Modulo Chain Evaluator
Thanks to @Bumpf for the interesting concept! I had a lot of fun thinking about this one.
The most efficient modulo chain of length n in the form (x, y) is (Fₙ, Fₙ₊₁), where Fₙ is the nth Fibonacci number. You should use the smaller number first to make the chain slightly longer!
The longest modulo chain with x and y < 2500 is (987, 1597), with length 16.