YES

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

Proof:
 Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {308,305,301,299,297,293,290,287,284,280,275,270,268,
                  265,261,258,255,251,247,242,240,235,230,227,224,220,
                  216,212,208,203,198,194,189,186,182,176,173,170,166,
                  162,158,157,155,151,146,143,139,138,137,132,127,124,
                  120,119,117,114,112,108,104,100,96,92,89,88,86,83,77,
                  72,68,63,59,55,51,50,46,44,39,38,34,30,25,20,19,13,
                  7,1}
   transitions:
    40(200) -> 201*
    40(225) -> 226*
    40(309) -> 308*
    40(113) -> 112*
    40(252) -> 253*
    40(2) -> 14*
    40(215) -> 212*
    40(245) -> 246*
    40(75) -> 76*
    40(111) -> 108*
    40(303) -> 304*
    40(199) -> 200*
    40(37) -> 34*
    40(228) -> 229*
    40(33) -> 30*
    40(262) -> 266*
    40(250) -> 247*
    40(175) -> 173*
    40(95) -> 92*
    40(292) -> 290*
    40(302) -> 303*
    40(219) -> 216*
    40(195) -> 196*
    40(229) -> 227*
    40(81) -> 82*
    40(62) -> 59*
    40(306) -> 307*
    40(3) -> 47*
    40(256) -> 257*
    40(103) -> 100*
    40(40) -> 73*
    40(14) -> 64*
    40(271) -> 272*
    40(52) -> 101*
    40(249) -> 269*
    40(232) -> 233*
    40(116) -> 114*
    40(15) -> 69*
    40(276) -> 281*
    40(248) -> 306*
    40(107) -> 104*
    40(161) -> 158*
    40(285) -> 286*
    40(22) -> 125*
    40(118) -> 117*
    40(207) -> 203*
    40(295) -> 300*
    40(128) -> 152*
    40(54) -> 51*
    40(226) -> 224*
    40(60) -> 105*
    40(11) -> 50*
    40(211) -> 208*
    40(53) -> 174*
    40(50) -> 119*
    40(172) -> 170*
    40(177) -> 276*
    40(192) -> 193*
    40(58) -> 55*
    40(223) -> 220*
    40(99) -> 96*
    40(78) -> 236*
    40(244) -> 245*
    40(47) -> 163*
    40(8) -> 56*
    40(191) -> 192*
    40(21) -> 35*
    40(42) -> 43*
    40(286) -> 284*
    20(47) -> 294*
    20(168) -> 169*
    20(273) -> 274*
    20(179) -> 228*
    20(16) -> 45*
    20(278) -> 279*
    20(60) -> 209*
    20(142) -> 157*
    20(154) -> 151*
    20(12) -> 7*
    20(40) -> 231*
    20(82) -> 77*
    20(205) -> 206*
    20(259) -> 260*
    20(165) -> 162*
    20(180) -> 181*
    20(15) -> 121*
    20(29) -> 25*
    20(295) -> 296*
    20(1) -> 19*
    20(218) -> 219*
    20(14) -> 133*
    20(6) -> 1*
    20(84) -> 85*
    20(17) -> 38*
    20(282) -> 283*
    20(150) -> 146*
    20(254) -> 251*
    20(76) -> 72*
    20(8) -> 243*
    20(43) -> 39*
    20(71) -> 68*
    20(131) -> 127*
    20(294) -> 295*
    20(24) -> 20*
    20(67) -> 63*
    20(48) -> 49*
    20(202) -> 198*
    20(49) -> 87*
    20(133) -> 159*
    20(257) -> 255*
    20(90) -> 91*
    20(156) -> 155*
    20(177) -> 190*
    20(237) -> 238*
    20(18) -> 13*
    20(2) -> 8*
    10(22) -> 23*
    10(272) -> 273*
    10(153) -> 154*
    10(52) -> 93*
    10(3) -> 4*
    10(130) -> 131*
    10(145) -> 143*
    10(15) -> 16*
    10(178) -> 179*
    10(53) -> 54*
    10(69) -> 70*
    10(221) -> 222*
    10(197) -> 194*
    10(62) -> 113*
    10(79) -> 80*
    10(57) -> 58*
    10(64) -> 65*
    10(56) -> 97*
    10(217) -> 218*
    10(163) -> 164*
    10(27) -> 28*
    10(14) -> 147*
    10(281) -> 282*
    10(277) -> 278*
    10(238) -> 239*
    10(36) -> 37*
    10(210) -> 211*
    10(126) -> 124*
    10(106) -> 107*
    10(214) -> 215*
    10(61) -> 62*
    10(187) -> 188*
    10(123) -> 120*
    10(190) -> 191*
    10(8) -> 9*
    10(47) -> 48*
    10(243) -> 244*
    10(140) -> 141*
    10(174) -> 175*
    10(115) -> 116*
    10(133) -> 134*
    10(249) -> 250*
    10(32) -> 33*
    10(16) -> 259*
    10(110) -> 111*
    10(167) -> 168*
    10(102) -> 103*
    10(74) -> 84*
    10(177) -> 204*
    10(160) -> 161*
    10(21) -> 183*
    10(2) -> 40*
    30(243) -> 248*
    30(38) -> 88*
    30(85) -> 83*
    30(164) -> 165*
    30(147) -> 148*
    30(185) -> 182*
    30(178) -> 217*
    30(23) -> 24*
    30(2) -> 78*
    30(22) -> 187*
    30(40) -> 41*
    30(28) -> 29*
    30(283) -> 280*
    30(4) -> 5*
    30(295) -> 298*
    30(10) -> 171*
    30(97) -> 98*
    30(204) -> 205*
    30(262) -> 263*
    30(179) -> 180*
    30(70) -> 71*
    30(289) -> 287*
    30(9) -> 10*
    30(199) -> 252*
    30(128) -> 129*
    30(134) -> 135*
    30(87) -> 86*
    30(80) -> 81*
    30(8) -> 52*
    30(93) -> 94*
    30(21) -> 31*
    30(61) -> 115*
    30(48) -> 90*
    30(58) -> 241*
    30(91) -> 89*
    30(45) -> 44*
    30(222) -> 223*
    30(195) -> 285*
    30(3) -> 26*
    30(49) -> 46*
    30(141) -> 142*
    30(169) -> 166*
    30(11) -> 118*
    30(65) -> 66*
    30(35) -> 144*
    30(16) -> 17*
    30(74) -> 75*
    00(190) -> 221*
    00(52) -> 53*
    00(66) -> 67*
    00(171) -> 172*
    00(39) -> 138*
    00(233) -> 234*
    00(2) -> 3*
    00(291) -> 292*
    00(10) -> 11*
    00(122) -> 123*
    00(17) -> 18*
    00(246) -> 242*
    00(5) -> 6*
    00(133) -> 140*
    00(31) -> 32*
    00(181) -> 176*
    00(21) -> 22*
    00(135) -> 136*
    00(253) -> 254*
    00(193) -> 189*
    00(94) -> 95*
    00(248) -> 249*
    00(101) -> 102*
    00(304) -> 301*
    00(196) -> 197*
    00(236) -> 237*
    00(184) -> 185*
    00(288) -> 289*
    00(121) -> 122*
    00(276) -> 277*
    00(243) -> 262*
    00(47) -> 167*
    00(266) -> 267*
    00(3) -> 128*
    00(195) -> 225*
    00(263) -> 264*
    00(56) -> 57*
    00(109) -> 110*
    00(129) -> 130*
    00(209) -> 210*
    00(201) -> 202*
    00(149) -> 150*
    00(152) -> 153*
    00(213) -> 214*
    00(60) -> 61*
    00(38) -> 137*
    00(11) -> 12*
    00(105) -> 106*
    00(125) -> 126*
    00(8) -> 21*
    00(35) -> 36*
    00(205) -> 256*
    00(136) -> 132*
    00(58) -> 156*
    00(142) -> 139*
    00(144) -> 145*
    00(159) -> 160*
    00(14) -> 15*
    00(78) -> 79*
    00(41) -> 42*
    00(26) -> 27*
    00(206) -> 207*
    00(73) -> 74*
    00(148) -> 149*
    00(177) -> 178*
    00(98) -> 99*
    50(248) -> 291*
    50(159) -> 288*
    50(106) -> 309*
    50(234) -> 230*
    50(52) -> 109*
    50(8) -> 60*
    50(264) -> 261*
    50(296) -> 293*
    50(298) -> 297*
    50(231) -> 232*
    50(3) -> 271*
    50(2) -> 177*
    50(300) -> 299*
    50(307) -> 305*
    50(279) -> 275*
    50(239) -> 235*
    50(241) -> 240*
    50(269) -> 268*
    50(183) -> 184*
    50(9) -> 195*
    50(243) -> 302*
    50(190) -> 213*
    50(260) -> 258*
    50(188) -> 186*
    50(40) -> 199*
    50(274) -> 270*
    50(267) -> 265*
    f60() -> 2*
    247 -> 3,21
    155 -> 3*
    151 -> 128*
    166 -> 3*
    194 -> 3*
    19 -> 3*
    92 -> 3*
    132 -> 3,128
    203 -> 3*
    68 -> 3*
    242 -> 3,21
    47 -> 3*
    198 -> 3*
    83 -> 3*
    240 -> 3*
    158 -> 3*
    189 -> 3*
    46 -> 3*
    216 -> 3*
    30 -> 3*
    182 -> 3*
    290 -> 177*
    7 -> 3*
    100 -> 3*
    104 -> 3*
    77 -> 3*
    112 -> 3*
    63 -> 3*
    114 -> 3*
    284 -> 177*
    258 -> 177,271
    212 -> 3*
    265 -> 177,271
    117 -> 3*
    301 -> 177*
    143 -> 128*
    270 -> 177,199
    230 -> 3*
    124 -> 3,128
    308 -> 177*
    220 -> 3*
    173 -> 3*
    251 -> 177,271
    72 -> 3*
    186 -> 3*
    268 -> 177,271
    208 -> 3*
    170 -> 3*
    91 -> 3*
    86 -> 21,3
    235 -> 3*
    38 -> 3*
    297 -> 177*
    261 -> 177,271
    26 -> 3*
    44 -> 3*
    139 -> 128*
    13 -> 3*
    127 -> 3,128
    305 -> 177*
    287 -> 177*
    1 -> 3*
    224 -> 3*
    293 -> 177*
    20 -> 3*
    255 -> 177,271
    55 -> 3*
    275 -> 177,199
    34 -> 3*
    59 -> 3*
    108 -> 177,271,3
    146 -> 128*
    50 -> 3*
    120 -> 3,128
    39 -> 3*
    227 -> 3*
    299 -> 177*
    96 -> 3*
    51 -> 3*
    128 -> 3*
    89 -> 3*
    25 -> 3*
    176 -> 3*
    280 -> 177*
    157 -> 3*
  problem:
   
  Qed