Even most algorithms would allow too many inputs. Even a simple algorithm computing the addition between two 64 bit numbers allow 2^128 possible input combinations, which would take billions of years to exhaustively check in the best case.

Making sure the test contains a sample from each class is the hard part. For example in your `if` example above it may happen that the code computing `a` is such that `a >= 5` is impossible, so that equivalence class is never going to happen. As such you can't have a test for it, and instead you'll have to prove that it can never happen, but this reduces to the halting problem and is not computable.

And even ignoring that problem, there may be an infinite amount of equivalence classes when you introduce loops/recursion, as the loops can run a different amount of times and thus lead to different executions.

Even just considering `if` statements, the amount of equivalence classes can be exponential in the amount of `if` (for example consider a series of `if` where each check a different bit of the input; ultimately you'll need any combination of bits to check every combination of `if`, and the number is 2^number of ifs).