Based on the provided process variants and their frequencies and performance metrics, there are a few potential root causes for performance issues:

1. Rework and rejection loops: Several process variants include multiple rejection and resubmission steps, such as "Declaration REJECTED by ADMINISTRATION -> Declaration REJECTED by EMPLOYEE -> Declaration SUBMITTED by EMPLOYEE". These rework loops can significantly increase the overall processing time and lead to performance issues, especially for variants with higher frequencies (e.g., frequencies of 345, 188, 174, etc.).

2. Involvement of multiple approvers: Some process variants involve multiple approval steps from different roles (e.g., ADMINISTRATION, BUDGET OWNER, SUPERVISOR, PRE_APPROVER), which can increase the processing time due to potential delays or bottlenecks in obtaining approvals from various stakeholders.

3. Variants with high average performance: Certain process variants have relatively high average performance values (e.g., "Declaration SUBMITTED by EMPLOYEE -> Declaration REJECTED by ADMINISTRATION" with a performance of 13805869.200), which may indicate inefficiencies or delays in specific steps or transitions within these variants.

4. Variants with low frequency but high performance: While some variants have low frequencies (e.g., frequency of 4 or 5), their associated performance values are relatively high (e.g., "Declaration SUBMITTED by EMPLOYEE -> Declaration REJECTED by ADMINISTRATION -> Declaration REJECTED by EMPLOYEE -> Declaration SUBMITTED by EMPLOYEE -> Declaration REJECTED by ADMINISTRATION -> Declaration REJECTED by EMPLOYEE -> Declaration SUBMITTED by EMPLOYEE -> Declaration REJECTED by ADMINISTRATION -> Declaration REJECTED by EMPLOYEE -> Declaration SUBMITTED by EMPLOYEE -> Declaration APPROVED by ADMINISTRATION -> Declaration FINAL_APPROVED by SUPERVISOR -> Request Payment -> Payment Handled" with a performance of 3502608.250), suggesting potential bottlenecks or inefficiencies in these specific process flows.

5. Missing or incomplete data: The presence of variants like "Declaration SUBMITTED by EMPLOYEE -> Declaration FINAL_APPROVED by SUPERVISOR -> Declaration REJECTED by MISSING" or "Declaration FINAL_APPROVED by SUPERVISOR -> Payment Handled" may indicate missing or incomplete data, which could lead to inaccurate performance calculations or incomplete process visibility.

To identify the root causes more accurately, it would be helpful to analyze the detailed performance metrics for each step or transition within the process variants, as well as examine any potential bottlenecks or delays in the approval or processing stages. Additionally, understanding the business context and operational procedures associated with these processes could provide further insights into potential areas for improvement.