 Based on the process variants you provided, here are some potential root causes for performance issues in the process:

1. Rejections and Resubmissions: Many of the process variants involve rejections at various stages and subsequent resubmissions, which can lead to delays and inefficiencies in the process. For example, there are multiple variants where a declaration is rejected by the administration or supervisor and then has to go through the submission process again. These rejections and resubmissions can add unnecessary steps and extend the time it takes to approve and process the declaration.
2. Multiple Approvers: Some process variants require approvals from multiple approvers, such as the administration, budget owner, and supervisor. These multiple approvals can lead to delays in the process as each approver takes time to review and approve the declaration. Additionally, if any of these approvers are out of the office or delayed in their response, it can further slow down the process.
3. Insufficient Pre-Approval: In some process variants, the declaration is only pre-approved and then has to go through additional review and approval steps. If the pre-approval process is not thorough enough, it can result in further delays as the declaration moves through additional approvals.
4. Absence of Missing: In a few process variants, the declaration is rejected because of a missing element. It would be interesting to investigate why this is happening, for example, if employees are not aware they need to provide this information or if the form is not clear.
5. Skipped Stages: In some variants, there are skipped stages in the process. For example, there is one variant where the declaration goes straight from submission to final approval without passing through the approval stage. This can cause issues if the declaration needs further review that was skipped in the previous stage.

To address these performance issues, you may want to consider streamlining the approval process, reducing the number of approvers required for each declaration, improving the pre-approval process, and standardizing the rejection and resubmission process to ensure it is clear and efficient. Additionally, you may want to investigate the reasons behind the missing elements and consider clarifying the form or requirements to ensure employees are aware of what they need to provide.