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The given Problem was:
a a b -> b b c a a 
a c -> a a 
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A self-embedding rewrite structure for the given SRS is:
   a a b c a b b c b b --(11)-> b b c b b c b b c a b b c a a b c a b b c b b c a a (#352242)
   OC+OC at 18
      OC: a a b c a b b --(8)-> b b c b b c b b c a b b c a a b c a a (#25589)
          OC+OC at 10
             OC: a a b c a b b --(6)-> b b c b b c b b c a a c b b c a a (#4242)
                 OC+OC at 12
                    OC: a a b c a b --(5)-> b b c b b c b b c a a c a a (#1653)
                        OC+OC at 6
                           OC: a a b c a b --(4)-> b b c b b c a a b c a a (#651)
                               OC+OC at 3
                                  OC: a a b c a b --(3)-> b b c a a b b c a a (#67)
                                      OC+OC at 4
                                         OC: a a b --(1)-> b b c a a (#1)
                                             Rule
                                         OC: a c a b --(2)-> a b b c a a (#7)
                                             OC+OC at 1
                                                OC: a c --(1)-> a a (#2)
                                                    Rule
                                                OC: a a b --(1)-> b b c a a (#1)
                                                    Rule
                                  OC: a a b --(1)-> b b c a a (#1)
                                      Rule
                           OC: a a b --(1)-> b b c a a (#1)
                               Rule
                    OC: a a b --(1)-> b b c a a (#1)
                        Rule
             OC: a c b --(2)-> b b c a a (#6)
                 OC+OC at 0
                    OC: a c --(1)-> a a (#2)
                        Rule
                    OC: a a b --(1)-> b b c a a (#1)
                        Rule
      OC: a c b b --(3)-> b b c b b c a a (#31)
          OC+OC at 0
             OC: a c --(1)-> a a (#2)
                 Rule
             OC: a a b b --(2)-> b b c b b c a a (#25)
                 OC+OC at 3
                    OC: a a b --(1)-> b b c a a (#1)
                        Rule
                    OC: a a b --(1)-> b b c a a (#1)
                        Rule
Hence, the SRS is non-terminating.