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The given Problem was:
b b -> b a 
a b -> b c c 
a c -> a a 
c a -> b a a 
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A self-embedding rewrite structure for the given SRS is:
   ba (c)^k ba --> ba (c)^2k+1 baa  (#42933)
   pattern overlapped by closure at r0
      RP: ba (c)^k b --> ba (c)^2k+1 c  (#4994)
          expand ->
             RP: ba (c)^k b --> ba (c)^2k+2  (#2131)
                 pattern overlapped by closure at l-1
                    RP: a (c)^k b --> b (c)^2k+2  (#619)
                        pattern overlapped by pattern
                           RP: a (c)^k --> (a)^k+1  (#2)
                               self-overlapping Closure at 1
                                  OC: a c --(1)-> a a (#3)
                                      Rule
                           RP: (a)^k+1 b --> b (c)^2k+2  (#19)
                               increment
                                  RP: (a)^k b --> b (c)^2k  (#3)
                                      self-overlapping Closure at -1
                                         OC: a b --(1)-> b c c (#2)
                                             Rule
                    OC: b b --(1)-> b a (#1)
                        Rule
      OC: c a --(1)-> b a a (#4)
          Rule
Hence, the SRS is non-terminating.