Problem:
 3(1(x1)) -> 4(1(x1))
 5(9(x1)) -> 2(6(5(x1)))
 3(5(x1)) -> 8(9(7(x1)))
 9(x1) -> 3(2(3(x1)))
 8(4(x1)) -> 6(x1)
 2(6(x1)) -> 4(3(x1))
 3(8(x1)) -> 3(2(7(x1)))
 9(x1) -> 5(0(2(x1)))
 8(8(4(x1))) -> 1(9(x1))
 7(1(x1)) -> 6(9(x1))
 3(9(x1)) -> 9(3(x1))
 7(5(x1)) -> 1(0(x1))

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {10,9,8,7,6,5}
   transitions:
    61(59) -> 60*
    61(61) -> 62*
    61(51) -> 52*
    61(53) -> 54*
    61(105) -> 106*
    91(107) -> 108*
    91(104) -> 105*
    91(113) -> 114*
    91(115) -> 116*
    51(87) -> 88*
    01(86) -> 87*
    21(85) -> 86*
    21(97) -> 98*
    21(89) -> 90*
    21(34) -> 35*
    21(95) -> 96*
    41(75) -> 76*
    41(15) -> 16*
    41(77) -> 78*
    41(67) -> 68*
    41(69) -> 70*
    31(45) -> 46*
    31(35) -> 36*
    31(37) -> 38*
    31(43) -> 44*
    31(33) -> 34*
    11(25) -> 26*
    11(17) -> 18*
    11(14) -> 15*
    11(23) -> 24*
    52(151) -> 152*
    52(143) -> 144*
    02(142) -> 143*
    02(150) -> 151*
    22(159) -> 160*
    22(149) -> 150*
    22(124) -> 125*
    22(141) -> 142*
    22(153) -> 154*
    22(128) -> 129*
    30(2) -> 5*
    30(4) -> 5*
    30(1) -> 5*
    30(3) -> 5*
    32(137) -> 138*
    32(127) -> 128*
    32(129) -> 130*
    32(123) -> 124*
    32(135) -> 136*
    32(125) -> 126*
    10(2) -> 1*
    10(4) -> 1*
    10(1) -> 1*
    10(3) -> 1*
    40(2) -> 2*
    40(4) -> 2*
    40(1) -> 2*
    40(3) -> 2*
    50(2) -> 6*
    50(4) -> 6*
    50(1) -> 6*
    50(3) -> 6*
    90(2) -> 7*
    90(4) -> 7*
    90(1) -> 7*
    90(3) -> 7*
    20(2) -> 9*
    20(4) -> 9*
    20(1) -> 9*
    20(3) -> 9*
    60(2) -> 3*
    60(4) -> 3*
    60(1) -> 3*
    60(3) -> 3*
    80(2) -> 8*
    80(4) -> 8*
    80(1) -> 8*
    80(3) -> 8*
    70(2) -> 10*
    70(4) -> 10*
    70(1) -> 10*
    70(3) -> 10*
    00(2) -> 4*
    00(4) -> 4*
    00(1) -> 4*
    00(3) -> 4*
    1 -> 113,89,59,37,23
    2 -> 104,97,51,45,14
    3 -> 115,85,61,33,25
    4 -> 107,95,53,43,17
    16 -> 124,38,75,34,77,5
    18 -> 15*
    24 -> 15*
    26 -> 15*
    34 -> 77*
    36 -> 7*
    38 -> 75,34
    44 -> 69,34
    46 -> 67,34
    52 -> 8*
    54 -> 8*
    60 -> 8*
    62 -> 8*
    68 -> 150,86,9
    70 -> 150,86,9
    76 -> 150,86,9
    78 -> 150,86,9
    88 -> 7*
    90 -> 86*
    96 -> 86*
    98 -> 86*
    104 -> 153,135
    106 -> 10*
    107 -> 159,137
    108 -> 105*
    113 -> 141,123
    114 -> 105*
    115 -> 149,127
    116 -> 105*
    126 -> 108,114
    130 -> 116*
    136 -> 124*
    138 -> 124*
    144 -> 108,114
    152 -> 116*
    154 -> 142*
    160 -> 142*
  problem:
   
  Qed