YES

Problem:
 1(2(1(1(0(0(1(0(2(1(1(0(2(x1))))))))))))) -> 1(2(2(1(0(0(2(0(1(2(2(0(1(0(0(2(2(x1)))))))))))))))))
 2(0(1(2(1(2(1(2(1(0(0(1(0(x1))))))))))))) -> 2(2(0(0(2(1(1(1(0(0(0(1(1(1(2(2(0(x1)))))))))))))))))
 2(1(0(0(2(1(1(1(0(1(2(2(0(x1))))))))))))) -> 0(0(2(1(0(0(1(1(2(2(2(2(2(1(2(1(0(x1)))))))))))))))))
 2(2(0(0(1(0(2(1(1(1(0(0(1(x1))))))))))))) -> 2(2(1(1(2(0(0(1(2(2(0(2(0(0(2(2(2(x1)))))))))))))))))
 2(2(1(0(1(0(1(1(0(0(0(2(0(x1))))))))))))) -> 0(2(2(1(0(0(1(0(0(1(1(1(1(0(0(2(0(x1)))))))))))))))))
 2(2(1(1(0(2(0(0(0(2(2(0(0(x1))))))))))))) -> 0(0(1(2(0(0(0(2(2(0(1(2(2(2(2(0(0(x1)))))))))))))))))
 2(2(2(1(0(2(0(0(1(0(1(0(2(x1))))))))))))) -> 0(2(2(0(0(2(2(2(1(2(0(0(2(2(0(2(2(x1)))))))))))))))))

Proof:
 Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {98,82,67,52,36,19,1}
   transitions:
    20(34) -> 35*
    20(4) -> 53*
    20(16) -> 17*
    20(40) -> 41*
    20(3) -> 4*
    20(79) -> 80*
    20(83) -> 84*
    20(102) -> 103*
    20(62) -> 63*
    20(43) -> 44*
    20(39) -> 40*
    20(9) -> 10*
    20(49) -> 50*
    20(65) -> 66*
    20(57) -> 58*
    20(37) -> 38*
    20(90) -> 91*
    20(21) -> 22*
    20(2) -> 3*
    20(12) -> 13*
    20(42) -> 43*
    20(31) -> 32*
    20(35) -> 19*
    20(89) -> 90*
    20(84) -> 85*
    20(55) -> 56*
    20(106) -> 107*
    20(86) -> 87*
    20(80) -> 81*
    20(20) -> 21*
    20(5) -> 99*
    20(17) -> 18*
    20(105) -> 106*
    20(85) -> 86*
    20(110) -> 111*
    20(99) -> 100*
    20(41) -> 42*
    20(58) -> 59*
    20(8) -> 9*
    20(104) -> 105*
    20(94) -> 95*
    20(109) -> 110*
    20(66) -> 52*
    00(21) -> 68*
    00(68) -> 69*
    00(32) -> 33*
    00(77) -> 78*
    00(13) -> 14*
    00(46) -> 47*
    00(60) -> 61*
    00(47) -> 48*
    00(56) -> 57*
    00(111) -> 98*
    00(33) -> 34*
    00(20) -> 83*
    00(73) -> 74*
    00(97) -> 82*
    00(27) -> 28*
    00(74) -> 75*
    00(25) -> 26*
    00(92) -> 93*
    00(108) -> 109*
    00(4) -> 5*
    00(2) -> 20*
    00(53) -> 54*
    00(107) -> 108*
    00(81) -> 67*
    00(91) -> 92*
    00(54) -> 55*
    00(100) -> 101*
    00(76) -> 77*
    00(88) -> 89*
    00(101) -> 102*
    00(26) -> 27*
    00(7) -> 8*
    00(5) -> 6*
    00(51) -> 36*
    00(93) -> 94*
    00(50) -> 51*
    00(14) -> 15*
    00(61) -> 62*
    00(11) -> 12*
    00(96) -> 97*
    10(78) -> 79*
    10(22) -> 23*
    10(75) -> 76*
    10(28) -> 29*
    10(48) -> 49*
    10(44) -> 45*
    10(38) -> 39*
    10(95) -> 96*
    10(72) -> 73*
    10(30) -> 31*
    10(103) -> 104*
    10(24) -> 25*
    10(6) -> 7*
    10(70) -> 71*
    10(23) -> 24*
    10(18) -> 1*
    10(15) -> 16*
    10(71) -> 72*
    10(69) -> 70*
    10(10) -> 11*
    10(87) -> 88*
    10(64) -> 65*
    10(45) -> 46*
    10(63) -> 64*
    10(29) -> 30*
    10(20) -> 37*
    10(59) -> 60*
    f30() -> 2*
    19 -> 3,21
    82 -> 3,4
    67 -> 3,4
    52 -> 3,4,22,85
    36 -> 3,38
    98 -> 3,4,53
  problem:
   
  Qed