Breadth First Search:

Given a set of operators o1, ..., on in a breadth first search, every time a new state is reached, an action for each operator on  s  is added to the bottom of the agenda, i.e., the pairs (s,o1), ..., (s,on) are added to the end of the agenda in that order.

However, once the 'D' state had been found, the actions: 

1.(empty,add'D')

2.(empty,add'N')

3. (empty,add 'A')

would be added to the top of the agenda, so it would look like this:

4. ('D',add 'D')

5. ('D',add 'N')

6. ('D',add 'A') 

However, we can remove the first agenda item as this action has been undertaken. Hence there are actually 5 actions on the agenda after the first step in the search space. Indeed, after every step, one action will be removed (the action just carried out), and three will be added, making a total addition of two actions to the agenda. It turns out that this kind of breadth first search leads to the name 'DAN' after 20 steps. Also, after the 20th step, there are 43 tasks still on the agenda to do.