YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {142,138,135,131,129,127,124,120,118,114,111,108,106,
                  103,99,96,92,87,82,76,74,69,68,65,64,63,62,61,57,53,
                  52,47,46,41,38,34,32,28,24,20,14,11,7,6,1}
   transitions:
    11(184) -> 185*
    11(150) -> 151*
    11(163) -> 164*
    11(176) -> 177*
    21(173) -> 174*
    21(183) -> 184*
    21(148) -> 149*
    21(164) -> 165*
    21(177) -> 178*
    00(122) -> 123*
    00(72) -> 73*
    00(5) -> 1*
    00(109) -> 110*
    00(16) -> 17*
    00(40) -> 38*
    00(20) -> 52*
    00(75) -> 74*
    00(45) -> 41*
    00(35) -> 100*
    00(29) -> 35*
    00(1) -> 6*
    00(81) -> 76*
    00(86) -> 82*
    00(17) -> 18*
    00(3) -> 83*
    00(8) -> 12*
    00(107) -> 106*
    00(113) -> 111*
    00(95) -> 92*
    00(50) -> 51*
    00(98) -> 96*
    00(110) -> 108*
    00(54) -> 55*
    00(10) -> 7*
    00(91) -> 87*
    00(123) -> 120*
    00(51) -> 47*
    f60() -> 2*
    50(25) -> 26*
    50(67) -> 65*
    50(35) -> 36*
    50(28) -> 64*
    50(3) -> 58*
    50(2) -> 21*
    50(83) -> 84*
    50(144) -> 142*
    50(84) -> 104*
    50(94) -> 95*
    50(21) -> 70*
    50(88) -> 139*
    50(132) -> 133*
    50(31) -> 28*
    50(90) -> 91*
    40(2) -> 15*
    40(104) -> 105*
    40(23) -> 136*
    40(126) -> 124*
    40(137) -> 135*
    40(70) -> 71*
    40(133) -> 134*
    40(102) -> 99*
    40(31) -> 125*
    40(3) -> 42*
    40(139) -> 140*
    40(20) -> 63*
    40(6) -> 46*
    40(84) -> 85*
    40(26) -> 27*
    40(88) -> 89*
    40(58) -> 59*
    40(21) -> 22*
    40(25) -> 93*
    20(22) -> 54*
    20(44) -> 45*
    20(4) -> 5*
    20(2) -> 29*
    20(93) -> 94*
    20(17) -> 143*
    20(71) -> 72*
    20(13) -> 11*
    20(49) -> 50*
    20(27) -> 24*
    20(15) -> 16*
    20(80) -> 81*
    20(9) -> 10*
    20(116) -> 119*
    20(140) -> 141*
    20(3) -> 8*
    20(105) -> 103*
    20(112) -> 113*
    20(59) -> 97*
    20(78) -> 79*
    20(42) -> 43*
    20(26) -> 109*
    30(35) -> 115*
    30(22) -> 23*
    30(30) -> 31*
    30(101) -> 102*
    30(29) -> 88*
    30(3) -> 25*
    30(130) -> 129*
    30(39) -> 40*
    30(66) -> 67*
    30(97) -> 98*
    30(27) -> 128*
    30(18) -> 19*
    30(125) -> 126*
    30(93) -> 112*
    30(141) -> 138*
    30(55) -> 56*
    30(1) -> 75*
    30(89) -> 90*
    30(85) -> 86*
    30(115) -> 116*
    30(59) -> 60*
    30(37) -> 34*
    30(28) -> 62*
    30(42) -> 121*
    30(78) -> 132*
    30(2) -> 77*
    30(20) -> 68*
    10(12) -> 13*
    10(100) -> 101*
    10(104) -> 107*
    10(17) -> 66*
    10(23) -> 20*
    10(2) -> 3*
    10(116) -> 117*
    10(43) -> 44*
    10(36) -> 37*
    10(28) -> 61*
    10(117) -> 114*
    10(5) -> 39*
    10(136) -> 137*
    10(119) -> 118*
    10(60) -> 57*
    10(79) -> 80*
    10(27) -> 130*
    10(18) -> 33*
    10(56) -> 53*
    10(128) -> 127*
    10(29) -> 30*
    10(134) -> 131*
    10(8) -> 9*
    10(143) -> 144*
    10(21) -> 48*
    10(121) -> 122*
    10(48) -> 49*
    10(77) -> 78*
    10(33) -> 32*
    10(3) -> 4*
    10(73) -> 69*
    10(19) -> 14*
    41(147) -> 148*
    31(185) -> 186*
    51(146) -> 147*
    51(186) -> 187*
    51(145) -> 146*
    01(175) -> 176*
    01(165) -> 166*
    01(149) -> 150*
    01(167) -> 168*
    151 -> 173,163,104
    166 -> 167,106
    24 -> 77*
    74 -> 83*
    131 -> 77*
    142 -> 146,21
    68 -> 146,21
    168 -> 106*
    47 -> 83*
    48 -> 77*
    46 -> 83*
    64 -> 146,21,58
    69 -> 146,21,147,70
    7 -> 83*
    63 -> 77*
    14 -> 77*
    114 -> 77*
    118 -> 77*
    28 -> 146,21,58
    11 -> 83*
    2 -> 145*
    53 -> 77,88
    174 -> 175,163
    124 -> 77,88
    6 -> 83*
    138 -> 146,21
    178 -> 106*
    38 -> 83*
    76 -> 83*
    135 -> 77*
    127 -> 77*
    1 -> 83*
    62 -> 77*
    20 -> 77*
    55 -> 183*
    65 -> 146,21
    34 -> 83*
    187 -> 139*
    57 -> 77*
    120 -> 77*
    41 -> 83*
    129 -> 77*
    32 -> 83*
    111 -> 77*
  problem:
   
  Qed