Algorithm 1${\mathcal{A}}_{DAG}$ (building of DAG $\Delta \left(T\right)$).

Input: A nonempty decision table T that has n conditional attributes $f_1,\dots ,f_n$. Output: Directed acyclic graph $\Delta \left(T\right)$. Build the graph consisting of one node T that is not tagged as processed. Check the processing of all nodes of the graph is completed or not. If yes, then the algorithm halts and returns the resulting graph as $\Delta \left(T\right)$. Otherwise, select a node (table) $\Theta$ which is yet unprocessed. Check node $\Theta$ is degenerate or not. (a) If yes, then tag the node $\Theta$ as processed and move to step 2. (b) If no, then draw a bundle of edges from the node $\Theta$ for each $f_i\in E(\Theta )$. Let $E(\Theta ,f_i)=\{a_1,\dots ,a_k\}$. Then draw k edges from $\Theta$ and attach to these edges systems of equations $\{f_i=a_1\},\dots ,\{f_i=a_k\}$. These edges enter nodes $\Theta \{f_i=a_1\},\dots ,\Theta \{f_i=a_k\}$, respectively. In case some of the nodes $\Theta \{f_i=a_1\},\dots ,\Theta \{f_i=a_k\}$ are not available in the graph, then add these nodes to the graph. Tag the node $\Theta$ as processed and move to step 2.