Algorithm 2${\mathcal{C}}_h$ (construction of the tree ${\Gamma }^{\left(k\right)}\left(T\right)$).

Input: T (a nonempty decision table), $\Delta \left(T\right)$ (the directed acyclic graph for T), and k (a natural number between 1 to 5). Output: A decision tree ${\Gamma }^{\left(k\right)}\left(T\right)$. Check all nodes of the DAG $\Delta \left(T\right)$ whether there is a decision tree attached to each node. If yes, then return the tree attached to the node T as ${\Gamma }^{\left(k\right)}\left(T\right)$ and break the algorithm. If not, select a node $\Theta$ of the graph $\Delta \left(T\right)$ that does not have an attached tree. It can be either a leaf node of $\Delta \left(T\right)$ or an internal node of $\Delta \left(T\right)$ where all children are tagged with trees. If $\Theta$ is a leaf node, then attach to it the decision tree ${\Gamma }^{\left(k\right)}(\Theta )$ that have only a single node. This node is tagged with the decision attached to all rows of $\Theta$. Move to step 1. If $\Theta$ is not a leaf node, then do the following according to the value k: When $k=1$, construct the tree ${\Gamma }_a^{\left(1\right)}(\Theta )$ and attach it to $\Theta$ as the tree ${\Gamma }^{\left(1\right)}(\Theta )$. When $k=2$, construct the tree ${\Gamma }_h^{\left(2\right)}(\Theta )$ and attach it to $\Theta$ as the tree ${\Gamma }^{\left(2\right)}(\Theta )$. When $k=3$, construct the trees ${\Gamma }_a^{\left(3\right)}(\Theta )$ and ${\Gamma }_h^{\left(3\right)}(\Theta )$, choose between them a tree with the minimum depth and attach it to $\Theta$ as the tree ${\Gamma }^{\left(3\right)}(\Theta )$. When $k=4$, construct the tree ${\Gamma }_p^{\left(4\right)}(\Theta )$ and attach it to $\Theta$ as the tree ${\Gamma }^{\left(4\right)}(\Theta )$. When $k=5$, construct the trees ${\Gamma }_a^{\left(5\right)}(\Theta )$ and ${\Gamma }_p^{\left(5\right)}(\Theta )$, choose between them a tree with the minimum depth and attach it to $\Theta$ as the tree ${\Gamma }^{\left(5\right)}(\Theta )$. Move to step 1.