========================================================
The given Problem was:
a -> 
a a -> b a b c 
c -> 
c b -> a c 
========================================================
A self-embedding rewrite structure for the given SRS is:
   c b b b b b a b --(19)-> b b c b b b b b a b c c (#4339105)
   OC+OC at 4
      OC: c b b b b b a b --(18)-> b b c b a b b b b a b c c (#3139690)
          OC+OC at 3
             OC: c b b --(4)-> b b c c (#123)
                 OC+OC at 0
                    OC: c b b --(2)-> a a c (#9)
                        OC+OC at 1
                           OC: c b --(1)-> a c (#4)
                               Rule
                           OC: c b --(1)-> a c (#4)
                               Rule
                    OC: a a --(2)-> b b c (#7)
                        OC+OC at 1
                           OC: a a --(1)-> b a b c (#2)
                               Rule
                           OC: a --(1)->  (#1)
                               Rule
             OC: c b b b a b --(14)-> b a b b b b a b c c (#247933)
                 OC+OC at 5
                    OC: c b b b a --(11)-> b a b b b c b (#18711)
                        OC+OC at 3
                           OC: c b b b a --(9)-> b a b a a b (#5737)
                               OC+OC at 3
                                  OC: c b b b a --(7)-> b a b c b a b (#1606)
                                      OC+OC at 4
                                         OC: c b b --(3)-> b a b c c (#122)
                                             OC+OC at 0
                                                OC: c b b --(2)-> a a c (#9)
                                                    OC+OC at 1
                                                       OC: c b --(1)-> a c (#4)
                                                           Rule
                                                       OC: c b --(1)-> a c (#4)
                                                           Rule
                                                OC: a a --(1)-> b a b c (#2)
                                                    Rule
                                         OC: c b a --(4)-> b a b (#26)
                                             OC+OC at 0
                                                OC: c b --(2)-> a (#6)
                                                    OC+OC at 1
                                                       OC: c b --(1)-> a c (#4)
                                                           Rule
                                                       OC: c --(1)->  (#3)
                                                           Rule
                                                OC: a a --(2)-> b a b (#8)
                                                    OC+OC at 3
                                                       OC: a a --(1)-> b a b c (#2)
                                                           Rule
                                                       OC: c --(1)->  (#3)
                                                           Rule
                                  OC: c b --(2)-> a (#6)
                                      OC+OC at 1
                                         OC: c b --(1)-> a c (#4)
                                             Rule
                                         OC: c --(1)->  (#3)
                                             Rule
                           OC: a a --(2)-> b b c (#7)
                               OC+OC at 1
                                  OC: a a --(1)-> b a b c (#2)
                                      Rule
                                  OC: a --(1)->  (#1)
                                      Rule
                    OC: c b b --(3)-> b a b c c (#122)
                        OC+OC at 0
                           OC: c b b --(2)-> a a c (#9)
                               OC+OC at 1
                                  OC: c b --(1)-> a c (#4)
                                      Rule
                                  OC: c b --(1)-> a c (#4)
                                      Rule
                           OC: a a --(1)-> b a b c (#2)
                               Rule
      OC: a --(1)->  (#1)
          Rule
Hence, the SRS is non-terminating.