# Give a context-free grammar

We know that $$L$$ = { $$w$$ $$in$$ {a, b}* $$|$$ $$|w|_{a}$$ > $$|w|_{b}$$ }

This is my answer: $$G$$ = ({$$S$$,$$A$$,$$B$$},{$$a$$,$$b$$},$$R$$,$$S$$)

$$R$$ = S $$to$$ $$AB$$

$$A$$ $$to$$ $$aA | Aa |B$$

$$A$$ $$to$$ $$a | abB | Bab | Bba |aBb|bBa$$

But after testing, it seems that writing like this is wrong.

So how should it be written?

https://web.stanford.edu/class/archive/cs/cs103/cs103.1156/tools/cfg/

This link can be used to simulate.