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The given Problem was:
a a a a -> a c a c c 
c c c -> a a a 
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A self-embedding rewrite structure for the given SRS is:
   a a a a c a a a c a a c a --(7)-> a c a a a a c a a a c a a c a c c (#3574)
   OC+OC at 5
      OC: a a a a c --(2)-> a c a a a a (#6)
          OC+OC at 3
             OC: a a a a --(1)-> a c a c c (#1)
                 Rule
             OC: c c c --(1)-> a a a (#2)
                 Rule
      OC: a a a a c a a c a --(5)-> a c a a a c a a c a c c (#241)
          OC+OC at 3
             OC: a a a a --(1)-> a c a c c (#1)
                 Rule
             OC: c c c a a c a --(4)-> a a c a a c a c c (#31)
                 OC+OC at 1
                    OC: c c c --(1)-> a a a (#2)
                        Rule
                    OC: a a a a c a --(3)-> a c a a c a c c (#15)
                        OC+OC at 3
                           OC: a a a a --(1)-> a c a c c (#1)
                               Rule
                           OC: c c c a --(2)-> a c a c c (#3)
                               OC+OC at 0
                                  OC: c c c --(1)-> a a a (#2)
                                      Rule
                                  OC: a a a a --(1)-> a c a c c (#1)
                                      Rule
Hence, the SRS is non-terminating.