YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {110,106,101,96,91,89,85,80,75,70,66,61,57,51,46,40,36,31,29,24,18,14,8,1}
   transitions:
    11(128) -> 129*
    11(119) -> 120*
    11(130) -> 131*
    11(129) -> 130*
    11(147) -> 148*
    41(158) -> 159*
    41(160) -> 161*
    41(143) -> 144*
    41(115) -> 116*
    41(145) -> 146*
    41(142) -> 143*
    41(117) -> 118*
    41(114) -> 115*
    00(13) -> 8*
    00(41) -> 42*
    00(108) -> 109*
    00(73) -> 74*
    00(45) -> 40*
    00(35) -> 31*
    00(52) -> 102*
    00(7) -> 1*
    00(23) -> 18*
    00(86) -> 87*
    00(3) -> 32*
    00(19) -> 62*
    00(48) -> 49*
    00(10) -> 111*
    00(28) -> 24*
    f60() -> 2*
    50(112) -> 113*
    50(104) -> 105*
    50(15) -> 16*
    50(39) -> 36*
    50(47) -> 67*
    50(27) -> 30*
    50(2) -> 41*
    50(63) -> 64*
    50(50) -> 46*
    50(22) -> 90*
    50(92) -> 93*
    30(2) -> 3*
    30(81) -> 82*
    30(3) -> 4*
    30(52) -> 53*
    30(9) -> 10*
    30(107) -> 108*
    30(67) -> 68*
    30(41) -> 97*
    30(84) -> 80*
    30(53) -> 54*
    30(88) -> 85*
    30(58) -> 59*
    30(47) -> 48*
    30(25) -> 26*
    30(19) -> 76*
    10(16) -> 17*
    10(2) -> 19*
    10(17) -> 14*
    10(62) -> 63*
    10(71) -> 72*
    10(20) -> 21*
    10(102) -> 103*
    10(83) -> 84*
    10(94) -> 95*
    10(25) -> 37*
    10(9) -> 92*
    10(111) -> 112*
    10(113) -> 110*
    10(64) -> 65*
    10(87) -> 88*
    10(56) -> 51*
    10(109) -> 106*
    10(55) -> 56*
    10(77) -> 78*
    10(43) -> 44*
    10(6) -> 7*
    10(38) -> 39*
    10(32) -> 33*
    10(11) -> 12*
    10(105) -> 101*
    10(34) -> 35*
    10(19) -> 20*
    10(30) -> 29*
    10(42) -> 43*
    10(98) -> 99*
    20(65) -> 61*
    20(22) -> 23*
    20(10) -> 15*
    20(3) -> 47*
    20(33) -> 34*
    20(53) -> 86*
    20(69) -> 66*
    20(90) -> 89*
    20(79) -> 75*
    20(27) -> 28*
    20(99) -> 100*
    20(60) -> 57*
    20(12) -> 13*
    20(4) -> 5*
    20(103) -> 104*
    20(44) -> 45*
    20(74) -> 70*
    20(21) -> 22*
    20(25) -> 107*
    20(2) -> 52*
    20(72) -> 73*
    40(54) -> 55*
    40(100) -> 96*
    40(2) -> 9*
    40(5) -> 6*
    40(10) -> 11*
    40(97) -> 98*
    40(76) -> 77*
    40(59) -> 60*
    40(82) -> 83*
    40(9) -> 25*
    40(68) -> 69*
    40(93) -> 94*
    40(26) -> 27*
    40(25) -> 58*
    40(3) -> 71*
    40(95) -> 91*
    40(37) -> 38*
    40(49) -> 50*
    40(78) -> 79*
    40(19) -> 81*
    31(116) -> 117*
    31(144) -> 145*
    01(133) -> 134*
    21(132) -> 133*
    21(131) -> 132*
    51(146) -> 147*
    51(118) -> 119*
    70 -> 52*
    24 -> 62*
    148 -> 102*
    159 -> 143*
    68 -> 158*
    46 -> 19*
    85 -> 3*
    106 -> 41*
    66 -> 52*
    75 -> 52*
    161 -> 143*
    36 -> 19*
    91 -> 9*
    26 -> 114*
    101 -> 41*
    40 -> 19*
    55 -> 128*
    110 -> 41*
    59 -> 142*
    134 -> 62*
    57 -> 52*
    120 -> 24*
    18 -> 62*
    96 -> 9*
    51 -> 19*
    80 -> 3*
    89 -> 9*
    29 -> 102*
    61 -> 52*
    78 -> 160*
  problem:
   
  Qed