YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {384,376,368,360,353,344,335,327,318,310,303,296,287,
                  278,270,262,254,245,237,229,221,213,204,196,188,179,
                  170,161,153,144,138,129,120,112,103,95,85,78,69,61,
                  52,42,32,22,12,1}
   transitions:
    40(309) -> 303*
    40(388) -> 389*
    40(168) -> 169*
    40(266) -> 267*
    40(272) -> 273*
    40(252) -> 253*
    40(2) -> 13*
    40(215) -> 216*
    40(178) -> 170*
    40(322) -> 323*
    40(75) -> 76*
    40(231) -> 232*
    40(325) -> 326*
    40(268) -> 269*
    40(104) -> 230*
    40(174) -> 175*
    40(23) -> 24*
    40(37) -> 38*
    40(130) -> 189*
    40(214) -> 215*
    40(33) -> 319*
    40(205) -> 206*
    40(38) -> 39*
    40(76) -> 77*
    40(51) -> 42*
    40(361) -> 362*
    40(79) -> 80*
    40(114) -> 115*
    40(367) -> 360*
    40(250) -> 251*
    40(18) -> 19*
    40(175) -> 176*
    40(274) -> 275*
    40(308) -> 309*
    40(329) -> 330*
    40(261) -> 254*
    40(206) -> 207*
    40(30) -> 31*
    40(35) -> 36*
    40(48) -> 49*
    40(145) -> 197*
    40(347) -> 348*
    40(154) -> 155*
    40(193) -> 194*
    40(194) -> 195*
    40(232) -> 233*
    40(334) -> 327*
    40(156) -> 157*
    40(148) -> 149*
    40(118) -> 119*
    40(323) -> 324*
    40(162) -> 263*
    40(13) -> 205*
    40(343) -> 335*
    40(365) -> 366*
    40(4) -> 96*
    40(54) -> 55*
    40(198) -> 199*
    40(96) -> 97*
    40(60) -> 52*
    40(333) -> 334*
    40(260) -> 261*
    40(59) -> 60*
    40(117) -> 118*
    40(320) -> 321*
    40(63) -> 64*
    40(86) -> 345*
    40(172) -> 173*
    40(122) -> 123*
    40(342) -> 343*
    40(255) -> 256*
    40(279) -> 280*
    40(374) -> 375*
    40(135) -> 136*
    40(97) -> 98*
    40(244) -> 237*
    40(142) -> 143*
    40(340) -> 341*
    40(246) -> 255*
    40(21) -> 12*
    40(25) -> 26*
    40(29) -> 30*
    40(19) -> 20*
    01(415) -> 416*
    01(470) -> 471*
    01(419) -> 420*
    01(449) -> 450*
    01(468) -> 469*
    01(450) -> 451*
    01(446) -> 447*
    01(406) -> 407*
    01(403) -> 404*
    01(409) -> 410*
    01(407) -> 408*
    01(471) -> 472*
    31(413) -> 414*
    31(453) -> 454*
    31(472) -> 473*
    31(420) -> 421*
    31(405) -> 406*
    31(448) -> 449*
    31(410) -> 411*
    30(171) -> 238*
    30(158) -> 159*
    30(68) -> 61*
    30(279) -> 311*
    30(285) -> 286*
    30(187) -> 179*
    30(34) -> 369*
    30(41) -> 32*
    30(209) -> 210*
    30(276) -> 277*
    30(57) -> 58*
    30(73) -> 74*
    30(126) -> 127*
    30(39) -> 40*
    30(20) -> 21*
    30(172) -> 354*
    30(240) -> 241*
    30(15) -> 16*
    30(290) -> 291*
    30(228) -> 221*
    30(208) -> 209*
    30(173) -> 174*
    30(324) -> 325*
    30(121) -> 214*
    30(379) -> 380*
    30(23) -> 171*
    30(238) -> 239*
    30(53) -> 62*
    30(100) -> 101*
    30(211) -> 212*
    30(218) -> 219*
    30(6) -> 7*
    30(86) -> 87*
    30(84) -> 78*
    30(11) -> 1*
    30(284) -> 285*
    30(264) -> 265*
    30(281) -> 282*
    30(89) -> 139*
    30(181) -> 182*
    30(150) -> 151*
    30(236) -> 229*
    30(159) -> 160*
    30(373) -> 374*
    30(92) -> 93*
    30(43) -> 44*
    30(131) -> 132*
    30(247) -> 248*
    30(348) -> 349*
    30(350) -> 351*
    30(80) -> 81*
    30(166) -> 167*
    30(246) -> 247*
    30(50) -> 51*
    30(375) -> 368*
    30(110) -> 111*
    30(202) -> 203*
    30(105) -> 106*
    30(197) -> 198*
    30(133) -> 134*
    30(346) -> 347*
    30(65) -> 66*
    30(288) -> 328*
    30(90) -> 91*
    30(224) -> 225*
    30(363) -> 364*
    30(177) -> 178*
    30(298) -> 299*
    30(337) -> 338*
    30(2) -> 33*
    10(294) -> 295*
    10(151) -> 152*
    10(272) -> 385*
    10(5) -> 6*
    10(43) -> 162*
    10(312) -> 313*
    10(3) -> 4*
    10(352) -> 344*
    10(130) -> 131*
    10(146) -> 147*
    10(33) -> 34*
    10(271) -> 272*
    10(241) -> 242*
    10(313) -> 314*
    10(216) -> 217*
    10(299) -> 300*
    10(304) -> 305*
    10(351) -> 352*
    10(265) -> 266*
    10(64) -> 65*
    10(134) -> 135*
    10(217) -> 218*
    10(163) -> 164*
    10(14) -> 15*
    10(305) -> 306*
    10(315) -> 316*
    10(141) -> 142*
    10(106) -> 107*
    10(176) -> 177*
    10(207) -> 208*
    10(336) -> 337*
    10(190) -> 191*
    10(316) -> 317*
    10(89) -> 90*
    10(267) -> 268*
    10(164) -> 165*
    10(280) -> 281*
    10(140) -> 141*
    10(369) -> 370*
    10(77) -> 69*
    10(292) -> 293*
    10(46) -> 47*
    10(24) -> 25*
    10(382) -> 383*
    10(87) -> 88*
    10(291) -> 292*
    10(28) -> 29*
    10(98) -> 99*
    10(293) -> 294*
    10(147) -> 148*
    10(44) -> 154*
    10(225) -> 226*
    10(311) -> 312*
    10(155) -> 156*
    10(160) -> 153*
    10(339) -> 340*
    10(2) -> 3*
    10(357) -> 358*
    41(474) -> 475*
    41(421) -> 422*
    41(445) -> 446*
    41(452) -> 453*
    41(454) -> 455*
    41(451) -> 452*
    41(418) -> 419*
    41(469) -> 470*
    20(219) -> 220*
    20(243) -> 244*
    20(331) -> 332*
    20(226) -> 227*
    20(104) -> 105*
    20(385) -> 386*
    20(34) -> 113*
    20(282) -> 283*
    20(242) -> 243*
    20(2) -> 43*
    20(43) -> 53*
    20(36) -> 37*
    20(14) -> 361*
    20(191) -> 192*
    20(81) -> 82*
    20(13) -> 70*
    20(233) -> 234*
    20(386) -> 387*
    20(149) -> 150*
    20(62) -> 63*
    20(119) -> 112*
    20(94) -> 85*
    20(9) -> 10*
    20(128) -> 120*
    20(326) -> 318*
    20(328) -> 329*
    20(362) -> 363*
    20(256) -> 257*
    20(26) -> 27*
    20(184) -> 185*
    20(121) -> 122*
    20(273) -> 274*
    20(364) -> 365*
    20(33) -> 288*
    20(195) -> 188*
    20(44) -> 45*
    20(251) -> 252*
    20(3) -> 336*
    20(359) -> 353*
    20(341) -> 342*
    20(162) -> 163*
    20(380) -> 381*
    20(127) -> 128*
    20(115) -> 116*
    20(137) -> 129*
    20(31) -> 22*
    20(355) -> 356*
    20(383) -> 376*
    11(402) -> 403*
    11(401) -> 402*
    11(447) -> 448*
    11(416) -> 417*
    11(404) -> 405*
    00(186) -> 187*
    00(16) -> 17*
    00(66) -> 67*
    00(157) -> 158*
    00(354) -> 355*
    00(4) -> 5*
    00(330) -> 331*
    00(2) -> 23*
    00(321) -> 322*
    00(10) -> 11*
    00(17) -> 18*
    00(67) -> 68*
    00(297) -> 298*
    00(71) -> 72*
    00(53) -> 54*
    00(13) -> 14*
    00(49) -> 50*
    00(27) -> 28*
    00(253) -> 245*
    00(189) -> 190*
    00(83) -> 84*
    00(300) -> 301*
    00(72) -> 73*
    00(180) -> 181*
    00(248) -> 249*
    00(54) -> 304*
    00(145) -> 146*
    00(288) -> 377*
    00(116) -> 117*
    00(377) -> 378*
    00(345) -> 346*
    00(154) -> 297*
    00(234) -> 235*
    00(286) -> 278*
    00(259) -> 260*
    00(40) -> 41*
    00(249) -> 250*
    00(389) -> 384*
    00(3) -> 121*
    00(222) -> 223*
    00(371) -> 372*
    00(263) -> 264*
    00(88) -> 89*
    00(56) -> 57*
    00(185) -> 186*
    00(109) -> 110*
    00(55) -> 56*
    00(314) -> 315*
    00(283) -> 284*
    00(201) -> 202*
    00(258) -> 259*
    00(107) -> 108*
    00(43) -> 145*
    00(257) -> 258*
    00(338) -> 339*
    00(277) -> 270*
    00(99) -> 100*
    00(358) -> 359*
    00(143) -> 138*
    00(332) -> 333*
    00(125) -> 126*
    00(34) -> 222*
    00(356) -> 357*
    00(210) -> 211*
    00(45) -> 46*
    00(8) -> 9*
    00(136) -> 137*
    00(372) -> 373*
    00(7) -> 8*
    00(199) -> 200*
    00(108) -> 109*
    00(230) -> 231*
    00(289) -> 290*
    00(123) -> 124*
    00(366) -> 367*
    00(200) -> 201*
    00(165) -> 166*
    00(239) -> 240*
    00(23) -> 130*
    00(124) -> 125*
    00(227) -> 228*
    00(33) -> 246*
    21(408) -> 409*
    21(412) -> 413*
    21(414) -> 415*
    21(467) -> 468*
    21(466) -> 467*
    51(473) -> 474*
    51(417) -> 418*
    50(220) -> 213*
    50(203) -> 196*
    50(301) -> 302*
    50(223) -> 224*
    50(15) -> 79*
    50(102) -> 95*
    50(47) -> 48*
    50(13) -> 279*
    50(288) -> 289*
    50(101) -> 102*
    50(319) -> 320*
    50(58) -> 59*
    50(2) -> 86*
    50(113) -> 114*
    50(43) -> 180*
    50(111) -> 103*
    50(82) -> 83*
    50(171) -> 172*
    50(307) -> 308*
    50(387) -> 388*
    50(74) -> 75*
    50(182) -> 183*
    50(192) -> 193*
    50(306) -> 307*
    50(212) -> 204*
    50(167) -> 168*
    50(269) -> 262*
    50(378) -> 379*
    50(23) -> 104*
    50(183) -> 184*
    50(91) -> 92*
    50(295) -> 287*
    50(381) -> 382*
    50(169) -> 161*
    50(34) -> 35*
    50(139) -> 140*
    50(370) -> 371*
    50(349) -> 350*
    50(152) -> 144*
    50(317) -> 310*
    50(93) -> 94*
    50(275) -> 276*
    50(302) -> 296*
    50(121) -> 271*
    50(132) -> 133*
    50(70) -> 71*
    50(235) -> 236*
    f60() -> 2*
    196 -> 43,53
    327 -> 33*
    262 -> 86*
    475 -> 421*
    144 -> 3,162
    422 -> 62*
    353 -> 13,205
    254 -> 33*
    168 -> 445*
    360 -> 13,205
    245 -> 33*
    278 -> 23,246
    310 -> 43,53
    42 -> 33,44,62
    69 -> 3*
    335 -> 33,87
    112 -> 43*
    85 -> 43,53
    12 -> 3,162
    318 -> 43,53
    188 -> 43,336
    344 -> 13,263
    204 -> 43,53
    368 -> 86,104
    270 -> 23,145
    237 -> 33,44,62
    22 -> 3,34
    455 -> 337*
    52 -> 33,44
    384 -> 86,279,320
    153 -> 3,34,370
    138 -> 23,145
    161 -> 3*
    170 -> 3*
    296 -> 3,162
    179 -> 43,336
    127 -> 412,401
    287 -> 3,4
    1 -> 43,53
    95 -> 43,53
    411 -> 53*
    219 -> 466*
    213 -> 43,53
    120 -> 43*
    129 -> 86,104
    303 -> 3*
    229 -> 33,338
    103 -> 43*
    32 -> 43,53
    61 -> 86*
    376 -> 86*
    221 -> 43*
    78 -> 43,336
  problem:
   
  Qed