Is following grammar LR(0)? I know how to verify whether grammar is LR(0) or not. But this particular case is little tricky and hence the question.


  Grammar:
  
  $SL \rightarrow SL ; S \space | \space \epsilon$
  
  $S \rightarrow s$
  
  (Note: $SL$ is single non-terminal.)


Now, LR(0) automaton for this grammar is as follow:



Now my question is whether to consider entry $start \rightarrow SL.$ in $State_1$ as SR conflict. 

Because I previously came to know that we don't consider conflicts due to augmented production.

Thanks.
You haven't actually augmented the grammar. The augmented grammar has the production $$start\to SL\;\$$$

With that change, state 1 is not a reduction state and there is no conflict.

If you did not intend to augment the grammar, then it is not $LR(0)$, because the language does not have the prefix property. But that's not very useful, so normally we augment grammars, turning the language $L$ into $L\$$, where $\$$ is a symbol not in the the alphabet for $L$. Clearly the augmented language has the prefix property.

There's a reasonable explanation with references on Wikipedia.