title: How to prove a Language is NOT Context Free
body: <p>I've been watching a lot of videos about how to prove this and I am getting mixed information about how to do so.</p>
  
  <p>In the case of contradiction, I am getting two different approaches and I want to know which  is correct.</p>
  
  <p>Example:</p>
  
  <p>L = {a^n b^n+1 c^n+1: n>=0}</p>
  
  <p>One source says I can Suppose that the language is context free, choose the sub-strings for  u,v,x,y while maintaining that three constraints, that being: </p>
  
  <ol>
  <li>uv^ixy^iz is in A for all i>=0</li>
  <li>|vy| > 0</li>
  <li>|vxy|&lt;= p</li>
  </ol>
  
  <p>and then show that the string that is pumped is not in the language, even while maintaining the constraints of a CFL. If the string pumped is not in the language, that how I can show the contradiction.</p>
  
  <p>Another Source says there are certain rules that must be followed when choosing vxy, that is vxy must straddle the midpoint...
  if you divided the string into 5 parts and a constraint isn't met, then that alone is proving that the language is not a CFL.</p>
  
  <p>Basically, which approach is right? what are the rules to dividing up u,v,x,y?</p>