ICMP - TTL - Trace Route

Given the following situation:

PC --- |aa RTR1 bb| --- |aa RTR2 bb| --- |aa RTR3 bb| etc

Each of the |aa rtr bb| is meant to be a router with two ports aa and bb.

My question is this. When you do a trace route from PC which router port address(aa or bb) will respond with time to live exceeded in transit message?

I seem to remember being taught to think of the router as being in as many parts as ports, so that in my scenario when aa is forwarding the packet to bb and decrements the ttl to 0, it will be the address of the aa port in the failure message. I am trying to find the definitive answer.

Thanks.