> in general we should assume it is always impossible to exhaustively test programs

The whole program? Yes.

For testing individual components, there's no need to assume. The answer is very likely either clearly yes (the input is a handful of booleans) or clearly no (the input is several integers or even unbounded) and for those cases where it's not immediately clear (one i16? Three u8s?) it's probably still not hard to think through for your particular case in your particular context.