YES

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

Proof:
 String Reversal Processor:
  4(0(x1)) -> 3(3(2(4(1(0(x1))))))
  4(0(x1)) -> 4(3(4(1(2(0(x1))))))
  4(0(0(x1))) -> 4(3(2(5(1(1(x1))))))
  1(1(0(x1))) -> 1(1(1(2(2(0(x1))))))
  3(1(0(x1))) -> 4(4(3(4(2(0(x1))))))
  4(2(0(x1))) -> 4(4(3(4(5(1(x1))))))
  0(4(0(x1))) -> 3(0(1(2(1(0(x1))))))
  3(2(1(x1))) -> 4(4(1(4(1(5(x1))))))
  3(3(1(x1))) -> 5(0(1(1(2(0(x1))))))
  3(3(1(x1))) -> 3(2(3(0(4(5(x1))))))
  5(3(1(x1))) -> 2(3(3(4(1(1(x1))))))
  0(0(2(x1))) -> 4(4(4(3(4(2(x1))))))
  1(0(2(x1))) -> 1(0(1(5(1(2(x1))))))
  1(0(2(x1))) -> 3(2(5(3(4(2(x1))))))
  4(0(2(x1))) -> 3(4(1(2(0(2(x1))))))
  4(0(2(x1))) -> 1(3(4(1(4(2(x1))))))
  1(0(3(x1))) -> 1(4(3(4(1(3(x1))))))
  5(0(3(x1))) -> 2(3(2(0(1(3(x1))))))
  0(0(4(x1))) -> 1(1(1(2(5(2(x1))))))
  5(0(4(x1))) -> 4(1(5(4(1(4(x1))))))
  5(0(4(x1))) -> 5(3(4(1(2(4(x1))))))
  2(0(5(x1))) -> 2(0(1(2(5(1(x1))))))
  4(0(5(x1))) -> 4(4(2(3(0(1(x1))))))
  4(0(5(x1))) -> 4(3(0(1(5(1(x1))))))
  Bounds Processor:
   bound: 3
   enrichment: match
   automaton:
    final states: {7}
    transitions:
     43(531) -> 532*
     43(528) -> 529*
     43(463) -> 464*
     43(530) -> 531*
     43(460) -> 461*
     43(462) -> 463*
     41(80) -> 81*
     41(157) -> 158*
     41(319) -> 320*
     41(516) -> 517*
     41(97) -> 98*
     41(17) -> 18*
     41(169) -> 170*
     41(159) -> 160*
     41(321) -> 322*
     41(89) -> 90*
     41(24) -> 25*
     41(141) -> 142*
     41(126) -> 127*
     41(66) -> 67*
     41(46) -> 47*
     41(26) -> 27*
     41(143) -> 144*
     41(123) -> 124*
     41(320) -> 321*
     41(487) -> 488*
     41(48) -> 49*
     41(240) -> 241*
     41(95) -> 96*
     41(489) -> 490*
     33(461) -> 462*
     33(529) -> 530*
     31(25) -> 26*
     31(20) -> 21*
     31(142) -> 143*
     31(127) -> 128*
     31(501) -> 502*
     31(82) -> 83*
     31(47) -> 48*
     31(139) -> 140*
     31(19) -> 20*
     31(181) -> 182*
     31(353) -> 354*
     31(318) -> 319*
     31(96) -> 97*
     31(91) -> 92*
     31(477) -> 478*
     31(392) -> 393*
     31(170) -> 171*
     31(90) -> 91*
     53(459) -> 460*
     53(527) -> 528*
     01(424) -> 425*
     01(15) -> 16*
     01(77) -> 78*
     01(471) -> 472*
     01(62) -> 63*
     01(174) -> 175*
     01(473) -> 474*
     01(106) -> 107*
     01(81) -> 82*
     01(475) -> 476*
     01(300) -> 301*
     01(185) -> 186*
     01(180) -> 181*
     01(569) -> 570*
     01(145) -> 146*
     01(120) -> 121*
     13(526) -> 527*
     13(458) -> 459*
     13(549) -> 550*
     11(65) -> 66*
     11(40) -> 41*
     11(122) -> 123*
     11(67) -> 68*
     11(32) -> 33*
     11(426) -> 427*
     11(184) -> 185*
     11(39) -> 40*
     11(161) -> 162*
     11(76) -> 77*
     11(61) -> 62*
     11(16) -> 17*
     11(173) -> 174*
     11(168) -> 169*
     11(158) -> 159*
     11(103) -> 104*
     11(38) -> 39*
     11(33) -> 34*
     11(23) -> 24*
     11(342) -> 343*
     11(140) -> 141*
     11(125) -> 126*
     11(105) -> 106*
     51(469) -> 470*
     51(50) -> 51*
     51(511) -> 512*
     51(558) -> 559*
     51(351) -> 352*
     51(104) -> 105*
     51(64) -> 65*
     51(34) -> 35*
     51(505) -> 506*
     51(298) -> 299*
     51(465) -> 466*
     51(108) -> 109*
     51(78) -> 79*
     51(467) -> 468*
     51(160) -> 161*
     51(155) -> 156*
     21(60) -> 61*
     21(35) -> 36*
     21(182) -> 183*
     21(172) -> 173*
     21(167) -> 168*
     21(92) -> 93*
     21(37) -> 38*
     21(22) -> 23*
     21(503) -> 504*
     21(94) -> 95*
     21(146) -> 147*
     21(121) -> 122*
     21(507) -> 508*
     21(83) -> 84*
     21(18) -> 19*
     21(352) -> 353*
     21(509) -> 510*
     22(344) -> 345*
     22(411) -> 412*
     22(211) -> 212*
     22(408) -> 409*
     22(365) -> 366*
     22(210) -> 211*
     40(7) -> 7*
     02(209) -> 210*
     02(348) -> 349*
     02(410) -> 411*
     02(432) -> 433*
     00(7) -> 7*
     12(479) -> 480*
     12(212) -> 213*
     12(409) -> 410*
     12(581) -> 582*
     12(571) -> 572*
     12(349) -> 350*
     12(441) -> 442*
     12(214) -> 215*
     12(406) -> 407*
     12(543) -> 544*
     12(443) -> 444*
     12(575) -> 576*
     12(545) -> 546*
     12(273) -> 274*
     12(258) -> 259*
     12(213) -> 214*
     12(395) -> 396*
     12(577) -> 578*
     12(552) -> 553*
     12(547) -> 548*
     12(345) -> 346*
     12(537) -> 538*
     12(447) -> 448*
     12(554) -> 555*
     12(347) -> 348*
     12(539) -> 540*
     30(7) -> 7*
     52(364) -> 365*
     52(551) -> 552*
     52(274) -> 275*
     52(259) -> 260*
     52(346) -> 347*
     52(407) -> 408*
     20(7) -> 7*
     42(277) -> 278*
     42(262) -> 263*
     42(242) -> 243*
     42(556) -> 557*
     42(481) -> 482*
     42(244) -> 245*
     42(396) -> 397*
     42(553) -> 554*
     42(398) -> 399*
     42(555) -> 556*
     42(278) -> 279*
     42(263) -> 264*
     42(275) -> 276*
     42(260) -> 261*
     42(245) -> 246*
     42(362) -> 363*
     10(7) -> 7*
     32(394) -> 395*
     32(491) -> 492*
     32(366) -> 367*
     32(276) -> 277*
     32(261) -> 262*
     32(363) -> 364*
     32(243) -> 244*
     32(397) -> 398*
     32(499) -> 500*
     50(7) -> 7*
     7 -> 157,139,94,64,32,15
     15 -> 273*
     16 -> 22*
     17 -> 60*
     18 -> 7,139,64,15,32,94,157
     20 -> 394*
     21 -> 582,259,570,274,33,50,17,180,140,16,22,158,7
     23 -> 501,46,37
     24 -> 76*
     25 -> 491*
     26 -> 158,7,139,64,15,32,94,157,167
     27 -> 559,570,65,80,16,22,96,140,158,7
     32 -> 569,558
     33 -> 274,7,157,94,32,15,64,139,273,180,50
     34 -> 89*
     36 -> 25*
     40 -> 551,300,298
     41 -> 582,259,570,572,407,274,16,22,158,167,17,33,50,34,180,7
     48 -> 509*
     49 -> 26*
     50 -> 571*
     51 -> 7,157,94,32,15,64,139,273,184,172,46
     61 -> 505*
     63 -> 20*
     65 -> 80*
     68 -> 48*
     78 -> 406*
     79 -> 559,65,80,140,7
     81 -> 318*
     84 -> 20*
     91 -> 489*
     92 -> 344*
     93 -> 559,23,37,95,46,65,80,7
     95 -> 155,120,103
     96 -> 125*
     97 -> 108*
     98 -> 48*
     104 -> 516*
     106 -> 209*
     107 -> 40*
     109 -> 83*
     124 -> 20*
     128 -> 40*
     141 -> 145*
     144 -> 40*
     145 -> 547*
     147 -> 91*
     156 -> 37*
     158 -> 511,167
     160 -> 577,392
     161 -> 473,467
     162 -> 26*
     171 -> 78*
     174 -> 258*
     175 -> 92*
     183 -> 48*
     185 -> 432*
     186 -> 342,25
     209 -> 458,443
     211 -> 242,240
     214 -> 471,465
     215 -> 582,572,576,274,17,159,34,60,33,50,7,180
     241 -> 47*
     246 -> 140*
     263 -> 503*
     264 -> 241,490,81,96,125,47,318,363,158,7,167
     275 -> 479*
     279 -> 241,47
     299 -> 65*
     300 -> 447*
     301 -> 22*
     319 -> 351*
     321 -> 507*
     322 -> 16,7,139,64,15,32,94,157,22
     342 -> 475,469
     343 -> 33,50,7,180
     345 -> 362*
     350 -> 17*
     353 -> 499*
     354 -> 33,50,7,180
     367 -> 17*
     393 -> 487,477,161
     399 -> 349*
     407 -> 424*
     408 -> 426*
     410 -> 526,441
     412 -> 481,23,37,7,95,46
     425 -> 181*
     427 -> 62*
     432 -> 549,537
     433 -> 210*
     442 -> 259*
     444 -> 274*
     448 -> 274*
     464 -> 243*
     466 -> 65*
     468 -> 65*
     470 -> 65*
     471 -> 545*
     472 -> 22*
     473 -> 543*
     474 -> 22*
     475 -> 539*
     476 -> 22*
     478 -> 92*
     480 -> 348*
     482 -> 363*
     488 -> 32*
     490 -> 32*
     492 -> 395*
     500 -> 395*
     502 -> 92*
     504 -> 155*
     506 -> 37*
     508 -> 155*
     510 -> 155*
     511 -> 575*
     512 -> 161*
     517 -> 20*
     532 -> 482*
     538 -> 259*
     540 -> 259*
     544 -> 259*
     546 -> 259*
     548 -> 259*
     550 -> 459*
     557 -> 502,92,344
     559 -> 65*
     569 -> 581*
     570 -> 22*
     572 -> 407*
     576 -> 407*
     578 -> 407*
     582 -> 259*
   problem:
    
   Qed