That's why you instead specify that if & when the program halts it travels back in time to let you know it has. Thus you would know immediately after starting t

That's why you instead specify that if & when the program halts it travels back in time to let you know it has. Thus you would know immediately after starting the computation if it's going to halt, how long it'll take, and what the result is. Of course you should still carry out the computation to prevent a paradox.