What subset of TMs are there where the halting problem is decidable?
If you don't look at turing machines in particularly: Sometimes you can make an argument &quot;if it halts at all, then it must halt within x steps&quot; where x can be calculated, so you decide the halting problem by calculating x and performing x steps.
One particular case: A program with nested loops, where an upper limit for the number of iterations of each loop can be calculated before the loop is executed, will halt. And if you take such a program and insert identifiable &quot;non-halting&quot; constructs, like &quot;for (;;) {}&quot; in a C program, then the halting problem is decidable.