Find a regular language that becomes non-regular if you cut away the middle third of all words Let $A$ be a regular language, let $A'=\{xz\}$ such that for some $y,|x|=|y|=|z|$ and $xyz\in A$.
Show that $A'$ is not necessarily regular language.

This is an excercise of Sipser, I've no idea how to construct $A,A'$ please help someone
Hint: Let $A = a^+ b^+ c^+$ and consider $A' \cap a^+c^+$.