YES

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

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