Recursion base case may not always be useful even if it's logically valid for the base case, is this true?

[sanjarcode]

This may make writing recursive functions more involved, and less obvious. Basically it'll add need for a basic test of whether the base case is valid for some cases.

This is undesirable, if true.

[sanjarcode]

A problem that has a base case that needs extra observations/test.

[sanjarcode]

In short, are non-intuitive base cases in recursion possible?