YES

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

Proof:
 Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {418,411,403,394,385,377,369,363,354,346,339,332,324,
                  315,307,298,289,281,272,264,256,249,240,232,223,214,
                  206,197,188,180,174,168,161,153,145,139,131,122,112,
                  103,95,88,78,69,59,50,41,32,22,12,1}
   transitions:
    50(421) -> 422*
    50(266) -> 267*
    50(113) -> 241*
    50(2) -> 60*
    50(215) -> 216*
    50(386) -> 387*
    50(233) -> 333*
    50(395) -> 396*
    50(328) -> 329*
    50(410) -> 403*
    50(313) -> 314*
    50(33) -> 96*
    50(331) -> 324*
    50(51) -> 347*
    50(134) -> 135*
    50(361) -> 362*
    50(79) -> 355*
    50(114) -> 115*
    50(85) -> 86*
    50(18) -> 19*
    50(110) -> 111*
    50(158) -> 159*
    50(190) -> 191*
    50(329) -> 330*
    50(30) -> 31*
    50(3) -> 4*
    50(16) -> 140*
    50(119) -> 120*
    50(273) -> 404*
    50(154) -> 162*
    50(290) -> 370*
    50(383) -> 384*
    50(357) -> 358*
    50(235) -> 236*
    50(276) -> 277*
    50(387) -> 388*
    50(181) -> 182*
    50(107) -> 108*
    50(316) -> 317*
    50(220) -> 221*
    50(234) -> 235*
    50(390) -> 391*
    50(393) -> 385*
    50(13) -> 189*
    50(56) -> 57*
    50(295) -> 296*
    50(4) -> 419*
    50(236) -> 237*
    50(54) -> 55*
    50(304) -> 305*
    50(60) -> 198*
    50(66) -> 67*
    50(27) -> 28*
    50(169) -> 170*
    50(26) -> 27*
    50(282) -> 283*
    50(378) -> 379*
    50(408) -> 409*
    50(86) -> 87*
    50(172) -> 173*
    50(203) -> 204*
    50(177) -> 178*
    50(372) -> 373*
    50(164) -> 165*
    50(120) -> 121*
    50(417) -> 411*
    50(47) -> 48*
    50(296) -> 297*
    50(218) -> 219*
    50(21) -> 12*
    50(238) -> 239*
    50(143) -> 144*
    00(171) -> 172*
    00(391) -> 392*
    00(200) -> 364*
    00(279) -> 280*
    00(13) -> 33*
    00(287) -> 288*
    00(144) -> 139*
    00(327) -> 328*
    00(219) -> 220*
    00(270) -> 271*
    00(60) -> 395*
    00(321) -> 322*
    00(396) -> 397*
    00(413) -> 414*
    00(57) -> 58*
    00(75) -> 76*
    00(45) -> 46*
    00(35) -> 36*
    00(374) -> 375*
    00(15) -> 16*
    00(312) -> 313*
    00(137) -> 138*
    00(305) -> 306*
    00(419) -> 420*
    00(173) -> 168*
    00(121) -> 112*
    00(379) -> 380*
    00(23) -> 24*
    00(62) -> 63*
    00(140) -> 141*
    00(147) -> 148*
    00(11) -> 1*
    00(38) -> 39*
    00(151) -> 152*
    00(104) -> 282*
    00(155) -> 156*
    00(61) -> 325*
    00(4) -> 5*
    00(373) -> 374*
    00(376) -> 369*
    00(355) -> 356*
    00(247) -> 248*
    00(323) -> 315*
    00(152) -> 145*
    00(225) -> 226*
    00(309) -> 310*
    00(79) -> 80*
    00(67) -> 68*
    00(314) -> 307*
    00(175) -> 176*
    00(49) -> 41*
    00(414) -> 415*
    00(425) -> 418*
    00(91) -> 92*
    00(362) -> 354*
    00(123) -> 132*
    00(424) -> 425*
    00(389) -> 390*
    00(46) -> 47*
    00(336) -> 337*
    00(274) -> 275*
    00(344) -> 345*
    00(167) -> 161*
    00(388) -> 389*
    00(2) -> 3*
    40(343) -> 344*
    40(5) -> 6*
    40(40) -> 32*
    40(288) -> 281*
    40(194) -> 195*
    40(104) -> 105*
    40(130) -> 122*
    40(15) -> 89*
    40(178) -> 179*
    40(384) -> 377*
    40(268) -> 269*
    40(299) -> 378*
    40(170) -> 171*
    40(262) -> 263*
    40(351) -> 352*
    40(63) -> 64*
    40(250) -> 251*
    40(13) -> 386*
    40(350) -> 351*
    40(23) -> 290*
    40(195) -> 196*
    40(342) -> 343*
    40(398) -> 399*
    40(358) -> 359*
    40(99) -> 100*
    40(405) -> 406*
    40(92) -> 93*
    40(406) -> 407*
    40(135) -> 136*
    40(210) -> 211*
    40(397) -> 398*
    40(176) -> 177*
    40(407) -> 408*
    40(303) -> 304*
    40(207) -> 208*
    40(123) -> 207*
    40(114) -> 181*
    40(89) -> 90*
    40(229) -> 230*
    40(185) -> 186*
    40(70) -> 71*
    40(267) -> 268*
    40(345) -> 339*
    40(100) -> 101*
    40(76) -> 77*
    40(80) -> 81*
    40(292) -> 293*
    40(291) -> 292*
    40(209) -> 210*
    40(42) -> 154*
    40(420) -> 421*
    40(293) -> 294*
    40(16) -> 169*
    40(375) -> 376*
    40(211) -> 212*
    40(129) -> 130*
    40(113) -> 215*
    40(6) -> 7*
    40(74) -> 75*
    40(160) -> 153*
    40(159) -> 160*
    40(338) -> 332*
    40(31) -> 22*
    40(2) -> 79*
    40(73) -> 74*
    30(370) -> 371*
    30(132) -> 133*
    30(404) -> 405*
    30(243) -> 244*
    30(422) -> 423*
    30(226) -> 227*
    30(156) -> 157*
    30(216) -> 217*
    30(400) -> 401*
    30(325) -> 326*
    30(241) -> 242*
    30(2) -> 13*
    30(182) -> 183*
    30(36) -> 37*
    30(28) -> 29*
    30(181) -> 340*
    30(191) -> 192*
    30(117) -> 118*
    30(4) -> 233*
    30(402) -> 394*
    30(349) -> 350*
    30(13) -> 51*
    30(149) -> 150*
    30(71) -> 72*
    30(96) -> 97*
    30(60) -> 61*
    30(79) -> 104*
    30(248) -> 240*
    30(302) -> 303*
    30(198) -> 199*
    30(208) -> 209*
    30(9) -> 10*
    30(64) -> 65*
    30(114) -> 257*
    30(108) -> 109*
    30(356) -> 357*
    30(409) -> 410*
    30(80) -> 146*
    30(275) -> 276*
    30(123) -> 124*
    30(58) -> 50*
    30(319) -> 320*
    30(280) -> 272*
    30(271) -> 264*
    30(25) -> 250*
    30(7) -> 8*
    30(3) -> 42*
    30(359) -> 360*
    30(200) -> 201*
    30(141) -> 142*
    30(19) -> 20*
    30(16) -> 17*
    30(221) -> 222*
    30(189) -> 190*
    20(52) -> 53*
    20(186) -> 187*
    20(364) -> 365*
    20(157) -> 158*
    20(254) -> 255*
    20(138) -> 131*
    20(39) -> 40*
    20(44) -> 45*
    20(237) -> 238*
    20(24) -> 25*
    20(290) -> 291*
    20(233) -> 234*
    20(330) -> 331*
    20(2) -> 113*
    20(10) -> 11*
    20(17) -> 18*
    20(360) -> 361*
    20(318) -> 319*
    20(133) -> 134*
    20(48) -> 49*
    20(297) -> 289*
    20(71) -> 412*
    20(380) -> 381*
    20(53) -> 54*
    20(13) -> 273*
    20(115) -> 116*
    20(20) -> 21*
    20(273) -> 274*
    20(337) -> 338*
    20(348) -> 349*
    20(253) -> 254*
    20(127) -> 128*
    20(193) -> 194*
    20(102) -> 95*
    20(83) -> 84*
    20(224) -> 225*
    20(61) -> 62*
    20(162) -> 163*
    20(94) -> 88*
    20(146) -> 147*
    20(261) -> 262*
    20(128) -> 129*
    20(334) -> 335*
    20(101) -> 102*
    20(196) -> 188*
    20(285) -> 286*
    20(311) -> 312*
    20(25) -> 26*
    20(163) -> 164*
    20(308) -> 309*
    20(399) -> 400*
    20(111) -> 103*
    20(113) -> 114*
    20(255) -> 249*
    20(416) -> 417*
    20(286) -> 287*
    20(340) -> 341*
    20(284) -> 285*
    20(299) -> 300*
    20(82) -> 83*
    20(392) -> 393*
    20(29) -> 30*
    20(401) -> 402*
    20(371) -> 372*
    20(90) -> 91*
    20(109) -> 110*
    20(228) -> 229*
    20(202) -> 203*
    20(294) -> 295*
    20(381) -> 382*
    20(201) -> 202*
    20(242) -> 243*
    20(187) -> 180*
    20(77) -> 69*
    20(79) -> 316*
    20(213) -> 206*
    20(341) -> 342*
    20(43) -> 44*
    20(257) -> 258*
    20(320) -> 321*
    20(277) -> 278*
    20(60) -> 224*
    20(6) -> 175*
    20(265) -> 266*
    20(353) -> 346*
    20(365) -> 366*
    20(335) -> 336*
    20(125) -> 126*
    20(423) -> 424*
    20(382) -> 383*
    20(352) -> 353*
    20(34) -> 35*
    20(84) -> 85*
    20(179) -> 174*
    20(8) -> 9*
    20(205) -> 197*
    20(136) -> 137*
    20(51) -> 52*
    20(217) -> 218*
    20(278) -> 279*
    20(368) -> 363*
    20(118) -> 119*
    20(142) -> 143*
    20(166) -> 167*
    20(199) -> 200*
    20(37) -> 38*
    20(183) -> 184*
    20(14) -> 15*
    20(252) -> 253*
    20(42) -> 43*
    20(123) -> 265*
    20(306) -> 298*
    20(412) -> 413*
    20(366) -> 367*
    20(301) -> 302*
    20(260) -> 261*
    20(245) -> 246*
    20(239) -> 232*
    20(23) -> 123*
    20(148) -> 149*
    20(124) -> 125*
    20(227) -> 228*
    20(65) -> 66*
    20(106) -> 107*
    20(98) -> 99*
    20(244) -> 245*
    20(326) -> 327*
    10(415) -> 416*
    10(246) -> 247*
    10(150) -> 151*
    10(283) -> 284*
    10(81) -> 82*
    10(204) -> 205*
    10(154) -> 155*
    10(347) -> 348*
    10(13) -> 14*
    10(33) -> 34*
    10(259) -> 260*
    10(116) -> 117*
    10(367) -> 368*
    10(231) -> 223*
    10(3) -> 299*
    10(2) -> 23*
    10(310) -> 311*
    10(300) -> 301*
    10(14) -> 308*
    10(192) -> 193*
    10(212) -> 213*
    10(126) -> 127*
    10(165) -> 166*
    10(269) -> 270*
    10(251) -> 252*
    10(23) -> 70*
    10(222) -> 214*
    10(258) -> 259*
    10(322) -> 323*
    10(97) -> 98*
    10(68) -> 59*
    10(55) -> 56*
    10(317) -> 318*
    10(72) -> 73*
    10(230) -> 231*
    10(105) -> 106*
    10(87) -> 78*
    10(93) -> 94*
    10(263) -> 256*
    10(333) -> 334*
    10(184) -> 185*
    f60() -> 2*
    307 -> 79,290
    403 -> 60,189
    354 -> 79*
    418 -> 60,198
    131 -> 79*
    324 -> 79,386
    206 -> 23,14
    168 -> 3,80
    256 -> 113,316
    240 -> 113*
    69 -> 23*
    112 -> 79*
    12 -> 3*
    281 -> 79*
    369 -> 79*
    188 -> 23,299
    232 -> 113*
    180 -> 23,299,34
    264 -> 113,224
    363 -> 79*
    249 -> 113,316,291
    174 -> 3,395
    394 -> 60,189
    22 -> 3*
    377 -> 60*
    88 -> 113*
    153 -> 3*
    346 -> 79*
    161 -> 3,24
    385 -> 60*
    139 -> 60*
    197 -> 23,14
    332 -> 79,386
    1 -> 3*
    59 -> 23,14
    95 -> 113,316
    411 -> 60,355,216
    298 -> 79,290,378
    50 -> 23,70
    41 -> 3,33
    122 -> 79,386,154
    145 -> 3*
    289 -> 79,81
    214 -> 23,14
    103 -> 13*
    315 -> 79,290
    32 -> 3*
    339 -> 79*
    223 -> 23*
    78 -> 23*
    272 -> 13*
  problem:
   
  Qed