YES
TRS:
 {b(d(x)) -> x,
  b(c(x)) -> c(d(a(b(x)))),
  a(d(x)) -> d(c(b(a(x)))),
  a(c(x)) -> x}
 DP:
  Strict:
   {b#(c(x)) -> b#(x),
    b#(c(x)) -> a#(b(x)),
    a#(d(x)) -> b#(a(x)),
    a#(d(x)) -> a#(x)}
  Weak:
  {b(d(x)) -> x,
   b(c(x)) -> c(d(a(b(x)))),
   a(d(x)) -> d(c(b(a(x)))),
   a(c(x)) -> x}
  EDG:
   {(a#(d(x)) -> a#(x), a#(d(x)) -> a#(x))
    (a#(d(x)) -> a#(x), a#(d(x)) -> b#(a(x)))
    (a#(d(x)) -> b#(a(x)), b#(c(x)) -> a#(b(x)))
    (a#(d(x)) -> b#(a(x)), b#(c(x)) -> b#(x))
    (b#(c(x)) -> a#(b(x)), a#(d(x)) -> b#(a(x)))
    (b#(c(x)) -> a#(b(x)), a#(d(x)) -> a#(x))
    (b#(c(x)) -> b#(x), b#(c(x)) -> b#(x))
    (b#(c(x)) -> b#(x), b#(c(x)) -> a#(b(x)))}
   SCCS:
    Scc:
     {b#(c(x)) -> b#(x),
      b#(c(x)) -> a#(b(x)),
      a#(d(x)) -> b#(a(x)),
      a#(d(x)) -> a#(x)}
    SCC:
     Strict:
      {b#(c(x)) -> b#(x),
       b#(c(x)) -> a#(b(x)),
       a#(d(x)) -> b#(a(x)),
       a#(d(x)) -> a#(x)}
     Weak:
     {b(d(x)) -> x,
      b(c(x)) -> c(d(a(b(x)))),
      a(d(x)) -> d(c(b(a(x)))),
      a(c(x)) -> x}
     UR:
      {b(d(x)) -> x,
       b(c(x)) -> c(d(a(b(x)))),
       a(d(x)) -> d(c(b(a(x)))),
       a(c(x)) -> x}
      BOUND:
       Bound: match(-raise)-DP-bounded by 1
       Automaton:
        {a#_1(43) -> 44*
         a#_1(41) -> 42*
         a#_1(31) -> 32*
         a#_0(26) -> 27*
         a#_0(15) -> 16*
          a_1(45) -> 46*
          a_1(24) -> 25*
          a_1(22) -> 23*
          a_1(20) -> 21*
          a_1(17) -> 18*
          a_0(12) -> 12*
          a_0(10) -> 12*
           a_0(9) -> 12*
           a_0(8) -> 12*
         b#_1(28) -> 29*
         b#_1(18) -> 19*
         b#_0(13) -> 14*
         b#_0(12) -> 6*
          b_1(37) -> 38*
          b_1(35) -> 36*
          b_1(33) -> 34*
          b_1(30) -> 31*
          b_0(12) -> 10*
          b_0(10) -> 10*
           b_0(9) -> 10*
           b_0(8) -> 10*
          c_1(47) -> 48*
          c_1(38) -> 39*
          c_0(12) -> 9*
          c_0(10) -> 9*
           c_0(9) -> 9*
           c_0(8) -> 9*
          d_1(46) -> 47*
          d_1(39) -> 40*
          d_0(12) -> 8*
          d_0(10) -> 8*
           d_0(9) -> 8*
           d_0(8) -> 8*
               48 -> 38 | 36 | 34
               47 -> 46*
               44 -> 32*
               42 -> 32*
               40 -> 46 | 25 | 23 | 18
               39 -> 38*
               36 -> 31*
               34 -> 31*
               32 -> 29 | 19
               31 -> 45*
               29 -> 19*
               27 -> 16*
               25 -> 18*
               23 -> 18*
               21 -> 18*
               19 -> 44 | 32 | 27 | 16
               18 -> 37*
               16 -> 27 | 6
               14 -> 6*
               12 -> 26 | 24 | 10
               10 -> 46 | 43 | 38 | 36 | 35 | 31 | 28 | 25 | 23 | 22 | 21 | 15 | 13 | 12
                9 -> 46 | 41 | 38 | 36 | 33 | 31 | 25 | 23 | 21 | 20 | 12 | 10
                8 -> 46 | 38 | 36 | 31 | 30 | 25 | 23 | 21 | 17 | 12 | 10
                6 -> 14*}
       Strict:
        {b#(c(x)) -> b#(x),
         b#(c(x)) -> a#(b(x)),
         a#(d(x)) -> a#(x)}
       EDG:
        {(a#(d(x)) -> a#(x), a#(d(x)) -> a#(x))
         (b#(c(x)) -> a#(b(x)), a#(d(x)) -> a#(x))
         (b#(c(x)) -> b#(x), b#(c(x)) -> b#(x))
         (b#(c(x)) -> b#(x), b#(c(x)) -> a#(b(x)))}
        SCCS:
         Scc:
          {a#(d(x)) -> a#(x)}
         Scc:
          {b#(c(x)) -> b#(x)}
         SCC:
          Strict:
           {a#(d(x)) -> a#(x)}
          Weak:
          {b(d(x)) -> x,
           b(c(x)) -> c(d(a(b(x)))),
           a(d(x)) -> d(c(b(a(x)))),
           a(c(x)) -> x}
          SPSC:
           Simple Projection:
            pi(a#) = 0
           Strict:
            {}
           Qed
         SCC:
          Strict:
           {b#(c(x)) -> b#(x)}
          Weak:
          {b(d(x)) -> x,
           b(c(x)) -> c(d(a(b(x)))),
           a(d(x)) -> d(c(b(a(x)))),
           a(c(x)) -> x}
          SPSC:
           Simple Projection:
            pi(b#) = 0
           Strict:
            {}
           Qed