YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {34,21,1}
   transitions:
    11(108) -> 109*
    11(251) -> 252*
    11(59) -> 60*
    11(195) -> 196*
    11(113) -> 114*
    11(143) -> 144*
    11(257) -> 258*
    11(166) -> 167*
    11(171) -> 172*
    11(151) -> 152*
    11(149) -> 150*
    11(152) -> 153*
    11(201) -> 202*
    11(51) -> 52*
    11(107) -> 108*
    11(57) -> 58*
    11(60) -> 61*
    11(252) -> 253*
    11(203) -> 204*
    11(163) -> 164*
    11(105) -> 106*
    11(204) -> 205*
    11(249) -> 250*
    11(165) -> 166*
    31(111) -> 112*
    31(141) -> 142*
    31(255) -> 256*
    31(155) -> 156*
    31(103) -> 104*
    31(147) -> 148*
    31(193) -> 194*
    31(49) -> 50*
    31(207) -> 208*
    31(169) -> 170*
    31(63) -> 64*
    31(161) -> 162*
    31(247) -> 248*
    31(55) -> 56*
    31(199) -> 200*
    00(13) -> 14*
    00(39) -> 40*
    00(20) -> 1*
    00(7) -> 8*
    00(26) -> 27*
    f60() -> 2*
    10(25) -> 26*
    10(15) -> 16*
    10(33) -> 21*
    10(28) -> 29*
    10(27) -> 28*
    10(41) -> 42*
    10(14) -> 15*
    10(38) -> 39*
    10(6) -> 7*
    10(46) -> 34*
    10(40) -> 41*
    10(12) -> 13*
    50(2) -> 3*
    50(16) -> 17*
    50(14) -> 22*
    50(27) -> 35*
    50(8) -> 9*
    50(42) -> 43*
    50(29) -> 30*
    20(24) -> 25*
    20(5) -> 6*
    20(32) -> 33*
    20(11) -> 12*
    20(45) -> 46*
    20(19) -> 20*
    20(37) -> 38*
    40(35) -> 36*
    40(22) -> 23*
    40(30) -> 31*
    40(43) -> 44*
    40(3) -> 4*
    40(17) -> 18*
    40(9) -> 10*
    30(23) -> 24*
    30(36) -> 37*
    30(4) -> 5*
    30(10) -> 11*
    30(18) -> 19*
    30(44) -> 45*
    30(31) -> 32*
    41(206) -> 207*
    41(110) -> 111*
    41(146) -> 147*
    41(254) -> 255*
    41(198) -> 199*
    41(168) -> 169*
    41(62) -> 63*
    41(246) -> 247*
    41(154) -> 155*
    41(102) -> 103*
    41(160) -> 161*
    41(48) -> 49*
    41(140) -> 141*
    41(54) -> 55*
    41(192) -> 193*
    01(250) -> 251*
    01(202) -> 203*
    01(209) -> 210*
    01(144) -> 145*
    01(196) -> 197*
    01(58) -> 59*
    01(65) -> 66*
    01(164) -> 165*
    01(157) -> 158*
    01(106) -> 107*
    01(150) -> 151*
    01(52) -> 53*
    51(191) -> 192*
    51(197) -> 198*
    51(263) -> 264*
    51(61) -> 62*
    51(153) -> 154*
    51(53) -> 54*
    51(139) -> 140*
    51(115) -> 116*
    51(167) -> 168*
    51(109) -> 110*
    51(205) -> 206*
    51(189) -> 190*
    51(159) -> 160*
    51(101) -> 102*
    51(245) -> 246*
    51(145) -> 146*
    51(47) -> 48*
    51(259) -> 260*
    51(253) -> 254*
    21(148) -> 149*
    21(162) -> 163*
    21(256) -> 257*
    21(142) -> 143*
    21(194) -> 195*
    21(50) -> 51*
    21(112) -> 113*
    21(64) -> 65*
    21(248) -> 249*
    21(170) -> 171*
    21(208) -> 209*
    21(104) -> 105*
    21(200) -> 201*
    21(56) -> 57*
    21(156) -> 157*
    151 -> 159*
    210 -> 40*
    203 -> 245*
    190 -> 160*
    158 -> 27*
    46 -> 263*
    113 -> 139*
    114 -> 14*
    66 -> 14*
    258 -> 40*
    264 -> 48*
    116 -> 102*
    171 -> 191*
    172 -> 27*
    251 -> 259*
    21 -> 8*
    165 -> 189*
    1 -> 8*
    107 -> 115*
    34 -> 8*
    59 -> 101*
    260 -> 246*
    33 -> 47*
  problem:
   
  Qed