YES
Time: 0.000478
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