Does Oblivion Ring create a loop if two of them are on the battlefield and each exiles the other?

When two Oblivion Rings (let's call them OR-A and OR-B) are both on the battlefield and each has exiled the other, the game reaches a stable state — not a loop. Each O-Ring's "when it enters the battlefield" trigger has already resolved, and its "when it leaves the battlefield" trigger hasn't fired yet, so nothing is continuously repeating. This is a static configuration, not a loop.

The complexity arises during resolution. When OR-A enters and its ETB trigger resolves, it exiles OR-B. OR-B leaving the battlefield triggers OR-B's "leaves the battlefield" ability, returning whatever OR-B had previously exiled. Then OR-B re-enters (if returned), creating a new ETB trigger chain. This ordering is governed by CR 603.6a — triggered abilities go on the stack and resolve in the order they are put there (LIFO), and the active player controls the order of their own simultaneous triggers (CR 603.3b).

A known exploit: if you control both O-Rings, you can manipulate the trigger order to permanently exile a permanent. If OR-A enters with nothing previously exiled by OR-B, you can arrange triggers so OR-B's LTB resolves (returning nothing) before OR-A's ETB resolves to exile OR-B, leaving OR-B in exile with no LTB trigger pending to return it.

Concrete example: OR-A is on the battlefield exiling your opponent's Titan. You play OR-B. OR-B's ETB trigger goes on the stack. You let it resolve — it exiles OR-A. OR-A leaving triggers its LTB, returning the Titan. The Titan returns to the battlefield. OR-B is now in a stable state exiling OR-A. No loop has occurred; the game just proceeds normally.

So the two O-Rings do NOT create an infinite loop — they simply end up in a locked configuration where each holds the other in exile, provided the trigger ordering doesn't allow one to escape permanently.