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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {6,5}
   transitions:
    51(142) -> 143*
    51(149) -> 150*
    41(55) -> 56*
    41(47) -> 48*
    41(119) -> 120*
    41(99) -> 100*
    41(49) -> 50*
    41(148) -> 149*
    41(78) -> 79*
    41(33) -> 34*
    11(25) -> 26*
    11(147) -> 148*
    11(37) -> 38*
    11(17) -> 18*
    11(12) -> 13*
    11(121) -> 122*
    11(76) -> 77*
    11(71) -> 72*
    11(36) -> 37*
    11(133) -> 134*
    11(23) -> 24*
    11(13) -> 14*
    11(145) -> 146*
    11(130) -> 131*
    21(75) -> 76*
    21(70) -> 71*
    21(87) -> 88*
    21(77) -> 78*
    21(57) -> 58*
    21(144) -> 145*
    21(89) -> 90*
    21(59) -> 60*
    21(14) -> 15*
    21(131) -> 132*
    21(100) -> 101*
    21(95) -> 96*
    31(35) -> 36*
    31(72) -> 73*
    31(31) -> 32*
    31(143) -> 144*
    31(98) -> 99*
    01(15) -> 16*
    01(117) -> 118*
    01(97) -> 98*
    01(109) -> 110*
    01(34) -> 35*
    01(111) -> 112*
    01(73) -> 74*
    01(58) -> 59*
    01(120) -> 121*
    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) -> 3*
    30(4) -> 3*
    30(1) -> 3*
    30(3) -> 3*
    40(2) -> 4*
    40(4) -> 4*
    40(1) -> 4*
    40(3) -> 4*
    50(2) -> 6*
    50(4) -> 6*
    50(1) -> 6*
    50(3) -> 6*
    1 -> 111,89,49,23
    2 -> 97,75,33,12
    3 -> 117,95,55,25
    4 -> 109,87,47,17
    13 -> 57*
    14 -> 31*
    16 -> 112,133,5
    18 -> 13*
    24 -> 13*
    26 -> 13*
    32 -> 15*
    34 -> 119,70
    38 -> 112,133,5
    48 -> 34*
    50 -> 34*
    56 -> 34*
    60 -> 37*
    74 -> 37*
    76 -> 142*
    78 -> 147*
    79 -> 73*
    88 -> 76*
    90 -> 76*
    96 -> 76*
    98 -> 133*
    99 -> 130*
    101 -> 36*
    110 -> 98*
    112 -> 98*
    118 -> 98*
    122 -> 59*
    132 -> 59*
    134 -> 35*
    146 -> 6*
    150 -> 6*
  problem:
   
  Qed