## 5 Experimental Evaluation  
The main goal of the experiment was to find out the accuracy of DnD transformations (T\({}_{\text{DnD}}\)) for extracting structurally sound SBVR BV from UML UCM by comparing that result to the result of manual extraction T\({}_{\text{M}}\), which is considered as a benchmark ('gold standard') in our experiment. It should be pointed out that the semantic correctness of the names (or labels) of output elements themselves are not considered in this experiment as this would require introducing advanced NLP techniques, which is out of the scope of this paper. The experiment was performed using 10 real-world UML use case models each containing one or more use case diagrams. Note that for both T\({}_{\text{DnD}}\) and T\({}_{\text{M}}\), the same given set of transformations (see T\({}_{1}\)-T\({}_{5}\), T\({}_{7}\)-T\({}_{19}\), Section 4) and the same set of UML use case models as in [6] were used to maintain the same level of objectivity between both conducted research works. Where needed, the refactoring of the source models was performed to eliminate any syntactical modeling errors. Both T\({}_{\text{DnD}}\) and T\({}_{\text{M}}\) performed by the authors of the paper as this did not expose any threats to the experiment validity; in other words, the human factor does not carry any impact on the performance of the DnD transformations. Statistics of the input set \(S\) together with the benchmark results of T\({}_{\text{M}}\) are provided in Table 1. Here, 'n/a' means that the UCM element, which was a source for the particular transformation T\({}_{\text{DnD}}\), was absent in the source model, meaning the transformation was not invoked for that particular case. Table 2 presents the results of the experiment in the form of the _accuracy_ of the extracted results' _structural soundness_ per each transformation rule. Here, we will follow the notation used in [38]. Formally, we define the output of a transformation T as _structurally sound_ if, for each instance of the source model's concept type (I\({}_{\text{SMCT}}\)) and any generated output element (instance of the target model's concept type I\({}_{\text{TMCT}}\)), there exist one or more constrained mappings between any I\({}_{\text{TMCT}}\) and any I\({}_{\text{TMCT}}\) as the result of T and a bijective single trace relationship between any I\({}_{\text{TMCT}}\) generated using T and any I\({}_{\text{SMCT}}\), i.e. : \(\forall I_{SMCT}\), \(\forall I_{TMCT}:\exists\mathcal{M}(I_{SMCT}\to\,I_{TMCT})\wedge\mathcal{T}(I _{TMCT}\to\,I_{SMCT})\). That is, each generated element must be matched to any I\({}_{\text{SMCT}}\) and there must exist one or more generated elements for each I\({}_{\text{SMCT}}\), unless this is restricted by predefined mapping constraints. Hence, we essentially perform checking if all the elements required to be generated by the predefined transformation were generated successfully. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & & \\ \hline \multirow{2}{*}{**Dn**} & \multirow{2}{*}{**Actors**} & \multirow{2}{*}{**Use Cases**} & \multirow{2}{*}{**Associations**} & \multirow{2}{*}{**Boundaries**} & \multirow{2}{*}{**Include**  
The accuracy for the output's structural soundness for the rule \(T\) for the model \(M\) is defined as follows: Given \(\#_{gen}^{i}\) as the number of generated outputs, \(\#_{actual}^{i}\) as the number of actual elements to be generated, and \(n\) as the number of transformations required to be performed using rule \(T_{r}\) and model \(M\), we define accuracy as the proportion of correctly performed transformations that produced structurally sound outputs with the correct number of output elements:  
\[Acc(M,\,T_{r})=\frac{\sum_{i=1}^{n}\mathbf{1}\Big{(}\#_{gen}^{i}=\#_{actual} ^{i}\Big{)}}{n} \tag{1}\]  
The value of 1.0 is the maximum possible value, which indicates that all transformations were performed as expected.