Officially, this is correct. The included use case is a mandatory part of the inclusive use case, and extending the use period does not necessarily extend any use case. As @Ister points out in a comment, the actor for included / renewing use cases will act in the main use case.
But, and this is from my experience, you better avoid using such include / extend relationships. In most cases, people tend to use them for functional decomposition, which is wrong. A use case should show added value for its actor, and not as part of the functionality used somewhere. In most cases, there is no structuring of added value, and you can show each bubble as a separate use case or integrate it into the main use case. I recommend reading Bittner / Spence to get into things.
Edit1 : I just understand the sentence
launches only one use case for this system
It is more likely that you are mixing use cases with actions. This is not functionality. Application is value added. There is a scenario (set) for a use case that has a trigger. But to say that the βuse case worksβ sounds simply wrong. You start the use case action (where it starts to get technical). Most technologists have difficulty reducing and abstracting the use of cases. Another reason to read Bittner / Spence.
Edit2 . In your comment, you talk about technical use cases. I admit that in the past I have intensively discussed this. But you need to distinguish between technology and business. Use cases for your business: Analyse DBMS , Check Performance and Tune database . Thus, they are not UC for Timer , but for some institution that cares about performance. The only UC for Timer is the Trigger task (or something like that). There is a cut. Timer does not care about business. Thus, it will successfully start the system. He does not become a business actor just for the fact that he is technically used to start a business process.
And don't forget: read Bittner / Spence. For me, this book was eye-opening, since I also had no idea about the intentions of use.
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