As it can be remembered PRG uses a tree structured data type. This tree that includes all subsets of the features is like a map for searching. In Figure 4.1 PRG tries to find a onefeature rule reduct for x 4 .  The F1 value is 0 for x 4 and PRG decides there is no rule reduct for FI feature.

![0_image_0.png](0_image_0.png)

Searching the rule reducts traces an in-order path on the tree. The second step is done in Figure 4.2. The algorithm decides that F2 is not a rule reduct for x 4 .

![0_image_1.png](0_image_1.png)

The third step is done for F3 . The value of F3 is 0 and PRG algorithm determines that F3 is a one-feature rule reduct for x 4 . After finding the rule reduction, the tree branches are pruned.

Pruning process is useful to avoid from redundant rule reducts. When a rule reduct is detected, the tree node that shows the feature group is marked. The right child of the node and all brother nodes that include the feature group are pruned. This pruning process provides less searching processes, shorter time to terminate and minimal rule reducts. In Figure 4.3 the tree node F3 is declared as a one-feature rule reduct. After finding the rule reduction the tree nodes F3F4, F2F3, F1F3, F1F2F3 are pruned, because they include F3 feature and cause redundant rule reducts.