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The given Problem was:
a a -> b a b c c 
c a -> 
c b -> a 
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A self-embedding rewrite structure for the given SRS is:
   a a b a b a b a a b --(22)-> b a b b a b a a b a b a b a a b c c (#176286)
   OC+OC at 13
      OC: a a b a b a b a a b --(21)-> b a b b a b a a b a b a b c b a b c c (#169940)
          OC+OC at 14
             OC: a a b a b a b a a b --(20)-> b a b b a b a a b a b a b c a a (#68243)
                 OC+OC at 14
                    OC: a a b a b a b a a b --(19)-> b a b b a b a a b a b a b c c b a (#65459)
                        OC+OC at 10
                           OC: a a b a b a b a a b --(18)-> b a b b a b a a b a a a b a (#24702)
                               OC+OC at 10
                                  OC: a a b a b a b a a b --(17)-> b a b b a b a a b a c b a b a (#13954)
                                      OC+OC at 11
                                         OC: a a b a b a --(13)-> b a b b a b a a b a c c (#10950)
                                             OC+OC at 3
                                                OC: a a b a b a --(7)-> b a b a a b a a b c c (#258)
                                                    OC+OC at 3
                                                       OC: a a b a b a --(6)-> b a b c b a b a a b c c (#122)
                                                           OC+OC at 4
                                                              OC: a a --(1)-> b a b c c (#1)
                                                                  Rule
                                                              OC: c b a b a --(5)-> b a b a a b c c (#80)
                                                                  OC+OC at 3
                                                                     OC: c b a b a --(4)-> b a b c b a b c c (#28)
                                                                         OC+OC at 0
                                                                            OC: c b --(1)-> a (#3)
                                                                                Rule
                                                                            OC: a a b a --(3)-> b a b c b a b c c (#19)
                                                                                OC+OC at 4
                                                                                   OC: a a --(1)-> b a b c c (#1)
                                                                                       Rule
                                                                                   OC: c b a --(2)-> b a b c c (#5)
                                                                                       OC+OC at 0
                                                                                          OC: c b --(1)-> a (#3)
                                                                                              Rule
                                                                                          OC: a a --(1)-> b a b c c (#1)
                                                                                              Rule
                                                                     OC: c b --(1)-> a (#3)
                                                                         Rule
                                                       OC: c b --(1)-> a (#3)
                                                           Rule
                                                OC: a a b a a b --(6)-> b a b a a b a (#97)
                                                    OC+OC at 3
                                                       OC: a a b a a b --(5)-> b a b c b a b a (#46)
                                                           OC+OC at 4
                                                              OC: a a --(1)-> b a b c c (#1)
                                                                  Rule
                                                              OC: c b a a b --(4)-> b a b a (#16)
                                                                  OC+OC at 0
                                                                     OC: c b --(1)-> a (#3)
                                                                         Rule
                                                                     OC: a a a b --(3)-> b a b a (#9)
                                                                         OC+OC at 3
                                                                            OC: a a a --(2)-> b a b c (#4)
                                                                                OC+OC at 4
                                                                                   OC: a a --(1)-> b a b c c (#1)
                                                                                       Rule
                                                                                   OC: c a --(1)->  (#2)
                                                                                       Rule
                                                                            OC: c b --(1)-> a (#3)
                                                                                Rule
                                                       OC: c b --(1)-> a (#3)
                                                           Rule
                                         OC: c b a a b --(4)-> b a b a (#16)
                                             OC+OC at 0
                                                OC: c b --(1)-> a (#3)
                                                    Rule
                                                OC: a a a b --(3)-> b a b a (#9)
                                                    OC+OC at 3
                                                       OC: a a a --(2)-> b a b c (#4)
                                                           OC+OC at 4
                                                              OC: a a --(1)-> b a b c c (#1)
                                                                  Rule
                                                              OC: c a --(1)->  (#2)
                                                                  Rule
                                                       OC: c b --(1)-> a (#3)
                                                           Rule
                                  OC: c b --(1)-> a (#3)
                                      Rule
                           OC: a a --(1)-> b a b c c (#1)
                               Rule
                    OC: c b --(1)-> a (#3)
                        Rule
             OC: a a --(1)-> b a b c c (#1)
                 Rule
      OC: c b --(1)-> a (#3)
          Rule
Hence, the SRS is non-terminating.