YES

Problem:
 a(a(x1)) -> b(b(b(x1)))
 a(x1) -> d(c(d(x1)))
 b(b(b(x1))) -> a(f(x1))
 b(b(x1)) -> c(c(c(x1)))
 c(c(x1)) -> d(d(d(x1)))
 c(d(d(x1))) -> f(x1)
 f(f(x1)) -> f(a(x1))

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {15,9,13,10,8,5,1}
   transitions:
    a2(138) -> 139*
    f50() -> 2*
    d3(140) -> 141*
    d3(142) -> 143*
    a1(34) -> 35*
    a1(120) -> 121*
    d2(96) -> 97*
    d2(86) -> 87*
    d2(81) -> 82*
    d2(97) -> 98*
    d2(123) -> 124*
    d2(125) -> 126*
    d2(82) -> 83*
    d2(87) -> 88*
    d2(73) -> 74*
    d2(83) -> 84*
    d2(75) -> 76*
    d2(85) -> 86*
    d2(102) -> 103*
    d2(100) -> 101*
    d2(98) -> 99*
    d2(101) -> 102*
    d0(7) -> 5*
    d0(14) -> 13*
    d0(6) -> 14*
    d0(2) -> 6*
    b0(4) -> 1*
    b0(2) -> 3*
    b0(3) -> 4*
    c1(47) -> 48*
    c1(44) -> 45*
    c1(30) -> 31*
    c1(45) -> 46*
    c1(43) -> 44*
    c1(49) -> 50*
    c1(18) -> 19*
    c1(48) -> 49*
    d1(62) -> 63*
    d1(31) -> 32*
    d1(154) -> 155*
    d1(156) -> 157*
    d1(155) -> 156*
    d1(59) -> 60*
    d1(63) -> 64*
    d1(61) -> 62*
    d1(58) -> 59*
    d1(17) -> 18*
    d1(29) -> 30*
    d1(19) -> 20*
    c0(2) -> 11*
    c0(12) -> 10*
    c0(6) -> 7*
    c0(11) -> 12*
    f0(16) -> 15*
    f0(2) -> 9*
    a0(2) -> 16*
    a0(9) -> 8*
    c2(74) -> 75*
    c2(124) -> 125*
    f3(134) -> 135*
    f2(110) -> 111*
    f2(150) -> 151*
    f2(116) -> 117*
    f2(166) -> 167*
    f2(162) -> 163*
    c3(141) -> 142*
    f1(121) -> 122*
    f1(33) -> 34*
    f1(108) -> 109*
    f1(170) -> 171*
    155 -> 166*
    151 -> 142*
    163 -> 48,85
    43 -> 100*
    47 -> 96*
    48 -> 85*
    35 -> 1*
    46 -> 4*
    64 -> 10*
    30 -> 58*
    126 -> 121*
    12 -> 154*
    11 -> 61*
    2 -> 43,33,29
    117 -> 50,1
    143 -> 139,134
    88 -> 50*
    109 -> 10*
    116 -> 120*
    6 -> 170*
    171 -> 45,12
    138 -> 140*
    58 -> 108*
    76 -> 35,1
    135 -> 125*
    44 -> 81*
    139 -> 134*
    60 -> 12*
    101 -> 110*
    13 -> 44,11,61,81
    8 -> 3,47,96,4
    1 -> 16*
    62 -> 162*
    99 -> 49*
    20 -> 8*
    34 -> 73*
    9 -> 44,11,61,81,31,7,17
    108 -> 138*
    50 -> 1*
    3 -> 47*
    120 -> 123*
    122 -> 15*
    167 -> 49*
    84 -> 46*
    96 -> 134*
    15 -> 151,142,34,9,17,73
    97 -> 116*
    10 -> 3,47,96
    103 -> 45*
    29 -> 150*
    32 -> 16*
    111 -> 46,4
    157 -> 48,85
  problem:
   
  Qed