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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {6,5,4}
   transitions:
    11(80) -> 81*
    11(37) -> 38*
    11(32) -> 33*
    11(9) -> 10*
    11(131) -> 132*
    11(111) -> 112*
    11(81) -> 82*
    11(46) -> 47*
    11(11) -> 12*
    11(68) -> 69*
    11(43) -> 44*
    11(120) -> 121*
    11(110) -> 111*
    21(45) -> 46*
    21(35) -> 36*
    21(10) -> 11*
    21(67) -> 68*
    21(119) -> 120*
    21(109) -> 110*
    21(79) -> 80*
    21(121) -> 122*
    21(66) -> 67*
    21(8) -> 9*
    21(130) -> 131*
    51(65) -> 66*
    51(97) -> 98*
    51(82) -> 83*
    51(77) -> 78*
    51(47) -> 48*
    51(64) -> 65*
    51(34) -> 35*
    51(96) -> 97*
    51(71) -> 72*
    51(108) -> 109*
    51(135) -> 136*
    41(107) -> 108*
    41(134) -> 135*
    41(99) -> 100*
    41(94) -> 95*
    41(49) -> 50*
    41(133) -> 134*
    41(48) -> 49*
    41(105) -> 106*
    01(147) -> 148*
    01(7) -> 8*
    01(69) -> 70*
    01(21) -> 22*
    01(33) -> 34*
    01(23) -> 24*
    01(95) -> 96*
    12(143) -> 144*
    12(145) -> 146*
    22(142) -> 143*
    22(144) -> 145*
    00(2) -> 4*
    00(1) -> 4*
    00(3) -> 4*
    02(141) -> 142*
    10(2) -> 1*
    10(1) -> 1*
    10(3) -> 1*
    20(2) -> 2*
    20(1) -> 2*
    20(3) -> 2*
    30(2) -> 5*
    30(1) -> 5*
    30(3) -> 5*
    40(2) -> 6*
    40(1) -> 6*
    40(3) -> 6*
    50(2) -> 3*
    50(1) -> 3*
    50(3) -> 3*
    1 -> 99,71,37,21
    2 -> 94,64,32,7
    3 -> 105,77,43,23
    12 -> 24,22,34,8,4
    22 -> 8*
    24 -> 8*
    33 -> 107,45
    34 -> 133*
    36 -> 10*
    38 -> 33*
    44 -> 33*
    50 -> 108,100,6
    65 -> 79*
    70 -> 24,8,4
    72 -> 65*
    78 -> 65*
    83 -> 69*
    96 -> 119*
    97 -> 130*
    98 -> 10*
    100 -> 95*
    106 -> 95*
    110 -> 141*
    111 -> 147*
    112 -> 108,100,6
    122 -> 96*
    132 -> 96*
    136 -> 121*
    146 -> 96,119
    148 -> 134*
  problem:
   
  Qed