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:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {6}
   transitions:
    51(479) -> 480*
    51(75) -> 76*
    51(469) -> 470*
    51(157) -> 158*
    51(97) -> 98*
    51(77) -> 78*
    51(471) -> 472*
    51(461) -> 462*
    51(401) -> 402*
    51(391) -> 392*
    51(386) -> 387*
    51(366) -> 367*
    51(493) -> 494*
    51(463) -> 464*
    51(453) -> 454*
    51(146) -> 147*
    51(91) -> 92*
    51(485) -> 486*
    51(455) -> 456*
    51(607) -> 608*
    51(355) -> 356*
    51(527) -> 528*
    51(517) -> 518*
    51(487) -> 488*
    51(83) -> 84*
    51(477) -> 478*
    51(599) -> 600*
    51(519) -> 520*
    51(85) -> 86*
    41(55) -> 56*
    41(197) -> 198*
    41(389) -> 390*
    41(229) -> 230*
    41(199) -> 200*
    41(189) -> 190*
    41(573) -> 574*
    41(134) -> 135*
    41(49) -> 50*
    41(191) -> 192*
    41(525) -> 526*
    41(96) -> 97*
    41(223) -> 224*
    41(183) -> 184*
    41(133) -> 134*
    41(53) -> 54*
    41(38) -> 39*
    41(145) -> 146*
    11(50) -> 51*
    11(35) -> 36*
    11(232) -> 233*
    11(15) -> 16*
    11(147) -> 148*
    11(339) -> 340*
    11(329) -> 330*
    11(117) -> 118*
    11(107) -> 108*
    11(37) -> 38*
    11(17) -> 18*
    11(109) -> 110*
    11(54) -> 55*
    11(353) -> 354*
    11(131) -> 132*
    11(323) -> 324*
    11(66) -> 67*
    11(345) -> 346*
    11(93) -> 94*
    11(362) -> 363*
    11(347) -> 348*
    11(337) -> 338*
    11(115) -> 116*
    11(307) -> 308*
    11(95) -> 96*
    01(65) -> 66*
    01(429) -> 430*
    01(207) -> 208*
    01(541) -> 542*
    01(511) -> 512*
    01(501) -> 502*
    01(249) -> 250*
    01(426) -> 427*
    01(623) -> 624*
    01(543) -> 544*
    01(533) -> 534*
    01(503) -> 504*
    01(94) -> 95*
    01(251) -> 252*
    01(443) -> 444*
    01(241) -> 242*
    01(231) -> 232*
    01(625) -> 626*
    01(221) -> 222*
    01(615) -> 616*
    01(363) -> 364*
    01(535) -> 536*
    01(495) -> 496*
    01(51) -> 52*
    01(243) -> 244*
    01(36) -> 37*
    01(435) -> 436*
    01(617) -> 618*
    01(16) -> 17*
    01(213) -> 214*
    01(597) -> 598*
    01(148) -> 149*
    01(123) -> 124*
    01(265) -> 266*
    01(437) -> 438*
    01(215) -> 216*
    01(609) -> 610*
    01(205) -> 206*
    01(377) -> 378*
    01(549) -> 550*
    01(125) -> 126*
    01(509) -> 510*
    21(25) -> 26*
    21(409) -> 410*
    21(591) -> 592*
    21(581) -> 582*
    21(299) -> 300*
    21(289) -> 290*
    21(264) -> 265*
    21(27) -> 28*
    21(411) -> 412*
    21(583) -> 584*
    21(331) -> 332*
    21(321) -> 322*
    21(291) -> 292*
    21(19) -> 20*
    21(403) -> 404*
    21(600) -> 601*
    21(575) -> 576*
    21(283) -> 284*
    21(445) -> 446*
    21(400) -> 401*
    21(375) -> 376*
    21(315) -> 316*
    21(33) -> 34*
    21(427) -> 428*
    21(417) -> 418*
    21(13) -> 14*
    21(589) -> 590*
    21(367) -> 368*
    21(297) -> 298*
    31(267) -> 268*
    31(257) -> 258*
    31(419) -> 420*
    31(167) -> 168*
    31(551) -> 552*
    31(67) -> 68*
    31(446) -> 447*
    31(159) -> 160*
    31(149) -> 150*
    31(281) -> 282*
    31(14) -> 15*
    31(181) -> 182*
    31(565) -> 566*
    31(151) -> 152*
    31(313) -> 314*
    31(273) -> 274*
    31(263) -> 264*
    31(233) -> 234*
    31(390) -> 391*
    31(385) -> 386*
    31(173) -> 174*
    31(567) -> 568*
    31(365) -> 366*
    31(557) -> 558*
    31(305) -> 306*
    31(275) -> 276*
    31(63) -> 64*
    31(387) -> 388*
    31(175) -> 176*
    31(165) -> 166*
    31(559) -> 560*
    02(665) -> 666*
    02(639) -> 640*
    00(5) -> 6*
    00(2) -> 6*
    00(4) -> 6*
    00(1) -> 6*
    00(3) -> 6*
    32(638) -> 639*
    32(664) -> 665*
    10(5) -> 1*
    10(2) -> 1*
    10(4) -> 1*
    10(1) -> 1*
    10(3) -> 1*
    52(663) -> 664*
    52(637) -> 638*
    20(5) -> 2*
    20(2) -> 2*
    20(4) -> 2*
    20(1) -> 2*
    20(3) -> 2*
    42(636) -> 637*
    42(662) -> 663*
    30(5) -> 3*
    30(2) -> 3*
    30(4) -> 3*
    30(1) -> 3*
    30(3) -> 3*
    12(661) -> 662*
    12(651) -> 652*
    12(641) -> 642*
    12(653) -> 654*
    12(635) -> 636*
    12(659) -> 660*
    40(5) -> 4*
    40(2) -> 4*
    40(4) -> 4*
    40(1) -> 4*
    40(3) -> 4*
    50(5) -> 5*
    50(2) -> 5*
    50(4) -> 5*
    50(1) -> 5*
    50(3) -> 5*
    1 -> 249,197,175,115,85,27
    2 -> 241,189,167,107,77,19
    3 -> 251,199,181,117,91,33
    4 -> 243,191,173,109,83,25
    5 -> 231,183,165,93,75,13
    14 -> 607,65,35
    15 -> 527*
    16 -> 49*
    18 -> 250,232,95,315,599,6
    20 -> 14*
    26 -> 14*
    28 -> 14*
    34 -> 14*
    36 -> 445,63,53
    37 -> 419,133
    39 -> 616,244,37,133,419,66,242,250,232,95,315,599,355,331,229,151,123,6
    52 -> 616,244,66,242,37,133,419,250,232,95,315,599,519,6
    54 -> 377*
    56 -> 51*
    64 -> 131,36
    67 -> 223*
    68 -> 37*
    75 -> 653*
    76 -> 283,263,205,35
    77 -> 635*
    78 -> 289,267,207,35
    83 -> 651*
    84 -> 291,273,213,35
    85 -> 659*
    86 -> 297,275,215,35
    91 -> 641*
    92 -> 299,281,221,35
    94 -> 313,145
    95 -> 385,157
    97 -> 321*
    98 -> 244,610,250,232,95,315,599,159,125,6
    108 -> 94*
    110 -> 94*
    116 -> 94*
    118 -> 94*
    124 -> 616,244,66,37,133,419,242,250,232,95,315,599,6
    126 -> 250,232,95,315,599,6
    132 -> 16*
    135 -> 616,244,66,242,250,232,95,315,599,6,17
    146 -> 525,375,365,329
    147 -> 597,257
    150 -> 616,244,250,232,95,315,599,6
    152 -> 250,232,95,315,599,6
    158 -> 427,252,250,232,95,315,599,37
    160 -> 250,232,95,315,599,6
    166 -> 426,400,75
    168 -> 429,403,75
    174 -> 435,409,75
    176 -> 437,411,75
    182 -> 443,417,75
    184 -> 609,575,75
    190 -> 615,581,75
    192 -> 617,583,75
    198 -> 623,589,75
    200 -> 625,591,75
    206 -> 551,533,477,66
    208 -> 557,535,479,66
    214 -> 559,541,485,66
    216 -> 565,543,487,66
    222 -> 567,549,493,66
    224 -> 37*
    230 -> 250,232,95,315,599,6
    232 -> 599,573,315
    233 -> 389*
    234 -> 95*
    242 -> 232*
    244 -> 232*
    250 -> 232*
    252 -> 232*
    258 -> 51*
    264 -> 307*
    265 -> 362,305
    266 -> 38*
    268 -> 264*
    274 -> 264*
    276 -> 264*
    282 -> 264*
    284 -> 455,337,36
    290 -> 461,339,36
    292 -> 463,345,36
    298 -> 469,347,36
    300 -> 471,353,36
    306 -> 265*
    308 -> 36*
    314 -> 323,94
    316 -> 616,244,37,133,419,250,232,95,315,599,517,66
    322 -> 38*
    324 -> 96*
    330 -> 96*
    332 -> 66,242,6
    338 -> 49*
    340 -> 49*
    346 -> 49*
    348 -> 49*
    354 -> 49*
    356 -> 6*
    364 -> 51*
    368 -> 51*
    376 -> 146*
    378 -> 331*
    388 -> 331*
    392 -> 331*
    401 -> 661*
    402 -> 36*
    404 -> 401*
    410 -> 401*
    412 -> 401*
    418 -> 401*
    420 -> 37*
    428 -> 157*
    430 -> 427*
    436 -> 427*
    438 -> 427*
    444 -> 427*
    446 -> 453*
    447 -> 367*
    454 -> 257*
    456 -> 495,37
    462 -> 501,37
    464 -> 503,37
    470 -> 509,37
    472 -> 511,37
    478 -> 37*
    480 -> 37*
    486 -> 37*
    488 -> 37*
    494 -> 37*
    496 -> 37*
    502 -> 37*
    504 -> 37*
    510 -> 37*
    512 -> 37*
    518 -> 157*
    520 -> 6*
    526 -> 366*
    528 -> 37*
    534 -> 37*
    536 -> 37*
    542 -> 37*
    544 -> 37*
    550 -> 37*
    552 -> 37*
    558 -> 37*
    560 -> 37*
    566 -> 37*
    568 -> 37*
    574 -> 157*
    576 -> 146*
    582 -> 146*
    584 -> 146*
    590 -> 146*
    592 -> 146*
    598 -> 149*
    601 -> 67*
    608 -> 35*
    610 -> 157*
    616 -> 157*
    618 -> 157*
    624 -> 157*
    626 -> 157*
    640 -> 37,133,419
    642 -> 636*
    652 -> 636*
    654 -> 636*
    660 -> 636*
    666 -> 17*
  problem:
   
  Qed