YES

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

Proof:
 String Reversal Processor:
  2(1(1(0(x1)))) -> 2(3(1(0(1(x1)))))
  2(1(1(0(x1)))) -> 2(1(0(1(4(x1)))))
  2(1(1(0(x1)))) -> 2(3(1(4(1(0(x1))))))
  2(1(1(0(x1)))) -> 2(1(4(1(4(0(x1))))))
  2(1(1(0(x1)))) -> 2(1(3(0(1(4(x1))))))
  2(1(1(0(x1)))) -> 2(0(1(3(1(4(x1))))))
  5(1(1(0(x1)))) -> 5(1(0(1(4(x1)))))
  5(1(1(0(x1)))) -> 1(0(1(4(5(x1)))))
  5(1(1(0(x1)))) -> 5(1(0(1(4(0(x1))))))
  5(1(1(0(x1)))) -> 1(0(1(4(5(0(x1))))))
  5(1(1(0(x1)))) -> 5(1(3(1(0(1(x1))))))
  5(1(1(0(x1)))) -> 5(1(0(4(4(1(x1))))))
  5(1(1(0(x1)))) -> 1(4(5(1(0(3(x1))))))
  5(1(1(0(x1)))) -> 5(1(0(1(4(3(x1))))))
  5(1(1(0(x1)))) -> 1(0(5(1(4(3(x1))))))
  5(1(1(0(x1)))) -> 1(0(1(4(5(3(x1))))))
  5(1(1(0(x1)))) -> 3(5(1(0(1(4(x1))))))
  5(1(1(0(x1)))) -> 4(5(1(0(1(4(x1))))))
  5(1(1(0(x1)))) -> 5(0(1(3(1(4(x1))))))
  5(1(1(0(x1)))) -> 5(0(1(4(1(4(x1))))))
  5(1(1(0(x1)))) -> 1(0(5(1(4(4(x1))))))
  5(1(1(0(x1)))) -> 0(1(3(1(4(5(x1))))))
  0(2(1(0(x1)))) -> 3(0(1(4(2(0(x1))))))
  5(3(1(0(x1)))) -> 1(4(5(3(0(x1)))))
  5(4(1(0(x1)))) -> 1(4(5(3(0(x1)))))
  5(4(1(0(x1)))) -> 3(5(1(0(4(4(x1))))))
  5(4(2(0(x1)))) -> 5(3(2(0(4(x1)))))
  5(4(2(0(x1)))) -> 5(2(0(4(4(x1)))))
  5(4(2(0(x1)))) -> 5(3(2(3(0(4(x1))))))
  5(1(2(0(0(x1))))) -> 1(4(5(2(0(0(x1))))))
  5(4(2(0(0(x1))))) -> 5(2(4(4(0(0(x1))))))
  5(4(0(1(0(x1))))) -> 5(1(0(0(4(0(x1))))))
  0(5(0(1(0(x1))))) -> 0(0(0(5(1(4(x1))))))
  5(0(1(1(0(x1))))) -> 5(1(0(4(0(1(x1))))))
  0(2(1(1(0(x1))))) -> 0(1(2(1(4(0(x1))))))
  0(2(1(1(0(x1))))) -> 0(0(1(2(1(4(x1))))))
  5(3(1(1(0(x1))))) -> 5(3(1(0(1(4(x1))))))
  5(3(1(1(0(x1))))) -> 1(3(0(1(4(5(x1))))))
  2(4(1(1(0(x1))))) -> 2(1(4(1(4(0(x1))))))
  2(4(1(1(0(x1))))) -> 0(2(1(3(1(4(x1))))))
  2(4(1(1(0(x1))))) -> 1(0(1(4(2(4(x1))))))
  5(4(1(1(0(x1))))) -> 1(3(1(4(5(0(x1))))))
  5(4(1(1(0(x1))))) -> 1(4(1(4(5(0(x1))))))
  5(4(1(1(0(x1))))) -> 5(1(0(1(4(2(x1))))))
  2(0(2(1(0(x1))))) -> 2(2(1(0(4(0(x1))))))
  5(1(2(1(0(x1))))) -> 5(2(1(4(1(0(x1))))))
  0(5(4(1(0(x1))))) -> 3(0(1(4(5(0(x1))))))
  5(1(5(1(0(x1))))) -> 5(1(0(1(4(5(x1))))))
  5(1(0(2(0(x1))))) -> 5(3(2(0(0(1(x1))))))
  5(4(0(2(0(x1))))) -> 5(1(4(2(0(0(x1))))))
  0(5(0(2(0(x1))))) -> 0(3(0(5(2(0(x1))))))
  5(1(3(2(0(x1))))) -> 5(3(2(1(0(0(x1))))))
  5(1(3(2(0(x1))))) -> 1(4(3(5(2(0(x1))))))
  5(1(3(2(0(x1))))) -> 1(4(2(5(3(0(x1))))))
  5(1(3(2(0(x1))))) -> 5(3(1(4(0(2(x1))))))
  5(1(3(2(0(x1))))) -> 3(5(1(4(0(2(x1))))))
  5(1(3(2(0(x1))))) -> 1(0(3(5(3(2(x1))))))
  5(1(3(2(0(x1))))) -> 0(1(4(3(5(2(x1))))))
  5(1(3(2(0(x1))))) -> 3(2(5(0(1(4(x1))))))
  5(1(3(2(0(x1))))) -> 5(2(0(3(1(4(x1))))))
  5(1(3(2(0(x1))))) -> 3(0(2(5(1(4(x1))))))
  2(1(5(2(0(x1))))) -> 5(1(2(3(2(0(x1))))))
  5(1(5(2(0(x1))))) -> 5(1(2(5(3(0(x1))))))
  5(1(5(2(0(x1))))) -> 5(2(5(1(4(0(x1))))))
  5(1(5(2(0(x1))))) -> 5(0(5(1(4(2(x1))))))
  5(1(5(2(0(x1))))) -> 5(2(5(0(1(4(x1))))))
  5(1(5(2(0(x1))))) -> 0(2(5(5(1(4(x1))))))
  5(1(5(3(0(x1))))) -> 1(4(5(3(0(5(x1))))))
  2(0(2(4(0(x1))))) -> 2(2(3(4(0(0(x1))))))
  5(1(2(4(0(x1))))) -> 1(4(4(5(2(0(x1))))))
  5(1(2(4(0(x1))))) -> 2(3(5(1(4(0(x1))))))
  5(1(2(4(0(x1))))) -> 5(0(0(1(4(2(x1))))))
  5(1(2(4(0(x1))))) -> 5(0(3(1(4(2(x1))))))
  5(1(2(4(0(x1))))) -> 0(4(5(1(4(2(x1))))))
  5(1(2(4(0(x1))))) -> 4(2(5(1(0(3(x1))))))
  5(1(2(4(0(x1))))) -> 1(4(2(5(0(3(x1))))))
  5(1(2(4(0(x1))))) -> 0(5(2(3(1(4(x1))))))
  5(1(2(4(0(x1))))) -> 2(5(1(0(4(4(x1))))))
  5(1(5(4(0(x1))))) -> 4(0(5(1(4(5(x1))))))
  Bounds Processor:
   bound: 1
   enrichment: match
   automaton:
    final states: {257,256,253,249,247,245,242,240,238,235,232,227,224,
                   223,220,217,215,211,208,205,202,197,192,190,185,182,
                   179,175,171,168,164,163,162,160,157,151,149,147,142,
                   140,138,136,132,129,125,121,117,113,108,104,102,98,
                   94,90,85,82,77,73,72,71,70,65,62,57,51,46,44,39,36,
                   31,30,26,23,18,12,7,1}
    transitions:
     11(280) -> 281*
     11(288) -> 289*
     11(264) -> 265*
     51(262) -> 263*
     51(286) -> 287*
     20(122) -> 209*
     20(115) -> 116*
     20(158) -> 159*
     20(13) -> 86*
     20(109) -> 110*
     20(16) -> 161*
     20(212) -> 213*
     20(97) -> 256*
     20(20) -> 130*
     20(22) -> 18*
     20(165) -> 166*
     20(27) -> 254*
     20(29) -> 26*
     20(203) -> 204*
     20(176) -> 177*
     20(218) -> 219*
     20(6) -> 1*
     20(11) -> 7*
     20(17) -> 12*
     20(206) -> 207*
     20(234) -> 232*
     20(233) -> 234*
     20(8) -> 143*
     20(159) -> 157*
     20(92) -> 183*
     20(25) -> 23*
     20(239) -> 238*
     20(55) -> 248*
     20(225) -> 226*
     20(99) -> 100*
     20(95) -> 103*
     20(105) -> 106*
     20(9) -> 133*
     20(28) -> 141*
     20(250) -> 251*
     20(2) -> 152*
     f60() -> 2*
     50(204) -> 223*
     50(154) -> 221*
     50(86) -> 172*
     50(219) -> 217*
     50(254) -> 255*
     50(178) -> 175*
     50(207) -> 205*
     50(13) -> 40*
     50(10) -> 203*
     50(110) -> 111*
     50(244) -> 242*
     50(161) -> 160*
     50(101) -> 98*
     50(52) -> 66*
     50(29) -> 72*
     50(103) -> 102*
     50(116) -> 113*
     50(122) -> 225*
     50(170) -> 168*
     50(107) -> 104*
     50(45) -> 44*
     50(2) -> 32*
     50(216) -> 215*
     50(241) -> 240*
     50(38) -> 36*
     50(76) -> 73*
     50(167) -> 164*
     50(11) -> 30*
     50(214) -> 211*
     50(50) -> 46*
     50(222) -> 220*
     50(9) -> 122*
     50(91) -> 92*
     50(61) -> 57*
     50(54) -> 55*
     50(188) -> 191*
     50(120) -> 117*
     50(34) -> 258*
     50(152) -> 198*
     50(193) -> 194*
     50(128) -> 125*
     50(79) -> 80*
     50(53) -> 250*
     50(137) -> 136*
     50(189) -> 185*
     50(20) -> 218*
     50(96) -> 97*
     50(229) -> 230*
     50(156) -> 151*
     50(59) -> 63*
     50(31) -> 163*
     40(221) -> 246*
     40(2) -> 8*
     40(55) -> 56*
     40(111) -> 112*
     40(259) -> 257*
     40(199) -> 200*
     40(109) -> 114*
     40(180) -> 181*
     40(114) -> 115*
     40(183) -> 184*
     40(110) -> 169*
     40(32) -> 33*
     40(30) -> 71*
     40(3) -> 47*
     40(40) -> 41*
     40(14) -> 15*
     40(251) -> 252*
     40(52) -> 58*
     40(9) -> 74*
     40(248) -> 247*
     40(20) -> 21*
     40(92) -> 93*
     40(13) -> 19*
     40(4) -> 126*
     40(236) -> 237*
     40(66) -> 67*
     40(152) -> 153*
     40(230) -> 231*
     40(86) -> 87*
     40(172) -> 236*
     40(47) -> 48*
     40(8) -> 78*
     40(186) -> 187*
     40(42) -> 150*
     40(143) -> 144*
     30(89) -> 85*
     30(16) -> 17*
     30(198) -> 199*
     30(188) -> 189*
     30(2) -> 52*
     30(10) -> 24*
     30(5) -> 6*
     30(13) -> 91*
     30(204) -> 202*
     30(191) -> 190*
     30(9) -> 27*
     30(154) -> 243*
     30(97) -> 94*
     30(172) -> 180*
     30(228) -> 229*
     30(194) -> 195*
     30(152) -> 193*
     30(43) -> 162*
     30(99) -> 105*
     30(11) -> 137*
     30(34) -> 83*
     30(210) -> 208*
     30(35) -> 139*
     30(173) -> 174*
     30(166) -> 167*
     30(86) -> 212*
     30(30) -> 70*
     30(42) -> 148*
     30(218) -> 239*
     30(100) -> 101*
     30(177) -> 178*
     30(106) -> 107*
     30(114) -> 233*
     00(122) -> 123*
     00(246) -> 245*
     00(75) -> 76*
     00(52) -> 53*
     00(3) -> 4*
     00(226) -> 224*
     00(145) -> 146*
     00(221) -> 222*
     00(84) -> 82*
     00(131) -> 129*
     00(63) -> 64*
     00(118) -> 119*
     00(13) -> 109*
     00(134) -> 135*
     00(154) -> 155*
     00(27) -> 206*
     00(195) -> 196*
     00(68) -> 69*
     00(9) -> 10*
     00(172) -> 173*
     00(135) -> 132*
     00(126) -> 127*
     00(141) -> 140*
     00(123) -> 124*
     00(258) -> 259*
     00(8) -> 99*
     00(243) -> 244*
     00(80) -> 81*
     00(174) -> 171*
     00(34) -> 35*
     00(59) -> 60*
     00(4) -> 165*
     00(209) -> 210*
     00(28) -> 29*
     00(42) -> 43*
     00(32) -> 228*
     00(88) -> 89*
     00(48) -> 49*
     00(19) -> 118*
     00(201) -> 197*
     00(152) -> 186*
     00(124) -> 121*
     00(155) -> 241*
     00(255) -> 253*
     00(78) -> 95*
     00(2) -> 13*
     00(20) -> 37*
     10(153) -> 154*
     10(69) -> 65*
     10(213) -> 214*
     10(2) -> 3*
     10(139) -> 138*
     10(43) -> 39*
     10(181) -> 179*
     10(4) -> 5*
     10(10) -> 11*
     10(81) -> 77*
     10(13) -> 14*
     10(196) -> 192*
     10(15) -> 16*
     10(148) -> 147*
     10(187) -> 188*
     10(109) -> 176*
     10(119) -> 120*
     10(60) -> 61*
     10(6) -> 45*
     10(27) -> 28*
     10(83) -> 84*
     10(118) -> 158*
     10(237) -> 235*
     10(64) -> 62*
     10(56) -> 51*
     10(155) -> 156*
     10(133) -> 134*
     10(87) -> 88*
     10(8) -> 9*
     10(93) -> 90*
     10(150) -> 149*
     10(21) -> 22*
     10(184) -> 182*
     10(24) -> 25*
     10(58) -> 59*
     10(231) -> 227*
     10(33) -> 34*
     10(95) -> 96*
     10(112) -> 108*
     10(252) -> 249*
     10(41) -> 42*
     10(144) -> 145*
     10(37) -> 38*
     10(49) -> 50*
     10(146) -> 142*
     10(200) -> 201*
     10(127) -> 128*
     10(78) -> 79*
     10(183) -> 216*
     10(169) -> 170*
     10(19) -> 20*
     10(53) -> 54*
     10(67) -> 68*
     10(35) -> 31*
     10(130) -> 131*
     10(74) -> 75*
     31(261) -> 262*
     31(285) -> 286*
     31(282) -> 283*
     21(278) -> 279*
     01(284) -> 285*
     01(260) -> 261*
     01(281) -> 282*
     41(287) -> 288*
     41(279) -> 280*
     41(263) -> 264*
     247 -> 32*
     238 -> 32*
     192 -> 32*
     94 -> 32*
     151 -> 32*
     163 -> 32*
     70 -> 32*
     142 -> 152,143
     132 -> 13,186
     215 -> 32*
     242 -> 32*
     168 -> 32*
     164 -> 32*
     190 -> 32*
     160 -> 32*
     245 -> 32*
     256 -> 32*
     240 -> 32*
     162 -> 13,228
     46 -> 32*
     30 -> 32*
     182 -> 32*
     113 -> 32*
     217 -> 32*
     7 -> 152*
     140 -> 152,143
     104 -> 32*
     77 -> 32*
     85 -> 13,186
     12 -> 152*
     232 -> 152,86
     265 -> 136*
     117 -> 32*
     82 -> 32*
     283 -> 186*
     249 -> 32*
     220 -> 32*
     171 -> 13,228
     121 -> 13,228
     257 -> 32*
     138 -> 32,66
     72 -> 32*
     208 -> 32*
     36 -> 32*
     253 -> 32*
     235 -> 32*
     125 -> 32,40
     261 -> 278*
     26 -> 152*
     179 -> 32*
     73 -> 32*
     44 -> 32*
     197 -> 32*
     1 -> 152*
     31 -> 32*
     62 -> 32*
     224 -> 32*
     90 -> 32,66
     175 -> 32*
     185 -> 32*
     65 -> 32*
     147 -> 32*
     9 -> 260*
     108 -> 32*
     57 -> 32*
     39 -> 32*
     227 -> 32*
     18 -> 143,152
     145 -> 284*
     211 -> 152*
     149 -> 32*
     136 -> 32,66
     129 -> 13,186
     289 -> 194*
     51 -> 32*
     98 -> 32*
     202 -> 32*
     205 -> 32*
     102 -> 32*
     23 -> 152*
     157 -> 152,86
     33 -> 32*
     223 -> 32*
   problem:
    
   Qed