If you can make the agencies believe you don't depend at all on how you plan your attempts to stop it, it depends on how the time continuum works. The success of the timetraveller is already determined by how he knows the world and he can't ever change that timeline, unless he did not travel both in time and into a different universe. Why? Causality!
Setting the stage
Let's assume our Timetraveller starts 2016 and manages to get a time machine for reasons directly or indirectly related to 9/11. He uses it to get to 2000 and somehow manages to prevent 9/11 the next year through some method, one or another. Now, how does the future unfurl? Here it comes into play how time is handled!
Case A: Instable Time Loop
This is also called the "grandfather Paradoxon" at times. Now, he has prevented 9/11. As he was directly motivated by 9/11 happening just how it happened, his younger self will never have reason to get a time machine and prevent 9/11. So he doesn't enter the time machine, which leads to him never going back in time to prevent 9/11. As he didn't go back to prevent 9/11, he is again motivated to go back in time to prevent 9/11. And we are back to the start of the loop.
It is easy to see, that either, our protagonist has no chance of succeeding or getting out of the loop: If time travel removes the reason for the time travel, you can't get a stable situation as it flickers between the two alternatives! It is like a Schrödinger's Cat parable, where the box can't be opened ever again once it is closed.... However, there is a solution:
Case B: Stable Time Loop
The Novikov self-consistency principle tells that any time travel is only possible if the time travel has only results that have been part of the history already. You can't go back in time to change it, but there might be an alternative universe (many worlds theory!), where somebody from the future of 9/11 did go back in time and did prevent 9/11 in a way that would make sure, that somebody in the future did discover that the evidence that was needed to prevent 9/11 did come from his time and then went back to become this person. This Logical Loop that is created must be a self-fulfilling prophecy: in this AU 9/11 never happened, in no way. Just one person has to undergo the stable loop.
However, this is not the only way, time travel can go on, there are other variants...
(original text: here)
Case C: Doctor Who
Now, Dr. Who is clearly not a non-stable or a stable time loop all the times, but somehow manages to have a roughly linear personal timestream (that the timeline of the world around him is an entangled yarn ball doesn't matter, he has personal timeline superiority!). He does adhere to some of the Novikov rules but breaks them at other points. Still, for him the Blinovitch Limitation Effect is governing (most of the time):
- You can't redo or fix anything you did yourself
- You can't have any contact with any of your earlier selves or face some heavy energy discharge
On itself, this would not prevent the time traveler from going back, but he can't go back to fix his own mistakes. So he can't just "try again", and if he doesn't manage to prevent 9/11, he can't try again. He could, however (under the paradigm), try to prevent some other thing, as long as it wouldn't void any of his prior time travels.
Conclusion: Causality needs to be maintained!
No matter how time travel is achieved or what method is taken to ensure the success, one has to adhere to the principles of 4D Logic, that is one has to advert time paradoxes at any cost. Maintaining the Causal Loops is essential!
In a world without 9/11, there wouldn't have been a War on Terror. Iraq wouldn't have been invaded. Possibly the Arabian Spring wouldn't have risen. Maybe there wouldn't have been the ISIS either.
Now, any reason that springs from these can't be a reason for the time travel or the result is a non-stable time loop, casual instability and time paradox. Our time travel reason needs to be something that ensures the time travel is being taken to fulfil Case B. If we add Case C, it is just a complication, that makes sure that the time traveler has to try his best to succeed - if he would not, nobody would be able to fix his mess, as those others wouldn't remember it any differently (and neither he), and at the same time he has still to ensure he did the time travel in the first place.
Now, If he remains in the same universe, the one he came from, then he can't change the path it will run down until the time he started his time travel - either because he would create a non-stable time loop and would end in the Schroedinger state of probable success and failure at the same time, or because he adheres to Novikov and ends up being ignored. However, there is a way out that I mentioned earlier: Many worlds Theory.
Instead of just going back in time, our "time traveller" ends in a branching universe that differs in at least one point from the one he came from, he is there. It might have more differences (Schwarzenegger was President?!), it might be otherwise identical - but this opens up the whole area: It is no longer creating causality errors to prevent or fail at preventing, as you don't try to change the system with the results of it. Instead, you know how system A played out and then alter the conditions in system B, that is the same in most but not all details.