Have a program use its own output as input, effectively letting you run programs for infinite amounts of time, which depending on how time travel is resolved may or may not give you a halting oracle.

Also you can now brute force most of mathematics:

one way to do this is using first order logic which is expressive enough to state most problems. First order logic is semi-decidable which means that there are algorithms which will eventually return a proof for correct statements. Since your computer will take at most ten seconds to do this, you will have a proof after ten seconds or know that the statement was incorrect if your computer remains silent.