YES

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

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