YES

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

Proof:
 String Reversal Processor:
  5(4(3(x1))) -> 0(4(0(3(0(1(3(0(5(3(x1))))))))))
  0(2(4(x1))) -> 0(3(0(3(0(1(0(3(1(3(x1))))))))))
  1(5(4(x1))) -> 4(5(0(5(0(5(3(0(3(0(x1))))))))))
  2(2(2(2(0(x1))))) -> 2(4(5(2(5(0(1(3(0(0(x1))))))))))
  0(5(2(2(2(x1))))) -> 5(0(5(3(2(0(3(3(3(2(x1))))))))))
  5(2(5(2(2(x1))))) -> 5(5(0(4(1(3(1(4(5(5(x1))))))))))
  2(0(2(2(3(x1))))) -> 3(4(5(5(3(5(3(1(2(4(x1))))))))))
  4(1(5(4(3(x1))))) -> 1(1(5(5(4(0(1(0(5(3(x1))))))))))
  5(1(4(1(4(x1))))) -> 5(1(4(0(4(1(3(5(5(5(x1))))))))))
  2(2(1(5(4(x1))))) -> 4(3(2(0(0(0(4(5(1(3(x1))))))))))
  2(2(5(4(5(x1))))) -> 1(0(0(4(3(5(5(2(1(5(x1))))))))))
  2(2(1(4(1(0(x1)))))) -> 4(5(5(5(5(0(2(4(0(0(x1))))))))))
  1(4(1(5(1(0(x1)))))) -> 0(0(0(4(5(4(5(5(5(4(x1))))))))))
  2(0(5(1(2(0(x1)))))) -> 2(3(3(1(0(5(5(5(3(3(x1))))))))))
  2(5(1(2(2(0(x1)))))) -> 3(3(5(2(1(2(0(0(5(0(x1))))))))))
  1(4(4(5(4(0(x1)))))) -> 3(5(0(2(5(5(4(0(2(3(x1))))))))))
  4(5(4(2(3(1(x1)))))) -> 4(0(1(1(2(4(5(0(2(1(x1))))))))))
  2(5(4(2(1(2(x1)))))) -> 2(2(2(1(3(4(1(5(5(0(x1))))))))))
  2(3(2(5(4(2(x1)))))) -> 3(3(2(0(2(5(3(4(0(2(x1))))))))))
  2(5(4(1(4(3(x1)))))) -> 3(1(3(0(5(5(5(5(3(5(x1))))))))))
  4(5(1(0(2(4(x1)))))) -> 1(1(4(3(0(1(1(5(1(0(x1))))))))))
  0(1(4(1(4(4(x1)))))) -> 0(1(3(4(5(2(0(0(2(0(x1))))))))))
  5(2(5(4(5(4(x1)))))) -> 3(4(5(1(3(3(0(0(5(0(x1))))))))))
  1(5(1(5(2(5(x1)))))) -> 5(0(5(4(0(1(3(4(0(5(x1))))))))))
  2(3(0(5(4(5(x1)))))) -> 2(5(1(1(5(3(1(1(5(5(x1))))))))))
  3(1(4(4(3(2(0(x1))))))) -> 3(3(1(4(0(3(1(1(3(0(x1))))))))))
  5(1(4(1(4(2(0(x1))))))) -> 2(5(5(0(0(2(1(1(4(0(x1))))))))))
  5(4(3(2(5(1(1(x1))))))) -> 0(4(1(1(1(2(0(1(3(4(x1))))))))))
  1(4(2(1(0(4(1(x1))))))) -> 2(0(3(2(0(4(3(5(0(1(x1))))))))))
  2(2(3(2(5(1(2(x1))))))) -> 5(5(5(2(1(3(3(5(1(2(x1))))))))))
  5(4(0(0(2(4(2(x1))))))) -> 0(2(3(5(4(3(1(5(5(3(x1))))))))))
  5(1(5(1(4(5(2(x1))))))) -> 5(2(0(4(0(4(4(0(2(2(x1))))))))))
  5(4(1(3(5(5(2(x1))))))) -> 2(0(1(0(0(0(4(0(3(2(x1))))))))))
  5(4(2(1(0(1(4(x1))))))) -> 5(4(5(3(4(3(2(4(5(5(x1))))))))))
  2(5(2(2(2(2(4(x1))))))) -> 1(5(0(1(4(2(0(3(3(4(x1))))))))))
  1(5(4(1(3(2(4(x1))))))) -> 1(4(1(2(1(5(0(1(4(0(x1))))))))))
  4(5(2(5(4(2(4(x1))))))) -> 0(2(3(2(2(4(5(3(3(0(x1))))))))))
  2(2(4(2(1(4(4(x1))))))) -> 0(4(5(1(3(0(3(3(3(0(x1))))))))))
  5(2(3(2(4(4(4(x1))))))) -> 5(0(5(1(4(0(4(3(1(0(x1))))))))))
  1(1(4(4(2(5(4(x1))))))) -> 0(5(0(2(3(0(5(2(5(4(x1))))))))))
  2(4(5(4(0(0(5(x1))))))) -> 2(4(0(2(3(3(5(3(1(5(x1))))))))))
  5(4(0(2(5(4(5(x1))))))) -> 5(1(4(3(1(1(1(0(0(5(x1))))))))))
  Bounds Processor:
   bound: 1
   enrichment: match
   automaton:
    final states: {353,345,337,329,322,314,307,299,292,284,275,267,258,
                   249,240,231,223,215,206,200,191,182,173,164,156,146,
                   137,128,119,110,102,93,85,77,70,60,50,40,31,21,12,
                   1}
    transitions:
     50(221) -> 222*
     50(266) -> 258*
     50(73) -> 74*
     50(2) -> 51*
     50(105) -> 106*
     50(264) -> 265*
     50(265) -> 266*
     50(111) -> 112*
     50(315) -> 316*
     50(259) -> 260*
     50(174) -> 175*
     50(37) -> 38*
     50(212) -> 213*
     50(214) -> 206*
     50(64) -> 65*
     50(51) -> 52*
     50(134) -> 135*
     50(326) -> 327*
     50(114) -> 115*
     50(144) -> 145*
     50(183) -> 184*
     50(250) -> 251*
     50(121) -> 122*
     50(175) -> 176*
     50(95) -> 96*
     50(176) -> 177*
     50(195) -> 196*
     50(308) -> 309*
     50(338) -> 339*
     50(74) -> 75*
     50(346) -> 347*
     50(3) -> 4*
     50(35) -> 36*
     50(298) -> 292*
     50(271) -> 272*
     50(52) -> 78*
     50(49) -> 40*
     50(149) -> 150*
     50(334) -> 335*
     50(107) -> 108*
     50(167) -> 168*
     50(67) -> 68*
     50(22) -> 129*
     50(305) -> 306*
     50(360) -> 353*
     50(13) -> 86*
     50(343) -> 344*
     50(84) -> 77*
     50(4) -> 268*
     50(96) -> 97*
     50(66) -> 67*
     50(27) -> 28*
     50(59) -> 50*
     50(129) -> 157*
     50(141) -> 142*
     50(237) -> 238*
     50(61) -> 111*
     50(122) -> 123*
     50(203) -> 204*
     50(177) -> 178*
     50(58) -> 59*
     50(336) -> 329*
     50(120) -> 121*
     50(47) -> 48*
     50(296) -> 297*
     50(218) -> 219*
     50(112) -> 113*
     50(283) -> 275*
     50(106) -> 107*
     50(238) -> 239*
     50(25) -> 26*
     50(108) -> 109*
     50(140) -> 141*
     50(29) -> 30*
     11(420) -> 421*
     11(417) -> 418*
     11(387) -> 388*
     11(439) -> 440*
     11(384) -> 385*
     11(442) -> 443*
     11(376) -> 377*
     31(491) -> 492*
     31(375) -> 376*
     31(440) -> 441*
     31(372) -> 373*
     31(389) -> 390*
     31(444) -> 445*
     31(453) -> 454*
     31(416) -> 417*
     31(459) -> 460*
     31(391) -> 392*
     31(418) -> 419*
     31(460) -> 461*
     31(463) -> 464*
     31(383) -> 384*
     31(378) -> 379*
     31(422) -> 423*
     31(451) -> 452*
     31(385) -> 386*
     31(458) -> 459*
     31(446) -> 447*
     31(438) -> 439*
     31(424) -> 425*
     31(493) -> 494*
     31(501) -> 502*
     00(116) -> 117*
     00(207) -> 354*
     00(339) -> 340*
     00(169) -> 170*
     00(193) -> 194*
     00(148) -> 149*
     00(88) -> 89*
     00(279) -> 280*
     00(286) -> 287*
     00(199) -> 191*
     00(287) -> 288*
     00(328) -> 322*
     00(210) -> 211*
     00(242) -> 243*
     00(253) -> 254*
     00(16) -> 17*
     00(44) -> 45*
     00(41) -> 165*
     00(34) -> 35*
     00(186) -> 187*
     00(226) -> 227*
     00(154) -> 155*
     00(321) -> 314*
     00(143) -> 144*
     00(276) -> 277*
     00(57) -> 58*
     00(342) -> 343*
     00(20) -> 12*
     00(42) -> 285*
     00(22) -> 32*
     00(129) -> 130*
     00(290) -> 291*
     00(7) -> 8*
     00(130) -> 131*
     00(81) -> 82*
     00(23) -> 24*
     00(304) -> 305*
     00(256) -> 257*
     00(118) -> 110*
     00(100) -> 101*
     00(87) -> 88*
     00(14) -> 15*
     00(192) -> 193*
     00(147) -> 250*
     00(11) -> 1*
     00(281) -> 282*
     00(89) -> 90*
     00(178) -> 179*
     00(248) -> 240*
     00(138) -> 139*
     00(104) -> 105*
     00(236) -> 237*
     00(26) -> 27*
     00(233) -> 308*
     00(4) -> 5*
     00(71) -> 72*
     00(235) -> 236*
     00(323) -> 324*
     00(350) -> 351*
     00(99) -> 100*
     00(48) -> 49*
     00(213) -> 214*
     00(300) -> 301*
     00(331) -> 332*
     00(288) -> 289*
     00(335) -> 336*
     00(9) -> 10*
     00(117) -> 118*
     00(123) -> 124*
     00(28) -> 29*
     00(274) -> 267*
     00(344) -> 337*
     00(18) -> 19*
     00(51) -> 207*
     00(2) -> 22*
     10(22) -> 183*
     10(153) -> 154*
     10(5) -> 71*
     10(246) -> 247*
     10(101) -> 93*
     10(75) -> 76*
     10(52) -> 216*
     10(3) -> 13*
     10(189) -> 190*
     10(33) -> 34*
     10(15) -> 16*
     10(53) -> 54*
     10(355) -> 356*
     10(180) -> 181*
     10(241) -> 242*
     10(306) -> 299*
     10(313) -> 307*
     10(184) -> 185*
     10(268) -> 269*
     10(216) -> 217*
     10(262) -> 263*
     10(244) -> 245*
     10(62) -> 63*
     10(219) -> 220*
     10(79) -> 80*
     10(359) -> 360*
     10(23) -> 224*
     10(356) -> 357*
     10(55) -> 56*
     10(333) -> 334*
     10(303) -> 304*
     10(190) -> 182*
     10(198) -> 199*
     10(185) -> 186*
     10(325) -> 326*
     10(232) -> 233*
     10(233) -> 234*
     10(220) -> 221*
     10(245) -> 246*
     10(83) -> 84*
     10(76) -> 70*
     10(224) -> 225*
     10(289) -> 290*
     10(309) -> 310*
     10(209) -> 210*
     10(202) -> 203*
     10(157) -> 158*
     10(51) -> 94*
     10(354) -> 355*
     10(152) -> 153*
     10(124) -> 125*
     10(311) -> 312*
     10(6) -> 7*
     10(160) -> 161*
     10(132) -> 133*
     10(2) -> 147*
     10(228) -> 229*
     10(41) -> 259*
     01(377) -> 378*
     01(381) -> 382*
     01(421) -> 422*
     01(390) -> 391*
     01(379) -> 380*
     01(492) -> 493*
     01(423) -> 424*
     01(445) -> 446*
     01(461) -> 462*
     01(447) -> 448*
     01(425) -> 426*
     01(386) -> 387*
     01(443) -> 444*
     01(490) -> 491*
     01(388) -> 389*
     01(419) -> 420*
     01(465) -> 466*
     01(497) -> 498*
     01(392) -> 393*
     01(374) -> 375*
     01(495) -> 496*
     01(441) -> 442*
     30(255) -> 256*
     30(217) -> 218*
     30(54) -> 55*
     30(69) -> 60*
     30(172) -> 164*
     30(241) -> 300*
     30(17) -> 18*
     30(348) -> 349*
     30(23) -> 315*
     30(2) -> 3*
     30(22) -> 23*
     30(357) -> 358*
     30(340) -> 341*
     30(43) -> 44*
     30(225) -> 226*
     30(181) -> 173*
     30(5) -> 6*
     30(261) -> 262*
     30(63) -> 64*
     30(295) -> 296*
     30(13) -> 14*
     30(97) -> 98*
     30(205) -> 200*
     30(171) -> 172*
     30(126) -> 127*
     30(269) -> 270*
     30(42) -> 43*
     30(230) -> 223*
     30(187) -> 188*
     30(136) -> 128*
     30(145) -> 137*
     30(94) -> 346*
     30(131) -> 201*
     30(179) -> 180*
     30(201) -> 202*
     30(208) -> 209*
     30(324) -> 325*
     30(272) -> 273*
     30(293) -> 294*
     30(315) -> 323*
     30(197) -> 198*
     30(347) -> 348*
     30(159) -> 160*
     30(135) -> 136*
     30(8) -> 9*
     30(61) -> 241*
     30(24) -> 25*
     30(91) -> 92*
     30(32) -> 33*
     30(319) -> 320*
     30(125) -> 126*
     30(251) -> 252*
     30(3) -> 120*
     30(41) -> 42*
     30(78) -> 79*
     30(229) -> 230*
     30(183) -> 330*
     30(166) -> 167*
     30(46) -> 47*
     30(19) -> 20*
     30(65) -> 66*
     30(260) -> 261*
     30(51) -> 174*
     51(464) -> 465*
     51(466) -> 467*
     51(373) -> 374*
     51(498) -> 499*
     51(494) -> 495*
     51(496) -> 497*
     40(52) -> 53*
     40(22) -> 232*
     40(211) -> 212*
     40(68) -> 69*
     40(188) -> 189*
     40(330) -> 331*
     40(302) -> 303*
     40(2) -> 61*
     40(10) -> 11*
     40(297) -> 298*
     40(115) -> 116*
     40(72) -> 73*
     40(80) -> 81*
     40(196) -> 197*
     40(204) -> 205*
     40(285) -> 286*
     40(113) -> 114*
     40(139) -> 140*
     40(82) -> 83*
     40(56) -> 57*
     40(109) -> 102*
     40(312) -> 313*
     40(92) -> 85*
     40(294) -> 295*
     40(158) -> 159*
     40(155) -> 146*
     40(247) -> 248*
     40(277) -> 278*
     40(38) -> 39*
     40(32) -> 103*
     40(358) -> 359*
     40(332) -> 333*
     40(207) -> 208*
     40(278) -> 279*
     40(351) -> 352*
     40(86) -> 87*
     40(30) -> 21*
     40(252) -> 253*
     40(270) -> 271*
     40(316) -> 317*
     40(327) -> 328*
     40(165) -> 166*
     40(150) -> 151*
     40(227) -> 228*
     40(280) -> 281*
     40(98) -> 99*
     21(457) -> 458*
     21(462) -> 463*
     41(499) -> 500*
     41(380) -> 381*
     20(257) -> 249*
     20(320) -> 321*
     20(301) -> 302*
     20(254) -> 255*
     20(39) -> 31*
     20(234) -> 235*
     20(282) -> 283*
     20(161) -> 162*
     20(103) -> 104*
     20(168) -> 169*
     20(291) -> 284*
     20(170) -> 171*
     20(142) -> 143*
     20(41) -> 276*
     20(36) -> 37*
     20(45) -> 46*
     20(3) -> 138*
     20(163) -> 156*
     20(2) -> 41*
     20(111) -> 338*
     20(310) -> 311*
     20(162) -> 163*
     20(151) -> 152*
     20(318) -> 319*
     20(239) -> 231*
     20(127) -> 119*
     20(133) -> 134*
     20(194) -> 195*
     20(222) -> 215*
     20(243) -> 244*
     20(22) -> 192*
     20(61) -> 62*
     20(341) -> 342*
     20(94) -> 95*
     20(349) -> 350*
     20(273) -> 274*
     20(352) -> 345*
     20(317) -> 318*
     20(53) -> 293*
     20(263) -> 264*
     20(147) -> 148*
     20(131) -> 132*
     20(90) -> 91*
     f60() -> 2*
     307 -> 147,94
     156 -> 41,338
     191 -> 22,250
     70 -> 61*
     351 -> 501*
     452 -> 439*
     92 -> 451*
     353 -> 51,111
     215 -> 41,138
     267 -> 51,111
     206 -> 147,94
     164 -> 41,138
     240 -> 51,111
     393 -> 105*
     231 -> 51*
     137 -> 147*
     30 -> 416*
     182 -> 61*
     77 -> 51*
     85 -> 41,276
     12 -> 22,165
     93 -> 41,276
     284 -> 51,111
     258 -> 41,276
     292 -> 51,111
     249 -> 147*
     345 -> 41,62
     109 -> 453*
     337 -> 147*
     173 -> 41,338
     21 -> 147,94
     161 -> 457*
     269 -> 372*
     38 -> 438*
     297 -> 490*
     426 -> 149*
     60 -> 41,192
     40 -> 22,207
     1 -> 51,111
     31 -> 41,276
     467 -> 340*
     275 -> 51*
     110 -> 147*
     146 -> 61*
     500 -> 94*
     382 -> 272*
     50 -> 51*
     299 -> 41*
     119 -> 41,192
     502 -> 439*
     448 -> 165,277
     454 -> 439*
     128 -> 41*
     32 -> 383*
     102 -> 41,276
     200 -> 51,339
     329 -> 51*
     322 -> 41,276
     314 -> 61*
     223 -> 3*
   problem:
    
   Qed