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I recently learned about the conversion, but I seem to be stuck.

I need to convert the following CFG to CNF:

$S → XY$

$X → abb|aXb|e$

$Y → c|cY$

  1. There is no S on the right side, so I did not need to add another
  2. I removed the null productions $X → e$

$S→XY|Y$

$X→abb|aXb|ab|$

$Y→c|cY|$

  1. I removed unit production $S→Y$ $Y→c$ with $S→c$

  2. There are no production rules which have more than 2 variables

  3. Here, I struggle. I am not allowed to have a terminal symbol and a variable together, but I am not sure how to get rid of these.

New grammar after step 4:

$S→XY|c$

$X→abb|aXb|ab$

$Y→ZY$

$Z→c$

I managed to replace the symbol c with Z, and added the new rule, so that seems fixed. However, I am unsure what do do with $aXb$.

Is this okay so far? if yes, what step should i take next?

Thank you in advance!

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