zaqtivi
It is not clear whether the 7513 is your router which is connected to the customer router and you want to find out what routing protocol is being run by the customer or what the relationship is.
Assuming that the 7513 is your router and that you can not ask the customer what routing protocol they are running, the most precise way that I know to discover the protocol is to do debug ip packet and look in the debug output to find routing protocol packets. You could consider an alternative (less processor intensive but not as precise) to assign an access list inbound on the customer facing interface which included:
permit ip any host 255.255.255.255 log-input
permit ip any 224.0.0.0 0.255.255.255 log-input
(if there is not an existing access list then you would also want permit ip any any as the last line of the access list).
The logged output would allow you to detect if the customer is sending RIPv1 (to the broadcast address), or to detect RIPv2, OSPF, or EIGRP (to the multicast destination). It would not detect BGP or ISIS.
HTH
Rick
HTH
Rick