The question is as follows:
Let's observe the following Post correspondence problem.
Input: Two finite lists of words $A$ and $B$ and a natural number $k$.
Question: Is there any words correspondence with a length of $k$ at the maximum?
Describe an algorithm to solve the problem and analyze its runtime.
I really don't understand how to solve this problem. From my understanding, the Post correspondence problem is undecidable so how come we can describe an algorithm to solve this question?