YES
TRS:
 {   a(c(d(x))) -> c(x),
  u(b(d(d(x)))) -> b(x),
        v(c(x)) -> b(x),
     v(a(c(x))) -> u(b(d(x))),
     v(a(a(x))) -> u(v(x)),
        w(c(x)) -> b(x),
     w(a(c(x))) -> u(b(d(x))),
     w(a(a(x))) -> u(w(x))}
 RUF:
  Strict:
   {u(b(d(d(x)))) -> b(x),
          v(c(x)) -> b(x),
          w(c(x)) -> b(x)}
  Weak:
   {}
  RUF:
   Strict:
    {}
   Weak:
    {}
   Qed