YES

Problem:
 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(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)))))))))))))))))))))))))

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {21,1}
   transitions:
    11(108) -> 109*
    11(58) -> 59*
    11(67) -> 68*
    11(102) -> 103*
    11(66) -> 67*
    11(111) -> 112*
    11(110) -> 111*
    11(116) -> 117*
    11(64) -> 65*
    11(72) -> 73*
    31(106) -> 107*
    31(56) -> 57*
    31(70) -> 71*
    31(62) -> 63*
    31(100) -> 101*
    31(114) -> 115*
    10(12) -> 13*
    10(20) -> 1*
    10(27) -> 28*
    10(15) -> 16*
    10(33) -> 21*
    10(14) -> 15*
    10(6) -> 7*
    10(25) -> 26*
    10(28) -> 29*
    f60() -> 2*
    00(13) -> 14*
    00(26) -> 27*
    00(7) -> 8*
    50(2) -> 3*
    50(16) -> 17*
    50(14) -> 22*
    50(8) -> 9*
    50(29) -> 30*
    20(24) -> 25*
    20(5) -> 6*
    20(32) -> 33*
    20(11) -> 12*
    20(19) -> 20*
    40(22) -> 23*
    40(30) -> 31*
    40(3) -> 4*
    40(17) -> 18*
    40(9) -> 10*
    30(23) -> 24*
    30(4) -> 5*
    30(10) -> 11*
    30(18) -> 19*
    30(31) -> 32*
    41(61) -> 62*
    41(99) -> 100*
    41(105) -> 106*
    41(55) -> 56*
    41(69) -> 70*
    41(113) -> 114*
    01(103) -> 104*
    01(65) -> 66*
    01(109) -> 110*
    01(59) -> 60*
    51(98) -> 99*
    51(118) -> 119*
    51(68) -> 69*
    51(112) -> 113*
    51(54) -> 55*
    51(104) -> 105*
    51(60) -> 61*
    51(74) -> 75*
    51(122) -> 123*
    21(115) -> 116*
    21(107) -> 108*
    21(101) -> 102*
    21(63) -> 64*
    21(71) -> 72*
    21(57) -> 58*
    66 -> 74*
    117 -> 27*
    75 -> 61*
    72 -> 98*
    21 -> 8*
    73 -> 14*
    123 -> 55*
    1 -> 8*
    20 -> 54*
    110 -> 118*
    119 -> 105*
    33 -> 122*
  problem:
   
  Qed