YES

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

Proof:
 String Reversal Processor:
  1(1(0(x1))) -> 1(4(3(2(1(0(x1))))))
  1(1(0(x1))) -> 0(4(3(1(3(1(x1))))))
  1(1(0(x1))) -> 1(3(0(3(1(5(x1))))))
  4(1(0(x1))) -> 4(3(1(0(x1))))
  4(1(0(x1))) -> 0(2(4(3(1(x1)))))
  4(1(0(x1))) -> 0(4(3(5(1(x1)))))
  4(1(0(x1))) -> 0(4(3(1(3(x1)))))
  4(1(0(x1))) -> 0(4(3(5(1(1(x1))))))
  4(1(0(x1))) -> 0(3(4(3(2(1(x1))))))
  4(1(0(x1))) -> 0(4(4(3(3(1(x1))))))
  4(1(0(x1))) -> 5(0(5(4(3(1(x1))))))
  4(1(0(x1))) -> 1(0(5(5(4(3(x1))))))
  4(2(1(x1))) -> 1(4(3(2(1(x1)))))
  4(2(1(x1))) -> 2(1(4(3(5(x1)))))
  4(2(1(x1))) -> 3(4(3(2(5(1(x1))))))
  4(2(1(x1))) -> 1(5(4(3(3(2(x1))))))
  1(2(5(x1))) -> 4(5(3(2(2(1(x1))))))
  1(2(5(x1))) -> 4(3(5(2(3(1(x1))))))
  4(2(5(x1))) -> 4(3(2(5(0(x1)))))
  4(2(5(x1))) -> 2(4(3(5(5(x1)))))
  4(2(5(x1))) -> 2(5(4(4(3(0(x1))))))
  4(2(5(x1))) -> 4(4(3(5(2(2(x1))))))
  4(2(5(x1))) -> 5(5(4(3(3(2(x1))))))
  4(2(5(x1))) -> 3(5(3(4(3(2(x1))))))
  4(2(5(x1))) -> 5(0(4(3(5(2(x1))))))
  4(2(5(x1))) -> 4(3(5(2(1(3(x1))))))
  4(2(5(x1))) -> 3(0(4(3(2(5(x1))))))
  4(2(0(0(x1)))) -> 2(0(3(4(0(x1)))))
  5(1(1(0(x1)))) -> 2(1(5(3(1(0(x1))))))
  4(2(1(0(x1)))) -> 4(3(3(2(1(0(x1))))))
  5(4(1(0(x1)))) -> 1(5(0(4(3(x1)))))
  5(4(1(0(x1)))) -> 1(0(3(5(4(3(x1))))))
  1(2(4(0(x1)))) -> 4(3(2(1(4(0(x1))))))
  4(1(5(0(x1)))) -> 1(4(5(3(0(0(x1))))))
  4(1(0(1(x1)))) -> 1(2(1(0(4(3(x1))))))
  4(2(1(1(x1)))) -> 2(1(4(3(1(x1)))))
  4(2(2(1(x1)))) -> 1(4(3(2(2(2(x1))))))
  2(4(2(1(x1)))) -> 3(2(4(3(2(1(x1))))))
  1(2(5(1(x1)))) -> 2(1(5(3(0(1(x1))))))
  4(2(5(1(x1)))) -> 4(1(5(3(2(3(x1))))))
  4(2(5(1(x1)))) -> 4(1(3(3(2(5(x1))))))
  4(1(0(5(x1)))) -> 1(3(5(0(4(3(x1))))))
  1(5(2(5(x1)))) -> 2(5(1(5(3(x1)))))
  4(5(1(1(0(x1))))) -> 1(1(4(5(0(0(x1))))))
  4(2(0(0(1(x1))))) -> 1(4(4(0(2(0(x1))))))
  1(2(4(0(1(x1))))) -> 0(1(4(3(2(1(x1))))))
  1(0(5(2(1(x1))))) -> 1(0(1(5(3(2(x1))))))
  4(0(3(5(1(x1))))) -> 4(0(4(3(1(5(x1))))))
  4(2(5(0(5(x1))))) -> 2(5(5(0(0(4(x1))))))
  2(4(2(3(5(x1))))) -> 2(4(3(5(1(2(x1))))))
  Bounds Processor:
   bound: 1
   enrichment: match
   automaton:
    final states: {193,187,184,180,179,174,170,166,164,161,156,151,149,
                   145,143,140,135,131,128,125,123,120,116,111,107,102,
                   98,97,92,87,83,79,75,71,65,61,57,56,51,48,44,39,34,
                   29,25,22,20,14,8,1}
    transitions:
     11(206) -> 207*
     11(214) -> 215*
     11(238) -> 239*
     11(288) -> 289*
     11(284) -> 285*
     11(233) -> 234*
     11(262) -> 263*
     11(210) -> 211*
     11(311) -> 312*
     11(292) -> 293*
     11(290) -> 291*
     11(318) -> 319*
     11(266) -> 267*
     11(212) -> 213*
     01(295) -> 296*
     01(205) -> 206*
     01(235) -> 236*
     01(313) -> 314*
     01(283) -> 284*
     01(263) -> 264*
     01(217) -> 218*
     10(148) -> 145*
     10(59) -> 60*
     10(162) -> 163*
     10(142) -> 140*
     10(154) -> 155*
     10(126) -> 141*
     10(183) -> 180*
     10(42) -> 56*
     10(127) -> 125*
     10(172) -> 173*
     10(165) -> 164*
     10(15) -> 16*
     10(7) -> 1*
     10(130) -> 128*
     10(139) -> 135*
     10(173) -> 170*
     10(121) -> 122*
     10(23) -> 144*
     10(70) -> 65*
     10(66) -> 194*
     10(3) -> 4*
     10(181) -> 182*
     10(178) -> 174*
     10(159) -> 160*
     10(55) -> 51*
     10(30) -> 31*
     10(19) -> 14*
     10(10) -> 11*
     10(9) -> 35*
     10(117) -> 132*
     10(167) -> 168*
     10(2) -> 9*
     f60() -> 2*
     50(153) -> 154*
     50(100) -> 101*
     50(67) -> 181*
     50(158) -> 159*
     50(15) -> 84*
     50(106) -> 102*
     50(136) -> 171*
     50(108) -> 109*
     50(52) -> 53*
     50(35) -> 36*
     50(168) -> 169*
     50(30) -> 167*
     50(3) -> 80*
     50(2) -> 15*
     50(76) -> 77*
     50(66) -> 103*
     50(126) -> 127*
     50(69) -> 70*
     50(50) -> 48*
     50(194) -> 195*
     50(191) -> 192*
     50(23) -> 49*
     50(9) -> 26*
     50(190) -> 191*
     50(73) -> 74*
     50(21) -> 121*
     50(53) -> 54*
     50(137) -> 138*
     50(93) -> 94*
     50(70) -> 97*
     50(90) -> 91*
     00(2) -> 3*
     00(105) -> 106*
     00(188) -> 189*
     00(33) -> 29*
     00(38) -> 34*
     00(24) -> 22*
     00(114) -> 115*
     00(185) -> 186*
     00(175) -> 176*
     00(3) -> 136*
     00(189) -> 190*
     00(52) -> 126*
     00(182) -> 183*
     00(49) -> 50*
     00(9) -> 152*
     00(118) -> 119*
     00(13) -> 8*
     00(43) -> 39*
     00(56) -> 179*
     00(28) -> 25*
     00(54) -> 55*
     00(129) -> 130*
     00(47) -> 44*
     00(17) -> 18*
     40(186) -> 184*
     40(89) -> 90*
     40(171) -> 172*
     40(138) -> 139*
     40(68) -> 69*
     40(2) -> 188*
     40(10) -> 23*
     40(17) -> 185*
     40(67) -> 99*
     40(74) -> 71*
     40(21) -> 20*
     40(27) -> 28*
     40(12) -> 13*
     40(96) -> 92*
     40(196) -> 197*
     40(163) -> 161*
     40(113) -> 114*
     40(104) -> 105*
     40(3) -> 117*
     40(82) -> 79*
     40(46) -> 47*
     40(88) -> 89*
     40(176) -> 177*
     40(110) -> 107*
     40(134) -> 131*
     40(6) -> 7*
     40(95) -> 96*
     40(32) -> 33*
     40(45) -> 46*
     40(58) -> 59*
     40(85) -> 86*
     40(37) -> 38*
     40(160) -> 156*
     40(147) -> 148*
     40(30) -> 52*
     40(63) -> 64*
     40(78) -> 75*
     40(41) -> 42*
     40(177) -> 178*
     40(124) -> 123*
     20(40) -> 72*
     20(122) -> 120*
     20(30) -> 157*
     20(10) -> 76*
     20(3) -> 175*
     20(86) -> 83*
     20(15) -> 112*
     20(66) -> 93*
     20(197) -> 193*
     20(169) -> 166*
     20(23) -> 24*
     20(93) -> 146*
     20(9) -> 40*
     20(141) -> 142*
     20(60) -> 57*
     20(91) -> 87*
     20(119) -> 116*
     20(80) -> 81*
     20(144) -> 143*
     20(4) -> 5*
     20(192) -> 187*
     20(42) -> 150*
     20(26) -> 62*
     20(155) -> 151*
     20(31) -> 108*
     20(132) -> 133*
     20(2) -> 66*
     30(103) -> 104*
     30(152) -> 153*
     30(2) -> 30*
     30(40) -> 41*
     30(36) -> 37*
     30(117) -> 118*
     30(4) -> 21*
     30(5) -> 6*
     30(10) -> 45*
     30(81) -> 82*
     30(42) -> 43*
     30(101) -> 98*
     30(15) -> 58*
     30(72) -> 73*
     30(62) -> 63*
     30(109) -> 110*
     30(136) -> 137*
     30(84) -> 85*
     30(94) -> 95*
     30(6) -> 124*
     30(99) -> 100*
     30(9) -> 10*
     30(113) -> 162*
     30(64) -> 61*
     30(18) -> 19*
     30(133) -> 134*
     30(26) -> 27*
     30(150) -> 149*
     30(77) -> 78*
     30(66) -> 67*
     30(195) -> 196*
     30(3) -> 88*
     30(112) -> 113*
     30(157) -> 158*
     30(146) -> 147*
     30(127) -> 165*
     30(11) -> 12*
     30(53) -> 129*
     30(67) -> 68*
     30(115) -> 111*
     30(16) -> 17*
     30(31) -> 32*
     51(317) -> 318*
     51(265) -> 266*
     51(310) -> 311*
     51(242) -> 243*
     51(259) -> 260*
     51(232) -> 233*
     41(294) -> 295*
     41(243) -> 244*
     41(216) -> 217*
     41(209) -> 210*
     41(287) -> 288*
     21(267) -> 268*
     21(285) -> 286*
     21(207) -> 208*
     21(319) -> 320*
     21(240) -> 241*
     21(239) -> 240*
     21(258) -> 259*
     31(264) -> 265*
     31(314) -> 315*
     31(257) -> 258*
     31(241) -> 242*
     31(213) -> 214*
     31(312) -> 313*
     31(236) -> 237*
     31(316) -> 317*
     31(286) -> 287*
     31(208) -> 209*
     31(291) -> 292*
     31(234) -> 235*
     31(293) -> 294*
     31(215) -> 216*
     31(260) -> 261*
     156 -> 188*
     151 -> 9,194
     56 -> 188*
     166 -> 9,16
     92 -> 188*
     131 -> 9,194
     285 -> 316*
     320 -> 36*
     168 -> 238*
     164 -> 188*
     48 -> 188*
     83 -> 188*
     182 -> 310,290,283
     140 -> 188*
     14 -> 9,35
     244 -> 35*
     180 -> 9,4
     143 -> 188*
     174 -> 188*
     237 -> 210*
     75 -> 9,194
     22 -> 188*
     116 -> 188*
     268 -> 35*
     161 -> 188*
     170 -> 188*
     79 -> 188*
     296 -> 35*
     125 -> 15*
     261 -> 243*
     179 -> 9,194
     135 -> 188*
     44 -> 188*
     71 -> 9,194
     8 -> 9,35
     123 -> 188*
     1 -> 9,35
     107 -> 188*
     193 -> 66*
     20 -> 188*
     65 -> 188*
     34 -> 188*
     187 -> 188*
     218 -> 16*
     57 -> 188*
     184 -> 188,117
     120 -> 15,26,36
     39 -> 188*
     145 -> 188*
     211 -> 16*
     149 -> 66*
     167 -> 262*
     129 -> 232,212,205
     289 -> 35*
     97 -> 188*
     51 -> 188*
     98 -> 188*
     87 -> 188*
     128 -> 15*
     315 -> 288*
     29 -> 188*
     102 -> 188*
     61 -> 188*
     25 -> 188*
     111 -> 188*
     239 -> 257*
   problem:
    
   Qed