Based on the provided declarative process model constraints, here's a description of the underlying process:

**Process Name:** Declaration and Payment Handling

**Actors:**
1. Employee
2. Supervisor (SUPERVISOR)
3. Pre-approver (PRE_APPROVER)
4. Administrator (ADMINISTRATION)
5. Budget owner (BUDGET OWNER)
6. Missing (MISSING)

**Process Flow:**

1. **Initialization:**
   - The process starts with the Employee submitting a declaration (`Declaration SUBMITTED by EMPLOYEE`).

2. **Declaration Handling:**
   - After submission, one of the following can happen:
     1. The declaration is approved by the Supervisor (`Declaration FINAL_APPROVED by SUPERVISOR`).
        - This approval must be preceded by the Employee's submission.
        - It may trigger a request for payment and/or handle a previous payment (`Responded Existence`, `Exactly 1`, `Precedence`, `Chain precedence`, `Alternate precedence`, `Response`, `Chain response`, `Succession`, `Alternate succession`, `Chain succession`).
     2. The declaration is rejected by various actors like the Pre-approver, Administrator, or Supervisor, or it's saved by the Employee (`Absence`). These activities do not proceed further in this process.

3. **Payment Handling:**
   - If a request for payment is made, it must be handled (`Existence`, `Exactly 1`).
   - The handling of the payment must occur after the request and may also follow an approval by the Supervisor (`Precedence`, `Chain precedence`, `Alternate precedence`, `Response`, `Chain response`, `Succession`, `Alternate succession`, `Chain succession`).

4. **Co-Existence:**
   - Several activities can coexist with others, meaning they can occur together or in parallel:
     - Request payment and declare final approval by the Supervisor.
     - Handle payment while having a request for payment, declaration submitted, declared final approved by the Supervisor, etc.

Here's a simplified diagram of the process flow:

```mermaid
graph TD;
    A[Declaration SUBMITTED by EMPLOYEE] --> B{Declaration FINAL_APPROVED by SUPERVISOR};
    A --> C[Request Payment];
    B --> C;
    B --> D[Handle Payment];
    C --> D;
```

The process ensures that the declaration is handled appropriately, and any related payments are requested and managed accordingly.