I think you don't know your own routes.
If a traceroute to NIC 3 is issued remotely, and comes in on the Real IP, Where is it routed to? Your routing tables will determine that.
Likewise, if a traceroute to www is issued via your 3rd NIC, what route will it take? If it has a choice, or no route at all, it's bad.
If you hit an infinite loop, you have 2 spots which each think they are the route to each other.
Box A says "Yes I have a route to C (via B)"
Box B says "Yes I have a route to C (via A)"
So A and B happily ping pong any packet until the Time To Live is expired.
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