YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {161,156,155,152,148,142,140,137,136,132,128,123,118,
                  116,113,112,109,108,104,100,98,95,91,87,86,82,78,73,
                  70,64,60,56,50,48,44,42,37,32,28,24,22,19,16,11,7,1}
   transitions:
    11(257) -> 258*
    11(241) -> 242*
    11(304) -> 305*
    11(168) -> 169*
    11(193) -> 194*
    11(252) -> 253*
    11(294) -> 295*
    11(229) -> 230*
    11(207) -> 208*
    01(268) -> 269*
    01(240) -> 241*
    01(209) -> 210*
    01(271) -> 272*
    01(219) -> 220*
    01(167) -> 168*
    01(206) -> 207*
    01(169) -> 170*
    01(292) -> 293*
    01(254) -> 255*
    01(266) -> 267*
    00(119) -> 149*
    00(160) -> 156*
    00(31) -> 28*
    00(143) -> 144*
    00(75) -> 76*
    00(101) -> 102*
    00(93) -> 94*
    00(52) -> 53*
    00(15) -> 11*
    00(130) -> 131*
    00(29) -> 30*
    00(139) -> 137*
    00(121) -> 122*
    00(6) -> 1*
    00(17) -> 18*
    00(164) -> 161*
    00(3) -> 25*
    00(38) -> 39*
    00(124) -> 125*
    00(8) -> 20*
    00(4) -> 5*
    00(36) -> 32*
    00(80) -> 81*
    00(79) -> 133*
    00(105) -> 106*
    00(10) -> 7*
    00(134) -> 135*
    00(65) -> 66*
    00(46) -> 47*
    00(2) -> 51*
    f60() -> 2*
    50(81) -> 78*
    50(153) -> 154*
    50(51) -> 83*
    50(102) -> 103*
    50(115) -> 113*
    50(30) -> 43*
    50(3) -> 119*
    50(2) -> 65*
    50(83) -> 88*
    50(162) -> 163*
    50(4) -> 96*
    50(144) -> 145*
    50(85) -> 82*
    50(76) -> 77*
    50(126) -> 127*
    50(9) -> 99*
    50(61) -> 62*
    50(157) -> 158*
    50(65) -> 157*
    50(135) -> 132*
    50(146) -> 147*
    50(31) -> 112*
    50(90) -> 87*
    40(2) -> 143*
    40(71) -> 72*
    40(111) -> 109*
    40(79) -> 80*
    40(163) -> 164*
    40(65) -> 124*
    40(133) -> 134*
    40(74) -> 75*
    40(3) -> 38*
    40(145) -> 146*
    40(159) -> 160*
    40(89) -> 90*
    40(92) -> 162*
    40(84) -> 85*
    40(4) -> 29*
    40(129) -> 130*
    10(138) -> 139*
    10(39) -> 40*
    10(141) -> 140*
    10(2) -> 74*
    10(122) -> 118*
    10(67) -> 68*
    10(103) -> 100*
    10(5) -> 6*
    10(62) -> 63*
    10(21) -> 19*
    10(27) -> 24*
    10(83) -> 84*
    10(94) -> 91*
    10(12) -> 13*
    10(54) -> 55*
    10(9) -> 10*
    10(57) -> 71*
    10(154) -> 152*
    10(97) -> 95*
    10(40) -> 49*
    10(18) -> 16*
    10(88) -> 89*
    10(131) -> 128*
    10(110) -> 111*
    10(77) -> 73*
    10(43) -> 42*
    10(99) -> 98*
    10(125) -> 126*
    10(34) -> 35*
    10(8) -> 45*
    10(58) -> 59*
    10(30) -> 31*
    10(78) -> 136*
    10(41) -> 37*
    10(81) -> 117*
    10(73) -> 86*
    10(23) -> 22*
    10(151) -> 148*
    10(65) -> 79*
    10(106) -> 107*
    10(114) -> 115*
    30(5) -> 23*
    30(96) -> 97*
    30(52) -> 57*
    30(3) -> 8*
    30(33) -> 34*
    30(53) -> 54*
    30(66) -> 67*
    30(57) -> 58*
    30(93) -> 110*
    30(92) -> 105*
    30(150) -> 151*
    30(4) -> 17*
    30(147) -> 142*
    30(26) -> 27*
    30(120) -> 138*
    30(95) -> 108*
    30(117) -> 116*
    30(21) -> 141*
    30(45) -> 46*
    30(25) -> 61*
    30(2) -> 12*
    20(12) -> 33*
    20(20) -> 21*
    20(69) -> 64*
    20(2) -> 3*
    20(40) -> 41*
    20(47) -> 44*
    20(14) -> 15*
    20(63) -> 60*
    20(107) -> 104*
    20(13) -> 14*
    20(55) -> 50*
    20(149) -> 150*
    20(39) -> 114*
    20(72) -> 70*
    20(119) -> 120*
    20(59) -> 56*
    20(68) -> 69*
    20(8) -> 9*
    20(66) -> 129*
    20(33) -> 101*
    20(25) -> 26*
    20(3) -> 4*
    20(95) -> 155*
    20(105) -> 153*
    20(158) -> 159*
    20(120) -> 121*
    20(49) -> 48*
    20(92) -> 93*
    20(127) -> 123*
    20(65) -> 92*
    20(35) -> 36*
    20(51) -> 52*
    41(239) -> 240*
    41(225) -> 226*
    41(305) -> 306*
    31(217) -> 218*
    31(293) -> 294*
    31(181) -> 182*
    31(279) -> 280*
    31(192) -> 193*
    31(253) -> 254*
    31(269) -> 270*
    31(205) -> 206*
    31(277) -> 278*
    31(228) -> 229*
    31(197) -> 198*
    21(195) -> 196*
    21(255) -> 256*
    21(319) -> 320*
    21(194) -> 195*
    21(179) -> 180*
    21(325) -> 326*
    21(227) -> 228*
    21(182) -> 183*
    21(165) -> 166*
    21(317) -> 318*
    21(295) -> 296*
    21(166) -> 167*
    21(309) -> 310*
    21(267) -> 268*
    21(210) -> 211*
    21(308) -> 309*
    51(307) -> 308*
    51(297) -> 298*
    51(243) -> 244*
    51(280) -> 281*
    51(291) -> 292*
    196 -> 169*
    156 -> 308,65,119
    56 -> 51*
    166 -> 307,239,219,181
    70 -> 51*
    19 -> 51*
    24 -> 51*
    92 -> 308,65,119
    142 -> 12*
    132 -> 51*
    320 -> 166*
    148 -> 65,83
    242 -> 257,210
    168 -> 243,217
    198 -> 193*
    48 -> 51*
    256 -> 133*
    115 -> 317*
    278 -> 304,269
    310 -> 206*
    64 -> 51*
    137 -> 272,267,51,66
    42 -> 51*
    182 -> 252,209
    113 -> 65*
    7 -> 51*
    100 -> 65*
    140 -> 12*
    104 -> 65*
    112 -> 65*
    306 -> 255*
    16 -> 51*
    318 -> 166*
    281 -> 257*
    258 -> 255*
    244 -> 207*
    118 -> 51*
    28 -> 51*
    11 -> 51*
    180 -> 166*
    2 -> 325*
    82 -> 51*
    270 -> 257*
    230 -> 195*
    22 -> 51*
    109 -> 65*
    220 -> 279,182
    116 -> 51*
    268 -> 277*
    161 -> 308,65,119
    208 -> 133*
    170 -> 133*
    91 -> 65*
    296 -> 255*
    86 -> 51*
    73 -> 51*
    44 -> 51*
    60 -> 51*
    183 -> 168*
    123 -> 51*
    1 -> 51*
    31 -> 319*
    107 -> 291,266,192,165
    193 -> 227*
    65 -> 297,271,197,179
    95 -> 65*
    37 -> 51*
    298 -> 292*
    108 -> 65*
    218 -> 207*
    50 -> 51*
    226 -> 167*
    211 -> 207*
    167 -> 225,205
    136 -> 51,133
    326 -> 166*
    98 -> 65*
    152 -> 65*
    87 -> 51*
    128 -> 51*
    32 -> 51*
    78 -> 51*
    272 -> 267*
  problem:
   
  Qed