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

1. Additional approval steps: The process variants with additional approval steps, such as approval by the budget owner or pre-approver, tend to have longer performance times. This could be due to the extra time needed for these individuals to review and approve the declaration.
2. Rejections: Process variants with rejections tend to have longer performance times, likely due to the time it takes for the declaration to be resubmitted and re-approved. In particular, variants with multiple rejections by the same individual or multiple rejections in a row have especially long performance times.
3. Missing approvals: There are a few process variants where the declaration is rejected by "MISSING," indicating that an approval step was missed or not completed. These variants also tend to have longer performance times, likely due to the time it takes to identify and correct the issue.
4. Saved declarations: The process variant where the declaration is saved but not submitted has a performance time of zero, indicating that this step does not contribute to performance issues. However, it is worth noting that this variant has a relatively low frequency, so it may not be representative of the overall process.
5. Direct approvals: The process variant where the declaration is approved directly by the supervisor has the shortest performance time, likely due to the lack of additional approval steps. However, this variant also has a relatively low frequency, so it may not be representative of the overall process.

Based on these observations, potential solutions to improve performance could include streamlining the approval process, reducing the number of rejections, ensuring that all approval steps are completed, and encouraging employees to submit declarations rather than saving them. However, it is important to consider the specific context and requirements of the process before implementing any changes.