YES

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

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