From the CCNA ICND2 Exam book: "Routers decrement the TTL by 1 every time they forward a packet; if a router decrements the TTL to 0, it throws away the packet. This prevents packets from rotating forever." I want to make it clear that before the router forwards a packet, the TTL is still remain the same. For example, in the topology above, pings to S0/1 and S0/0 of Router 2 have the same TTL.
The picture below shows TTL values for each interface of each router and for HostB. Notice that Host A initializes ICMP packet with a TTL of 255: