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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {6,5}
   transitions:
    51(55) -> 56*
    51(134) -> 135*
    51(39) -> 40*
    51(201) -> 202*
    51(151) -> 152*
    51(183) -> 184*
    51(153) -> 154*
    51(143) -> 144*
    51(88) -> 89*
    51(145) -> 146*
    51(130) -> 131*
    21(187) -> 188*
    21(67) -> 68*
    21(47) -> 48*
    21(174) -> 175*
    21(79) -> 80*
    21(69) -> 70*
    21(49) -> 50*
    21(81) -> 82*
    21(41) -> 42*
    21(133) -> 134*
    21(73) -> 74*
    21(38) -> 39*
    21(200) -> 201*
    21(105) -> 106*
    41(197) -> 198*
    41(92) -> 93*
    41(219) -> 220*
    41(89) -> 90*
    41(221) -> 222*
    41(19) -> 20*
    41(211) -> 212*
    41(213) -> 214*
    41(173) -> 174*
    41(68) -> 69*
    41(195) -> 196*
    41(185) -> 186*
    41(135) -> 136*
    11(70) -> 71*
    11(172) -> 173*
    11(57) -> 58*
    11(37) -> 38*
    11(27) -> 28*
    11(199) -> 200*
    11(169) -> 170*
    11(159) -> 160*
    11(94) -> 95*
    11(29) -> 30*
    11(14) -> 15*
    11(186) -> 187*
    11(161) -> 162*
    11(131) -> 132*
    11(91) -> 92*
    11(21) -> 22*
    11(16) -> 17*
    11(198) -> 199*
    11(18) -> 19*
    31(15) -> 16*
    31(162) -> 163*
    31(107) -> 108*
    31(17) -> 18*
    31(171) -> 172*
    31(121) -> 122*
    31(71) -> 72*
    31(123) -> 124*
    31(113) -> 114*
    31(93) -> 94*
    31(115) -> 116*
    31(95) -> 96*
    42(237) -> 238*
    12(257) -> 258*
    12(232) -> 233*
    12(234) -> 235*
    12(251) -> 252*
    12(236) -> 237*
    12(253) -> 254*
    12(243) -> 244*
    12(245) -> 246*
    00(2) -> 5*
    00(4) -> 5*
    00(1) -> 5*
    00(3) -> 5*
    32(233) -> 234*
    32(235) -> 236*
    10(2) -> 1*
    10(4) -> 1*
    10(1) -> 1*
    10(3) -> 1*
    20(2) -> 2*
    20(4) -> 2*
    20(1) -> 2*
    20(3) -> 2*
    30(2) -> 3*
    30(4) -> 3*
    30(1) -> 3*
    30(3) -> 3*
    40(2) -> 6*
    40(4) -> 6*
    40(1) -> 6*
    40(3) -> 6*
    50(2) -> 4*
    50(4) -> 4*
    50(1) -> 4*
    50(3) -> 4*
    1 -> 213,151,121,79,27
    2 -> 197,143,113,67,14
    3 -> 219,153,123,81,29
    4 -> 211,145,115,73,21
    14 -> 245*
    15 -> 133,37
    17 -> 185,47
    20 -> 220,212,222,214,198,200,57,6
    21 -> 251*
    22 -> 15*
    27 -> 232*
    28 -> 15*
    29 -> 243*
    30 -> 15*
    37 -> 253*
    38 -> 221,171,169
    39 -> 49*
    40 -> 159,55,41,19
    42 -> 19*
    48 -> 195,39
    50 -> 39*
    56 -> 19*
    58 -> 220,222,214,198,200,6
    68 -> 105,91,88
    69 -> 130*
    72 -> 57*
    74 -> 68*
    80 -> 68*
    82 -> 68*
    90 -> 70*
    92 -> 107*
    95 -> 183*
    96 -> 220,198,6
    106 -> 16*
    108 -> 17*
    114 -> 16*
    116 -> 16*
    122 -> 16*
    124 -> 16*
    132 -> 94*
    135 -> 161*
    136 -> 94*
    144 -> 15*
    146 -> 15*
    152 -> 15*
    154 -> 15*
    160 -> 19*
    163 -> 19*
    169 -> 257*
    170 -> 38*
    175 -> 212,198,6
    184 -> 212,198,6
    188 -> 183*
    196 -> 183*
    202 -> 183*
    212 -> 198*
    214 -> 198*
    220 -> 198*
    222 -> 200*
    238 -> 222,200
    244 -> 233*
    246 -> 233*
    252 -> 233*
    254 -> 233*
    258 -> 233*
  problem:
   
  Qed