YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {252,250,246,244,240,235,231,228,227,226,224,218,217,
                  215,211,206,201,198,195,193,190,186,181,177,174,169,
                  165,164,162,159,158,155,151,148,145,141,138,134,128,
                  125,121,119,116,114,110,106,102,99,98,96,95,94,93,91,
                  89,88,85,82,80,79,76,72,69,66,64,61,58,54,51,48,43,
                  39,35,30,27,22,18,12,8,1}
   transitions:
    41(481) -> 482*
    41(442) -> 443*
    41(436) -> 437*
    41(302) -> 303*
    41(414) -> 415*
    41(384) -> 385*
    41(457) -> 458*
    41(400) -> 401*
    41(454) -> 455*
    41(427) -> 428*
    41(490) -> 491*
    41(300) -> 301*
    41(275) -> 276*
    41(422) -> 423*
    41(494) -> 495*
    41(466) -> 467*
    41(510) -> 511*
    41(255) -> 256*
    41(290) -> 291*
    41(360) -> 361*
    41(470) -> 471*
    41(398) -> 399*
    41(318) -> 319*
    41(410) -> 411*
    51(412) -> 413*
    51(452) -> 453*
    51(444) -> 445*
    51(289) -> 290*
    51(304) -> 305*
    51(294) -> 295*
    51(336) -> 337*
    51(390) -> 391*
    51(321) -> 322*
    51(382) -> 383*
    51(292) -> 293*
    51(272) -> 273*
    51(375) -> 376*
    51(279) -> 280*
    51(504) -> 505*
    00(171) -> 172*
    00(182) -> 183*
    00(153) -> 154*
    00(207) -> 208*
    00(13) -> 14*
    00(31) -> 111*
    00(59) -> 60*
    00(242) -> 243*
    00(44) -> 45*
    00(34) -> 30*
    00(229) -> 230*
    00(108) -> 109*
    00(40) -> 41*
    00(103) -> 104*
    00(129) -> 130*
    00(101) -> 99*
    00(15) -> 16*
    00(7) -> 1*
    00(32) -> 156*
    00(23) -> 24*
    00(62) -> 90*
    00(238) -> 239*
    00(3) -> 9*
    00(38) -> 35*
    00(233) -> 234*
    00(63) -> 115*
    00(21) -> 18*
    00(4) -> 5*
    00(24) -> 25*
    00(19) -> 28*
    00(67) -> 68*
    00(202) -> 241*
    00(204) -> 205*
    00(133) -> 128*
    00(9) -> 10*
    00(117) -> 118*
    00(123) -> 124*
    00(56) -> 57*
    00(196) -> 225*
    00(149) -> 150*
    00(2) -> 3*
    f60() -> 2*
    50(81) -> 80*
    50(178) -> 179*
    50(33) -> 34*
    50(28) -> 29*
    50(122) -> 123*
    50(37) -> 38*
    50(41) -> 42*
    50(45) -> 46*
    50(3) -> 31*
    50(2) -> 23*
    50(4) -> 52*
    50(62) -> 83*
    50(183) -> 184*
    50(19) -> 36*
    50(118) -> 116*
    50(68) -> 79*
    50(18) -> 226*
    50(55) -> 59*
    50(137) -> 134*
    50(77) -> 78*
    50(135) -> 196*
    50(131) -> 132*
    50(90) -> 163*
    40(2) -> 44*
    40(245) -> 244*
    40(71) -> 69*
    40(187) -> 199*
    40(253) -> 252*
    40(75) -> 72*
    40(127) -> 158*
    40(188) -> 189*
    40(111) -> 112*
    40(115) -> 114*
    40(23) -> 207*
    40(199) -> 200*
    40(37) -> 98*
    40(214) -> 211*
    40(205) -> 201*
    40(77) -> 81*
    40(51) -> 217*
    40(109) -> 106*
    40(180) -> 177*
    40(24) -> 40*
    40(210) -> 206*
    40(144) -> 141*
    40(18) -> 227*
    40(176) -> 174*
    40(219) -> 220*
    40(216) -> 215*
    40(65) -> 95*
    40(31) -> 32*
    40(3) -> 19*
    40(14) -> 212*
    40(52) -> 53*
    40(249) -> 246*
    40(182) -> 232*
    40(49) -> 50*
    40(9) -> 135*
    40(248) -> 249*
    40(166) -> 167*
    40(20) -> 117*
    40(239) -> 235*
    40(13) -> 236*
    40(60) -> 93*
    40(66) -> 88*
    40(124) -> 121*
    40(44) -> 202*
    40(152) -> 153*
    40(230) -> 228*
    40(63) -> 94*
    40(78) -> 76*
    40(97) -> 96*
    40(160) -> 161*
    40(100) -> 101*
    40(112) -> 113*
    40(25) -> 26*
    40(140) -> 138*
    40(87) -> 85*
    40(170) -> 171*
    10(16) -> 17*
    10(44) -> 55*
    10(4) -> 77*
    10(2) -> 219*
    10(17) -> 12*
    10(5) -> 126*
    10(62) -> 63*
    10(31) -> 142*
    10(53) -> 51*
    10(74) -> 100*
    10(135) -> 136*
    10(127) -> 125*
    10(189) -> 186*
    10(83) -> 84*
    10(50) -> 48*
    10(161) -> 159*
    10(236) -> 237*
    10(191) -> 192*
    10(163) -> 162*
    10(113) -> 110*
    10(154) -> 151*
    10(234) -> 231*
    10(139) -> 140*
    10(40) -> 65*
    10(175) -> 176*
    10(47) -> 43*
    10(3) -> 73*
    10(28) -> 146*
    10(29) -> 27*
    10(36) -> 37*
    10(46) -> 97*
    10(185) -> 181*
    10(209) -> 210*
    10(120) -> 119*
    10(213) -> 214*
    10(203) -> 204*
    10(220) -> 221*
    10(167) -> 168*
    10(6) -> 7*
    10(32) -> 33*
    10(143) -> 144*
    10(11) -> 8*
    10(105) -> 102*
    10(112) -> 253*
    10(132) -> 133*
    10(179) -> 180*
    10(45) -> 247*
    10(136) -> 137*
    10(130) -> 131*
    10(173) -> 169*
    10(156) -> 157*
    10(199) -> 216*
    10(86) -> 87*
    10(19) -> 20*
    10(14) -> 107*
    10(42) -> 39*
    10(26) -> 22*
    10(81) -> 194*
    10(200) -> 198*
    10(70) -> 71*
    10(73) -> 122*
    10(23) -> 170*
    10(65) -> 120*
    30(5) -> 160*
    30(237) -> 238*
    30(178) -> 191*
    30(241) -> 242*
    30(221) -> 229*
    30(197) -> 195*
    30(90) -> 89*
    30(107) -> 108*
    30(156) -> 245*
    30(212) -> 213*
    30(14) -> 15*
    30(251) -> 250*
    30(68) -> 66*
    30(92) -> 91*
    30(126) -> 127*
    30(55) -> 56*
    30(223) -> 218*
    30(150) -> 164*
    30(232) -> 233*
    30(247) -> 248*
    30(147) -> 145*
    30(19) -> 103*
    30(157) -> 155*
    30(225) -> 224*
    30(74) -> 75*
    30(2) -> 129*
    30(20) -> 21*
    30(73) -> 152*
    20(243) -> 240*
    20(104) -> 105*
    20(194) -> 193*
    20(20) -> 149*
    20(168) -> 165*
    20(172) -> 173*
    20(192) -> 190*
    20(57) -> 54*
    20(2) -> 13*
    20(28) -> 92*
    20(202) -> 203*
    20(4) -> 70*
    20(5) -> 6*
    20(63) -> 61*
    20(10) -> 11*
    20(196) -> 197*
    20(55) -> 67*
    20(62) -> 175*
    20(187) -> 188*
    20(84) -> 82*
    20(60) -> 58*
    20(208) -> 209*
    20(9) -> 166*
    20(142) -> 143*
    20(52) -> 86*
    20(150) -> 148*
    20(184) -> 185*
    20(24) -> 187*
    20(77) -> 139*
    20(45) -> 62*
    20(222) -> 223*
    20(33) -> 251*
    20(44) -> 182*
    20(3) -> 4*
    20(146) -> 147*
    20(73) -> 74*
    20(46) -> 47*
    20(19) -> 178*
    20(65) -> 64*
    20(31) -> 49*
    20(221) -> 222*
    21(320) -> 321*
    21(411) -> 412*
    21(512) -> 513*
    21(479) -> 480*
    21(392) -> 393*
    21(317) -> 318*
    21(343) -> 344*
    21(456) -> 457*
    21(305) -> 306*
    21(354) -> 355*
    21(358) -> 359*
    21(334) -> 335*
    21(467) -> 468*
    21(371) -> 372*
    31(257) -> 258*
    31(482) -> 483*
    31(332) -> 333*
    31(356) -> 357*
    31(493) -> 494*
    31(372) -> 373*
    01(480) -> 481*
    01(254) -> 255*
    01(273) -> 274*
    01(426) -> 427*
    01(258) -> 259*
    01(333) -> 334*
    01(435) -> 436*
    01(355) -> 356*
    01(303) -> 304*
    01(409) -> 410*
    01(453) -> 454*
    01(274) -> 275*
    01(502) -> 503*
    01(443) -> 444*
    01(278) -> 279*
    11(492) -> 493*
    11(256) -> 257*
    11(359) -> 360*
    11(346) -> 347*
    11(331) -> 332*
    11(374) -> 375*
    11(484) -> 485*
    11(418) -> 419*
    11(276) -> 277*
    11(306) -> 307*
    11(451) -> 452*
    11(468) -> 469*
    11(370) -> 371*
    11(344) -> 345*
    11(291) -> 292*
    307 -> 490,232
    513 -> 480*
    228 -> 202*
    415 -> 202,236,44,232
    94 -> 44,202
    155 -> 44,220
    151 -> 44,220
    321 -> 374,358
    27 -> 3,45
    43 -> 44,236
    19 -> 202*
    195 -> 44,236
    375 -> 384*
    399 -> 232*
    259 -> 45,241
    215 -> 44,236,232
    413 -> 359*
    148 -> 44,19,212
    206 -> 44,236,232
    159 -> 44,236
    250 -> 44,207
    164 -> 44,236
    190 -> 44,236
    198 -> 44,236,232
    48 -> 44,236
    256 -> 294,278
    240 -> 202*
    393 -> 359*
    458 -> 484,318
    231 -> 202*
    158 -> 44,220
    35 -> 3,45
    162 -> 44,236
    64 -> 44,236
    30 -> 3,45
    290 -> 426,317
    69 -> 44,236
    295 -> 291*
    335 -> 232*
    169 -> 44,236
    85 -> 44,236
    12 -> 3*
    357 -> 398,232
    93 -> 44,202
    373 -> 360*
    114 -> 3,45,241
    106 -> 3,45
    66 -> 44,236
    252 -> 44,207
    419 -> 360*
    244 -> 202*
    344 -> 390*
    301 -> 346,278
    82 -> 44,236
    437 -> 45,241
    485 -> 360*
    292 -> 422*
    174 -> 44,236
    22 -> 3,45
    455 -> 247*
    54 -> 44,236
    345 -> 435,334
    88 -> 44,236
    153 -> 479,302,272,254
    116 -> 3,45,241
    337 -> 333*
    277 -> 45,241
    121 -> 219,73,247
    257 -> 442*
    138 -> 219,55,237
    141 -> 44,236,219,55,237
    72 -> 44,236
    186 -> 44,236
    177 -> 44,236
    201 -> 44,236,232
    385 -> 382*
    58 -> 44,236
    91 -> 44*
    233 -> 512,510,504,502
    79 -> 44,236
    235 -> 202*
    76 -> 44,236
    125 -> 219*
    423 -> 202,236,44,232
    428 -> 275*
    505 -> 273*
    334 -> 414*
    332 -> 354,336
    165 -> 44,236
    305 -> 418*
    8 -> 3*
    1 -> 3,9
    246 -> 202*
    31 -> 44*
    224 -> 44*
    293 -> 258*
    304 -> 492,343
    495 -> 360*
    445 -> 45,241
    99 -> 3,45
    193 -> 44,236
    255 -> 370,320,289
    361 -> 202,236,44,232
    483 -> 291*
    319 -> 306*
    110 -> 3,45,241
    95 -> 44,202
    134 -> 219,55,221
    347 -> 334*
    218 -> 44*
    39 -> 3,45
    469 -> 333*
    18 -> 3,45
    491 -> 232*
    145 -> 219,55
    119 -> 219,73
    511 -> 303*
    211 -> 44,236,232
    391 -> 344*
    371 -> 451*
    471 -> 303*
    383 -> 232*
    303 -> 466,331
    96 -> 44,202
    181 -> 44,236
    401 -> 254*
    273 -> 470*
    274 -> 456,300
    51 -> 44,236
    98 -> 44,202
    152 -> 409,400
    80 -> 44,236
    356 -> 382*
    202 -> 44,236,232
    128 -> 219*
    89 -> 44*
    102 -> 3,45
    61 -> 44,236
    280 -> 276*
    376 -> 360*
    322 -> 392,318
    503 -> 255*
  problem:
   
  Qed