YES

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

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