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The given Problem was:
R b -> b R 
R c -> L c 
b L -> L b 
a L -> a b R 
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A self-embedding rewrite structure for the given SRS is:
   a (b)^k Lc --> a (b)^k+1 Lc  (#8052)
   pattern overlapped by closure at r0
      RP: a (b)^k L --> a (b)^k+1 R  (#6118)
          pattern overlapped by pattern
             RP: a (b)^k L --> abR (b)^k  (#130)
                 pattern overlapped by closure at l-1
                    RP: (b)^k L --> L (b)^k  (#4)
                        self-overlapping Closure at -1
                           OC: b L --(1)-> L b (#3)
                               Rule
                    OC: a L --(1)-> a b R (#4)
                        Rule
             RP: R (b)^k --> (b)^k R  (#1)
                 self-overlapping Closure at 1
                    OC: R b --(1)-> b R (#1)
                        Rule
      OC: R c --(1)-> L c (#2)
          Rule
Hence, the SRS is non-terminating.