Anything that you think might break your code.  Or rather, demonstrate that no reasonable situation exists which will break your code. 

Honestly though I don't have a good specific answer for this.  Mostly this is because I'm not sure what is going on here.  This solution seems to solve the problems you've posed but I'm not able to understand it well enough to have confidence that it works in all situations.  You may be trying to solve a difficult problem here. 

For example

What if we know that 
x - 2 > 0
y - 1 > 0
and we ask if 
x + y > 1

It sounds like you're trying to implement a fairly general constraint solver.  I wonder if there are more theoretical methods to accomplish this task.