YES

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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {7}
   transitions:
    31(75) -> 76*
    31(60) -> 61*
    31(25) -> 26*
    31(20) -> 21*
    31(359) -> 360*
    31(132) -> 133*
    31(117) -> 118*
    31(92) -> 93*
    31(72) -> 73*
    31(57) -> 58*
    31(42) -> 43*
    31(366) -> 367*
    31(119) -> 120*
    31(104) -> 105*
    31(295) -> 296*
    31(347) -> 348*
    31(145) -> 146*
    01(55) -> 56*
    01(35) -> 36*
    01(399) -> 400*
    01(162) -> 163*
    01(147) -> 148*
    01(159) -> 160*
    01(134) -> 135*
    01(79) -> 80*
    01(44) -> 45*
    01(106) -> 107*
    01(51) -> 52*
    01(400) -> 401*
    01(325) -> 326*
    01(123) -> 124*
    01(33) -> 34*
    01(105) -> 106*
    01(297) -> 298*
    41(80) -> 81*
    41(15) -> 16*
    41(414) -> 415*
    41(364) -> 365*
    41(102) -> 103*
    41(294) -> 295*
    41(77) -> 78*
    41(27) -> 28*
    41(59) -> 60*
    41(161) -> 162*
    41(131) -> 132*
    41(101) -> 102*
    41(41) -> 42*
    41(365) -> 366*
    41(355) -> 356*
    41(148) -> 149*
    41(118) -> 119*
    41(78) -> 79*
    41(402) -> 403*
    41(125) -> 126*
    51(416) -> 417*
    51(144) -> 145*
    51(124) -> 125*
    51(323) -> 324*
    51(143) -> 144*
    51(88) -> 89*
    51(53) -> 54*
    51(160) -> 161*
    51(357) -> 358*
    51(90) -> 91*
    21(40) -> 41*
    21(324) -> 325*
    21(122) -> 123*
    21(87) -> 88*
    21(52) -> 53*
    21(17) -> 18*
    21(406) -> 407*
    21(361) -> 362*
    21(99) -> 100*
    21(483) -> 484*
    21(74) -> 75*
    21(54) -> 55*
    21(34) -> 35*
    21(136) -> 137*
    21(293) -> 294*
    21(26) -> 27*
    21(16) -> 17*
    21(73) -> 74*
    21(472) -> 473*
    21(58) -> 59*
    21(38) -> 39*
    21(412) -> 413*
    21(362) -> 363*
    11(45) -> 46*
    11(242) -> 243*
    11(404) -> 405*
    11(137) -> 138*
    11(37) -> 38*
    11(22) -> 23*
    11(204) -> 205*
    11(296) -> 297*
    11(89) -> 90*
    11(468) -> 469*
    11(24) -> 25*
    11(19) -> 20*
    11(363) -> 364*
    11(298) -> 299*
    11(86) -> 87*
    11(61) -> 62*
    11(36) -> 37*
    11(133) -> 134*
    11(93) -> 94*
    11(43) -> 44*
    11(23) -> 24*
    11(18) -> 19*
    11(120) -> 121*
    11(100) -> 101*
    32(434) -> 435*
    32(349) -> 350*
    32(481) -> 482*
    32(421) -> 422*
    32(209) -> 210*
    32(169) -> 170*
    32(478) -> 479*
    32(353) -> 354*
    32(480) -> 481*
    32(445) -> 446*
    32(437) -> 438*
    32(397) -> 398*
    32(352) -> 353*
    10(7) -> 7*
    42(439) -> 440*
    42(436) -> 437*
    42(396) -> 397*
    42(164) -> 165*
    42(423) -> 424*
    42(211) -> 212*
    42(395) -> 396*
    40(7) -> 7*
    12(429) -> 430*
    12(419) -> 420*
    12(207) -> 208*
    12(394) -> 395*
    12(167) -> 168*
    12(269) -> 270*
    12(229) -> 230*
    12(438) -> 439*
    12(428) -> 429*
    12(418) -> 419*
    12(206) -> 207*
    12(228) -> 229*
    12(420) -> 421*
    12(208) -> 209*
    12(168) -> 169*
    12(270) -> 271*
    30(7) -> 7*
    22(479) -> 480*
    22(267) -> 268*
    22(426) -> 427*
    22(351) -> 352*
    22(271) -> 272*
    22(226) -> 227*
    22(393) -> 394*
    22(166) -> 167*
    22(435) -> 436*
    22(430) -> 431*
    22(350) -> 351*
    22(230) -> 231*
    22(422) -> 423*
    22(210) -> 211*
    22(392) -> 393*
    22(165) -> 166*
    20(7) -> 7*
    02(227) -> 228*
    02(266) -> 267*
    02(268) -> 269*
    02(425) -> 426*
    02(432) -> 433*
    02(427) -> 428*
    02(225) -> 226*
    50(7) -> 7*
    52(476) -> 477*
    52(477) -> 478*
    00(7) -> 7*
    7 -> 143,57,40,33,22,15
    16 -> 355,117,51
    17 -> 468,92
    21 -> 403,119,145,144,16,51,132,117,23,122,7
    23 -> 131,122,72
    27 -> 445,392,361,347,206,204,164
    28 -> 58,144,7
    33 -> 483,266
    34 -> 7,143,40,22,15,33,57,266,416,104,86,77
    35 -> 323*
    39 -> 267,400,144,34,86,77,104,7
    41 -> 359,159,99
    46 -> 267,144,34,86,77,104,7
    55 -> 425,412
    56 -> 484,267,41,99,159,34,86,77,104,23,122,72,131,7
    58 -> 402,399
    62 -> 27*
    76 -> 20*
    78 -> 136*
    81 -> 38*
    90 -> 476,404,293
    91 -> 144,7
    94 -> 61*
    100 -> 147*
    103 -> 20*
    107 -> 54*
    121 -> 55*
    123 -> 357*
    126 -> 55*
    134 -> 406*
    135 -> 55*
    138 -> 125*
    144 -> 414*
    146 -> 74*
    149 -> 44*
    160 -> 242*
    162 -> 225*
    163 -> 20*
    170 -> 7,22,40,143,57,33,15,23,122
    205 -> 23*
    207 -> 349*
    211 -> 434,418
    212 -> 145,144
    231 -> 267,52,34,86,7,77,104
    243 -> 229*
    272 -> 400,106
    299 -> 267,34,86,7,57,33,15,22,40,143,77,104
    325 -> 472,432
    326 -> 23,122,7,57,33,15,22,40,143,72,131
    348 -> 58*
    354 -> 132*
    356 -> 79*
    358 -> 89*
    360 -> 93*
    367 -> 7,22,40,143,57,33,15,144
    398 -> 145*
    401 -> 38*
    403 -> 119*
    405 -> 131*
    407 -> 99*
    413 -> 99*
    415 -> 162*
    417 -> 161*
    424 -> 145*
    431 -> 106,400
    433 -> 426*
    440 -> 146*
    446 -> 435*
    469 -> 125*
    473 -> 99*
    482 -> 403,119
    484 -> 99*
  problem:
   
  Qed