Procedure: Start a secondary TM in parallel with the first, but have the second perform exactly 1 step each 2 steps the first TM performs (i.e. it runs at half speed). If the second machine ever reaches the same configuration as the first, a loop was detected (obviously).
Claim: All infinite local loops in a TM can be detected in the above manner.
Local loop, in this context, refers to a machine running within a certain tape interval without ever stopping. To clarify, in particular this excludes any machines which extend the tape in any direction without bounds.
Has this been proven? I'm pretty sure I found this claim in a paper, I believe one of Marxen's, though I can't seem to find it.