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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {6,5}
   transitions:
    31(32) -> 33*
    31(7) -> 8*
    31(179) -> 180*
    31(29) -> 30*
    31(21) -> 22*
    31(138) -> 139*
    31(23) -> 24*
    51(97) -> 98*
    51(77) -> 78*
    51(119) -> 120*
    51(181) -> 182*
    51(76) -> 77*
    51(163) -> 164*
    51(103) -> 104*
    51(190) -> 191*
    51(175) -> 176*
    51(140) -> 141*
    51(105) -> 106*
    51(95) -> 96*
    51(85) -> 86*
    11(50) -> 51*
    11(127) -> 128*
    11(189) -> 190*
    11(149) -> 150*
    11(129) -> 130*
    11(9) -> 10*
    11(161) -> 162*
    11(121) -> 122*
    11(116) -> 117*
    11(178) -> 179*
    11(73) -> 74*
    11(115) -> 116*
    01(75) -> 76*
    01(152) -> 153*
    01(52) -> 53*
    01(164) -> 165*
    01(139) -> 140*
    01(11) -> 12*
    01(188) -> 189*
    01(118) -> 119*
    41(65) -> 66*
    41(10) -> 11*
    41(187) -> 188*
    41(182) -> 183*
    41(117) -> 118*
    41(74) -> 75*
    41(49) -> 50*
    41(151) -> 152*
    41(141) -> 142*
    41(71) -> 72*
    41(51) -> 52*
    41(143) -> 144*
    41(63) -> 64*
    21(177) -> 178*
    21(87) -> 88*
    21(47) -> 48*
    21(39) -> 40*
    21(176) -> 177*
    21(86) -> 87*
    21(41) -> 42*
    21(31) -> 32*
    21(153) -> 154*
    21(53) -> 54*
    21(8) -> 9*
    00(2) -> 5*
    00(4) -> 5*
    00(1) -> 5*
    00(3) -> 5*
    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) -> 6*
    30(4) -> 6*
    30(1) -> 6*
    30(3) -> 6*
    40(2) -> 3*
    40(4) -> 3*
    40(1) -> 3*
    40(3) -> 3*
    50(2) -> 4*
    50(4) -> 4*
    50(1) -> 4*
    50(3) -> 4*
    1 -> 127,97,65,41,23
    2 -> 115,85,49,31,7
    3 -> 129,103,71,47,29
    4 -> 121,95,63,39,21
    8 -> 143*
    12 -> 30,8,143,6,5
    22 -> 8*
    24 -> 8*
    30 -> 8*
    32 -> 187,105,73
    33 -> 9*
    40 -> 32*
    42 -> 32*
    48 -> 32*
    50 -> 175*
    54 -> 5*
    64 -> 50*
    66 -> 50*
    72 -> 50*
    75 -> 163*
    77 -> 5*
    78 -> 5*
    87 -> 181*
    88 -> 149,10
    96 -> 86*
    98 -> 86*
    104 -> 86*
    106 -> 161,87
    116 -> 151*
    117 -> 138*
    120 -> 53*
    122 -> 116*
    128 -> 116*
    130 -> 116*
    142 -> 5*
    144 -> 8*
    150 -> 10*
    154 -> 75*
    162 -> 74*
    165 -> 11*
    180 -> 22,33,8,143,9,6
    183 -> 178*
    191 -> 179*
  problem:
   
  Qed