Infinite CFLs and Another Pumping Theorem

Intuitive reasoning behind the pumping theorem for CFLs

Now that we know how to determine if a context-free grammar generates an infinite language, let’s look a little closer at such languages. Suppose $A$ is a recursive variable in some CFG. Beginning with the start variable until the time $A$ first appears in a working derivation, symbols will have accumulated around $A$. Look at the CFG below and the following derivation: