You&#x27;re asking for a loop invariant to prove that a non-terminating loop terminates?  That seems... somewhat contradictory.  Either you can&#x27;t prove that with a loop invariant, or the proof must be invalid.<p>As you said, the machine eventually runs out of memory.  But &quot;loop invariants&quot; don&#x27;t usually include the machine running out of memory as the termination condition, because that&#x27;s more a crash than a loop termination.  (That is, whatever part of the program you wanted to execute after the zeno loop won&#x27;t execute, because the <i>program</i> terminated, not just the loop.)  So when we talk about loop termination, program-crashing events are usually out of scope.  (That&#x27;s something we <i>also</i> need to prove - no undesirable side effects - but that&#x27;s actually a separate issue.)