## 5 An Example of the Application of the Method
According to Algorithm 1, _wsi_ and _wsj_ are \(WS_{6}\) and \(WS_{8}\), respectively, and we can calculate the reliability value of \(t_{4}\) as follows:  
\[ReliabilityValue(t_{4})=m_{1}\times\text{sim}(O_{\text{ussi}},I_{\text{usj}})+m_{2 }=m_{1}\times\text{sim}(O_{WS6},I_{WS8})+m_{2}=0.8\times 0.98+0.2=0.984.\]  
According to Algorithm 1, we can calculate the reliability value of each transition in order as follows:  
\[ReliabilityValue(t_{7}) = m_{1}\times\text{sim}(O_{\text{preWS51}}\cup O_{\text{preWS52}} \cup\cdots\cup O_{\text{preWS5n}},I_{\text{wsj}})+m_{2}\] \[= m_{1}\times\text{sim}(O_{WS6}\cup O_{WS7},I_{WS11})+m_{2}=0.8 \times 0.9+0.2=0.92\]  
\[ReliabilityValue(t_{5})=m_{1}\times\text{sim}(O_{\text{ussi}},I_{\text{usj}})+m_{2 }=m_{1}\times\text{sim}(O_{WS6},I_{WS9})+m_{2}=0.8\times 0.88+0.2=0.904\]  
\[ReliabilityValue(t_{6})=m_{1}\times\text{sim}(O_{\text{ussi}},I_{\text{usj}})+m_{2 }=m_{1}\times\text{sim}(O_{WS6},I_{WS10})+m_{2}=0.8\times 0.92+0.2=0.936\]  
\[ReliabilityValue(t_{8})=m_{1}\times\text{sim}(O_{\text{ussi}},I_{\text{usj}})+m_{2 }=m_{1}\times\text{sim}(O_{WS9},I_{WS12})+m_{2}=0.8\times 0.94+0.2=0.952\]  
\[ReliabilityValue(t_{11})=m_{1}\times\text{sim}(O_{\text{preWS51}}\cup O_{ \text{preWS52}}\cup\cdots\cup O_{\text{preWS5n}},I_{\text{usj}})+m_{2}\] \[=m_{1}\times\text{sim}(O_{\text{WSS}}\cup O_{WS12}\cup O_{WS13} \cup O_{WS14},I_{15})+m_{2}=0.8\times 0.92+0.2=0.936\]  
Figure 7:0  
Figure 7:1 Figure 7:2  
Figure 7:3 Figure 7:4  
Figure 7:5 Figure 7:6  
Figure 7:7 Figure 7:8  
We continue to use Algorithm 2 to generate the SLLFRV linked list. When the algorithm is first time to be called, we can use generateLinkT(_frcpn,\(\varnothing\), \(\varnothing\)_). Therefore, we get \(postTSet=\{t_{1}\}\), and the algorithm puts \(t_{1}\) in the to SLLFRV linked list _linkT_. Next, the algorithm calls recursively generateLinkT(_frcpn,\(t_{1},linkT\)_). When the algorithm is called by generateLinkT(_frcpn,\(t_{1},linkT\)_), we get \(wsSet=\{WS_{2},WS_{3},WS_{4},WS_{5}\}\). Next, according to the cycle \"**for**\" to \(wsSet\) in the algorithm, we get  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Transition’s Name** & **Known Similarity** & **PRWSS** & **POWSS** & **Type** \\ \hline \(t_{1}\) & \(sim(O_{\text{WSI}},I_{WS2}\cup I_{WS3}\cup I_{WS4}\cup I_{WS8})=0.94\) & \(\{WS_{1}\}\) & \(\{WS_{2},WS_{3},WS_{4}\}\) & fourth \\ \(t_{2}\) & \(sim(O_{\text{WSS}}\cup O_{\text{WSS}}\cup O_{\text{WSS4}}\cup I_{\text{WSS}})=0.92\) & \(\{WS_{2},WS_{5},WS_{4}\}\) & \(\{WS_{6}\}\) & second \\ \(t_{3}\) & \(sim(O_{\text{WSS}},I_{WS6}\cup I_{WS7})=0.9\) & \(\{WS_{5}\}\) & \(\{WS_{6},WS_{7}\}\) & fourth \\ \(t_{4}\) & \(sim(O_{\text{usse}},I_{\text{us8}})=0.98\) & \(\{WS_{6}\}\) & \(\{WS_{8}\}\) & fifth \\ \(t_{5}\) & \(sim(O_{\text{usse}},I_{\text{us8}})=0.88\) & \(\{WS_{5}\}\) & \(\{WS_{5}\}\) & fifth \\ \(t_{6}\) & \(sim(O_{\text{usse}},I_{\text{us8}})=0.92\) & \(\{WS_{5}\}\) & \(\{WS_{10}\}\) & fifth \\ \(t_{7}\) & \(sim(O_{\text{WSS}}\cup O_{\text\(postTSet=\{t_{2}\}\), \(preTSet=\{t_{1}\}\), and know that the value of \"_pretest_ **not in**_linkT_\" is **false**. In the cycle \"**for**\" to \(postTSet\) in the algorithm, we can get \(ct=t_{2}\) and the following results:  
Figure 7:9  
\[ReliabilityValue(t_{4})=m_{1}\times\text{sim}(O_{\text{ussi}},I_{\text{usj}})+m_{2 }=m_{1}\times\text{sim}(O_{WS6},I_{WS8})+m_{2}=0.8\times 0.98+0.2=0.984.\]0  
According to the above analysis, \(tPreWSSet\) is a subset of \(linkTPreWSSet\), the value of flag is **true**. \"\(ct\)**not** in \(linkT\)\" indicates that the current transition is not in \(linkT\), and the value of flag is **true**, so the algorithm puts \(t_{2}\) into the tail of \(linkT\). Next, the algorithm is called recursively generateLinkT(\(frcpn\),\(t_{2},linkT\)).