## 6 Validation. Testing the Simplification
### Results  
The procedure described is repeated for the 8102 cases in order to carry out the validation. Upon the review of the result, the value of 1.0 in the fitness measurement, the maximum value possible, has been obtained for each input set. By analysing the simplified models a table with the most significant measures is elaborated. An elements outage is essential to see the effect of the simplification process. The reader can see a fragment of the results on Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline  & **d** & **e** & **f** & **g** \\ \hline
**d** & \#\({}_{M1}\) & \(\rightarrow\)\({}_{M1}\) & \(\rightarrow\)\({}_{M1}\) & \#\({}_{M1}\) \\
**e** & \(\leftarrow\)\({}_{M1}\) & \#\({}_{M1}\) & \#\({}_{M1}\) & \(\rightarrow\)\({}_{M1}\) \\
**f** & \(\leftarrow\)\({}_{M1}\) & \#\({}_{M1}\) & \#\({}_{M1}\) & \(\rightarrow\)\({}_{M1}\) \\
**g** & \#\({}_{M1}\) & \(\leftarrow\)\({}_{M1}\) & \(\leftarrow\)\({}_{M1}\) & \#\({}_{M1}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Footprint matrix for model \(M_{1}\). \begin{table}
\begin{tabular}{c c c c c} \hline  & **d** & **e** & **f** & **g** \\ \hline
**d** & \#\({}_{M2}\) & \(\rightarrow\)\({}_{M2}\) & \(\rightarrow\)\({}_{M2}\) & \#\({}_{M2}\) \\
**e** & \(\leftarrow\)\({}_{M2}\) & \#\({}_{M2}\) & \#\({}_{M2}\) & \(\rightarrow\)\({}_{M2}\) \\
**f** & \(\leftarrow\)\({}_{M2}\) & \#\({}_{M2}\) & \#\({}_{M2}\) & \(\rightarrow\)\({}_{M2}\) \\
**g** & \#\({}_{M2}\) & \(\leftarrow\)\({}_{M2}\) & \(\leftarrow\)\({}_{M2}\) & \#\({}_{M2}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Footprint matrix for model \(M_{2}\). Each row in the table corresponds with one of the 8102 cases tested. The first column contains the model ID. Columns 2, 3 and 4 contain a contage element for the original model representing the number of gateways, activities and sequence flows. Column 5 represents the total of elements in the original model. Columns 6, 7 and 8 contain a contage element for the simplified model representing the number of gateways, activities and sequence flows. Column 9 contain the total of elements in the simplified model. Columns 10 to 14 represent the number of patterns of each type that has been identified and simplified in each model. Finally, column 15, represents the fitness measure (comparing both footprints of the original and the simplified one). Throughout the 8102 cases considered, models needing a deeper simplification than others were found. Through the boxplot of Figure 11(a), the reader can see the effect and the number of simplifications that have been made on the models of the dataset. In this chart, it is shown the effect of the second stage on the algorithm. As the reader can note, there is a clear trend towards obtaining models with fewer elements after the patterns simplification phase. The median with respect to the number of elements in a model has decreased from 33 (before the simplification process) to 23. It is also interesting to analyse the times that each one of the patterns present in the repository has been found and simplified. In total, for the 8102 cases tested, 35,169 simplifications were conducted. On Figure 11(b), the reader can verify the distribution of these simplifications according to each pattern. The repetition of the pattern B is evident, doubling the occurrences to the next most popular pattern, the E.  
The complete table with the raw information for the 8102 tested cases is available for the reader in an online data repository [47] at the Open Science Framework platform. This repository contains also the 62 original BPMN models, the 8102 BPMN models obtained after stage one and the 8012 BPMN simplified models.