YES

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

Proof:
 String Reversal Processor:
  1(0(0(x1))) -> 3(1(2(0(0(x1)))))
  1(0(0(x1))) -> 1(3(2(2(0(0(x1))))))
  1(4(0(x1))) -> 1(2(2(4(0(x1)))))
  1(4(0(x1))) -> 2(4(1(3(2(0(x1))))))
  1(0(1(x1))) -> 1(1(2(0(x1))))
  1(0(1(x1))) -> 2(1(1(2(0(x1)))))
  1(0(1(x1))) -> 1(2(3(0(1(x1)))))
  0(4(1(x1))) -> 2(4(2(3(0(1(x1))))))
  1(4(1(x1))) -> 1(1(2(4(x1))))
  1(4(1(x1))) -> 1(2(1(1(2(4(x1))))))
  1(0(4(x1))) -> 1(2(0(4(x1))))
  1(0(5(x1))) -> 1(2(0(5(x1))))
  1(0(5(x1))) -> 3(5(1(2(0(x1)))))
  1(0(5(x1))) -> 5(5(1(2(3(0(x1))))))
  1(0(5(x1))) -> 1(5(3(2(0(3(x1))))))
  5(0(5(x1))) -> 5(3(5(2(3(0(x1))))))
  1(4(5(x1))) -> 3(1(5(2(4(2(x1))))))
  1(4(5(x1))) -> 3(3(1(2(5(4(x1))))))
  5(4(0(0(x1)))) -> 2(4(2(0(5(0(x1))))))
  0(2(1(0(x1)))) -> 0(1(2(0(2(x1)))))
  1(0(2(0(x1)))) -> 3(1(2(0(0(x1)))))
  0(4(3(0(x1)))) -> 3(0(0(4(2(3(x1))))))
  4(0(4(0(x1)))) -> 4(4(2(3(0(0(x1))))))
  4(1(0(1(x1)))) -> 0(4(1(1(3(2(x1))))))
  1(3(0(1(x1)))) -> 0(1(1(3(2(4(x1))))))
  4(0(2(1(x1)))) -> 2(3(0(2(4(1(x1))))))
  4(0(3(1(x1)))) -> 3(1(2(3(0(4(x1))))))
  5(1(4(1(x1)))) -> 4(1(5(2(1(2(x1))))))
  1(5(0(4(x1)))) -> 5(1(2(4(2(0(x1))))))
  0(0(1(4(x1)))) -> 0(0(4(1(2(3(x1))))))
  4(0(1(4(x1)))) -> 1(2(0(4(4(x1)))))
  1(0(0(5(x1)))) -> 0(1(5(2(3(0(x1))))))
  1(3(0(5(x1)))) -> 1(2(3(5(0(x1)))))
  1(3(0(5(x1)))) -> 1(2(2(5(3(0(x1))))))
  1(5(0(5(x1)))) -> 0(1(3(5(2(5(x1))))))
  1(4(2(5(x1)))) -> 5(2(4(1(2(x1)))))
  5(1(4(5(x1)))) -> 1(2(5(5(4(x1)))))
  5(1(4(5(x1)))) -> 5(2(4(5(1(2(x1))))))
  1(3(4(5(x1)))) -> 3(1(2(4(5(x1)))))
  1(3(4(5(x1)))) -> 1(2(4(2(5(3(x1))))))
  1(3(4(5(x1)))) -> 1(2(3(4(2(5(x1))))))
  4(0(5(5(x1)))) -> 2(4(5(2(0(5(x1))))))
  1(3(3(0(0(x1))))) -> 3(2(1(0(3(0(x1))))))
  1(3(4(2(0(x1))))) -> 2(4(1(3(2(0(x1))))))
  1(1(4(5(0(x1))))) -> 1(1(5(2(0(4(x1))))))
  1(3(4(2(1(x1))))) -> 4(1(3(3(2(1(x1))))))
  1(3(0(0(4(x1))))) -> 0(1(2(3(0(4(x1))))))
  1(3(0(0(4(x1))))) -> 1(0(0(2(3(4(x1))))))
  5(0(0(1(5(x1))))) -> 5(1(2(0(0(5(x1))))))
  1(0(2(4(5(x1))))) -> 1(2(0(4(5(2(x1))))))
  Bounds Processor:
   bound: 1
   enrichment: match
   automaton:
    final states: {184,180,175,174,169,166,162,159,155,150,146,142,139,
                   136,131,127,124,122,118,114,110,105,101,96,92,87,83,
                   78,74,69,64,58,55,49,44,42,38,35,33,29,27,22,21,19,
                   14,10,7,1}
    transitions:
     40(2) -> 30*
     40(115) -> 116*
     40(23) -> 97*
     40(109) -> 105*
     40(79) -> 80*
     40(85) -> 86*
     40(185) -> 186*
     40(173) -> 169*
     40(30) -> 119*
     40(3) -> 11*
     40(72) -> 73*
     40(15) -> 111*
     40(39) -> 147*
     40(90) -> 91*
     40(59) -> 60*
     40(26) -> 28*
     40(152) -> 153*
     40(86) -> 83*
     40(160) -> 161*
     40(132) -> 156*
     40(106) -> 137*
     40(17) -> 18*
     40(143) -> 144*
     31(260) -> 261*
     31(246) -> 247*
     31(218) -> 219*
     31(274) -> 275*
     31(202) -> 203*
     31(225) -> 226*
     31(199) -> 200*
     41(227) -> 228*
     41(220) -> 221*
     41(262) -> 263*
     41(276) -> 277*
     41(248) -> 249*
     30(171) -> 172*
     30(68) -> 64*
     30(31) -> 93*
     30(59) -> 88*
     30(82) -> 78*
     30(52) -> 53*
     30(165) -> 162*
     30(15) -> 16*
     30(70) -> 125*
     30(6) -> 1*
     30(3) -> 45*
     30(104) -> 101*
     30(63) -> 58*
     30(8) -> 9*
     30(4) -> 84*
     30(43) -> 42*
     30(24) -> 25*
     30(36) -> 102*
     30(30) -> 176*
     30(170) -> 171*
     30(99) -> 100*
     30(67) -> 68*
     30(133) -> 134*
     30(156) -> 157*
     30(56) -> 57*
     30(149) -> 146*
     30(2) -> 50*
     00(40) -> 181*
     00(30) -> 36*
     00(104) -> 174*
     00(81) -> 82*
     00(3) -> 4*
     00(178) -> 179*
     00(39) -> 40*
     00(116) -> 117*
     00(23) -> 24*
     00(135) -> 131*
     00(123) -> 122*
     00(91) -> 87*
     00(70) -> 71*
     00(119) -> 120*
     00(80) -> 81*
     00(77) -> 74*
     00(59) -> 75*
     00(50) -> 51*
     00(98) -> 99*
     00(186) -> 187*
     00(177) -> 178*
     00(95) -> 92*
     00(117) -> 114*
     00(45) -> 163*
     00(2) -> 3*
     21(226) -> 227*
     21(197) -> 198*
     21(221) -> 222*
     21(201) -> 202*
     21(228) -> 229*
     21(275) -> 276*
     21(247) -> 248*
     21(219) -> 220*
     21(263) -> 264*
     21(249) -> 250*
     21(277) -> 278*
     21(261) -> 262*
     20(153) -> 154*
     20(12) -> 13*
     20(100) -> 96*
     20(176) -> 177*
     20(164) -> 165*
     20(147) -> 148*
     20(23) -> 170*
     20(2) -> 59*
     20(40) -> 41*
     20(36) -> 37*
     20(28) -> 27*
     20(181) -> 182*
     20(4) -> 5*
     20(5) -> 8*
     20(97) -> 98*
     20(161) -> 159*
     20(39) -> 132*
     20(102) -> 103*
     20(71) -> 72*
     20(75) -> 76*
     20(187) -> 188*
     20(84) -> 85*
     20(60) -> 61*
     20(151) -> 152*
     20(18) -> 14*
     20(128) -> 129*
     20(111) -> 112*
     20(29) -> 34*
     20(106) -> 107*
     20(140) -> 141*
     20(50) -> 79*
     20(125) -> 126*
     20(45) -> 46*
     20(129) -> 130*
     20(25) -> 26*
     20(3) -> 15*
     20(144) -> 145*
     20(120) -> 121*
     20(157) -> 158*
     20(30) -> 31*
     20(73) -> 69*
     20(11) -> 12*
     20(19) -> 21*
     20(65) -> 66*
     20(137) -> 138*
     20(51) -> 52*
     11(244) -> 245*
     11(258) -> 259*
     11(198) -> 199*
     11(203) -> 204*
     11(272) -> 273*
     11(216) -> 217*
     11(223) -> 224*
     10(89) -> 90*
     10(16) -> 17*
     10(66) -> 67*
     10(188) -> 184*
     10(141) -> 139*
     10(2) -> 23*
     10(93) -> 94*
     10(103) -> 104*
     10(5) -> 6*
     10(62) -> 63*
     10(31) -> 32*
     10(13) -> 10*
     10(20) -> 19*
     10(15) -> 20*
     10(94) -> 95*
     10(54) -> 49*
     10(163) -> 164*
     10(9) -> 7*
     10(154) -> 150*
     10(121) -> 118*
     10(172) -> 173*
     10(46) -> 47*
     10(88) -> 89*
     10(56) -> 123*
     10(158) -> 155*
     10(79) -> 115*
     10(134) -> 135*
     10(167) -> 168*
     10(32) -> 29*
     10(168) -> 166*
     10(112) -> 113*
     10(34) -> 33*
     10(179) -> 175*
     10(130) -> 127*
     10(108) -> 109*
     10(37) -> 35*
     10(59) -> 106*
     10(76) -> 77*
     10(41) -> 38*
     10(26) -> 22*
     10(148) -> 149*
     10(126) -> 124*
     10(182) -> 183*
     01(196) -> 197*
     01(259) -> 260*
     01(224) -> 225*
     01(273) -> 274*
     01(217) -> 218*
     01(245) -> 246*
     01(195) -> 196*
     50(57) -> 55*
     50(106) -> 143*
     50(47) -> 48*
     50(37) -> 167*
     50(107) -> 108*
     50(30) -> 65*
     50(41) -> 160*
     50(45) -> 128*
     50(3) -> 70*
     50(2) -> 39*
     50(113) -> 110*
     50(145) -> 142*
     50(50) -> 151*
     50(183) -> 180*
     50(46) -> 56*
     50(61) -> 62*
     50(53) -> 54*
     50(20) -> 43*
     50(65) -> 140*
     50(48) -> 44*
     50(132) -> 133*
     50(59) -> 185*
     50(138) -> 136*
     f60() -> 2*
     155 -> 23*
     166 -> 23*
     27 -> 3,36
     19 -> 23*
     92 -> 23*
     74 -> 3,75
     131 -> 23*
     142 -> 39*
     159 -> 30,11
     250 -> 40*
     198 -> 201*
     83 -> 30,11
     278 -> 24*
     35 -> 23*
     162 -> 23*
     64 -> 23*
     42 -> 23*
     69 -> 39,65
     7 -> 23*
     169 -> 23*
     14 -> 23*
     114 -> 3,4
     118 -> 30,11
     180 -> 39,70
     204 -> 175*
     264 -> 120*
     174 -> 23*
     124 -> 23*
     105 -> 39*
     22 -> 23*
     121 -> 258*
     172 -> 272*
     150 -> 23*
     21 -> 23*
     177 -> 195*
     58 -> 23*
     79 -> 223*
     38 -> 23*
     44 -> 23*
     139 -> 39*
     101 -> 30,11
     222 -> 87*
     127 -> 23*
     1 -> 23*
     49 -> 23*
     175 -> 23*
     55 -> 39,70
     110 -> 23*
     108 -> 244*
     146 -> 23*
     184 -> 23*
     122 -> 23*
     136 -> 23*
     96 -> 30,11
     10 -> 23*
     229 -> 117*
     87 -> 30,97
     89 -> 216*
     29 -> 23*
     200 -> 175*
     33 -> 23*
     78 -> 3,36
   problem:
    
   Qed