Computable only means effective. I can write an effective spaghetti code solution that works and is very effective.
Efficiency is on a different axis. Computable doesn’t have to be efficient. For example, if you do the wrong things in the right way, (Low effective, high efficient), it won’t be computable because you did the wrong things. Doesn’t matter if you did it the right way: you did the wrong things.
So, that’s proof-by-… by where-it-doesn’t work… whatever that’s called.