YES

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

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {4,12,7,1}
   transitions:
    f50() -> 2*
    d3(40) -> 41*
    d3(44) -> 45*
    d3(75) -> 76*
    b1(20) -> 21*
    b1(22) -> 23*
    b1(28) -> 29*
    b1(26) -> 27*
    b1(25) -> 26*
    b1(29) -> 30*
    c3(42) -> 43*
    a2(38) -> 39*
    c1(21) -> 22*
    c1(67) -> 68*
    b0(5) -> 6*
    b0(11) -> 7*
    b0(3) -> 4*
    b0(8) -> 9*
    b0(10) -> 11*
    b0(2) -> 8*
    a0(3) -> 12*
    d1(19) -> 20*
    d1(23) -> 24*
    f0(9) -> 10*
    b3(55) -> 56*
    b3(41) -> 42*
    b3(43) -> 44*
    b3(59) -> 60*
    b3(58) -> 59*
    b3(56) -> 57*
    c0(4) -> 5*
    f3(57) -> 58*
    d2(73) -> 74*
    d2(37) -> 38*
    f1(27) -> 28*
    d0(6) -> 1*
    d0(2) -> 3*
    43 -> 73*
    24 -> 12*
    74 -> 38*
    68 -> 22*
    30 -> 12*
    12 -> 8,21,4,26
    45 -> 39,27
    4 -> 20,3
    2 -> 19*
    22 -> 37*
    38 -> 55*
    76 -> 41*
    26 -> 67*
    73 -> 75*
    60 -> 39,27
    37 -> 40*
    3 -> 25*
    39 -> 21,4,3,25,26,9,27
  problem:
   
  Qed