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The given Problem was:
a a b -> b b c a c 
a c -> a a 
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A self-embedding rewrite structure for the given SRS is:
   a c c a b b c b b --(18)-> b b c b b c a b b c b b c a c c a b b c b b c a c (#1345782)
   OC+OC at 17
      OC: a c c a b b --(14)-> b b c b b c a b b c b b c a c c a a (#83598)
          OC+OC at 10
             OC: a c c a b b --(12)-> b b c b b c a b b c a c b c a a (#26269)
                 OC+OC at 7
                    OC: a c c a b b --(10)-> b b c b b c a a c b b c a a (#4435)
                        OC+OC at 9
                           OC: a c c a b --(7)-> b b c b b c a a c a c (#956)
                               OC+OC at 3
                                  OC: a c c a b --(4)-> b b c a c b c a c (#226)
                                      OC+OC at 0
                                         OC: a c c a b --(3)-> a a b b c a c (#19)
                                             OC+OC at 1
                                                OC: a c --(1)-> a a (#2)
                                                    Rule
                                                OC: a c a b --(2)-> a b b c a c (#7)
                                                    OC+OC at 1
                                                       OC: a c --(1)-> a a (#2)
                                                           Rule
                                                       OC: a a b --(1)-> b b c a c (#1)
                                                           Rule
                                         OC: a a b --(1)-> b b c a c (#1)
                                             Rule
                                  OC: a c b --(3)-> b b c a a (#10)
                                      OC+OC at 0
                                         OC: a c --(1)-> a a (#2)
                                             Rule
                                         OC: a a b --(2)-> b b c a a (#8)
                                             OC+OC at 3
                                                OC: a a b --(1)-> b b c a c (#1)
                                                    Rule
                                                OC: a c --(1)-> a a (#2)
                                                    Rule
                           OC: a c b --(3)-> b b c a a (#10)
                               OC+OC at 0
                                  OC: a c --(1)-> a a (#2)
                                      Rule
                                  OC: a a b --(2)-> b b c a a (#8)
                                      OC+OC at 3
                                         OC: a a b --(1)-> b b c a c (#1)
                                             Rule
                                         OC: a c --(1)-> a a (#2)
                                             Rule
                    OC: a c b --(2)-> b b c a c (#6)
                        OC+OC at 0
                           OC: a c --(1)-> a a (#2)
                               Rule
                           OC: a a b --(1)-> b b c a c (#1)
                               Rule
             OC: a c b --(2)-> b b c a c (#6)
                 OC+OC at 0
                    OC: a c --(1)-> a a (#2)
                        Rule
                    OC: a a b --(1)-> b b c a c (#1)
                        Rule
      OC: a c b b --(4)-> b b c b b c a c (#50)
          OC+OC at 0
             OC: a c --(1)-> a a (#2)
                 Rule
             OC: a a b b --(3)-> b b c b b c a c (#41)
                 OC+OC at 3
                    OC: a a b --(1)-> b b c a c (#1)
                        Rule
                    OC: a c b --(2)-> b b c a c (#6)
                        OC+OC at 0
                           OC: a c --(1)-> a a (#2)
                               Rule
                           OC: a a b --(1)-> b b c a c (#1)
                               Rule
Hence, the SRS is non-terminating.