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The given Problem was:
a a a a -> b a a a 
b b -> a a b 
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A self-embedding rewrite structure for the given SRS is:
   (a)^k+4 --> (a)^2k baaa  (#1032)
   pattern overlapped by pattern
      RP: (a)^k+4 --> (b)^k+1 aaa  (#41)
          increment
             RP: (a)^k+3 --> (b)^k aaa  (#2)
                 self-overlapping Closure at 1
                    OC: a a a a --(1)-> b a a a (#1)
                        Rule
      RP: (b)^k+1 --> (a)^2k b  (#1)
          self-overlapping Closure at 2
             OC: b b --(1)-> a a b (#2)
                 Rule
Hence, the SRS is non-terminating.