YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {383,374,366,359,351,343,335,327,320,312,304,295,287,
                  278,272,264,256,249,241,232,223,214,205,195,187,181,
                  175,166,157,148,139,131,122,114,104,95,85,76,67,58,
                  49,41,31,22,12,1}
   transitions:
    40(309) -> 310*
    40(243) -> 244*
    40(266) -> 267*
    40(73) -> 74*
    40(2) -> 3*
    40(105) -> 106*
    40(268) -> 269*
    40(303) -> 295*
    40(23) -> 24*
    40(313) -> 314*
    40(332) -> 333*
    40(51) -> 52*
    40(361) -> 362*
    40(24) -> 25*
    40(250) -> 251*
    40(110) -> 111*
    40(310) -> 311*
    40(292) -> 293*
    40(81) -> 82*
    40(197) -> 352*
    40(224) -> 328*
    40(308) -> 309*
    40(133) -> 134*
    40(306) -> 307*
    40(206) -> 207*
    40(3) -> 23*
    40(189) -> 190*
    40(319) -> 312*
    40(145) -> 146*
    40(289) -> 290*
    40(182) -> 183*
    40(385) -> 386*
    40(220) -> 221*
    40(280) -> 281*
    40(288) -> 289*
    40(376) -> 377*
    40(284) -> 285*
    40(13) -> 50*
    40(270) -> 271*
    40(196) -> 197*
    40(260) -> 261*
    40(26) -> 27*
    40(124) -> 125*
    40(136) -> 137*
    40(63) -> 64*
    40(237) -> 238*
    40(86) -> 149*
    40(61) -> 62*
    40(336) -> 337*
    40(142) -> 143*
    40(47) -> 48*
    40(375) -> 376*
    40(201) -> 202*
    40(106) -> 242*
    40(238) -> 239*
    40(42) -> 43*
    40(25) -> 26*
    41(440) -> 441*
    41(402) -> 403*
    41(424) -> 425*
    41(435) -> 436*
    41(439) -> 440*
    41(436) -> 437*
    41(409) -> 410*
    41(437) -> 438*
    41(438) -> 439*
    21(457) -> 458*
    21(429) -> 430*
    21(408) -> 409*
    21(465) -> 466*
    21(460) -> 461*
    21(431) -> 432*
    21(441) -> 442*
    21(403) -> 404*
    21(405) -> 406*
    21(443) -> 444*
    21(410) -> 411*
    21(466) -> 467*
    21(461) -> 462*
    21(406) -> 407*
    30(265) -> 266*
    30(339) -> 340*
    30(68) -> 69*
    30(200) -> 201*
    30(13) -> 206*
    30(77) -> 78*
    30(283) -> 284*
    30(188) -> 189*
    30(219) -> 220*
    30(253) -> 254*
    30(44) -> 45*
    30(34) -> 35*
    30(186) -> 181*
    30(126) -> 127*
    30(120) -> 121*
    30(35) -> 36*
    30(33) -> 34*
    30(228) -> 229*
    30(387) -> 388*
    30(262) -> 263*
    30(347) -> 348*
    30(32) -> 140*
    30(203) -> 204*
    30(86) -> 215*
    30(11) -> 1*
    30(17) -> 18*
    30(282) -> 283*
    30(3) -> 77*
    30(206) -> 305*
    30(150) -> 151*
    30(341) -> 342*
    30(352) -> 353*
    30(236) -> 237*
    30(4) -> 5*
    30(239) -> 240*
    30(79) -> 80*
    30(378) -> 379*
    30(191) -> 192*
    30(314) -> 315*
    30(48) -> 41*
    30(213) -> 205*
    30(105) -> 158*
    30(65) -> 66*
    30(90) -> 91*
    30(371) -> 372*
    30(363) -> 364*
    30(318) -> 319*
    30(384) -> 385*
    30(18) -> 19*
    30(163) -> 164*
    30(2) -> 196*
    50(153) -> 154*
    50(158) -> 336*
    50(127) -> 128*
    50(75) -> 67*
    50(3) -> 4*
    50(370) -> 371*
    50(240) -> 232*
    50(33) -> 188*
    50(178) -> 179*
    50(307) -> 308*
    50(344) -> 345*
    50(204) -> 195*
    50(274) -> 275*
    50(365) -> 359*
    50(156) -> 148*
    50(300) -> 301*
    50(118) -> 119*
    50(350) -> 343*
    50(322) -> 323*
    50(212) -> 213*
    50(346) -> 347*
    50(281) -> 282*
    50(68) -> 288*
    50(356) -> 357*
    50(296) -> 297*
    50(390) -> 383*
    50(279) -> 384*
    50(108) -> 109*
    50(141) -> 142*
    50(176) -> 177*
    50(89) -> 90*
    50(325) -> 326*
    50(243) -> 273*
    50(119) -> 120*
    50(379) -> 380*
    50(254) -> 255*
    50(222) -> 214*
    50(369) -> 370*
    50(174) -> 166*
    50(173) -> 174*
    50(59) -> 115*
    50(382) -> 374*
    50(87) -> 257*
    50(50) -> 51*
    50(32) -> 296*
    50(19) -> 20*
    50(364) -> 365*
    50(386) -> 387*
    50(71) -> 72*
    50(340) -> 341*
    50(188) -> 321*
    50(177) -> 178*
    50(160) -> 161*
    50(338) -> 339*
    50(235) -> 236*
    50(78) -> 79*
    50(2) -> 105*
    50(323) -> 324*
    51(464) -> 465*
    51(407) -> 408*
    51(425) -> 426*
    51(411) -> 412*
    20(132) -> 133*
    20(188) -> 250*
    20(255) -> 249*
    20(367) -> 368*
    20(38) -> 39*
    20(297) -> 298*
    20(103) -> 95*
    20(152) -> 153*
    20(291) -> 292*
    20(194) -> 187*
    20(20) -> 21*
    20(69) -> 70*
    20(172) -> 173*
    20(154) -> 155*
    20(277) -> 272*
    20(257) -> 258*
    20(57) -> 49*
    20(2) -> 13*
    20(330) -> 331*
    20(259) -> 260*
    20(43) -> 44*
    20(36) -> 37*
    20(14) -> 265*
    20(117) -> 118*
    20(342) -> 335*
    20(261) -> 262*
    20(349) -> 350*
    20(107) -> 108*
    20(13) -> 59*
    20(269) -> 270*
    20(149) -> 150*
    20(258) -> 259*
    20(161) -> 162*
    20(15) -> 16*
    20(72) -> 73*
    20(109) -> 110*
    20(247) -> 248*
    20(84) -> 76*
    20(60) -> 61*
    20(94) -> 85*
    20(27) -> 28*
    20(198) -> 199*
    20(151) -> 152*
    20(70) -> 71*
    20(208) -> 209*
    20(59) -> 60*
    20(9) -> 10*
    20(199) -> 200*
    20(311) -> 304*
    20(29) -> 30*
    20(140) -> 141*
    20(165) -> 157*
    20(362) -> 363*
    20(285) -> 286*
    20(87) -> 88*
    20(167) -> 168*
    20(377) -> 378*
    20(80) -> 81*
    20(93) -> 94*
    20(21) -> 12*
    20(123) -> 124*
    20(207) -> 208*
    20(32) -> 96*
    20(45) -> 46*
    20(224) -> 225*
    20(271) -> 264*
    20(86) -> 87*
    20(7) -> 8*
    20(333) -> 334*
    20(3) -> 68*
    20(105) -> 233*
    20(37) -> 38*
    20(353) -> 354*
    20(210) -> 211*
    20(162) -> 163*
    20(316) -> 317*
    20(372) -> 373*
    20(78) -> 360*
    20(245) -> 246*
    20(130) -> 122*
    20(16) -> 17*
    20(74) -> 75*
    20(211) -> 212*
    11(427) -> 428*
    11(432) -> 433*
    11(428) -> 429*
    11(444) -> 445*
    11(430) -> 431*
    11(458) -> 459*
    11(459) -> 460*
    10(52) -> 53*
    10(66) -> 58*
    10(138) -> 131*
    10(354) -> 355*
    10(233) -> 234*
    10(302) -> 303*
    10(2) -> 32*
    10(321) -> 322*
    10(10) -> 11*
    10(360) -> 361*
    10(246) -> 247*
    10(5) -> 6*
    10(317) -> 318*
    10(62) -> 63*
    10(380) -> 381*
    10(53) -> 54*
    10(13) -> 14*
    10(135) -> 136*
    10(115) -> 116*
    10(337) -> 338*
    10(215) -> 216*
    10(348) -> 349*
    10(102) -> 103*
    10(275) -> 276*
    10(83) -> 84*
    10(305) -> 306*
    10(61) -> 176*
    10(180) -> 175*
    10(192) -> 193*
    10(128) -> 129*
    10(334) -> 327*
    10(101) -> 102*
    10(388) -> 389*
    10(196) -> 279*
    10(184) -> 185*
    10(116) -> 117*
    10(111) -> 112*
    10(345) -> 346*
    10(113) -> 104*
    10(324) -> 325*
    10(234) -> 235*
    10(121) -> 114*
    10(276) -> 277*
    10(286) -> 278*
    10(164) -> 165*
    10(389) -> 390*
    10(3) -> 224*
    10(331) -> 332*
    10(197) -> 198*
    10(46) -> 47*
    10(88) -> 89*
    10(56) -> 57*
    10(129) -> 130*
    10(209) -> 210*
    10(55) -> 56*
    10(202) -> 203*
    10(92) -> 93*
    10(294) -> 287*
    10(381) -> 382*
    10(158) -> 159*
    10(155) -> 156*
    10(43) -> 182*
    10(134) -> 135*
    10(231) -> 223*
    10(6) -> 7*
    10(99) -> 100*
    10(32) -> 33*
    10(168) -> 169*
    10(143) -> 144*
    10(125) -> 126*
    10(112) -> 113*
    10(179) -> 180*
    10(8) -> 9*
    10(217) -> 218*
    10(368) -> 369*
    10(357) -> 358*
    10(169) -> 170*
    10(86) -> 123*
    10(144) -> 145*
    10(159) -> 160*
    10(183) -> 184*
    10(30) -> 22*
    10(14) -> 15*
    10(252) -> 253*
    10(91) -> 92*
    10(279) -> 280*
    10(216) -> 217*
    10(301) -> 302*
    10(298) -> 299*
    10(170) -> 171*
    10(315) -> 316*
    10(225) -> 226*
    10(137) -> 138*
    10(33) -> 344*
    10(106) -> 107*
    10(98) -> 99*
    10(244) -> 245*
    10(226) -> 227*
    10(326) -> 320*
    01(442) -> 443*
    31(462) -> 463*
    31(404) -> 405*
    31(426) -> 427*
    31(433) -> 434*
    31(463) -> 464*
    00(355) -> 356*
    00(248) -> 241*
    00(86) -> 375*
    00(100) -> 101*
    00(329) -> 330*
    00(39) -> 40*
    00(33) -> 42*
    00(28) -> 29*
    00(221) -> 222*
    00(299) -> 300*
    00(2) -> 86*
    00(358) -> 351*
    00(82) -> 83*
    00(218) -> 219*
    00(171) -> 172*
    00(373) -> 366*
    00(251) -> 252*
    00(140) -> 313*
    00(242) -> 243*
    00(190) -> 191*
    00(32) -> 167*
    00(54) -> 55*
    00(40) -> 31*
    00(97) -> 98*
    00(227) -> 228*
    00(193) -> 194*
    00(273) -> 274*
    00(185) -> 186*
    00(328) -> 329*
    00(230) -> 231*
    00(96) -> 97*
    00(229) -> 230*
    00(290) -> 291*
    00(293) -> 294*
    00(263) -> 256*
    00(147) -> 139*
    00(59) -> 132*
    00(146) -> 147*
    00(64) -> 65*
    00(224) -> 367*
    00(267) -> 268*
    f60() -> 2*
    327 -> 3,197
    312 -> 3,149,376
    166 -> 86*
    351 -> 105*
    412 -> 275*
    195 -> 105,4
    131 -> 105,297
    320 -> 3,149
    148 -> 86*
    254 -> 457*
    242 -> 402*
    47 -> 424*
    256 -> 86*
    278 -> 32,14
    434 -> 375*
    295 -> 196*
    335 -> 3,197
    104 -> 3,197
    85 -> 196,77
    12 -> 196,206
    114 -> 3,106
    359 -> 105,296
    232 -> 105*
    264 -> 86*
    67 -> 105*
    230 -> 435*
    249 -> 86*
    22 -> 3*
    58 -> 3,106
    343 -> 105*
    76 -> 86*
    139 -> 86,375
    287 -> 32,279
    1 -> 86*
    49 -> 196,77
    31 -> 86,375
    304 -> 196,158
    467 -> 215*
    445 -> 106*
    175 -> 196,215
    241 -> 86*
    95 -> 3,197
    187 -> 105*
    41 -> 86*
    122 -> 105,4
    383 -> 105,4
    374 -> 105*
    181 -> 196,158
    214 -> 105,4
    205 -> 105,4
    366 -> 105,257
    157 -> 86*
    223 -> 105,4
    272 -> 86*
  problem:
   
  Qed