YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {380,371,363,356,348,339,332,324,316,308,301,293,285,
                  277,268,259,253,246,238,231,223,216,208,199,191,184,
                  175,167,158,149,139,131,122,113,105,96,87,78,69,59,
                  49,40,30,22,12,1}
   transitions:
    40(168) -> 169*
    40(2) -> 13*
    40(71) -> 72*
    40(337) -> 338*
    40(264) -> 265*
    40(322) -> 323*
    40(377) -> 378*
    40(366) -> 367*
    40(37) -> 38*
    40(130) -> 122*
    40(77) -> 69*
    40(326) -> 327*
    40(79) -> 80*
    40(367) -> 368*
    40(18) -> 19*
    40(95) -> 87*
    40(176) -> 364*
    40(302) -> 303*
    40(150) -> 151*
    40(219) -> 220*
    40(311) -> 312*
    40(3) -> 97*
    40(256) -> 257*
    40(48) -> 40*
    40(347) -> 339*
    40(154) -> 155*
    40(209) -> 210*
    40(67) -> 68*
    40(166) -> 158*
    40(20) -> 21*
    40(93) -> 94*
    40(239) -> 247*
    40(323) -> 316*
    40(360) -> 361*
    40(275) -> 276*
    40(90) -> 91*
    40(295) -> 296*
    40(128) -> 129*
    40(157) -> 149*
    40(378) -> 379*
    40(50) -> 51*
    40(257) -> 258*
    40(263) -> 264*
    40(330) -> 331*
    40(61) -> 294*
    40(177) -> 232*
    40(281) -> 282*
    40(99) -> 100*
    40(327) -> 328*
    40(244) -> 245*
    40(142) -> 143*
    40(375) -> 376*
    40(296) -> 297*
    40(364) -> 365*
    40(100) -> 101*
    40(106) -> 302*
    40(17) -> 18*
    40(25) -> 26*
    51(470) -> 471*
    51(551) -> 552*
    51(405) -> 406*
    51(552) -> 553*
    51(545) -> 546*
    51(474) -> 475*
    51(404) -> 405*
    51(400) -> 401*
    51(475) -> 476*
    21(546) -> 547*
    21(542) -> 543*
    21(514) -> 515*
    21(481) -> 482*
    21(472) -> 473*
    21(402) -> 403*
    21(418) -> 419*
    21(441) -> 442*
    21(476) -> 477*
    21(488) -> 489*
    21(443) -> 444*
    21(537) -> 538*
    21(438) -> 439*
    21(411) -> 412*
    21(540) -> 541*
    21(521) -> 522*
    21(406) -> 407*
    00(207) -> 199*
    00(160) -> 161*
    00(148) -> 139*
    00(200) -> 239*
    00(13) -> 340*
    00(210) -> 211*
    00(261) -> 262*
    00(242) -> 243*
    00(162) -> 163*
    00(321) -> 322*
    00(368) -> 369*
    00(73) -> 74*
    00(319) -> 320*
    00(201) -> 202*
    00(129) -> 130*
    00(45) -> 46*
    00(33) -> 34*
    00(305) -> 306*
    00(161) -> 162*
    00(111) -> 112*
    00(32) -> 33*
    00(136) -> 137*
    00(218) -> 219*
    00(86) -> 78*
    00(84) -> 85*
    00(11) -> 1*
    00(3) -> 159*
    00(272) -> 273*
    00(89) -> 90*
    00(178) -> 179*
    00(254) -> 255*
    00(138) -> 131*
    00(292) -> 285*
    00(234) -> 235*
    00(61) -> 62*
    00(63) -> 64*
    00(124) -> 125*
    00(4) -> 132*
    00(291) -> 292*
    00(220) -> 221*
    00(170) -> 171*
    00(351) -> 352*
    00(306) -> 307*
    00(9) -> 10*
    00(123) -> 309*
    00(196) -> 197*
    00(336) -> 337*
    00(237) -> 231*
    00(2) -> 140*
    30(294) -> 295*
    30(35) -> 36*
    30(151) -> 152*
    30(194) -> 195*
    30(278) -> 279*
    30(171) -> 172*
    30(81) -> 254*
    30(248) -> 249*
    30(341) -> 342*
    30(43) -> 44*
    30(29) -> 22*
    30(252) -> 246*
    30(312) -> 313*
    30(3) -> 4*
    30(352) -> 353*
    30(240) -> 241*
    30(349) -> 350*
    30(145) -> 146*
    30(15) -> 16*
    30(38) -> 39*
    30(180) -> 181*
    30(241) -> 242*
    30(385) -> 386*
    30(62) -> 63*
    30(107) -> 108*
    30(250) -> 251*
    30(156) -> 157*
    30(57) -> 58*
    30(97) -> 98*
    30(13) -> 14*
    30(54) -> 55*
    30(217) -> 218*
    30(14) -> 106*
    30(342) -> 343*
    30(181) -> 182*
    30(125) -> 126*
    30(290) -> 291*
    30(36) -> 37*
    30(298) -> 299*
    30(334) -> 335*
    30(106) -> 107*
    30(230) -> 223*
    30(55) -> 56*
    30(329) -> 330*
    30(60) -> 150*
    30(374) -> 375*
    30(114) -> 224*
    30(123) -> 124*
    30(190) -> 184*
    30(89) -> 357*
    30(229) -> 230*
    30(185) -> 186*
    30(70) -> 286*
    30(267) -> 259*
    30(376) -> 377*
    30(140) -> 269*
    30(369) -> 370*
    30(80) -> 81*
    30(112) -> 105*
    30(115) -> 116*
    30(50) -> 176*
    30(266) -> 267*
    30(247) -> 248*
    30(16) -> 17*
    30(361) -> 362*
    30(88) -> 192*
    30(310) -> 311*
    30(19) -> 20*
    30(318) -> 319*
    30(211) -> 212*
    30(71) -> 381*
    30(152) -> 153*
    30(6) -> 7*
    30(74) -> 75*
    30(159) -> 160*
    30(373) -> 374*
    30(31) -> 88*
    30(132) -> 133*
    30(2) -> 50*
    30(284) -> 277*
    31(416) -> 417*
    31(483) -> 484*
    31(436) -> 437*
    31(548) -> 549*
    31(515) -> 516*
    31(407) -> 408*
    31(412) -> 413*
    31(513) -> 514*
    31(413) -> 414*
    31(480) -> 481*
    31(477) -> 478*
    31(482) -> 483*
    31(439) -> 440*
    31(486) -> 487*
    31(535) -> 536*
    31(538) -> 539*
    31(519) -> 520*
    31(469) -> 470*
    31(399) -> 400*
    31(410) -> 411*
    31(516) -> 517*
    10(331) -> 324*
    10(297) -> 298*
    10(104) -> 96*
    10(325) -> 326*
    10(85) -> 86*
    10(164) -> 165*
    10(147) -> 148*
    10(23) -> 24*
    10(358) -> 359*
    10(2) -> 3*
    10(182) -> 183*
    10(265) -> 266*
    10(117) -> 118*
    10(4) -> 5*
    10(88) -> 89*
    10(233) -> 234*
    10(126) -> 127*
    10(42) -> 43*
    10(101) -> 102*
    10(102) -> 103*
    10(344) -> 345*
    10(75) -> 76*
    10(236) -> 237*
    10(274) -> 275*
    10(60) -> 123*
    10(287) -> 288*
    10(379) -> 371*
    10(179) -> 180*
    10(198) -> 191*
    10(118) -> 119*
    10(384) -> 385*
    10(82) -> 83*
    10(68) -> 59*
    10(304) -> 305*
    10(114) -> 115*
    10(140) -> 141*
    10(228) -> 229*
    10(215) -> 208*
    10(206) -> 207*
    10(135) -> 136*
    10(50) -> 200*
    10(276) -> 268*
    10(143) -> 144*
    10(313) -> 314*
    10(58) -> 49*
    10(66) -> 67*
    10(365) -> 366*
    10(44) -> 45*
    10(280) -> 281*
    10(186) -> 187*
    10(7) -> 8*
    10(333) -> 334*
    10(359) -> 360*
    10(174) -> 167*
    10(144) -> 145*
    10(300) -> 293*
    10(212) -> 213*
    10(183) -> 175*
    10(203) -> 204*
    10(239) -> 240*
    10(31) -> 32*
    10(221) -> 222*
    11(536) -> 537*
    11(471) -> 472*
    11(547) -> 548*
    11(549) -> 550*
    11(435) -> 436*
    11(539) -> 540*
    11(401) -> 402*
    11(437) -> 438*
    11(440) -> 441*
    11(534) -> 535*
    20(52) -> 53*
    20(39) -> 30*
    20(362) -> 356*
    20(354) -> 355*
    20(188) -> 189*
    20(24) -> 25*
    20(153) -> 154*
    20(214) -> 215*
    20(2) -> 31*
    20(10) -> 11*
    20(5) -> 6*
    20(21) -> 12*
    20(13) -> 70*
    20(127) -> 128*
    20(193) -> 194*
    20(224) -> 225*
    20(72) -> 73*
    20(192) -> 193*
    20(94) -> 95*
    20(343) -> 344*
    20(146) -> 147*
    20(204) -> 205*
    20(235) -> 236*
    20(163) -> 164*
    20(116) -> 117*
    20(345) -> 346*
    20(255) -> 256*
    20(97) -> 325*
    20(243) -> 244*
    20(249) -> 250*
    20(28) -> 29*
    20(195) -> 196*
    20(222) -> 216*
    20(282) -> 283*
    20(88) -> 317*
    20(56) -> 57*
    20(109) -> 110*
    20(202) -> 203*
    20(92) -> 93*
    20(176) -> 177*
    20(314) -> 315*
    20(283) -> 284*
    20(155) -> 156*
    20(120) -> 121*
    20(110) -> 111*
    20(187) -> 188*
    20(307) -> 301*
    20(338) -> 332*
    20(320) -> 321*
    20(60) -> 61*
    20(335) -> 336*
    20(386) -> 380*
    20(34) -> 35*
    20(262) -> 263*
    20(383) -> 384*
    20(8) -> 9*
    20(357) -> 358*
    20(173) -> 174*
    20(169) -> 170*
    20(108) -> 109*
    20(14) -> 15*
    20(270) -> 271*
    20(91) -> 92*
    20(279) -> 280*
    20(76) -> 77*
    20(41) -> 42*
    20(81) -> 82*
    20(245) -> 238*
    20(165) -> 166*
    20(315) -> 308*
    20(150) -> 209*
    20(70) -> 71*
    20(225) -> 226*
    20(346) -> 347*
    20(177) -> 217*
    20(137) -> 138*
    20(124) -> 185*
    20(65) -> 66*
    20(98) -> 99*
    01(442) -> 443*
    01(543) -> 544*
    01(541) -> 542*
    01(550) -> 551*
    01(444) -> 445*
    41(414) -> 415*
    41(512) -> 513*
    41(518) -> 519*
    41(487) -> 488*
    41(479) -> 480*
    41(403) -> 404*
    41(553) -> 554*
    41(473) -> 474*
    41(417) -> 418*
    41(409) -> 410*
    41(485) -> 486*
    41(484) -> 485*
    41(398) -> 399*
    41(468) -> 469*
    41(520) -> 521*
    41(517) -> 518*
    41(433) -> 434*
    41(415) -> 416*
    50(355) -> 348*
    50(141) -> 142*
    50(309) -> 310*
    50(51) -> 52*
    50(382) -> 383*
    50(289) -> 290*
    50(47) -> 48*
    50(13) -> 260*
    50(226) -> 227*
    50(134) -> 135*
    50(288) -> 289*
    50(103) -> 104*
    50(286) -> 287*
    50(168) -> 333*
    50(27) -> 28*
    50(271) -> 272*
    50(372) -> 373*
    50(26) -> 27*
    50(3) -> 41*
    50(299) -> 300*
    50(2) -> 60*
    50(83) -> 84*
    50(177) -> 178*
    50(14) -> 23*
    50(4) -> 349*
    50(119) -> 120*
    50(213) -> 214*
    50(269) -> 270*
    50(251) -> 252*
    50(133) -> 134*
    50(140) -> 372*
    50(50) -> 114*
    50(114) -> 168*
    50(260) -> 261*
    50(46) -> 47*
    50(258) -> 253*
    50(350) -> 351*
    50(381) -> 382*
    50(97) -> 278*
    50(205) -> 206*
    50(232) -> 233*
    50(172) -> 173*
    50(227) -> 228*
    50(370) -> 363*
    50(273) -> 274*
    50(200) -> 201*
    50(317) -> 318*
    50(197) -> 198*
    50(328) -> 329*
    50(53) -> 54*
    50(189) -> 190*
    50(353) -> 354*
    50(121) -> 113*
    50(31) -> 79*
    50(64) -> 65*
    50(303) -> 304*
    50(340) -> 341*
    f60() -> 2*
    408 -> 361*
    238 -> 140*
    191 -> 3*
    544 -> 309*
    358 -> 398*
    259 -> 140*
    489 -> 159*
    131 -> 140*
    285 -> 140,340
    324 -> 3*
    48 -> 409*
    231 -> 60,372
    158 -> 140,340
    434 -> 410*
    216 -> 31*
    30 -> 140,159
    182 -> 468,435
    113 -> 60,41,142
    69 -> 140,340
    12 -> 140,159
    348 -> 50,269
    535 -> 545*
    379 -> 534*
    478 -> 97*
    419 -> 309*
    301 -> 3,141
    363 -> 60,372
    522 -> 239*
    105 -> 50,4
    22 -> 13,97
    308 -> 3,141
    554 -> 310*
    277 -> 140,340
    268 -> 140*
    208 -> 3,123
    253 -> 140*
    330 -> 479*
    139 -> 140,159
    332 -> 31*
    316 -> 3*
    40 -> 60,372
    1 -> 140,159
    380 -> 60,168
    246 -> 140,159
    49 -> 140*
    293 -> 3,141
    445 -> 159*
    130 -> 433*
    175 -> 3*
    199 -> 3,123
    59 -> 140,159
    347 -> 512*
    184 -> 3*
    122 -> 60,260
    149 -> 140,159
    167 -> 3,141
    371 -> 60,41
    96 -> 3*
    87 -> 3*
    356 -> 13*
    339 -> 50,269,133
    223 -> 50,14,98
    78 -> 3,141
  problem:
   
  Qed