How to make string test cases by using class partitioning?

I'm learning S/W testing and practicing to make test case. But I have no idea, when inputs are strings. I have a example. please give me some advise how to partition classes, and determine boundaries...

My program has to inputs that are 2 non empty Strings. And It determines which one has more vowels characters and prints the string.

For example, when 'mike' and 'hi' is entered, the program prints mike. If both strings have same number of vowels, the program prints equal.

I understand that the number of inputs can be a class. And I and I knows that 2 and 4 can be boundary invalid vales of the class. But That's all I know....