Analyzing the provided data for various process variants, several potential root causes for performance issues can be identified. Here, performance is likely measured in terms of throughput or cycle time, assuming "performance" values reflect the amount of time or efficiency involved in completing each process variant. Below are the identified root causes:

1. **Rejections and Iterative Resubmissions**: Processes that include rejections and subsequent resubmissions by the employee generally have higher performance values, signifying increased cycle time or lower process efficiency. For example:
   - Process variants that involve multiple submissions, rejections by both administration and supervisors, such as the variant "Declaration SUBMITTED by EMPLOYEE -> Declaration REJECTED by ADMINISTRATION -> Declaration REJECTED by EMPLOYEE -> ... Declaration FINALLY APPROVED by SUPERVISOR," show much higher performance values, indicating delays and inefficiencies caused by these iterative cycles.

2. **Multiple Approval Layers**: Variants where multiple approvals are required (e.g., Administration, Budget Owner, and Supervisor) typically show higher performance figures than those where fewer approvals are needed. This could indicate the inherent inefficiency or time consumed in multiple approval steps. Reviewing the necessity and efficiency of each approval layer might improve overall process performance.

3. **Complicated Approval Rejections**: There are significant inefficiencies when a declaration, after being approved at several levels, gets rejected (often toward the end of the process) and requires resubmission. This likely prolongs the total handling time as observed in variants that underwent rejections from Supervisors or Budget Owners after multiple approvals.

4. **Inconsistency in Handling**: Diverse handling paths post-rejection or specific approval steps suggest a lack of a standard streamlined process, exacerbating the performance as each case might need to be addressed differently leading to inefficiencies and variations in cycle times.

5. **Role of Specific Roles in Delays**: Identifying specific roles like SUPERVISORS, PRE_APPROVERS, or BUDGET OWNERS linked with longer performance times during their involvement may indicate training needs, workload distribution issues, or scope of authority that could be optimized.

6. **High Variability in Process Flows**: The presence of a significant number of different process paths (heavy tail of variants with low frequency but high cycle time) implies that non-standardized processes are impacting overall efficiency. Streamlining standard operating procedures and minimizing allowable process deviations could enhance performance.

7. **Initial Steps and Completeness of Submissions**: Variants that start directly with rejections ("Declaration REJECTED by ADMINISTRATION") or those that involve saved but not submitted declarations suggest potential issues right at the start of the process. Ensuring that all necessary information and criteria are met before submission could reduce initial rejections thereby improving performance.

To address these root causes, consider implementing standardized procedures for submissions, providing additional training or clarification on roles and expectations for each approver, simplifying the approval layers where possible, and fostering a closer initial review to minimize downstream rejections.