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The given Problem was:
a -> b 
a a b c -> b c c a a a 
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A self-embedding rewrite structure for the given SRS is:
   a a b c a b c c b c c --(12)-> b c c b c c b c c a b c c a a b c a b c c b c c a a a (#673815)
   OC+OC at 18
      OC: a a b c a b c c --(9)-> b c c b c c b c c a b c c a a b c a a a (#41656)
          OC+OC at 10
             OC: a a b c a b c c --(7)-> b c c b c c b c c a a a b c c a a a (#6534)
                 OC+OC at 12
                    OC: a a b c a b c --(6)-> b c c b c c b c c a a a a a b (#2172)
                        OC+OC at 6
                           OC: a a b c a b c --(5)-> b c c b c c a a b c a a b (#924)
                               OC+OC at 3
                                  OC: a a b c a b c --(3)-> b c c a a b c c a a b (#20)
                                      OC+OC at 5
                                         OC: a a b c --(1)-> b c c a a a (#2)
                                             Rule
                                         OC: a a b c --(2)-> b c c a a b (#5)
                                             OC+OC at 5
                                                OC: a a b c --(1)-> b c c a a a (#2)
                                                    Rule
                                                OC: a --(1)-> b (#1)
                                                    Rule
                                  OC: a a b c --(2)-> b c c a a b (#5)
                                      OC+OC at 5
                                         OC: a a b c --(1)-> b c c a a a (#2)
                                             Rule
                                         OC: a --(1)-> b (#1)
                                             Rule
                           OC: a a b c --(1)-> b c c a a a (#2)
                               Rule
                    OC: a a b c --(1)-> b c c a a a (#2)
                        Rule
             OC: a a b c --(2)-> b c c a a b (#5)
                 OC+OC at 5
                    OC: a a b c --(1)-> b c c a a a (#2)
                        Rule
                    OC: a --(1)-> b (#1)
                        Rule
      OC: a a b c c --(3)-> b c c b c c a a a (#25)
          OC+OC at 3
             OC: a a b c --(2)-> b c c a a b (#5)
                 OC+OC at 5
                    OC: a a b c --(1)-> b c c a a a (#2)
                        Rule
                    OC: a --(1)-> b (#1)
                        Rule
             OC: a a b c --(1)-> b c c a a a (#2)
                 Rule
Hence, the SRS is non-terminating.