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The given Problem was:
a b c -> c b a 
a c -> a a d a 
d a b -> b a d 
d a c -> b c c 
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A self-embedding rewrite structure for the given SRS is:
   a (ab)^k+1 cc --> a (ab)^k+2 cc  (#119220)
   pattern overlapped by closure at r0
      RP: a (ab)^k+1 c --> aa (ba)^k+1 da  (#70270)
          pattern overlapped by pattern
             RP: a (ab)^k+1 c --> aad (ab)^k+1 a  (#868)
                 pattern overlapped by closure at l-1
                    RP: (ab)^k+1 c --> c (ba)^k ba  (#29)
                        expand ->
                           RP: (ab)^k+1 c --> c (ba)^k+1  (#7)
                               increment
                                  RP: (ab)^k c --> c (ba)^k  (#5)
                                      self-overlapping Closure at -2
                                         OC: a b c --(1)-> c b a (#1)
                                             Rule
                    OC: a c --(1)-> a a d a (#2)
                        Rule
             RP: d (ab)^k+1 --> (ba)^k+1 d  (#8)
                 increment
                    RP: d (ab)^k --> (ba)^k d  (#1)
                        self-overlapping Closure at 2
                           OC: d a b --(1)-> b a d (#3)
                               Rule
      OC: d a c --(1)-> b c c (#4)
          Rule
Hence, the SRS is non-terminating.