YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {430,422,413,405,397,388,379,372,364,356,349,341,332,
                  323,315,307,299,291,282,273,266,258,250,241,233,224,
                  215,206,198,189,181,172,163,154,148,139,131,121,113,
                  105,97,88,79,70,60,50,40,31,22,12,1}
   transitions:
    11(447) -> 448*
    11(441) -> 442*
    31(445) -> 446*
    31(442) -> 443*
    31(463) -> 464*
    10(69) -> 60*
    10(168) -> 169*
    10(326) -> 327*
    10(265) -> 258*
    10(301) -> 302*
    10(13) -> 71*
    10(400) -> 401*
    10(327) -> 328*
    10(185) -> 186*
    10(328) -> 329*
    10(5) -> 6*
    10(190) -> 191*
    10(109) -> 110*
    10(188) -> 181*
    10(261) -> 262*
    10(219) -> 220*
    10(41) -> 324*
    10(343) -> 344*
    10(278) -> 279*
    10(321) -> 322*
    10(73) -> 74*
    10(289) -> 290*
    10(381) -> 382*
    10(333) -> 334*
    10(342) -> 373*
    10(42) -> 199*
    10(127) -> 128*
    10(103) -> 104*
    10(93) -> 94*
    10(401) -> 402*
    10(251) -> 267*
    10(228) -> 229*
    10(387) -> 379*
    10(132) -> 133*
    10(53) -> 54*
    10(118) -> 119*
    10(211) -> 212*
    10(218) -> 219*
    10(84) -> 85*
    10(11) -> 1*
    10(17) -> 18*
    10(164) -> 308*
    10(3) -> 225*
    10(383) -> 384*
    10(281) -> 273*
    10(89) -> 234*
    10(254) -> 255*
    10(76) -> 77*
    10(155) -> 156*
    10(292) -> 293*
    10(61) -> 62*
    10(4) -> 316*
    10(373) -> 374*
    10(43) -> 44*
    10(25) -> 149*
    10(294) -> 295*
    10(55) -> 56*
    10(235) -> 236*
    10(350) -> 351*
    10(309) -> 310*
    10(80) -> 106*
    10(166) -> 167*
    10(314) -> 307*
    10(95) -> 96*
    10(353) -> 354*
    10(54) -> 55*
    10(359) -> 360*
    10(271) -> 272*
    10(128) -> 129*
    10(90) -> 91*
    10(416) -> 417*
    10(227) -> 228*
    10(362) -> 363*
    10(123) -> 124*
    10(329) -> 330*
    10(28) -> 29*
    10(434) -> 435*
    10(406) -> 407*
    10(51) -> 80*
    10(167) -> 168*
    10(2) -> 122*
    f60() -> 2*
    20(415) -> 416*
    20(257) -> 250*
    20(412) -> 405*
    20(203) -> 204*
    20(159) -> 160*
    20(104) -> 97*
    20(187) -> 188*
    20(398) -> 399*
    20(106) -> 107*
    20(285) -> 286*
    20(102) -> 103*
    20(226) -> 227*
    20(391) -> 392*
    20(259) -> 260*
    20(288) -> 289*
    20(108) -> 109*
    20(210) -> 211*
    20(29) -> 30*
    20(44) -> 45*
    20(367) -> 368*
    20(122) -> 190*
    20(129) -> 130*
    20(423) -> 424*
    20(27) -> 28*
    20(231) -> 232*
    20(334) -> 335*
    20(41) -> 173*
    20(357) -> 358*
    20(3) -> 216*
    20(2) -> 61*
    20(89) -> 90*
    20(83) -> 84*
    20(256) -> 257*
    20(201) -> 202*
    20(279) -> 280*
    20(63) -> 64*
    20(14) -> 132*
    20(4) -> 182*
    20(74) -> 75*
    20(80) -> 81*
    20(117) -> 118*
    20(212) -> 213*
    20(119) -> 120*
    20(214) -> 206*
    20(133) -> 134*
    20(140) -> 342*
    20(354) -> 355*
    20(365) -> 366*
    20(222) -> 223*
    20(277) -> 278*
    20(260) -> 261*
    20(322) -> 315*
    20(98) -> 99*
    20(270) -> 271*
    20(205) -> 198*
    20(152) -> 153*
    20(18) -> 19*
    20(72) -> 73*
    20(197) -> 189*
    20(435) -> 436*
    20(137) -> 138*
    20(65) -> 66*
    20(230) -> 231*
    20(229) -> 230*
    20(407) -> 408*
    20(87) -> 79*
    20(16) -> 17*
    20(293) -> 294*
    20(330) -> 331*
    20(275) -> 276*
    20(48) -> 49*
    20(428) -> 429*
    20(263) -> 264*
    20(123) -> 406*
    20(284) -> 285*
    50(437) -> 430*
    50(421) -> 413*
    50(324) -> 325*
    50(272) -> 266*
    50(2) -> 51*
    50(337) -> 338*
    50(389) -> 390*
    50(409) -> 410*
    50(91) -> 92*
    50(51) -> 283*
    50(134) -> 135*
    50(85) -> 86*
    50(392) -> 393*
    50(173) -> 174*
    50(158) -> 159*
    50(396) -> 388*
    50(62) -> 98*
    50(3) -> 4*
    50(145) -> 146*
    50(290) -> 282*
    50(436) -> 437*
    50(249) -> 241*
    50(49) -> 40*
    50(89) -> 292*
    50(276) -> 277*
    50(305) -> 306*
    50(376) -> 377*
    50(390) -> 391*
    50(433) -> 434*
    50(13) -> 389*
    50(429) -> 422*
    50(157) -> 158*
    50(169) -> 170*
    50(59) -> 50*
    50(378) -> 372*
    50(335) -> 336*
    50(61) -> 274*
    50(122) -> 123*
    50(342) -> 343*
    50(120) -> 113*
    50(318) -> 319*
    50(375) -> 376*
    50(186) -> 187*
    50(404) -> 397*
    50(21) -> 12*
    00(52) -> 398*
    00(417) -> 418*
    00(2) -> 13*
    00(10) -> 11*
    00(360) -> 361*
    00(296) -> 297*
    00(374) -> 375*
    00(297) -> 298*
    00(71) -> 72*
    00(13) -> 14*
    00(115) -> 116*
    00(20) -> 21*
    00(300) -> 301*
    00(427) -> 428*
    00(304) -> 305*
    00(191) -> 192*
    00(232) -> 224*
    00(363) -> 356*
    00(311) -> 312*
    00(425) -> 426*
    00(308) -> 309*
    00(57) -> 58*
    00(111) -> 112*
    00(345) -> 346*
    00(140) -> 141*
    00(255) -> 256*
    00(64) -> 65*
    00(286) -> 287*
    00(164) -> 165*
    00(47) -> 48*
    00(3) -> 23*
    00(82) -> 83*
    00(274) -> 275*
    00(36) -> 37*
    00(331) -> 323*
    00(371) -> 364*
    00(46) -> 47*
    00(56) -> 57*
    00(202) -> 203*
    00(92) -> 93*
    00(194) -> 195*
    00(283) -> 284*
    00(420) -> 421*
    00(149) -> 150*
    00(77) -> 78*
    00(338) -> 339*
    00(38) -> 39*
    00(143) -> 144*
    00(344) -> 345*
    00(382) -> 383*
    00(352) -> 353*
    00(34) -> 35*
    00(174) -> 175*
    00(51) -> 207*
    00(310) -> 311*
    00(351) -> 352*
    00(156) -> 157*
    00(142) -> 143*
    00(86) -> 87*
    00(183) -> 184*
    00(251) -> 252*
    00(216) -> 217*
    00(41) -> 380*
    00(316) -> 317*
    00(306) -> 299*
    00(366) -> 367*
    00(200) -> 201*
    00(100) -> 101*
    00(126) -> 127*
    00(124) -> 125*
    00(151) -> 152*
    00(280) -> 281*
    00(182) -> 183*
    00(244) -> 245*
    00(114) -> 115*
    40(35) -> 36*
    40(7) -> 8*
    40(246) -> 247*
    40(432) -> 433*
    40(208) -> 209*
    40(30) -> 22*
    40(419) -> 420*
    40(96) -> 88*
    40(171) -> 163*
    40(408) -> 409*
    40(94) -> 95*
    40(248) -> 249*
    40(75) -> 76*
    40(264) -> 265*
    40(52) -> 53*
    40(312) -> 313*
    40(3) -> 32*
    40(240) -> 233*
    40(146) -> 147*
    40(355) -> 349*
    40(180) -> 172*
    40(385) -> 386*
    40(39) -> 31*
    40(393) -> 394*
    40(313) -> 314*
    40(221) -> 222*
    40(184) -> 185*
    40(67) -> 68*
    40(268) -> 269*
    40(66) -> 67*
    40(170) -> 171*
    40(262) -> 263*
    40(418) -> 419*
    40(236) -> 237*
    40(320) -> 321*
    40(13) -> 155*
    40(217) -> 218*
    40(346) -> 347*
    40(195) -> 196*
    40(14) -> 15*
    40(347) -> 348*
    40(238) -> 239*
    40(302) -> 303*
    40(253) -> 254*
    40(403) -> 404*
    40(135) -> 136*
    40(399) -> 400*
    40(141) -> 142*
    40(176) -> 177*
    40(61) -> 89*
    40(207) -> 208*
    40(89) -> 431*
    40(8) -> 9*
    40(426) -> 427*
    40(317) -> 318*
    40(325) -> 326*
    40(150) -> 151*
    40(267) -> 268*
    40(242) -> 243*
    40(220) -> 221*
    40(243) -> 244*
    40(245) -> 246*
    40(165) -> 166*
    40(80) -> 259*
    40(112) -> 105*
    40(144) -> 145*
    40(24) -> 25*
    40(4) -> 5*
    40(37) -> 38*
    40(209) -> 210*
    40(395) -> 396*
    40(42) -> 43*
    40(348) -> 341*
    40(98) -> 350*
    40(162) -> 154*
    40(247) -> 248*
    40(32) -> 33*
    40(361) -> 362*
    40(386) -> 387*
    40(51) -> 333*
    40(58) -> 59*
    40(179) -> 180*
    40(225) -> 357*
    40(340) -> 332*
    40(161) -> 162*
    40(160) -> 161*
    40(269) -> 270*
    40(175) -> 176*
    40(25) -> 26*
    40(78) -> 70*
    40(2) -> 3*
    40(213) -> 214*
    40(410) -> 411*
    40(41) -> 42*
    30(370) -> 371*
    30(411) -> 412*
    30(153) -> 148*
    30(192) -> 193*
    30(223) -> 215*
    30(147) -> 139*
    30(242) -> 423*
    30(178) -> 179*
    30(23) -> 24*
    30(358) -> 359*
    30(298) -> 291*
    30(2) -> 41*
    30(122) -> 164*
    30(116) -> 117*
    30(225) -> 226*
    30(295) -> 296*
    30(402) -> 403*
    30(107) -> 108*
    30(81) -> 82*
    30(13) -> 242*
    30(196) -> 197*
    30(414) -> 415*
    30(101) -> 102*
    30(15) -> 16*
    30(62) -> 63*
    30(368) -> 369*
    30(431) -> 432*
    30(177) -> 178*
    30(204) -> 205*
    30(110) -> 111*
    30(136) -> 137*
    30(287) -> 288*
    30(6) -> 7*
    30(336) -> 337*
    30(99) -> 100*
    30(384) -> 385*
    30(9) -> 10*
    30(237) -> 238*
    30(199) -> 200*
    30(68) -> 69*
    30(138) -> 131*
    30(339) -> 340*
    30(140) -> 251*
    30(89) -> 114*
    30(424) -> 425*
    30(377) -> 378*
    30(26) -> 27*
    30(123) -> 300*
    30(319) -> 320*
    30(125) -> 126*
    30(45) -> 46*
    30(33) -> 34*
    30(303) -> 304*
    30(3) -> 140*
    30(193) -> 194*
    30(252) -> 253*
    30(41) -> 414*
    30(234) -> 235*
    30(380) -> 381*
    30(173) -> 365*
    30(19) -> 20*
    30(130) -> 121*
    30(369) -> 370*
    30(239) -> 240*
    30(394) -> 395*
    30(51) -> 52*
    41(462) -> 463*
    41(461) -> 462*
    41(444) -> 445*
    41(460) -> 461*
    41(440) -> 441*
    41(443) -> 444*
    41(469) -> 470*
    41(438) -> 439*
    41(465) -> 466*
    41(467) -> 468*
    51(439) -> 440*
    01(464) -> 465*
    01(468) -> 469*
    01(466) -> 467*
    01(446) -> 447*
    307 -> 41,52
    291 -> 41,242,126
    430 -> 51,283
    163 -> 13*
    70 -> 61,173
    372 -> 51,389
    266 -> 51,283
    422 -> 51,283
    388 -> 51*
    131 -> 51,283
    215 -> 41,52
    413 -> 51,283,390
    148 -> 13,125
    206 -> 61,182
    154 -> 13,125
    250 -> 51,283
    198 -> 61,216
    189 -> 61*
    113 -> 51,389
    282 -> 122,80,124
    12 -> 51,389
    379 -> 51,274
    419 -> 460*
    470 -> 333*
    258 -> 51,283
    105 -> 3,42
    22 -> 13,72
    377 -> 438*
    88 -> 3*
    121 -> 51*
    172 -> 13,380,165
    349 -> 3,89
    233 -> 3,42,53
    79 -> 61*
    323 -> 3,259
    139 -> 51,283
    60 -> 122,80
    332 -> 3,259
    40 -> 51,283
    1 -> 41,52
    31 -> 3,333
    224 -> 3*
    397 -> 51,4
    241 -> 51,389
    341 -> 3,89
    405 -> 51,283,390
    50 -> 51,283
    299 -> 41*
    448 -> 52*
    181 -> 122,80
    97 -> 3,259
    273 -> 122,71
    356 -> 3,333
    315 -> 3,155,208
    364 -> 3,333
  problem:
   
  Qed