Here are two scenarios to test failures and the count to infinity problem.


c2inf.net contains a network where the count to infinity problem arises if
node 4 fails.


    +---+         +---+
    | 1 | ------- | 2 | 
    +-+-+         +-+-+
      \            /
       \          /
        \        /
         \      /
          \    /
           \  /
          ++-++
          | 3 |
          +-+-+
            |
            |
            |
            |
          +-+-+
          | 4 |
          +-+-+
            |
            |
            |
            |
          +-+-+
          | 5 |
          +-+-+


notc2inf.net contains a network where the count-to-infinity problem does not
arise if node 4 fails.  It is similar to c2inf.net, but there's an extra
link between nodes 2 and 5.

    +---+         +---+
    | 1 | ------- | 2 | 
    +-+-+         +-+++
      \            / |
       \          /  | 
        \        /   |
         \      /    |
          \    /     |
           \  /      |
          ++-++      |
          | 3 |      |
          +-+-+      |
            |        |
            |        |
            |        |
            |        |
          +-+-+      |
          | 4 |      |
          +-+-+      |
            |        |
            |        |
            |        |
            |        |
          +-+-+      |
          | 5 +------+
          +-+-+