YES

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

Proof:
 String Reversal Processor:
  1(0(0(x1))) -> 0(0(4(1(3(2(x1))))))
  0(0(1(x1))) -> 0(1(3(2(0(x1)))))
  1(0(1(x1))) -> 1(3(2(1(2(0(x1))))))
  1(0(1(x1))) -> 1(3(2(5(0(1(x1))))))
  1(0(1(x1))) -> 1(3(2(0(1(2(x1))))))
  0(0(4(x1))) -> 0(4(3(2(0(x1)))))
  1(0(4(x1))) -> 4(1(2(2(0(x1)))))
  1(0(4(x1))) -> 1(4(3(2(0(x1)))))
  0(1(5(x1))) -> 0(1(3(2(5(x1)))))
  0(1(5(x1))) -> 0(1(3(3(2(5(x1))))))
  1(1(5(x1))) -> 5(1(4(1(3(2(x1))))))
  1(1(5(x1))) -> 1(1(3(2(3(5(x1))))))
  0(3(0(0(x1)))) -> 0(3(2(0(0(4(x1))))))
  1(0(3(0(x1)))) -> 3(1(2(2(0(0(x1))))))
  1(3(0(1(x1)))) -> 3(1(3(2(1(0(x1))))))
  1(3(0(1(x1)))) -> 1(3(2(1(4(0(x1))))))
  1(5(2(1(x1)))) -> 1(1(3(2(4(5(x1))))))
  1(1(0(4(x1)))) -> 1(1(4(2(0(x1)))))
  5(1(0(4(x1)))) -> 4(1(3(2(0(5(x1))))))
  5(1(0(4(x1)))) -> 0(4(3(1(4(5(x1))))))
  0(3(0(4(x1)))) -> 5(4(0(3(2(0(x1))))))
  5(3(0(4(x1)))) -> 5(1(4(3(2(0(x1))))))
  0(5(2(4(x1)))) -> 0(3(2(5(4(x1)))))
  0(5(2(4(x1)))) -> 4(5(3(2(0(4(x1))))))
  0(0(3(4(x1)))) -> 0(3(4(3(2(0(x1))))))
  1(0(3(4(x1)))) -> 3(2(0(4(1(x1)))))
  1(0(3(4(x1)))) -> 1(4(2(2(0(3(x1))))))
  1(1(1(5(x1)))) -> 1(5(1(1(2(2(x1))))))
  5(2(1(0(0(x1))))) -> 0(0(5(1(3(2(x1))))))
  0(0(3(1(0(x1))))) -> 0(0(0(1(3(2(x1))))))
  1(3(5(2(0(x1))))) -> 3(1(4(5(0(2(x1))))))
  1(5(5(2(0(x1))))) -> 5(4(5(1(2(0(x1))))))
  1(5(0(3(0(x1))))) -> 0(0(3(5(1(2(x1))))))
  1(5(3(4(0(x1))))) -> 5(0(1(3(4(2(x1))))))
  5(1(1(5(0(x1))))) -> 5(5(1(2(1(0(x1))))))
  0(3(1(5(0(x1))))) -> 0(0(5(3(1(2(x1))))))
  5(1(4(0(1(x1))))) -> 0(5(1(2(1(4(x1))))))
  1(5(4(2(1(x1))))) -> 3(2(5(1(4(1(x1))))))
  0(3(5(2(1(x1))))) -> 0(5(3(2(4(1(x1))))))
  0(4(0(3(1(x1))))) -> 0(4(1(3(2(0(x1))))))
  5(1(3(0(4(x1))))) -> 1(0(5(3(4(4(x1))))))
  0(0(5(2(4(x1))))) -> 4(4(0(2(5(0(x1))))))
  0(0(5(2(4(x1))))) -> 0(0(4(3(2(5(x1))))))
  0(3(5(2(4(x1))))) -> 3(2(5(2(0(4(x1))))))
  0(3(5(2(4(x1))))) -> 0(1(3(4(2(5(x1))))))
  1(3(5(2(4(x1))))) -> 2(4(5(1(3(2(x1))))))
  1(0(0(3(4(x1))))) -> 0(0(1(3(4(2(x1))))))
  0(5(2(3(4(x1))))) -> 5(4(3(2(4(0(x1))))))
  1(3(1(5(4(x1))))) -> 1(4(5(3(1(4(x1))))))
  1(3(4(1(5(x1))))) -> 1(1(4(2(3(5(x1))))))
  Bounds Processor:
   bound: 2
   enrichment: match
   automaton:
    final states: {192,188,184,183,181,177,174,171,166,161,159,155,151,
                   146,142,139,134,130,127,122,119,116,111,105,101,99,
                   95,91,90,87,83,78,75,70,65,60,55,49,44,42,39,34,33,
                   30,28,23,17,13,8,1}
    transitions:
     02(445) -> 446*
     02(449) -> 450*
     20(2) -> 3*
     20(71) -> 72*
     20(51) -> 96*
     20(45) -> 46*
     20(79) -> 80*
     20(175) -> 176*
     20(57) -> 58*
     20(102) -> 156*
     20(3) -> 112*
     20(35) -> 36*
     20(103) -> 104*
     20(14) -> 15*
     20(52) -> 53*
     20(182) -> 181*
     20(9) -> 10*
     20(107) -> 108*
     20(167) -> 168*
     20(67) -> 68*
     20(20) -> 21*
     20(92) -> 93*
     20(147) -> 148*
     20(10) -> 31*
     20(56) -> 57*
     20(66) -> 185*
     20(153) -> 154*
     20(61) -> 62*
     20(25) -> 26*
     20(108) -> 109*
     42(448) -> 449*
     31(412) -> 413*
     31(275) -> 276*
     31(233) -> 234*
     31(251) -> 252*
     31(298) -> 299*
     31(387) -> 388*
     31(209) -> 210*
     31(227) -> 228*
     31(203) -> 204*
     31(404) -> 405*
     31(369) -> 370*
     31(407) -> 408*
     31(281) -> 282*
     31(373) -> 374*
     31(385) -> 386*
     31(257) -> 258*
     41(382) -> 383*
     41(414) -> 415*
     41(518) -> 519*
     41(276) -> 277*
     41(252) -> 253*
     41(319) -> 320*
     41(228) -> 229*
     41(370) -> 371*
     41(234) -> 235*
     41(323) -> 324*
     00(102) -> 103*
     00(168) -> 169*
     00(160) -> 159*
     00(158) -> 155*
     00(106) -> 107*
     00(144) -> 145*
     00(145) -> 142*
     00(5) -> 120*
     00(41) -> 39*
     00(12) -> 8*
     00(120) -> 121*
     00(172) -> 173*
     00(35) -> 79*
     00(180) -> 177*
     00(7) -> 1*
     00(137) -> 138*
     00(29) -> 28*
     00(173) -> 171*
     00(121) -> 119*
     00(132) -> 133*
     00(94) -> 91*
     00(118) -> 116*
     00(100) -> 99*
     00(6) -> 7*
     00(86) -> 83*
     00(11) -> 88*
     00(164) -> 165*
     00(3) -> 123*
     00(38) -> 34*
     00(150) -> 146*
     00(138) -> 183*
     00(24) -> 25*
     00(50) -> 51*
     00(54) -> 49*
     00(133) -> 130*
     00(9) -> 56*
     00(117) -> 118*
     00(18) -> 19*
     00(51) -> 52*
     00(2) -> 9*
     30(35) -> 45*
     30(96) -> 97*
     30(104) -> 101*
     30(29) -> 100*
     30(10) -> 11*
     30(3) -> 4*
     30(15) -> 16*
     30(178) -> 179*
     30(53) -> 54*
     30(84) -> 85*
     30(131) -> 132*
     30(62) -> 63*
     30(156) -> 157*
     30(64) -> 60*
     30(154) -> 151*
     30(68) -> 69*
     30(93) -> 94*
     30(36) -> 37*
     30(135) -> 136*
     30(126) -> 122*
     30(176) -> 174*
     30(185) -> 186*
     30(80) -> 81*
     30(46) -> 47*
     30(24) -> 143*
     30(59) -> 55*
     30(37) -> 40*
     30(162) -> 163*
     30(147) -> 189*
     30(26) -> 27*
     30(21) -> 22*
     30(2) -> 106*
     30(72) -> 73*
     01(283) -> 284*
     01(231) -> 232*
     01(253) -> 254*
     01(487) -> 488*
     01(259) -> 260*
     01(315) -> 316*
     01(302) -> 303*
     01(507) -> 508*
     01(453) -> 454*
     01(279) -> 280*
     01(349) -> 350*
     01(273) -> 274*
     01(201) -> 202*
     01(477) -> 478*
     01(225) -> 226*
     01(427) -> 428*
     01(229) -> 230*
     01(501) -> 502*
     01(205) -> 206*
     01(415) -> 416*
     01(523) -> 524*
     01(388) -> 389*
     01(371) -> 372*
     01(255) -> 256*
     01(367) -> 368*
     01(459) -> 460*
     01(211) -> 212*
     01(249) -> 250*
     01(277) -> 278*
     01(207) -> 208*
     01(383) -> 384*
     01(235) -> 236*
     10(194) -> 192*
     10(69) -> 65*
     10(2) -> 18*
     10(22) -> 17*
     10(40) -> 41*
     10(47) -> 48*
     10(191) -> 188*
     10(4) -> 5*
     10(63) -> 64*
     10(10) -> 14*
     10(81) -> 82*
     10(76) -> 77*
     10(102) -> 152*
     10(148) -> 149*
     10(71) -> 84*
     10(62) -> 140*
     10(110) -> 105*
     10(136) -> 137*
     10(6) -> 43*
     10(27) -> 23*
     10(179) -> 180*
     10(9) -> 61*
     10(113) -> 114*
     10(29) -> 33*
     10(165) -> 161*
     10(50) -> 147*
     10(48) -> 44*
     10(58) -> 59*
     10(77) -> 75*
     10(66) -> 67*
     10(125) -> 126*
     10(3) -> 24*
     10(193) -> 194*
     10(112) -> 113*
     10(37) -> 38*
     10(73) -> 74*
     10(11) -> 12*
     10(115) -> 111*
     10(16) -> 13*
     10(74) -> 70*
     10(31) -> 32*
     11(282) -> 283*
     11(413) -> 414*
     11(299) -> 300*
     11(301) -> 302*
     11(343) -> 344*
     11(493) -> 494*
     11(331) -> 332*
     11(322) -> 323*
     11(467) -> 468*
     11(258) -> 259*
     11(519) -> 520*
     11(296) -> 297*
     11(337) -> 338*
     11(405) -> 406*
     11(204) -> 205*
     11(355) -> 356*
     11(335) -> 336*
     11(485) -> 486*
     11(314) -> 315*
     11(521) -> 522*
     11(210) -> 211*
     40(190) -> 191*
     40(186) -> 187*
     40(2) -> 50*
     40(10) -> 76*
     40(5) -> 6*
     40(117) -> 182*
     40(50) -> 162*
     40(128) -> 129*
     40(12) -> 160*
     40(9) -> 66*
     40(3) -> 135*
     40(82) -> 78*
     40(18) -> 102*
     40(36) -> 178*
     40(46) -> 193*
     40(88) -> 89*
     40(109) -> 110*
     40(32) -> 30*
     40(11) -> 29*
     40(35) -> 71*
     40(169) -> 170*
     40(85) -> 86*
     40(37) -> 172*
     40(170) -> 166*
     40(124) -> 125*
     40(98) -> 95*
     51(303) -> 304*
     51(522) -> 523*
     51(402) -> 403*
     51(433) -> 434*
     21(425) -> 426*
     21(455) -> 456*
     21(357) -> 358*
     21(313) -> 314*
     21(280) -> 281*
     21(226) -> 227*
     21(411) -> 412*
     21(471) -> 472*
     21(479) -> 480*
     21(256) -> 257*
     21(403) -> 404*
     21(384) -> 385*
     21(435) -> 436*
     21(297) -> 298*
     21(274) -> 275*
     21(321) -> 322*
     21(390) -> 391*
     21(345) -> 346*
     21(202) -> 203*
     21(232) -> 233*
     21(250) -> 251*
     21(368) -> 369*
     21(389) -> 390*
     21(520) -> 521*
     21(495) -> 496*
     21(465) -> 466*
     21(503) -> 504*
     21(208) -> 209*
     50(141) -> 139*
     50(187) -> 184*
     50(33) -> 90*
     50(149) -> 150*
     50(129) -> 127*
     50(143) -> 144*
     50(163) -> 164*
     50(2) -> 35*
     50(89) -> 87*
     50(43) -> 42*
     50(14) -> 128*
     50(5) -> 117*
     50(140) -> 141*
     50(50) -> 92*
     50(114) -> 115*
     50(9) -> 167*
     50(19) -> 20*
     50(157) -> 158*
     50(97) -> 98*
     50(24) -> 131*
     50(152) -> 153*
     50(189) -> 190*
     50(96) -> 175*
     50(123) -> 124*
     50(138) -> 134*
     32(447) -> 448*
     22(446) -> 447*
     f60() -> 2*
     408 -> 405*
     228 -> 477,335
     192 -> 18*
     155 -> 232,9,107
     151 -> 18*
     166 -> 232,9,56
     70 -> 18*
     210 -> 255*
     372 -> 79*
     144 -> 455*
     358 -> 314*
     142 -> 232,9,107
     320 -> 373,331,283
     324 -> 61*
     254 -> 1*
     206 -> 183*
     159 -> 232,9,51
     17 -> 18,61
     414 -> 445*
     83 -> 35*
     278 -> 19*
     434 -> 297*
     42 -> 18*
     30 -> 18,61
     282 -> 319*
     236 -> 56,52
     450 -> 254,1
     85 -> 367*
     12 -> 459*
     504 -> 314*
     114 -> 402*
     508 -> 403*
     281 -> 321,296
     300 -> 61*
     252 -> 273*
     188 -> 18*
     478 -> 226*
     284 -> 56*
     258 -> 435,427
     212 -> 121*
     344 -> 302*
     28 -> 232,9,56
     4 -> 207*
     11 -> 387,313,301,279
     2 -> 231*
     204 -> 518,507
     350 -> 226*
     336 -> 283*
     230 -> 171*
     174 -> 232,9,107
     386 -> 61*
     105 -> 18,61
     75 -> 18*
     468 -> 61*
     116 -> 35*
     302 -> 382*
     171 -> 232,9,56
     172 -> 471*
     346 -> 314*
     493 -> 503,501
     177 -> 9,107
     161 -> 35*
     91 -> 232,9,79
     233 -> 465*
     235 -> 467*
     179 -> 495,493,487
     488 -> 226*
     480 -> 322*
     426 -> 412*
     44 -> 18*
     428 -> 226*
     139 -> 35*
     60 -> 18*
     416 -> 253*
     183 -> 18,61
     524 -> 153*
     101 -> 18,61
     332 -> 61*
     13 -> 18,61
     316 -> 297*
     127 -> 18*
     8 -> 232,9,56
     40 -> 357,355,349
     1 -> 18,61
     49 -> 232,9,107
     304 -> 297*
     99 -> 232,9,56
     90 -> 35*
     130 -> 18*
     55 -> 18,61
     456 -> 412*
     65 -> 18*
     34 -> 232,9,19
     95 -> 232,9,79
     37 -> 345,343,225
     5 -> 249*
     134 -> 18*
     146 -> 35*
     406 -> 277*
     405 -> 407*
     460 -> 232*
     184 -> 232,9,79
     120 -> 425*
     39 -> 232,9,19
     227 -> 479,337
     260 -> 433,119
     466 -> 322*
     122 -> 18*
     119 -> 232,9,56
     502 -> 226*
     436 -> 314*
     211 -> 411*
     391 -> 319*
     472 -> 412*
     136 -> 201*
     374 -> 283*
     448 -> 453*
     181 -> 18*
     496 -> 314*
     229 -> 485*
     87 -> 232,9,107
     338 -> 297*
     356 -> 302*
     454 -> 274*
     486 -> 61*
     494 -> 259*
     111 -> 18*
     23 -> 18,61
     33 -> 18,61
     78 -> 35*
   problem:
    
   Qed