What makes a case complex?

An indirect recursion.

Recursion is just spiral reasoning. It looks like circular reasoning, but if you keep going with it the curve keeps getting smaller until eventually you reach the trivial case.

Honestly, this is the best single-line definition for a non-specialist I have ever seen.

How many single line definitions for non-specialists have you seen?

I have myself tried to explain recursion many times to those who do not understand it. While I do well, this is significantly more succinct than what it would take for me to succeed with most, and provides a clear visual. Nicely done.

I’ll probably be stealing that metaphor.

Please, credit it to Euler.

I don’t think recursion is that hard to reason about. You need an understanding of how to work with it. This requires practice in the same way dealing with trigonometry required that.

If you are a programmer and feel that dealing with recursion is hard I think you’ve got an opportunity for growth there.

It’s true that recursion is harder to deal with than loops. I generally use loops and recursion for a different class of problems.

Working with trees of arbitrary depth is much easier when using recursion.

Unless you are working in a functional language and don't have loops.