special case of best first search algorithms
Consider a node $u$ such that $depth(u)=l$.

In Best first Search when you evaluate $u$ with the evaluation function you defined, you have $f(u)=−l$.

queue

╔═══╤═══╤═════╤═══╗
║ r │ a │ ... │ u ║
╚═══╧═══╧═════╧═══╝


When you expand $u$ and you evaluate the first child of $u$ (suppose it is Node $v$) you have $f(v)=−(l+1)&lt;−l=f(u)$ so now you expand $v$ (that means that you put $v$ in the front of the queue) and you continue. 

queue

╔═══╤═══╤═════╤═══╤═══╗
║ r │ a │ ... │ u │ v ║
╚═══╧═══╧═════╧═══╧═══╝


This corresponds to what you do when you use Depth First Search.