Running only RIP? Probably not. Most routing loops occur because of the wrong application of "Default Route(s)" or other statics.
For example, if router1 in your example had a default route to router2, and router2 had a route (static or otherwise) that pointed to a network that the he believed exists behind router1 (that doesn't exist). Router1 would send the traffic to router2, router2 would ultimately send it back ... repeat until the TTL expires.
It is possible to have an loop exist briefly in RIP when a driectly-attached network on router1 drops and router2 hasn't received an update. Router1 doesn't have a good path anymore, so it forwards the traffic out the default, router2 gets the packet, still has a route in the table saying that router1 is the best path and he sends it back ... repeat until TTL expires or the route gets updated (on router2).
I'm sure there are some other circumstances, but hopefully, you get the idea.
Basically it boils down to: If you start getting "TTL Expired" messages, chances are good that you have a loop. If you have a loop, evaluate your Default and Static routes (starting on either side of the router passing the message to the host getting TTL expired).
Good Luck
Scott
