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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {6,5}
   transitions:
    51(80) -> 81*
    51(167) -> 168*
    51(117) -> 118*
    51(159) -> 160*
    51(171) -> 172*
    51(161) -> 162*
    51(101) -> 102*
    51(153) -> 154*
    51(123) -> 124*
    51(170) -> 171*
    51(150) -> 151*
    51(115) -> 116*
    21(62) -> 63*
    21(169) -> 170*
    21(104) -> 105*
    21(99) -> 100*
    21(79) -> 80*
    21(91) -> 92*
    21(93) -> 94*
    11(50) -> 51*
    11(10) -> 11*
    11(82) -> 83*
    11(77) -> 78*
    11(69) -> 70*
    11(59) -> 60*
    11(71) -> 72*
    11(61) -> 62*
    11(133) -> 134*
    11(103) -> 104*
    31(132) -> 133*
    31(102) -> 103*
    31(49) -> 50*
    31(9) -> 10*
    31(151) -> 152*
    31(141) -> 142*
    31(81) -> 82*
    31(143) -> 144*
    31(135) -> 136*
    41(45) -> 46*
    41(47) -> 48*
    41(37) -> 38*
    41(39) -> 40*
    41(31) -> 32*
    41(48) -> 49*
    41(8) -> 9*
    41(125) -> 126*
    01(7) -> 8*
    01(29) -> 30*
    01(21) -> 22*
    01(11) -> 12*
    01(23) -> 24*
    01(105) -> 106*
    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) -> 6*
    20(4) -> 6*
    20(1) -> 6*
    20(3) -> 6*
    30(2) -> 2*
    30(4) -> 2*
    30(1) -> 2*
    30(3) -> 2*
    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 -> 117,93,39,23
    2 -> 101,79,31,7
    3 -> 123,99,45,29
    4 -> 115,91,37,21
    9 -> 59,47
    10 -> 167*
    12 -> 22,30,8,5
    22 -> 8*
    24 -> 8*
    30 -> 8*
    32 -> 150,132,61,8
    38 -> 153,135,69,8
    40 -> 159,141,71,8
    46 -> 161,143,77,8
    51 -> 8,5
    60 -> 11*
    63 -> 11*
    70 -> 62*
    72 -> 62*
    78 -> 62*
    82 -> 125*
    83 -> 80,6
    92 -> 80*
    94 -> 80*
    100 -> 80*
    106 -> 80,6
    116 -> 102*
    118 -> 102*
    124 -> 102*
    126 -> 82*
    134 -> 169,8
    136 -> 133*
    142 -> 133*
    144 -> 133*
    152 -> 8*
    154 -> 151*
    160 -> 151*
    162 -> 151*
    168 -> 10*
    172 -> 92,80,6
  problem:
   
  Qed