title: How to prove left-recursive grammar is not in LL(1) using parsing table
body: <p>I have a grammar and would like to prove that it is not in LL(1):</p>
  
  <pre><code>S-&gt;SA|A
  A-&gt;a
  </code></pre>
  
  <p>As it is a left-recursive grammarm, to find the first and follow sets I eliminated the left recursion and got:</p>
  
  <pre><code>S-&gt;AS'
  S'-&gt;AS'|Empty
  A-&gt;a
  
  first of A={a}      follow of S={$}
  first of s'={a,ε}   follow of S'={$}
  first of S={a}       follow of A={a,$}
  </code></pre>
  
  <p>But when I filled in the parsing table, I did not get any cell with 2 entries. Then how is one to prove that the given grammar is not in LL(1)?  </p>