========================================================
The given Problem was:
a -> 
a b -> b c a 
c a c -> b a a 
========================================================
A self-embedding rewrite structure for the given SRS is:
   c a c b b c b c --(15)-> b b b b c a c b b c b c a (#562424)
   OC+OC at 3
      OC: c a c b b c b c --(14)-> b b b a b c b b c b c a (#231682)
          OC+OC at 6
             OC: c a c b b --(7)-> b b b a b c c a (#1321)
                 OC+OC at 4
                    OC: c a c b b --(5)-> b b b a a b c a (#264)
                        OC+OC at 5
                           OC: c a c b --(4)-> b b b a a a (#226)
                               OC+OC at 1
                                  OC: c a c b --(2)-> b a b c a (#16)
                                      OC+OC at 2
                                         OC: c a c --(1)-> b a a (#3)
                                             Rule
                                         OC: a b --(1)-> b c a (#2)
                                             Rule
                                  OC: a b c --(2)-> b b a a (#11)
                                      OC+OC at 1
                                         OC: a b --(1)-> b c a (#2)
                                             Rule
                                         OC: c a c --(1)-> b a a (#3)
                                             Rule
                           OC: a b --(1)-> b c a (#2)
                               Rule
                    OC: a b --(2)-> b c (#4)
                        OC+OC at 2
                           OC: a b --(1)-> b c a (#2)
                               Rule
                           OC: a --(1)->  (#1)
                               Rule
             OC: c a c b c --(7)-> b b c b c a (#594)
                 OC+OC at 3
                    OC: c a c b c --(6)-> b b c a b (#262)
                        OC+OC at 1
                           OC: c a c b c --(5)-> b a b b (#51)
                               OC+OC at 4
                                  OC: c a c b c --(4)-> b a b b a (#42)
                                      OC+OC at 2
                                         OC: c a c --(1)-> b a a (#3)
                                             Rule
                                         OC: a b c --(3)-> b b a (#10)
                                             OC+OC at 1
                                                OC: a b --(1)-> b c a (#2)
                                                    Rule
                                                OC: c a c --(2)-> b a (#5)
                                                    OC+OC at 1
                                                       OC: c a c --(1)-> b a a (#3)
                                                           Rule
                                                       OC: a --(1)->  (#1)
                                                           Rule
                                  OC: a --(1)->  (#1)
                                      Rule
                           OC: a b --(1)-> b c a (#2)
                               Rule
                    OC: a b --(1)-> b c a (#2)
                        Rule
      OC: a b --(1)-> b c a (#2)
          Rule
Hence, the SRS is non-terminating.