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The given Problem was:
a a -> b 
a b c -> a c c a a a 
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A self-embedding rewrite structure for the given SRS is:
   a b c b c c a c c --(16)-> a c c a c c a c c a a c c a b c b c c a c c a a a (#623345)
   OC+OC at 14
      OC: a b c b c c a c c --(15)-> a c c a c c a c c a a c c a a a c b c c a c c a a a (#506334)
          OC+OC at 20
             OC: a b c b c c a c --(14)-> a c c a c c a c c a a c c a a a c b c c a b (#103579)
                 OC+OC at 17
                    OC: a b c b c c a c --(13)-> a c c a c c a c c a a c c a a a c a a c c a b (#85606)
                        OC+OC at 18
                           OC: a b c b c c a --(11)-> a c c a c c a c c a a c c a a a c a a b (#27902)
                               OC+OC at 10
                                  OC: a b c b c c a --(10)-> a c c a c c a c c a a b c c a a b (#5877)
                                      OC+OC at 11
                                         OC: a b c b c c a --(9)-> a c c a c c a c c a a a a c c a a b (#2848)
                                             OC+OC at 17
                                                OC: a b c b c c --(8)-> a c c a c c a c c a a a a c c a a a (#2278)
                                                    OC+OC at 12
                                                       OC: a b c b c --(7)-> a c c a c c a c c a a a a b (#649)
                                                           OC+OC at 6
                                                              OC: a b c b c --(6)-> a c c a c c a b c a b (#183)
                                                                  OC+OC at 3
                                                                     OC: a b c b c --(4)-> a c c a b c c a b (#45)
                                                                         OC+OC at 4
                                                                            OC: a b c b c --(3)-> a c c a a a c c a b (#13)
                                                                                OC+OC at 5
                                                                                   OC: a b c --(1)-> a c c a a a (#2)
                                                                                       Rule
                                                                                   OC: a b c --(2)-> a c c a b (#4)
                                                                                       OC+OC at 4
                                                                                          OC: a b c --(1)-> a c c a a a (#2)
                                                                                              Rule
                                                                                          OC: a a --(1)-> b (#1)
                                                                                              Rule
                                                                            OC: a a --(1)-> b (#1)
                                                                                Rule
                                                                     OC: a b c --(2)-> a c c a b (#4)
                                                                         OC+OC at 4
                                                                            OC: a b c --(1)-> a c c a a a (#2)
                                                                                Rule
                                                                            OC: a a --(1)-> b (#1)
                                                                                Rule
                                                              OC: a b c --(1)-> a c c a a a (#2)
                                                                  Rule
                                                       OC: a b c --(1)-> a c c a a a (#2)
                                                           Rule
                                                OC: a a --(1)-> b (#1)
                                                    Rule
                                         OC: a a --(1)-> b (#1)
                                             Rule
                                  OC: a b c --(1)-> a c c a a a (#2)
                                      Rule
                           OC: a b c --(2)-> a c c a b (#4)
                               OC+OC at 4
                                  OC: a b c --(1)-> a c c a a a (#2)
                                      Rule
                                  OC: a a --(1)-> b (#1)
                                      Rule
                    OC: a a --(1)-> b (#1)
                        Rule
             OC: a b c --(1)-> a c c a a a (#2)
                 Rule
      OC: a a --(1)-> b (#1)
          Rule
Hence, the SRS is non-terminating.