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The given Problem was:
a -> 
a b -> 
b b -> c 
c a -> a a b c 
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A self-embedding rewrite structure for the given SRS is:
   c a a a a a --(15)-> a c a a a a a b c b c (#140963)
   OC+OC at 2
      OC: c a a --(6)-> a c c (#140)
          OC+OC at 1
             OC: c a a --(5)-> a b b c (#65)
                 OC+OC at 2
                    OC: c a a --(4)-> a b a b c (#45)
                        OC+OC at 2
                           OC: c a --(2)-> a b c (#5)
                               OC+OC at 0
                                  OC: c a --(1)-> a a b c (#4)
                                      Rule
                                  OC: a --(1)->  (#1)
                                      Rule
                           OC: c a --(2)-> a b c (#5)
                               OC+OC at 0
                                  OC: c a --(1)-> a a b c (#4)
                                      Rule
                                  OC: a --(1)->  (#1)
                                      Rule
                    OC: a --(1)->  (#1)
                        Rule
             OC: b b --(1)-> c (#3)
                 Rule
      OC: c a a a --(9)-> a a a a a b c b c (#7952)
          OC+OC at 3
             OC: c a a a --(8)-> a a a c a b c (#2512)
                 OC+OC at 2
                    OC: c a a a --(6)-> a a c a a b c (#501)
                        OC+OC at 3
                           OC: c a a --(5)-> a a c c (#141)
                               OC+OC at 2
                                  OC: c a a --(4)-> a a b b c (#63)
                                      OC+OC at 3
                                         OC: c a a --(3)-> a a b a b c (#47)
                                             OC+OC at 3
                                                OC: c a --(1)-> a a b c (#4)
                                                    Rule
                                                OC: c a --(2)-> a b c (#5)
                                                    OC+OC at 0
                                                       OC: c a --(1)-> a a b c (#4)
                                                           Rule
                                                       OC: a --(1)->  (#1)
                                                           Rule
                                         OC: a --(1)->  (#1)
                                             Rule
                                  OC: b b --(1)-> c (#3)
                                      Rule
                           OC: c a --(1)-> a a b c (#4)
                               Rule
                    OC: c a --(2)-> a c (#8)
                        OC+OC at 1
                           OC: c a --(1)-> a a b c (#4)
                               Rule
                           OC: a b --(1)->  (#2)
                               Rule
             OC: c a --(1)-> a a b c (#4)
                 Rule
Hence, the SRS is non-terminating.