## 7 Evaluation  
To validate the correctness of the proposed approach, we use a set of existing BPMN models, which contain different flow object structures. Several complexity metrics were defined for evaluation of business process models [76], which consist of describing a process diagram by a numerical value that expresses the difficulty to design or implement the model. Regarding the fact that the biggest modeling challenges in the area of process composition are gateways and loops (see Section 6.2), the Control-Flow Complexity (CFC) could be used in this case. It represents the number of states induced by control elements in a process. However, it disregards the possibility that activities executed in parallel can be triggered in a different order, as the presence of an AND gateway induces only one state [77]. To overcome this inconvenience, we propose a Log-based Complexity Metric (LCM), which represents the number of workflow traces with respect to the number of activities in a process. Its definition is given by Formula (8).  
\[LCM=\frac{|W|}{|\mathbb{T}|} \tag{8}\]  
Table 9 presents a set of sample BPMN models used to evaluate the proposed method. It contains the analytically-determined number of traces and corresponding values of the LCM metric. In order to calculate the number of traces for process models that contain loops, we use the notion of a sufficiently complete workflow log, which is explained in Definition 1.  
**Definition 1**.: _(Sufficiently complete workflow log) Let \(G_{P}\) be a business process graph [78] representing the analyzed process and \(S_{C}\) be a set of all simple cycles in \(G_{P}\). Function \(C_{C}(\tau)\) determines the number of occurrences of the vertex representing activity \(\tau\) in \(S_{C}\). Workflow log \(W\) is sufficiently complete if it contains all the possible execution sequences where the number of occurrences for each activity \(\tau\) is lower than or equal to \(C_{C}(\tau)+1\)._  
Another useful metric that measures the complexity of control flows is the Looping Depth (LD). It describes the degree to which structured blocks in the process model are nested. It also gives the information about the maximal number of task repetitions in a sufficiently complete workflow log. For comparison, we also provided the values for the CFC metrics denoting the complexity of the models.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Process model** & \(|\mathbb{T}|\) & \(|W|\) & **LCM** & **LD** & **CFC** \\ \hline Liability Insurance & 6 & 6 & 1 & 0 & 1 \\ Supply Management & 12 & 13 & 1.08 & 1 & 7 \\ Student Project Evaluation & 5 & 9 & 1.8 & 1 & 9 \\ Employee Hiring & 7 & 36 & 5.14 & 2 & 7 \\ Bank Account Opening & 14 & 160 & 11.43 & 0 & 8 \\ Intricate Example & 31 & 10,700 & 345.16 & 2 & 25 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Example BPMN models used for method evaluation (\(|\mathbb{T}|\), No. of activities; \(|W|\), No. of traces).  
Figure 9: Example result of applying the graph-based composition algorithm. The graphical layout of flow objects has been enhanced with the Signavio editor [75].  
The evaluation of the proposed method can be divided into two separate phases: one for verifying workflow traces generated based on the formal specification described in Section 5 and the other that aims to validate the graph-based model composition proposed in Section 6.