YES

Problem:
 a(c(d(x))) -> c(x)
 u(b(d(d(x)))) -> b(x)
 v(a(a(x))) -> u(v(x))
 v(a(c(x))) -> u(b(d(x)))
 v(c(x)) -> b(x)
 w(a(a(x))) -> u(w(x))
 w(a(c(x))) -> u(b(d(x)))
 w(c(x)) -> b(x)

Proof:
 DP Processor:
  DPs:
   v#(a(a(x))) -> v#(x)
   v#(a(a(x))) -> u#(v(x))
   v#(a(c(x))) -> u#(b(d(x)))
   w#(a(a(x))) -> w#(x)
   w#(a(a(x))) -> u#(w(x))
   w#(a(c(x))) -> u#(b(d(x)))
  TRS:
   a(c(d(x))) -> c(x)
   u(b(d(d(x)))) -> b(x)
   v(a(a(x))) -> u(v(x))
   v(a(c(x))) -> u(b(d(x)))
   v(c(x)) -> b(x)
   w(a(a(x))) -> u(w(x))
   w(a(c(x))) -> u(b(d(x)))
   w(c(x)) -> b(x)
  TDG Processor:
   DPs:
    v#(a(a(x))) -> v#(x)
    v#(a(a(x))) -> u#(v(x))
    v#(a(c(x))) -> u#(b(d(x)))
    w#(a(a(x))) -> w#(x)
    w#(a(a(x))) -> u#(w(x))
    w#(a(c(x))) -> u#(b(d(x)))
   TRS:
    a(c(d(x))) -> c(x)
    u(b(d(d(x)))) -> b(x)
    v(a(a(x))) -> u(v(x))
    v(a(c(x))) -> u(b(d(x)))
    v(c(x)) -> b(x)
    w(a(a(x))) -> u(w(x))
    w(a(c(x))) -> u(b(d(x)))
    w(c(x)) -> b(x)
   graph:
    w#(a(a(x))) -> w#(x) -> w#(a(c(x))) -> u#(b(d(x)))
    w#(a(a(x))) -> w#(x) -> w#(a(a(x))) -> u#(w(x))
    w#(a(a(x))) -> w#(x) -> w#(a(a(x))) -> w#(x)
    v#(a(a(x))) -> v#(x) -> v#(a(c(x))) -> u#(b(d(x)))
    v#(a(a(x))) -> v#(x) -> v#(a(a(x))) -> u#(v(x))
    v#(a(a(x))) -> v#(x) -> v#(a(a(x))) -> v#(x)
   CDG Processor:
    DPs:
     v#(a(a(x))) -> v#(x)
     v#(a(a(x))) -> u#(v(x))
     v#(a(c(x))) -> u#(b(d(x)))
     w#(a(a(x))) -> w#(x)
     w#(a(a(x))) -> u#(w(x))
     w#(a(c(x))) -> u#(b(d(x)))
    TRS:
     a(c(d(x))) -> c(x)
     u(b(d(d(x)))) -> b(x)
     v(a(a(x))) -> u(v(x))
     v(a(c(x))) -> u(b(d(x)))
     v(c(x)) -> b(x)
     w(a(a(x))) -> u(w(x))
     w(a(c(x))) -> u(b(d(x)))
     w(c(x)) -> b(x)
    graph:
     
    Qed