Context-Free Grammar from this language I'm having difficulties with an exercise in a theoretical CS class.
The problem is:

let $L_{2}$ be a language defined as follows: after every "a" come atleast two "b" or after every "b" comes atleast one "a". 

What is the CFG that creates $L_{2}$?

I'm struggling since 2h... I've found out that for example "abba" is not in the language, but to write it formally is quite difficult. Help would be much appreciated.
As Aspass.Jack wrote in the comments, let's first define $L_3$ to be the language where each $a$ is followed by at least 2 $b$'s, and $L_4$ to be the language where each $b$ is followed by at least one $a$.

Now, if let's say you can define CFGs for $L_3$ and $L_4$ with start symbols $S_3$ and $S_4$. Then, we simply need to define a grammer with the transition:
$$S \rightarrow S_3|S_4$$
together with all the transitions from the other 2 CFGs. Hopefully this simplifies your problem.