# Context Free Grammar for language L

Can someone help with this:

$L=\{a^ib^j \mid i,j \ge 1 \text{ and } i \ne j \text{ and } i<2j\}$

I'm trying to write a grammar for this language? I tried this:

$S \to S_1 \mid S_2 \\ S_1 \to aXb \\ X \to aXb \mid aaXb \mid aab \\ S_2 \to aYb \\ Y \to aYb \mid Yb \mid b \\$

What do you think?

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Seems correct. Is there a problem? – Karolis Juodelė Feb 16 at 11:46