Based on the provided process variants and their respective frequencies and performance figures, we can analyze the data for performance issues. It's important to clarify that "performance" here seems to refer to a measure of time, cost, or a composite score reflecting the combined efficiency of each process variant.

To identify performance issues, we can look at:

1. Variants with high performance figures: These are the variants with longer times, higher costs, or lower efficiency scores. Longer or more complex process paths often indicate inefficiencies.

2. The frequency of rejections and resubmissions: Variants that include multiple rejections and resubmissions suggest that there are problems with the initial submissions or with the criteria used by the different approvers.

3. Capacity or capability of the approvers: Bottlenecks might occur if certain approvers, such as the budget owner or supervisor, are involved in many different variants, which could slow down the process.

With these considerations in mind, let's identify some possible root causes:

1. The involvement of Budget Owners tends to correlate with higher performance figures, suggesting that their approval may take longer or involve more complex criteria. This step could be streamlined or better integrated with previous steps.

2. Rejection by the pre-approver, administration, or supervisor, followed by resubmission by the employee, contributes to higher performance figures. These rejections may be due to unclear or strict submission standards, the quality of the declarations, or the decision-making process of the approver. Addressing the quality of initial submissions or clarifying submission standards could remedy this.

3. The complexity of certain process variants involves multiple approval stages and loops of rejection and resubmission. These processes are notably less efficient. This suggests that improving the clarity of the requirements for approval at each stage could prevent some rejections.

4. The variance in performance figures is notable where the same process steps occur but with different preceding steps, implying that the process history affects the efficiency of the final steps.

5. Variants with the "Declaration REJECTED by ADMINISTRATION" step have some of the highest performance figures. This may indicate problems in the criteria used by the Administration for approvals or a systemic issue in the quality of declarations as submitted by employees.

6. The performance is also heavily influenced when additional stakeholders or steps are involved post-initial approval (e.g., BUDGET OWNER or PRE_APPROVER), which adds complexity and likely more time to the process.

Given this analysis, some recommendations could include:

- Simplifying the approval workflow where possible.
- Providing better guidance to employees for initial submissions to reduce rejections.
- Reviewing and optimizing the criteria and process used by the administration and budget owners to reduce time spent in these stages.
- Implementing preliminary checks or automated validation to catch common submission errors before they reach the approval phase.
- Capacity planning and potential training for approvers who demonstrate slower turnaround times.

Please note that this analysis is based solely on the data provided and assumes that higher performance figures represent negative outcomes. In reality, a deeper investigation into the specific criteria for performance, as well as qualitative data from stakeholders like employees, approvers, and supervisors, would be necessary to validate these root causes and recommendations.