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The given Problem was:
a a b -> c c a a a 
a c -> b a 
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A self-embedding rewrite structure for the given SRS is:
   a a b b a b b --(10)-> c c b b a a b b a b b a a a a (#10376)
   OC+OC at 10
      OC: a a b b a b b --(9)-> c c b b a a b b a b a c a a a (#6839)
          OC+OC at 7
             OC: a a b b a b b --(8)-> c c b b a a b a c b a c a a a (#4752)
                 OC+OC at 6
                    OC: a a b b a b b --(7)-> c c b b a a a c c b a c a a a (#1483)
                        OC+OC at 7
                           OC: a a b b --(4)-> c c b b a a a a (#37)
                               OC+OC at 3
                                  OC: a a b b --(3)-> c c b a c a a a (#24)
                                      OC+OC at 2
                                         OC: a a b b --(2)-> c c a c c a a a (#17)
                                             OC+OC at 3
                                                OC: a a b --(1)-> c c a a a (#1)
                                                    Rule
                                                OC: a a b --(1)-> c c a a a (#1)
                                                    Rule
                                         OC: a c --(1)-> b a (#2)
                                             Rule
                                  OC: a c --(1)-> b a (#2)
                                      Rule
                           OC: a a b b --(3)-> c c b a c a a a (#24)
                               OC+OC at 2
                                  OC: a a b b --(2)-> c c a c c a a a (#17)
                                      OC+OC at 3
                                         OC: a a b --(1)-> c c a a a (#1)
                                             Rule
                                         OC: a a b --(1)-> c c a a a (#1)
                                             Rule
                                  OC: a c --(1)-> b a (#2)
                                      Rule
                    OC: a c --(1)-> b a (#2)
                        Rule
             OC: a c --(1)-> b a (#2)
                 Rule
      OC: a c --(1)-> b a (#2)
          Rule
Hence, the SRS is non-terminating.