than the one present at the vertex $11$.

In this situation we consider every active edge originating from $11$ and create a phantom edge through which this new water will flow. We will create a new vertex $11'$ with label $L(11')=L(7)-f_2(7,11)=9$ and connect it with each of the neighbors of $11$ that can get their label increased with the new flow. The only one such neighbor is $12$ and we obtain the graph as shown in the right portion of Figure [fi:figure 4]{}.

![\[fi:figure 4\] The configurations after the seconds 11 and 13.](graph05.png "fig:") ![\[fi:figure 4\] The configurations after the seconds 11 and 13.](graph06.png "fig:")

Variables
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In this section we will describe the memory management of variables necessary for the implementation of the algorithm. Before providing the precise set of variables let us describe the information that has to be carried throughout the execution process. As we have seen before, the vertices will have labels assigned to them. Denote by $L(P)$ the label of the vertex $P$. Initially we label each vertex of $G$ with $0$ except for vertices in $A$ which are labeled by $M$. Each vertex in $V$ and each edge in $E$ has a [*state*]{} assigned 