YES
Time: 0.000604
TRS:
 {a b x -> b a x,
  a c x -> x}
 RUF:
  Strict:
   {a b x -> b a x}
  Weak:
   {}
  DP:
   DP:
    {a# b x -> a# x}
   TRS:
   {a b x -> b a x}
   EDG:
    {(a# b x -> a# x, a# b x -> a# x)}
    SCCS (1):
     Scc:
      {a# b x -> a# x}
     SCC (1):
      Strict:
       {a# b x -> a# x}
      Weak:
      {a b x -> b a x}
      SPSC:
       Simple Projection:
        pi(a#) = 0
       Strict:
        {}
       Qed