Which form of the verb is correct after the verb "continue"?
If police didn't arrest him, he would continue robbing.
If police didn't arrest him, he would continue to rob.
(These sentences are written by me.)
Both forms are accepted, although if you're still learning, and didn't make it a habit, the '-ing' form is less ambiguous.
The problem is that the 'verb to verb' in some contexts may mean two different things.
I stopped smoking
It means unambiguously that I don't smoke (cigarettes or whatever) any more.
I was raking dry leaves all morning, and while doing it, I came to a life-changing decision. I stopped to smoke, and decided to quit my current job and take up a hobby.
And here we don't know: was the decision to stop smoking? Or - conversely - he stopped raking leaves, in order to smoke a cigarette, and then, while smoking, came up with the remaining decisions.
In other words, the negatives - 'stop', 'pause', 'cease', etc connected with 'to verb' may relate either to stopping/pausing/etc that specific activity, or pausing a previous activity, in order to start the given activity!
The '-ing' bears no such ambiguity and is equally valid as a grammar construct, so if you have no specific reasons for writing otherwise, '-ing' is safer.