Time complexity for a for loop with a multi-variable condition statement

A. What is the complexity (big-O) of the following code fragment?

for (i = 0; (i < n) || (i < m); i++) {
sequence of statements

The best i could come up with is the following.. if n is less then m O(n) else O(m) I have no clue how to write big-o in the case where there are two variables.

I know this is a very corner case and basic time complexity question so i do not mind removing it after I get some clarification.