YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {401,383,366,347,330,313,296,280,265,248,232,216,202,
                  190,175,162,150,140,132,123,115,106,97,88,82,73,65,
                  58,50,45,39,32,27,23,18,15,12,9,5,1}
   transitions:
    21(421) -> 422*
    21(436) -> 437*
    21(452) -> 453*
    21(454) -> 455*
    21(434) -> 435*
    41(422) -> 423*
    41(456) -> 457*
    41(438) -> 439*
    00(69) -> 70*
    00(153) -> 154*
    00(339) -> 340*
    00(169) -> 170*
    00(393) -> 394*
    00(13) -> 14*
    00(286) -> 287*
    00(400) -> 383*
    00(231) -> 216*
    00(185) -> 186*
    00(328) -> 329*
    00(59) -> 249*
    00(367) -> 368*
    00(34) -> 46*
    00(270) -> 271*
    00(243) -> 244*
    00(413) -> 414*
    00(174) -> 162*
    00(289) -> 290*
    00(40) -> 41*
    00(319) -> 320*
    00(85) -> 86*
    00(205) -> 206*
    00(165) -> 166*
    00(374) -> 375*
    00(407) -> 408*
    00(180) -> 181*
    00(405) -> 406*
    00(33) -> 40*
    00(295) -> 280*
    00(1) -> 116*
    00(387) -> 388*
    00(203) -> 204*
    00(66) -> 67*
    00(100) -> 101*
    00(135) -> 136*
    00(282) -> 283*
    00(164) -> 217*
    00(3) -> 4*
    00(38) -> 32*
    00(178) -> 179*
    00(352) -> 353*
    00(37) -> 38*
    00(61) -> 62*
    00(4) -> 1*
    00(107) -> 108*
    00(239) -> 240*
    00(131) -> 123*
    00(55) -> 56*
    00(113) -> 114*
    00(309) -> 310*
    00(19) -> 20*
    00(378) -> 379*
    00(67) -> 68*
    00(133) -> 134*
    00(257) -> 258*
    00(28) -> 29*
    00(336) -> 337*
    00(318) -> 319*
    00(406) -> 407*
    00(237) -> 238*
    00(51) -> 52*
    00(410) -> 411*
    00(397) -> 398*
    00(2) -> 13*
    f60() -> 2*
    50(355) -> 356*
    50(412) -> 413*
    50(159) -> 160*
    50(320) -> 321*
    50(283) -> 284*
    50(301) -> 302*
    50(204) -> 205*
    50(86) -> 87*
    50(25) -> 26*
    50(51) -> 203*
    50(219) -> 220*
    50(382) -> 366*
    50(187) -> 188*
    50(398) -> 399*
    50(207) -> 208*
    50(136) -> 137*
    50(196) -> 197*
    50(33) -> 66*
    50(244) -> 245*
    50(161) -> 150*
    50(56) -> 57*
    50(375) -> 376*
    50(264) -> 248*
    50(402) -> 403*
    50(122) -> 115*
    50(399) -> 400*
    50(30) -> 31*
    50(36) -> 37*
    50(3) -> 74*
    50(2) -> 10*
    50(43) -> 44*
    50(310) -> 311*
    50(218) -> 219*
    50(14) -> 297*
    50(4) -> 83*
    50(373) -> 374*
    50(411) -> 412*
    50(314) -> 315*
    50(76) -> 77*
    50(252) -> 253*
    50(389) -> 390*
    50(11) -> 331*
    50(109) -> 110*
    50(6) -> 384*
    50(199) -> 200*
    50(217) -> 218*
    50(360) -> 361*
    50(277) -> 278*
    50(181) -> 182*
    50(22) -> 18*
    50(54) -> 55*
    50(92) -> 93*
    50(125) -> 126*
    50(188) -> 189*
    50(322) -> 323*
    50(98) -> 99*
    50(34) -> 35*
    50(253) -> 254*
    50(268) -> 269*
    50(361) -> 362*
    50(342) -> 343*
    50(278) -> 279*
    50(166) -> 167*
    50(128) -> 129*
    50(79) -> 80*
    50(247) -> 232*
    50(385) -> 386*
    50(297) -> 298*
    50(305) -> 306*
    50(96) -> 88*
    50(353) -> 354*
    50(290) -> 291*
    50(302) -> 303*
    50(263) -> 264*
    50(59) -> 314*
    50(70) -> 71*
    50(184) -> 185*
    50(64) -> 58*
    50(267) -> 268*
    20(324) -> 325*
    20(168) -> 169*
    20(221) -> 222*
    20(2) -> 6*
    20(71) -> 72*
    20(359) -> 360*
    20(409) -> 410*
    20(233) -> 234*
    20(259) -> 260*
    20(33) -> 107*
    20(331) -> 332*
    20(134) -> 135*
    20(183) -> 184*
    20(110) -> 111*
    20(163) -> 367*
    20(229) -> 230*
    20(158) -> 159*
    20(381) -> 382*
    20(396) -> 397*
    20(308) -> 309*
    20(206) -> 207*
    20(240) -> 241*
    20(346) -> 330*
    20(3) -> 141*
    20(35) -> 36*
    20(416) -> 417*
    20(384) -> 385*
    20(14) -> 12*
    20(119) -> 120*
    20(271) -> 272*
    20(154) -> 155*
    20(235) -> 236*
    20(83) -> 84*
    20(156) -> 157*
    20(89) -> 151*
    20(139) -> 132*
    20(276) -> 277*
    20(285) -> 286*
    20(316) -> 317*
    20(20) -> 21*
    20(348) -> 349*
    20(220) -> 221*
    20(10) -> 11*
    20(288) -> 289*
    20(234) -> 235*
    20(93) -> 94*
    20(356) -> 357*
    20(13) -> 233*
    20(84) -> 85*
    20(365) -> 347*
    20(4) -> 19*
    20(146) -> 147*
    20(226) -> 227*
    20(242) -> 243*
    20(333) -> 334*
    20(260) -> 261*
    20(59) -> 402*
    20(124) -> 125*
    20(129) -> 130*
    20(230) -> 231*
    20(414) -> 415*
    20(222) -> 223*
    20(349) -> 350*
    20(164) -> 165*
    20(46) -> 133*
    20(344) -> 345*
    20(417) -> 418*
    20(287) -> 288*
    20(171) -> 172*
    20(112) -> 113*
    20(17) -> 15*
    20(42) -> 43*
    20(108) -> 191*
    20(87) -> 82*
    10(157) -> 158*
    10(211) -> 212*
    10(269) -> 270*
    10(2) -> 3*
    10(10) -> 28*
    10(246) -> 247*
    10(62) -> 63*
    10(117) -> 118*
    10(74) -> 75*
    10(325) -> 326*
    10(127) -> 128*
    10(224) -> 225*
    10(80) -> 81*
    10(94) -> 95*
    10(390) -> 391*
    10(304) -> 305*
    10(236) -> 237*
    10(57) -> 50*
    10(340) -> 341*
    10(299) -> 300*
    10(370) -> 371*
    10(392) -> 393*
    10(274) -> 275*
    10(404) -> 405*
    10(75) -> 76*
    10(46) -> 47*
    10(228) -> 229*
    10(294) -> 295*
    10(201) -> 190*
    10(120) -> 121*
    10(149) -> 140*
    10(107) -> 266*
    10(341) -> 342*
    10(338) -> 339*
    10(167) -> 168*
    10(95) -> 96*
    10(358) -> 359*
    10(11) -> 16*
    10(386) -> 387*
    10(350) -> 351*
    10(51) -> 124*
    10(130) -> 131*
    10(368) -> 369*
    10(357) -> 358*
    10(394) -> 395*
    10(212) -> 213*
    10(160) -> 161*
    10(144) -> 145*
    10(59) -> 60*
    10(279) -> 265*
    10(327) -> 328*
    10(81) -> 73*
    10(200) -> 201*
    10(170) -> 171*
    10(376) -> 377*
    10(151) -> 152*
    10(227) -> 228*
    10(33) -> 348*
    10(182) -> 183*
    10(303) -> 304*
    40(7) -> 8*
    40(215) -> 202*
    40(208) -> 209*
    40(419) -> 401*
    40(101) -> 102*
    40(335) -> 336*
    40(408) -> 409*
    40(391) -> 392*
    40(104) -> 105*
    40(29) -> 30*
    40(52) -> 53*
    40(3) -> 51*
    40(33) -> 34*
    40(145) -> 146*
    40(49) -> 45*
    40(53) -> 54*
    40(121) -> 122*
    40(307) -> 308*
    40(138) -> 139*
    40(363) -> 364*
    40(197) -> 198*
    40(262) -> 263*
    40(418) -> 419*
    40(351) -> 352*
    40(63) -> 64*
    40(250) -> 251*
    40(300) -> 301*
    40(195) -> 196*
    40(315) -> 316*
    40(251) -> 252*
    40(238) -> 239*
    40(68) -> 69*
    40(298) -> 299*
    40(172) -> 173*
    40(11) -> 9*
    40(210) -> 211*
    40(126) -> 127*
    40(141) -> 142*
    40(176) -> 177*
    40(329) -> 313*
    40(60) -> 61*
    40(332) -> 333*
    40(89) -> 90*
    40(379) -> 380*
    40(254) -> 255*
    40(369) -> 370*
    40(292) -> 293*
    40(173) -> 174*
    40(4) -> 24*
    40(209) -> 210*
    40(266) -> 267*
    40(395) -> 396*
    40(103) -> 104*
    40(147) -> 148*
    40(186) -> 187*
    40(179) -> 180*
    40(377) -> 378*
    40(311) -> 312*
    40(6) -> 163*
    40(177) -> 178*
    40(31) -> 27*
    40(255) -> 256*
    40(78) -> 79*
    40(2) -> 33*
    40(323) -> 324*
    40(380) -> 381*
    40(284) -> 285*
    30(152) -> 153*
    30(291) -> 292*
    30(306) -> 307*
    30(194) -> 195*
    30(241) -> 242*
    30(192) -> 193*
    30(223) -> 224*
    30(213) -> 214*
    30(2) -> 59*
    30(116) -> 117*
    30(47) -> 48*
    30(163) -> 164*
    30(403) -> 404*
    30(225) -> 226*
    30(343) -> 344*
    30(191) -> 192*
    30(261) -> 262*
    30(90) -> 91*
    30(10) -> 98*
    30(13) -> 176*
    30(281) -> 282*
    30(214) -> 215*
    30(233) -> 281*
    30(258) -> 259*
    30(148) -> 149*
    30(102) -> 103*
    30(72) -> 65*
    30(345) -> 346*
    30(6) -> 7*
    30(249) -> 250*
    30(198) -> 199*
    30(99) -> 100*
    30(118) -> 119*
    30(59) -> 89*
    30(155) -> 156*
    30(142) -> 143*
    30(114) -> 106*
    30(272) -> 273*
    30(108) -> 109*
    30(293) -> 294*
    30(111) -> 112*
    30(388) -> 389*
    30(326) -> 327*
    30(334) -> 335*
    30(362) -> 363*
    30(256) -> 257*
    30(8) -> 5*
    30(26) -> 23*
    30(275) -> 276*
    30(143) -> 144*
    30(21) -> 22*
    30(24) -> 25*
    30(48) -> 49*
    30(273) -> 274*
    30(312) -> 296*
    30(337) -> 338*
    30(91) -> 92*
    30(77) -> 78*
    30(364) -> 365*
    30(321) -> 322*
    30(354) -> 355*
    30(44) -> 39*
    30(193) -> 194*
    30(105) -> 97*
    30(41) -> 42*
    30(415) -> 416*
    30(317) -> 318*
    30(372) -> 373*
    30(245) -> 246*
    30(371) -> 372*
    30(16) -> 17*
    30(137) -> 138*
    30(189) -> 175*
    51(420) -> 421*
    31(439) -> 440*
    31(437) -> 438*
    31(455) -> 456*
    31(457) -> 458*
    01(433) -> 434*
    01(432) -> 433*
    01(450) -> 451*
    01(451) -> 452*
    435 -> 44*
    27 -> 10,384
    132 -> 10,314
    190 -> 10,314
    17 -> 436*
    458 -> 176,250
    115 -> 10,66
    162 -> 13,14,434
    453 -> 331*
    216 -> 13,249
    113 -> 450*
    140 -> 13,4
    12 -> 10,384,403
    106 -> 10,314
    45 -> 59,89
    440 -> 109*
    232 -> 59*
    265 -> 3*
    313 -> 10*
    82 -> 6,402
    88 -> 10*
    150 -> 6,107
    248 -> 10*
    58 -> 6,402
    296 -> 10,384
    330 -> 6,233,133
    423 -> 185*
    73 -> 3*
    123 -> 13,14
    40 -> 432*
    1 -> 13,4
    175 -> 59,176
    65 -> 59,98
    5 -> 59,176
    9 -> 10,384
    347 -> 6*
    50 -> 3,266
    39 -> 59,176
    18 -> 59*
    383 -> 13,249
    15 -> 33*
    181 -> 420*
    401 -> 13,40,432
    97 -> 10*
    229 -> 454*
    202 -> 33,90
    32 -> 13,4
    280 -> 3*
    366 -> 33,34
    23 -> 59,7
  problem:
   
  Qed