[SyzygyRhythm]

Even with the visualization, I found the minimal solution hard to visualize. I came up with this instead:

Suppose you start with two separated intervals. The left one starts sliding rightward. At what point do they contact? That's easy, it's just when (end1 > start2).

As it continues sliding, at what point do they lose contact? Again, easy: it's where (start1 >= end2).

So the solution is the first condition and the negation of the second, i.e.: (end1 > start2) && (start1 < end2)