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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {6,5}
   transitions:
    51(15) -> 16*
    51(97) -> 98*
    51(67) -> 68*
    51(139) -> 140*
    51(74) -> 75*
    51(59) -> 60*
    51(176) -> 177*
    51(61) -> 62*
    51(123) -> 124*
    51(43) -> 44*
    51(135) -> 136*
    31(45) -> 46*
    31(137) -> 138*
    31(191) -> 192*
    31(186) -> 187*
    31(100) -> 101*
    01(27) -> 28*
    01(154) -> 155*
    01(29) -> 30*
    01(14) -> 15*
    01(136) -> 137*
    01(96) -> 97*
    01(46) -> 47*
    01(21) -> 22*
    01(148) -> 149*
    01(73) -> 74*
    01(190) -> 191*
    11(70) -> 71*
    11(167) -> 168*
    11(122) -> 123*
    11(47) -> 48*
    11(17) -> 18*
    11(189) -> 190*
    11(99) -> 100*
    11(41) -> 42*
    11(173) -> 174*
    11(153) -> 154*
    11(18) -> 19*
    11(165) -> 166*
    11(155) -> 156*
    41(85) -> 86*
    41(187) -> 188*
    41(87) -> 88*
    41(149) -> 150*
    41(69) -> 70*
    41(39) -> 40*
    41(156) -> 157*
    41(121) -> 122*
    41(71) -> 72*
    41(16) -> 17*
    41(98) -> 99*
    41(93) -> 94*
    41(48) -> 49*
    41(185) -> 186*
    41(150) -> 151*
    21(40) -> 41*
    21(72) -> 73*
    21(124) -> 125*
    21(119) -> 120*
    21(44) -> 45*
    21(19) -> 20*
    21(151) -> 152*
    21(111) -> 112*
    21(113) -> 114*
    21(38) -> 39*
    21(175) -> 176*
    21(95) -> 96*
    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 -> 167,113,87,61,27
    2 -> 153,95,69,43,14
    3 -> 173,119,93,67,29
    4 -> 165,111,85,59,21
    15 -> 121*
    16 -> 38*
    20 -> 28,15,155,121,5
    22 -> 15*
    28 -> 15*
    30 -> 15*
    42 -> 30,149,28,155,121,5
    49 -> 28,155,121,5
    60 -> 44*
    62 -> 44*
    68 -> 44*
    70 -> 148*
    71 -> 135*
    75 -> 22,30,149,28,155,121,5
    86 -> 70*
    88 -> 70*
    94 -> 70*
    101 -> 30,15,149,121,5
    112 -> 96*
    114 -> 96*
    120 -> 96*
    123 -> 175*
    125 -> 100*
    137 -> 139*
    138 -> 74*
    140 -> 74*
    152 -> 74*
    154 -> 189,185
    157 -> 137*
    166 -> 154*
    168 -> 154*
    174 -> 154*
    177 -> 48*
    188 -> 73*
    192 -> 139*
  problem:
   
  Qed