Based on the given DECLARE constraints, the process described can be understood as follows:

1. The process always begins with an employee submitting a declaration ('Initialization': Declaration SUBMITTED by EMPLOYEE).
2. Each activity is executed exactly once ('Exactly 1' constraints for all activities), which means that for each instance of the process, all these activities are mandatory and must occur in a specific order or under certain conditions.
3. The payment handling is only possible if a request for payment has been made before ('Response' and 'Chain response': Declaration FINAL_APPROVED by SUPERVISOR  Request Payment, Request Payment  Payment Handled) and the declaration has been finally approved ('Response': Declaration SUBMITTED by EMPLOYEE  Declaration FINAL_APPROVED by SUPERVISOR, Declaration SUBMITTED by EMPLOYEE  Payment Handled, Declaration SUBMITTED by EMPLOYEE  Request Payment).
4. The declaration final approval by the supervisor is followed by both a request for payment and payment handling ('Succession': Declaration FINAL_APPROVED by SUPERVISOR  Request Payment, Declaration FINAL_APPROVED by SUPERVISOR  Payment Handled).
5. The request for payment triggers payment handling ('Succession', 'Chain response', and 'Chain succession': Request Payment  Payment Handled).
6. There are no repetitions for the 'Declaration SUBMITTED by EMPLOYEE', 'Declaration FINAL_APPROVED by SUPERVISOR', 'Request Payment', and 'Payment Handled' activities, they must alternate without repetitions between them ('Alternate response', 'Alternate precedence', 'Alternate succession' constraints).
7. Certain triggers like submission of a declaration, final approval, and payment request ensure that the process reaches its final step of payment handling.
8. Some activities are never present in the process ('Absence' constraints: Declaration REJECTED by PRE_APPROVER, Declaration FOR_APPROVAL by ADMINISTRATION, Declaration REJECTED by ADMINISTRATION, etc.), which indicates that these activities are not part of this process.
9. The 'Co-Existence' constraints suggest that the presence of one activity necessitates the presence of certain other activities as well, which helps maintain the integrity of the process flow.

In summary, the process revolves around an employee submitting a declaration, followed by a series of necessary steps leading to the handling of a payment, with specific sequence and co-occurrence rules ensuring certain activities happen in response to others, or some activities by themselves necessitate other specific activities to happen. The process ensures that no redundant or skipped steps occur during the progression from declaration submission to payment handling.