YES

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

Proof:
 Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {420,413,404,396,388,380,372,364,356,349,340,332,323,
                  314,306,297,288,279,272,265,256,247,238,229,221,213,
                  204,195,187,178,169,161,155,146,138,129,119,110,101,
                  93,85,76,67,60,50,42,32,22,12,1}
   transitions:
    40(371) -> 364*
    40(168) -> 161*
    40(73) -> 74*
    40(113) -> 114*
    40(2) -> 33*
    40(105) -> 106*
    40(412) -> 404*
    40(389) -> 390*
    40(127) -> 128*
    40(188) -> 189*
    40(386) -> 387*
    40(315) -> 316*
    40(233) -> 234*
    40(395) -> 388*
    40(23) -> 248*
    40(418) -> 419*
    40(313) -> 306*
    40(130) -> 162*
    40(228) -> 221*
    40(33) -> 239*
    40(205) -> 381*
    40(294) -> 295*
    40(64) -> 65*
    40(51) -> 280*
    40(180) -> 181*
    40(425) -> 426*
    40(367) -> 368*
    40(250) -> 251*
    40(379) -> 372*
    40(173) -> 174*
    40(308) -> 309*
    40(338) -> 339*
    40(48) -> 49*
    40(16) -> 17*
    40(289) -> 290*
    40(14) -> 86*
    40(154) -> 146*
    40(159) -> 160*
    40(193) -> 194*
    40(52) -> 214*
    40(350) -> 351*
    40(232) -> 233*
    40(235) -> 236*
    40(15) -> 61*
    40(167) -> 168*
    40(20) -> 21*
    40(92) -> 85*
    40(148) -> 149*
    40(39) -> 40*
    40(411) -> 412*
    40(275) -> 276*
    40(393) -> 394*
    40(13) -> 257*
    40(343) -> 344*
    40(184) -> 185*
    40(373) -> 374*
    40(4) -> 5*
    40(54) -> 55*
    40(226) -> 227*
    40(27) -> 28*
    40(124) -> 125*
    40(320) -> 321*
    40(208) -> 209*
    40(98) -> 99*
    40(153) -> 154*
    40(172) -> 173*
    40(151) -> 152*
    40(336) -> 337*
    40(82) -> 83*
    40(99) -> 100*
    40(417) -> 418*
    40(318) -> 319*
    40(399) -> 400*
    40(423) -> 424*
    40(25) -> 26*
    40(299) -> 300*
    40(170) -> 373*
    40(363) -> 356*
    00(194) -> 187*
    00(13) -> 102*
    00(286) -> 287*
    00(283) -> 284*
    00(106) -> 107*
    00(185) -> 186*
    00(210) -> 211*
    00(31) -> 22*
    00(261) -> 262*
    00(78) -> 79*
    00(34) -> 35*
    00(162) -> 163*
    00(243) -> 244*
    00(108) -> 109*
    00(321) -> 322*
    00(40) -> 41*
    00(381) -> 382*
    00(319) -> 320*
    00(75) -> 67*
    00(409) -> 410*
    00(267) -> 268*
    00(259) -> 260*
    00(377) -> 378*
    00(290) -> 291*
    00(33) -> 34*
    00(345) -> 346*
    00(137) -> 129*
    00(29) -> 30*
    00(347) -> 348*
    00(125) -> 126*
    00(94) -> 95*
    00(140) -> 141*
    00(141) -> 142*
    00(83) -> 84*
    00(135) -> 136*
    00(11) -> 1*
    00(284) -> 285*
    00(181) -> 182*
    00(248) -> 249*
    00(244) -> 245*
    00(403) -> 396*
    00(402) -> 403*
    00(234) -> 235*
    00(390) -> 391*
    00(107) -> 108*
    00(215) -> 216*
    00(30) -> 31*
    00(260) -> 261*
    00(49) -> 42*
    00(10) -> 11*
    00(258) -> 259*
    00(134) -> 135*
    00(351) -> 352*
    00(227) -> 228*
    00(56) -> 57*
    00(329) -> 330*
    00(344) -> 345*
    00(51) -> 341*
    00(410) -> 411*
    00(337) -> 338*
    00(2) -> 120*
    30(7) -> 8*
    30(171) -> 172*
    30(391) -> 392*
    30(368) -> 369*
    30(301) -> 302*
    30(43) -> 44*
    30(264) -> 256*
    30(252) -> 253*
    30(3) -> 4*
    30(240) -> 241*
    30(130) -> 131*
    30(33) -> 230*
    30(327) -> 328*
    30(145) -> 138*
    30(121) -> 139*
    30(241) -> 242*
    30(282) -> 283*
    30(384) -> 385*
    30(285) -> 286*
    30(66) -> 60*
    30(90) -> 91*
    30(116) -> 117*
    30(276) -> 277*
    30(13) -> 315*
    30(139) -> 140*
    30(322) -> 314*
    30(217) -> 218*
    30(23) -> 298*
    30(128) -> 119*
    30(305) -> 297*
    30(342) -> 343*
    30(143) -> 144*
    30(302) -> 303*
    30(398) -> 399*
    30(358) -> 359*
    30(324) -> 325*
    30(298) -> 389*
    30(296) -> 288*
    30(406) -> 407*
    30(287) -> 279*
    30(397) -> 398*
    30(270) -> 271*
    30(421) -> 422*
    30(374) -> 375*
    30(123) -> 124*
    30(223) -> 224*
    30(91) -> 92*
    30(198) -> 199*
    30(426) -> 427*
    30(317) -> 318*
    30(242) -> 243*
    30(383) -> 384*
    30(165) -> 166*
    30(254) -> 255*
    30(369) -> 370*
    30(77) -> 78*
    30(289) -> 357*
    30(112) -> 113*
    30(46) -> 47*
    30(24) -> 25*
    30(59) -> 50*
    30(263) -> 264*
    30(309) -> 310*
    30(37) -> 38*
    30(28) -> 29*
    30(310) -> 311*
    30(401) -> 402*
    30(51) -> 289*
    30(326) -> 327*
    30(179) -> 333*
    30(120) -> 421*
    30(117) -> 118*
    30(175) -> 176*
    30(132) -> 133*
    30(2) -> 13*
    30(72) -> 73*
    20(218) -> 219*
    20(346) -> 347*
    20(255) -> 247*
    20(331) -> 323*
    20(291) -> 292*
    20(385) -> 386*
    20(69) -> 70*
    20(192) -> 193*
    20(266) -> 267*
    20(176) -> 177*
    20(257) -> 258*
    20(147) -> 307*
    20(375) -> 376*
    20(360) -> 361*
    20(298) -> 299*
    20(2) -> 51*
    20(330) -> 331*
    20(357) -> 358*
    20(376) -> 377*
    20(36) -> 37*
    20(202) -> 203*
    20(191) -> 192*
    20(4) -> 94*
    20(5) -> 6*
    20(63) -> 64*
    20(13) -> 14*
    20(281) -> 282*
    20(214) -> 215*
    20(55) -> 56*
    20(126) -> 127*
    20(15) -> 16*
    20(102) -> 103*
    20(230) -> 231*
    20(136) -> 137*
    20(84) -> 76*
    20(274) -> 275*
    20(96) -> 97*
    20(94) -> 273*
    20(79) -> 80*
    20(131) -> 132*
    20(6) -> 7*
    20(179) -> 180*
    20(405) -> 406*
    20(416) -> 417*
    20(199) -> 200*
    20(18) -> 19*
    20(142) -> 143*
    20(293) -> 294*
    20(170) -> 171*
    20(133) -> 134*
    20(339) -> 332*
    20(206) -> 207*
    20(52) -> 53*
    20(424) -> 425*
    20(80) -> 81*
    20(8) -> 9*
    20(268) -> 269*
    20(21) -> 12*
    20(61) -> 62*
    20(307) -> 308*
    20(224) -> 225*
    20(33) -> 196*
    20(354) -> 355*
    20(303) -> 304*
    20(186) -> 178*
    20(271) -> 265*
    20(86) -> 87*
    20(3) -> 68*
    20(359) -> 360*
    20(174) -> 175*
    20(95) -> 96*
    20(144) -> 145*
    20(120) -> 170*
    20(415) -> 416*
    20(157) -> 158*
    20(300) -> 301*
    20(209) -> 210*
    20(200) -> 201*
    20(292) -> 293*
    20(166) -> 167*
    20(19) -> 20*
    20(180) -> 266*
    20(115) -> 116*
    20(74) -> 75*
    20(355) -> 349*
    20(394) -> 395*
    20(427) -> 428*
    20(51) -> 147*
    20(189) -> 190*
    50(89) -> 90*
    50(422) -> 423*
    50(44) -> 45*
    50(68) -> 69*
    50(4) -> 43*
    50(269) -> 270*
    50(2) -> 3*
    50(378) -> 379*
    50(122) -> 123*
    50(17) -> 18*
    50(246) -> 238*
    50(62) -> 63*
    50(71) -> 72*
    50(53) -> 54*
    50(325) -> 326*
    50(273) -> 274*
    50(328) -> 329*
    50(348) -> 340*
    50(253) -> 254*
    50(9) -> 10*
    50(111) -> 112*
    50(104) -> 105*
    50(121) -> 122*
    50(164) -> 165*
    50(97) -> 98*
    50(47) -> 48*
    50(419) -> 413*
    50(3) -> 130*
    50(392) -> 393*
    50(87) -> 88*
    50(222) -> 223*
    50(197) -> 198*
    50(88) -> 89*
    50(312) -> 313*
    50(414) -> 415*
    50(201) -> 202*
    50(120) -> 121*
    50(149) -> 150*
    50(152) -> 153*
    50(77) -> 188*
    50(307) -> 350*
    50(231) -> 232*
    50(277) -> 278*
    50(220) -> 213*
    50(38) -> 39*
    50(428) -> 420*
    50(335) -> 336*
    50(382) -> 383*
    50(352) -> 353*
    50(262) -> 263*
    50(35) -> 36*
    50(51) -> 52*
    50(130) -> 397*
    50(207) -> 208*
    50(408) -> 409*
    50(278) -> 272*
    50(58) -> 59*
    50(160) -> 155*
    50(183) -> 184*
    50(14) -> 15*
    50(216) -> 217*
    50(316) -> 317*
    50(26) -> 27*
    50(81) -> 82*
    50(170) -> 222*
    50(245) -> 246*
    50(239) -> 240*
    50(150) -> 151*
    50(225) -> 226*
    50(23) -> 24*
    50(177) -> 169*
    50(33) -> 179*
    50(65) -> 66*
    50(280) -> 281*
    50(114) -> 115*
    50(295) -> 296*
    10(249) -> 250*
    10(203) -> 195*
    10(57) -> 58*
    10(51) -> 405*
    10(100) -> 93*
    10(219) -> 220*
    10(158) -> 159*
    10(400) -> 401*
    10(13) -> 205*
    10(196) -> 197*
    10(33) -> 111*
    10(103) -> 104*
    10(35) -> 414*
    10(362) -> 363*
    10(304) -> 305*
    10(334) -> 335*
    10(41) -> 32*
    10(45) -> 46*
    10(163) -> 164*
    10(2) -> 23*
    10(387) -> 380*
    10(182) -> 183*
    10(212) -> 204*
    10(109) -> 101*
    10(251) -> 252*
    10(237) -> 229*
    10(23) -> 77*
    10(365) -> 366*
    10(190) -> 191*
    10(211) -> 212*
    10(341) -> 342*
    10(120) -> 324*
    10(311) -> 312*
    10(205) -> 206*
    10(361) -> 362*
    10(118) -> 110*
    10(370) -> 371*
    10(353) -> 354*
    10(156) -> 157*
    10(407) -> 408*
    10(77) -> 365*
    10(366) -> 367*
    10(236) -> 237*
    10(147) -> 148*
    10(333) -> 334*
    10(132) -> 156*
    10(70) -> 71*
    f60() -> 2*
    420 -> 3,130,397
    247 -> 51,170
    238 -> 23*
    155 -> 33,257
    396 -> 33,239
    372 -> 33,248
    195 -> 23,205
    388 -> 33,257
    340 -> 33*
    413 -> 3,179
    256 -> 51*
    42 -> 13,421
    169 -> 3,130
    85 -> 120,34
    12 -> 13,230
    306 -> 13,421
    93 -> 23,324
    265 -> 51,147,266
    204 -> 23,111
    67 -> 3,179
    288 -> 13,421
    22 -> 120,102
    404 -> 33,239
    178 -> 120*
    138 -> 13,315
    161 -> 33*
    349 -> 33,248
    297 -> 13,421
    76 -> 120*
    323 -> 13,230
    60 -> 13,4,139
    101 -> 23,324
    332 -> 33*
    1 -> 13,421
    380 -> 33,257
    110 -> 23*
    187 -> 120*
    146 -> 33*
    213 -> 23,111
    50 -> 13,230
    119 -> 51,196
    129 -> 13,421
    229 -> 23*
    356 -> 33,248
    32 -> 23*
    221 -> 23*
    364 -> 33,248
    314 -> 13,230
    279 -> 13,421
    272 -> 51,68
  problem:
   
  Qed