Suppose that there exists a natural number that diverges to infinity under the Collatz map. Then the Collatz conjecture would be false, but your machine would s

Suppose that there exists a natural number that diverges to infinity under the Collatz map. Then the Collatz conjecture would be false, but your machine would still run forever on that diverging number. As far as I am aware, there is no known machine that halts iff the Collatz conjecture is false.