How can I efficiently construct a CFG from a language
The best way is to learn is to look at examples, and see how they work.
One of the simplest &quot;real&quot; context-free languages is $\{\; a^mb^n \mid n = m \;\}$
Its grammar is $S\to aSb\mid \varepsilon$.
Now add in steps, the extra 3, and the more than ...
$\{\; a^mb^n \mid n = m+3 \;\}$
$\{\; a^mb^n \mid n \le m+3 \;\}$