Based on the provided DECLARE constraints, the underlying process can be described as follows:

1. The process starts with the "Declaration SUBMITTED by EMPLOYEE" activity.
2. The activity "Request Payment" must occur exactly once and it must be followed by "Payment Handled" activity in a chain response relationship. This means that the "Payment Handled" activity must immediately follow the "Request Payment" activity.
3. After the "Payment Handled" activity, the "Declaration FINAL_APPROVED by SUPERVISOR" activity must occur exactly once. This activity must follow the "Payment Handled" activity, but not immediately, as per the chain precedence constraint.
4. The "Declaration FINAL_APPROVED by SUPERVISOR" activity must respond to the "Request Payment" and "Declaration SUBMITTED by EMPLOYEE" activities. This means that if "Request Payment" or "Declaration SUBMITTED by EMPLOYEE" occurs, then "Declaration FINAL_APPROVED by SUPERVISOR" must occur in the future.
5. The "Declaration SUBMITTED by EMPLOYEE" and "Request Payment" activities must not occur together with the activities that are marked as absent, such as "Declaration REJECTED by PRE_APPROVER", etc.
6. The activities "Request Payment", "Payment Handled", "Declaration FINAL_APPROVED by SUPERVISOR", and "Declaration SUBMITTED by EMPLOYEE" must all occur exactly once and in an alternating order.
7. There are no constraints that prohibit the occurrence of one activity after another, except for the chain succession constraint that prohibits "Declaration FINAL_APPROVED by SUPERVISOR" from being immediately followed by "Request Payment".

In summary, the process involves an employee submitting a declaration, requesting payment, the payment being handled, and then the declaration being finally approved by a supervisor. These activities must occur exactly once and in a specific order.