*
    20(253) -> 245*
    20(16) -> 17*
    20(44) -> 45*
    20(60) -> 61*
    20(226) -> 227*
    20(142) -> 143*
    20(154) -> 246*
    20(97) -> 297*
    20(126) -> 127*
    20(201) -> 202*
    20(42) -> 43*
    20(22) -> 50*
    20(101) -> 102*
    20(27) -> 28*
    20(290) -> 291*
    20(33) -> 88*
    20(307) -> 308*
    20(295) -> 288*
    20(208) -> 209*
    20(173) -> 174*
    20(111) -> 104*
    20(81) -> 82*
    20(32) -> 33*
    20(94) -> 87*
    20(70) -> 71*
    20(304) -> 305*
    20(218) -> 219*
    20(11) -> 1*
    20(249) -> 250*
    20(164) -> 165*
    20(3) -> 304*
    20(89) -> 90*
    20(38) -> 39*
    20(74) -> 75*
    20(341) -> 342*
    20(234) -> 235*
    20(4) -> 5*
    20(43) -> 44*
    20(217) -> 218*
    20(107) -> 108*
    20(71) -> 72*
    20(113) -> 114*
    20(380) -> 381*
    20(79) -> 313*
    20(246) -> 264*
    20(191) -> 192*
    20(314) -> 315*
    20(260) -> 261*
    20(375) -> 376*
    20(54) -> 55*
    20(105) -> 106*
    20(146) -> 147*
    20(356) -> 357*
    20(134) -> 135*
    20(363) -> 364*
    20(332) -> 333*
    20(299) -> 300*
    20(91) -> 92*
    20(250) -> 251*
    20(384) -> 385*
    20(18) -> 19*
    20(337) -> 338*
    20(157) -> 158*
    20(2) -> 32*
    40(151) -> 152*
    40(22) -> 137*
    40(158) -> 159*
    40(30) -> 21*
    40(335) -> 327*
    40(29) -> 30*
    40(252) -> 253*
    40(3) -> 79*
    40(33) -> 34*
    40(372) -> 373*
    40(166) -> 167*
    40(206) -> 207*
    40(53) -> 54*
    40(355) -> 356*
    40(259) -> 260*
    40(39) -> 40*
    40(69) -> 96*
    40(285) -> 286*
    40(66) -> 67*
    40(90) -> 91*
    40(262) -> 254*
    40(244) -> 236*
    40(62) -> 63*
    40(79) -> 172*
    40(118) -> 119*
    40(17) -> 18*
    40(148) -> 149*
    40(97) -> 98*
    40(139) -> 140*
    40(322) -> 323*
    40(154) -> 155*
    40(23) -> 24*
    40(346) -> 347*
    40(315) -> 316*
    40(347) -> 348*
    40(238) -> 239*
    40(36) -> 37*
    40(172) -> 173*
    40(106) -> 107*
    40(230) -> 231*
    40(214) -> 215*
    40(329) -> 330*
    40(61) -> 62*
    40(60) -> 363*
    40(207) -> 208*
    40(308) -> 309*
    40(123) -> 124*
    40(223) -> 224*
    40(8) -> 9*
    40(229) -> 230*
    40(383) -> 384*
    40(233) -> 234*
    40(140) -> 141*
    40(222) -> 223*
    40(83) -> 84*
    40(80) -> 81*
    40(289) -> 290*
    40(371) -> 372*
    40(4) -> 42*
    40(382) -> 383*
    40(133) -> 134*
    40(192) -> 193*
    40(28) -> 29*
    40(98) -> 99*
    40(293) -> 294*
    40(32) -> 188*
    40(297) -> 298*
    40(19) -> 20*
    40(211) -> 203*
    40(167) -> 168*
    40(326) -> 320*
    40(261) -> 262*
    40(188) -> 221*
    40(177) -> 178*
    40(235) -> 228*
    40(2) -> 22*
    40(213) -> 214*
    40(20) -> 12*
    11(763) -> 764*
    11(572) -> 573*
    11(531) -> 532*
    11(487) -> 488*
    11(446) -> 447*
    11(534) -> 535*
    11(776) -> 777*
    11(727) -> 728*
    11(740) -> 741*
    11(445) -> 446*
    11(456) -> 457*
    11(894) -> 895*
    11(457) -> 458*
    11(412) -> 413*
    11(533) -> 534*
    11(767) -> 768*
    11(695) -> 696*
    11(582) -> 583*
    11(402) -> 403*
    11(413) -> 414*
    11(489) -> 490*
    11(799) -> 800*
    11(443) -> 444*
    11(803) -> 804*
    11(612) -> 613*
    11(691) -> 692*
    11(454) -> 455*
    11(401) -> 402*
    11(811) -> 812*
    11(542) -> 543*
    11(490) -> 491*
    11(622) -> 623*
    11(731) -> 732*
    11(500) -> 501*
    11(501) -> 502*
    11(772) -> 773*
    11(700) -> 701*
    11(498) -> 499*
    11(813) -> 814*
    11(652) -> 653*
    11(736) -> 737*
    11(860) -> 861*
    11(704) -> 705*
    11(849) -> 850*
    11(399) -> 400*
    11(891) -> 892*
    11(662) -> 663*
    11(410) -> 411*
    30(264) -> 265*
    30(216) -> 217*
    30(69) -> 70*
    30(168) -> 169*
    30(34) -> 35*
    30(241) -> 242*
    30(266) -> 267*
    30(351) -> 352*
    30(242) -> 243*
    30(185) -> 186*
    30(23) -> 213*
    30(2) -> 3*
    30(330) -> 331*
    30(22) -> 272*
    30(182) -> 183*
    30(340) -> 341*
    30(14) -> 15*
    30(202) -> 196*
    30(343) -> 344*
    30(181) -> 182*
    30(117) -> 118*
    30(4) -> 355*
    30(63) -> 64*
    30(309) -> 310*
    30(318) -> 319*
    30(55) -> 56*
    30(269) -> 270*
    30(149) -> 150*
    30(161) -> 162*
    30(15) -> 16*
    30(344) -> 336*
    30(361) -> 354*
    30(110) -> 111*
    30(96) -> 97*
    30(302) -> 296*
    30(59) -> 60*
    30(9) -> 10*
    30(108) -> 109*
    30(339) -> 340*
    30(334) -> 335*
    30(352) -> 353*
    30(52) -> 53*
    30(286) -> 287*
    30(80) -> 122*
    30(135) -> 128*
    30(50) -> 51*
    30(323) -> 324*
    30(275) -> 276*
    30(143) -> 144*
    30(24) -> 25*
    30(48) -> 41*
    30(77) -> 68*
    30(267) -> 268*
    30(364) -> 365*
    30(319) -> 312*
    30(45) -> 46*
    30(224) -> 225*
    30(240) -> 241*
    30(7) -> 8*
    30(3) -> 13*
    30(120) -> 112*
    30(374) -> 375*
    30(353) -> 345*
    30(270) -> 263*
    30(278) -> 279*
    30(92) -> 93*
    30(127) -> 121*
    30(183) -> 184*
    30(65) -> 66*
    41(578) -> 579*
    41(840) -> 841*
    41(503) -> 504*
    41(851) -> 852*
    41(800) -> 801*
    41(536) -> 537*
    41(666) -> 667*
    41(895) -> 896*
    41(762) -> 763*
    41(726) -> 727*
    41(618) -> 619*
    41(626) -> 627*
    41(809) -> 810*
    41(548) -> 549*
    41(589) -> 590*
    41(692) -> 693*
    41(549) -> 550*
    41(764) -> 765*
    41(697) -> 698*
    41(658) -> 659*
    41(771) -> 772*
    41(690) -> 691*
    41(588) -> 589*
    41(735) -> 736*
    41(656) -> 657*
    41(939) -> 940*
    41(701) -> 702*
    41(769) -> 770*
    41(919) -> 920*
    41(706) -> 707*
    41(415) -> 416*
    41(616) -> 617*
    41(628) -> 629*
    41(742) -> 743*
    41(812) -> 813*
    41(586) -> 587*
    41(492) -> 493*
    41(805) -> 806*
    41(778) -> 779*
    41(668) -> 669*
    41(773) -> 774*
    41(576) -> 577*
    41(728) -> 729*
    41(448) -> 449*
    41(733) -> 734*
    41(887) -> 888*
    41(579) -> 580*
    41(927) -> 928*
    41(798) -> 799*
    41(856) -> 857*
    41(546) -> 547*
    41(404) -> 405*
    41(669) -> 670*
    41(815) -> 816*
    41(629) -> 630*
    41(845) -> 846*
    41(659) -> 660*
    41(459) -> 460*
    41(619) -> 620*
    41(737) -> 738*
    41(699) -> 700*
    00(186) -> 179*
    00(237) -> 238*
    00(2) -> 154*
    00(93) -> 94*
    00(10) -> 11*
    00(103) -> 95*
    00(273) -> 274*
    00(189) -> 190*
    00(367) -> 368*
    00(180) -> 181*
    00(248) -> 249*
    00(96) -> 105*
    00(204) -> 205*
    00(232) -> 233*
    00(184) -> 185*
    00(25) -> 26*
    00(64) -> 65*
    00(69) -> 255*
    00(47) -> 48*
    00(282) -> 283*
    00(268) -> 269*
    00(46) -> 47*
    00(109) -> 110*
    00(194) -> 195*
    00(283) -> 284*
    00(257) -> 258*
    00(277) -> 278*
    00(265) -> 266*
    00(365) -> 366*
    00(125) -> 126*
    00(34) -> 321*
    00(205) -> 206*
    00(51) -> 52*
    00(130) -> 131*
    00(368) -> 369*
    00(156) -> 157*
    00(59) -> 113*
    00(76) -> 77*
    00(316) -> 317*
    00(306) -> 307*
    00(366) -> 367*
    00(298) -> 299*
    00(150) -> 151*
    00(100) -> 101*
    00(219) -> 212*
    01(505) -> 506*
    01(494) -> 495*
    01(417) -> 418*
    01(703) -> 704*
    01(843) -> 844*
    01(854) -> 855*
    01(802) -> 803*
    01(739) -> 740*
    01(450) -> 451*
    01(900) -> 901*
    01(406) -> 407*
    01(775) -> 776*
    01(766) -> 767*
    01(694) -> 695*
    01(730) -> 731*
    01(538) -> 539*
    01(885) -> 886*
    01(901) -> 902*
    01(461) -> 462*
    21(933) -> 934*
    21(741) -> 742*
    21(615) -> 616*
    21(852) -> 853*
    21(455) -> 456*
    21(532) -> 533*
    21(667) -> 668*
    21(627) -> 628*
    21(499) -> 500*
    21(411) -> 412*
    21(462) -> 463*
    21(577) -> 578*
    21(896) -> 897*
    21(857) -> 858*
    21(657) -> 658*
    21(655) -> 656*
    21(897) -> 898*
    21(777) -> 778*
    21(804) -> 805*
    21(732) -> 733*
    21(768) -> 769*
    21(665) -> 666*
    21(935) -> 936*
    21(488) -> 489*
    21(400) -> 401*
    21(705) -> 706*
    21(575) -> 576*
    21(539) -> 540*
    21(451) -> 452*
    21(444) -> 445*
    21(883) -> 884*
    21(846) -> 847*
    21(888) -> 889*
    21(545) -> 546*
    21(587) -> 588*
    21(506) -> 507*
    21(625) -> 626*
    21(841) -> 842*
    21(418) -> 419*
    21(495) -> 496*
    21(814) -> 815*
    21(696) -> 697*
    21(547) -> 548*
    21(807) -> 808*
    21(898) -> 899*
    21(808) -> 809*
    21(407) -> 408*
    21(585) -> 586*
    21(617) -> 618*
    50(141) -> 142*
    50(246) -> 247*
    50(379) -> 380*
    50(195) -> 187*
    50(377) -> 370*
    50(294) -> 295*
    50(13) -> 371*
    50(272) -> 273*
    50(56) -> 57*
    50(359) -> 360*
    50(292) -> 293*
    50(129) -> 130*
    50(124) -> 125*
    50(170) -> 163*
    50(75) -> 76*
    50(221) -> 222*
    50(2) -> 59*
    50(174) -> 175*
    50(281) -> 282*
    50(310) -> 311*
    50(300) -> 301*
    50(279) -> 271*
    50(386) -> 378*
    50(239) -> 240*
    50(144) -> 136*
    50(80) -> 197*
    50(84) -> 85*
    50(324) -> 325*
    50(165) -> 166*
    50(325) -> 326*
    50(69) -> 328*
    50(215) -> 216*
    50(50) -> 281*
    50(369) -> 362*
    50(22) -> 346*
    50(32) -> 379*
    50(40) -> 31*
    50(311) -> 303*
    50(175) -> 176*
    50(152) -> 145*
    50(193) -> 194*
    50(247) -> 248*
    50(88) -> 89*
    50(305) -> 306*
    50(99) -> 100*
    50(147) -> 148*
    50(348) -> 349*
    50(59) -> 237*
    50(176) -> 177*
    f60() -> 2*
    196 -> 154*
    408 -> 181*
    228 -> 32,246
    327 -> 32,884,50
    312 -> 154*
    155 -> 735,453
    163 -> 154*
    507 -> 255,205
    354 -> 3,410,572,13
    660 -> 255,205
    903 -> 206*
    452 -> 278*
    399 -> 541*
    358 -> 851*
    378 -> 59,379
    670 -> 190*
    928 -> 935,772
    203 -> 154*
    320 -> 154*
    254 -> 32*
    68 -> 154*
    926 -> 498*
    245 -> 32*
    707 -> 578*
    256 -> 762,486
    531 -> 661*
    362 -> 59*
    630 -> 258*
    806 -> 668*
    934 -> 808*
    69 -> 807,771,497
    370 -> 59,328
    236 -> 32*
    104 -> 154*
    112 -> 3,410
    12 -> 154*
    580 -> 255*
    188 -> 798,530
    419 -> 255*
    850 -> 198*
    212 -> 154*
    463 -> 157*
    2 -> 699,409
    336 -> 3,410
    498 -> 651*
    288 -> 154*
    345 -> 3,410,572,13
    220 -> 69,771,204
    153 -> 154*
    171 -> 154*
    121 -> 3,410
    779 -> 658*
    918 -> 410*
    540 -> 190*
    21 -> 154*
    58 -> 154,255
    79 -> 840*
    920 -> 700*
    296 -> 154,255
    179 -> 154,255
    590 -> 278*
    505 -> 893*
    410 -> 571*
    770 -> 628*
    940 -> 883*
    936 -> 884*
    1 -> 154*
    49 -> 69,771,337
    700 -> 883*
    31 -> 154*
    892 -> 337,329
    698 -> 548*
    95 -> 154*
    443 -> 581*
    620 -> 157*
    861 -> 361*
    187 -> 154*
    817 -> 206*
    57 -> 919,917
    41 -> 154*
    227 -> 933,927,925
    550 -> 181*
    276 -> 726,442
    145 -> 59,346
    136 -> 59,371
    303 -> 154,255
    743 -> 618*
    487 -> 621*
    734 -> 588*
    496 -> 258*
    87 -> 22,700
    271 -> 3,410,60
    263 -> 3,410,70,498
    454 -> 611*
    128 -> 3,410,572,13
    280 -> 154*
    376 -> 939*
    23 -> 690,398
    78 -> 154*
  problem:
   
  Qed