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The given Problem was:
a a -> a b 
b a c -> c c a a a 
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A self-embedding rewrite structure for the given SRS is:
   b a c a a c c a c c --(16)-> c c a c c a c c a a c c a b a c a a c c a c c a a a (#508692)
   OC+OC at 18
      OC: b a c a a c c --(13)-> c c a c c a c c a a c c a b a c a a b (#47771)
          OC+OC at 10
             OC: b a c a a c c --(11)-> c c a c c a c c a a b a c c a a b (#8981)
                 OC+OC at 12
                    OC: b a c a a c --(9)-> c c a c c a c c a a b a b a (#2966)
                        OC+OC at 6
                           OC: b a c a a c --(7)-> c c a c c a b a c a b a (#916)
                               OC+OC at 3
                                  OC: b a c a a c --(5)-> c c a b a c c a b a (#80)
                                      OC+OC at 4
                                         OC: b a c --(2)-> c c a b a (#4)
                                             OC+OC at 2
                                                OC: b a c --(1)-> c c a a a (#2)
                                                    Rule
                                                OC: a a --(1)-> a b (#1)
                                                    Rule
                                         OC: a a a c --(3)-> a c c a b a (#7)
                                             OC+OC at 1
                                                OC: a a --(1)-> a b (#1)
                                                    Rule
                                                OC: b a c --(2)-> c c a b a (#4)
                                                    OC+OC at 2
                                                       OC: b a c --(1)-> c c a a a (#2)
                                                           Rule
                                                       OC: a a --(1)-> a b (#1)
                                                           Rule
                                  OC: b a c --(2)-> c c a b a (#4)
                                      OC+OC at 2
                                         OC: b a c --(1)-> c c a a a (#2)
                                             Rule
                                         OC: a a --(1)-> a b (#1)
                                             Rule
                           OC: b a c --(2)-> c c a a b (#5)
                               OC+OC at 3
                                  OC: b a c --(1)-> c c a a a (#2)
                                      Rule
                                  OC: a a --(1)-> a b (#1)
                                      Rule
                    OC: b a c --(2)-> c c a a b (#5)
                        OC+OC at 3
                           OC: b a c --(1)-> c c a a a (#2)
                               Rule
                           OC: a a --(1)-> a b (#1)
                               Rule
             OC: b a c --(2)-> c c a b a (#4)
                 OC+OC at 2
                    OC: b a c --(1)-> c c a a a (#2)
                        Rule
                    OC: a a --(1)-> a b (#1)
                        Rule
      OC: b a c c --(3)-> c c a c c a a a (#24)
          OC+OC at 3
             OC: b a c --(2)-> c c a b a (#4)
                 OC+OC at 2
                    OC: b a c --(1)-> c c a a a (#2)
                        Rule
                    OC: a a --(1)-> a b (#1)
                        Rule
             OC: b a c --(1)-> c c a a a (#2)
                 Rule
Hence, the SRS is non-terminating.