Comp Sci How to build logic to make context free grammar?

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The discussion revolves around building logic for context-free grammar, with the user sharing their solution and expressing confusion about understanding the derivation process. They acknowledge having memorized the grammar rules but seek clarity on the underlying logic behind them. The user notes that while there are exhaustive methods for machines, human understanding feels more like solving a puzzle. They emphasize the importance of intuition in grasping the solutions rather than relying solely on mechanical processes. Overall, the conversation highlights the challenge of comprehending context-free grammar beyond mere memorization.
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Homework Statement
Context free grammar
Relevant Equations
None
1636738772910.png

I already have the solution.

I also have another solution for this-:

S->AB

A->aA/a

B->ab/aBb

But my issue is I am memorizing them, I am not understanding how this came up. Please explain the logic building behind this.
 
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I don't think there is any "logic" to deriving a specific string of terminals from the "rules". I am sure there are exhaustive methods that can be performed by a machine. For us, it is kind of a puzzle.
 
I mean just some initution to understand why we came to this solution I mean would be helpful. I know there is no mechanical process for this. It is all practice. But my problem is I am confused while practicing. (I am clear about this tho so don't waste time on this now).
 
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