YES

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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {179,175,170,166,162,158,153,151,149,144,140,135,131,
                  128,126,124,122,120,115,112,108,104,101,98,93,90,88,
                  84,79,75,72,67,63,58,55,52,49,45,40,34,32,29,25,21,
                  15,11,7,1}
   transitions:
    52(467) -> 468*
    52(464) -> 465*
    52(323) -> 324*
    52(320) -> 321*
    12(322) -> 323*
    12(321) -> 322*
    12(465) -> 466*
    12(466) -> 467*
    51(282) -> 283*
    51(390) -> 391*
    51(445) -> 446*
    51(314) -> 315*
    51(438) -> 439*
    51(258) -> 259*
    51(349) -> 350*
    51(313) -> 314*
    51(444) -> 445*
    51(411) -> 412*
    51(419) -> 420*
    51(285) -> 286*
    51(266) -> 267*
    51(441) -> 442*
    01(363) -> 364*
    01(397) -> 398*
    01(420) -> 421*
    01(259) -> 260*
    01(405) -> 406*
    01(393) -> 394*
    01(289) -> 290*
    01(339) -> 340*
    01(296) -> 297*
    01(337) -> 338*
    01(446) -> 447*
    01(474) -> 475*
    01(315) -> 316*
    01(482) -> 483*
    01(391) -> 392*
    01(241) -> 242*
    01(205) -> 206*
    01(267) -> 268*
    01(235) -> 236*
    01(443) -> 444*
    01(281) -> 282*
    01(184) -> 185*
    01(292) -> 293*
    01(362) -> 363*
    01(331) -> 332*
    01(375) -> 376*
    01(212) -> 213*
    01(437) -> 438*
    01(351) -> 352*
    01(312) -> 313*
    00(69) -> 70*
    00(102) -> 103*
    00(168) -> 169*
    00(5) -> 6*
    00(59) -> 113*
    00(16) -> 17*
    00(142) -> 143*
    00(143) -> 140*
    00(127) -> 126*
    00(33) -> 32*
    00(111) -> 108*
    00(132) -> 133*
    00(94) -> 95*
    00(6) -> 1*
    00(3) -> 4*
    00(89) -> 88*
    00(181) -> 182*
    00(38) -> 39*
    00(74) -> 72*
    00(26) -> 171*
    00(8) -> 176*
    00(24) -> 21*
    00(36) -> 159*
    00(30) -> 31*
    00(64) -> 65*
    00(105) -> 106*
    00(10) -> 7*
    00(65) -> 150*
    00(9) -> 10*
    00(28) -> 25*
    00(157) -> 153*
    00(2) -> 12*
    f60() -> 2*
    50(150) -> 149*
    50(78) -> 75*
    50(8) -> 64*
    50(27) -> 105*
    50(41) -> 167*
    50(2) -> 68*
    50(148) -> 144*
    50(80) -> 81*
    50(85) -> 132*
    50(182) -> 179*
    50(73) -> 74*
    50(130) -> 128*
    50(139) -> 135*
    50(172) -> 173*
    50(12) -> 85*
    50(87) -> 84*
    50(16) -> 50*
    50(59) -> 60*
    50(176) -> 177*
    50(138) -> 139*
    40(2) -> 35*
    40(51) -> 121*
    40(180) -> 181*
    40(85) -> 163*
    40(65) -> 152*
    40(3) -> 22*
    40(35) -> 94*
    40(48) -> 45*
    40(16) -> 59*
    40(9) -> 102*
    40(20) -> 15*
    40(10) -> 89*
    40(4) -> 99*
    40(60) -> 61*
    40(11) -> 125*
    40(117) -> 118*
    40(50) -> 53*
    40(171) -> 172*
    40(8) -> 73*
    40(106) -> 107*
    40(125) -> 124*
    10(16) -> 80*
    10(44) -> 40*
    10(68) -> 116*
    10(4) -> 5*
    10(2) -> 3*
    10(17) -> 18*
    10(133) -> 134*
    10(62) -> 58*
    10(71) -> 67*
    10(53) -> 54*
    10(13) -> 14*
    10(27) -> 46*
    10(83) -> 79*
    10(146) -> 147*
    10(12) -> 145*
    10(96) -> 97*
    10(57) -> 55*
    10(113) -> 114*
    10(154) -> 155*
    10(47) -> 48*
    10(3) -> 8*
    10(28) -> 33*
    10(82) -> 83*
    10(18) -> 19*
    10(36) -> 141*
    10(56) -> 57*
    10(109) -> 110*
    10(129) -> 130*
    10(92) -> 90*
    10(155) -> 156*
    10(110) -> 111*
    10(134) -> 131*
    10(167) -> 168*
    10(99) -> 129*
    10(35) -> 36*
    10(136) -> 137*
    10(51) -> 49*
    10(173) -> 174*
    10(118) -> 119*
    10(85) -> 86*
    10(86) -> 87*
    10(19) -> 20*
    10(37) -> 38*
    10(91) -> 92*
    10(76) -> 77*
    10(41) -> 76*
    10(42) -> 43*
    10(26) -> 27*
    10(165) -> 162*
    10(70) -> 71*
    10(23) -> 24*
    10(137) -> 138*
    10(65) -> 66*
    30(35) -> 41*
    30(22) -> 23*
    30(81) -> 82*
    30(145) -> 146*
    30(121) -> 120*
    30(39) -> 34*
    30(66) -> 63*
    30(107) -> 104*
    30(169) -> 166*
    30(17) -> 91*
    30(54) -> 52*
    30(163) -> 164*
    30(99) -> 100*
    30(61) -> 62*
    30(123) -> 122*
    30(114) -> 112*
    30(12) -> 13*
    30(70) -> 123*
    30(164) -> 165*
    30(119) -> 115*
    30(4) -> 109*
    30(50) -> 51*
    30(103) -> 101*
    30(51) -> 56*
    30(26) -> 154*
    30(152) -> 151*
    30(161) -> 158*
    30(177) -> 178*
    30(95) -> 96*
    30(31) -> 29*
    30(2) -> 26*
    30(41) -> 42*
    20(100) -> 98*
    20(156) -> 157*
    20(147) -> 148*
    20(178) -> 175*
    20(2) -> 16*
    20(116) -> 117*
    20(43) -> 44*
    20(160) -> 161*
    20(36) -> 37*
    20(14) -> 11*
    20(97) -> 93*
    20(76) -> 127*
    20(27) -> 28*
    20(68) -> 69*
    20(159) -> 160*
    20(80) -> 180*
    20(8) -> 9*
    20(77) -> 78*
    20(3) -> 30*
    20(174) -> 170*
    20(141) -> 142*
    20(46) -> 47*
    20(16) -> 136*
    41(209) -> 210*
    41(238) -> 239*
    41(265) -> 266*
    41(188) -> 189*
    41(372) -> 373*
    41(216) -> 217*
    41(232) -> 233*
    41(389) -> 390*
    31(293) -> 294*
    31(373) -> 374*
    31(261) -> 262*
    31(239) -> 240*
    31(422) -> 423*
    31(475) -> 476*
    31(233) -> 234*
    21(211) -> 212*
    21(477) -> 478*
    21(361) -> 362*
    21(204) -> 205*
    21(481) -> 482*
    21(350) -> 351*
    21(183) -> 184*
    02(463) -> 464*
    02(319) -> 320*
    02(355) -> 356*
    02(413) -> 414*
    11(352) -> 353*
    11(237) -> 238*
    11(440) -> 441*
    11(256) -> 257*
    11(359) -> 360*
    11(264) -> 265*
    11(489) -> 490*
    11(284) -> 285*
    11(185) -> 186*
    11(294) -> 295*
    11(353) -> 354*
    11(257) -> 258*
    11(374) -> 375*
    11(317) -> 318*
    11(283) -> 284*
    11(295) -> 296*
    11(418) -> 419*
    11(213) -> 214*
    11(439) -> 440*
    11(207) -> 208*
    11(403) -> 404*
    11(206) -> 207*
    11(417) -> 418*
    11(476) -> 477*
    11(214) -> 215*
    11(421) -> 422*
    11(240) -> 241*
    11(316) -> 317*
    11(360) -> 361*
    11(448) -> 449*
    11(480) -> 481*
    11(231) -> 232*
    11(479) -> 480*
    11(447) -> 448*
    11(208) -> 209*
    11(263) -> 264*
    11(291) -> 292*
    11(371) -> 372*
    11(234) -> 235*
    11(187) -> 188*
    11(186) -> 187*
    11(388) -> 389*
    11(215) -> 216*
    11(260) -> 261*
    238 -> 337*
    312 -> 319*
    262 -> 178*
    151 -> 26,13,109
    166 -> 26*
    442 -> 283,85
    354 -> 321,314
    210 -> 182*
    372 -> 388*
    144 -> 282,12
    412 -> 350*
    74 -> 359*
    131 -> 68,132
    142 -> 405,403
    340 -> 313*
    324 -> 315*
    267 -> 489*
    398 -> 282*
    242 -> 101*
    160 -> 474*
    414 -> 320*
    115 -> 26*
    158 -> 26*
    35 -> 231*
    162 -> 26*
    189 -> 113*
    64 -> 443*
    126 -> 35*
    290 -> 282*
    217 -> 103*
    7 -> 12,185,17
    236 -> 96*
    140 -> 12*
    104 -> 26,13
    112 -> 26*
    63 -> 26*
    93 -> 282,12,171
    318 -> 132*
    45 -> 26*
    478 -> 171*
    449 -> 283,85
    11 -> 282,12,171
    180 -> 263*
    2 -> 281,183
    143 -> 397*
    67 -> 68,283,85
    124 -> 35*
    394 -> 282*
    75 -> 68,50
    52 -> 26*
    88 -> 12*
    153 -> 26,13
    468 -> 446*
    404 -> 292*
    6 -> 289*
    141 -> 411*
    72 -> 68,283,85
    21 -> 26,13
    268 -> 179*
    170 -> 68*
    36 -> 479*
    58 -> 26*
    79 -> 68*
    297 -> 146*
    423 -> 13*
    179 -> 68,60
    135 -> 68*
    392 -> 283,85
    490 -> 360*
    101 -> 26,13,91
    332 -> 282*
    8 -> 349,256,211
    40 -> 26*
    1 -> 12*
    49 -> 26*
    90 -> 282,12,171
    175 -> 68,105
    55 -> 26*
    483 -> 474*
    65 -> 437,417
    34 -> 26*
    443 -> 463*
    5 -> 312,291
    9 -> 339,237
    108 -> 26,146
    406 -> 313*
    405 -> 413*
    120 -> 26*
    122 -> 26*
    149 -> 282,12
    84 -> 68*
    15 -> 282,12
    10 -> 371,331
    286 -> 132*
    98 -> 282,12
    80 -> 204*
    338 -> 293*
    356 -> 320*
    128 -> 68*
    89 -> 393*
    29 -> 26*
    32 -> 26*
    25 -> 26*
    376 -> 13*
    364 -> 70*
    339 -> 355*
  problem:
   
  Qed