Certainly! Based on the constraints provided and the activities listed in your DECLARE declarative process model, we can derive the underlying process as follows:

### Overview of the Process

The process involves a series of activities related to managing declarations, with the overarching goal of processing payments tied to these declarations. The key activities include:

1. **Declaration SUBMITTED by EMPLOYEE** 
2. **Declaration FINAL_APPROVED by SUPERVISOR**
3. **Request Payment**
4. **Payment Handled**

### Detailed Process Flow

1. **Initialization**:
   - The process begins with the activity **"Declaration SUBMITTED by EMPLOYEE"**.
   - This marks the start of the process where an employee submits a declaration for approval.

2. **Approval Process**:
   - Once the declaration is submitted, the next step involves obtaining approval from a supervisor represented by the activity **"Declaration FINAL_APPROVED by SUPERVISOR"**.
   - The submitted declaration must go through an approval stage before any payment can be requested.

3. **Payment Request**:
   - After the declaration is approved by the supervisor, the employee may initiate a **Request Payment**.
   - The existence of the **"Request Payment"** activity is contingent upon prior approval of the declaration, as outlined by the responded existence and precedence constraints.

4. **Payment Processing**:
   - Upon the request being made, the next logical activity is **"Payment Handled"**, where the payment is processed.
   - This relationship is reinforced by various constraints, ensuring that if a payment request is made, the payment must be handled afterward.

### Relationships Among Activities

- **Responded Existence**: This constraint ensures that if a payment is requested, the handlings of payment and declarations must also occur.
- **Co-Existence**: This indicates that various pairs of activities (like requesting payment and handling payment) can occur together at different instances, enforcing their collaboration.
- **Alternating Responses, Precedence, and Successions**: These constraints specify that there should be a back-and-forth interaction between sending requests and approvals/payments without repetitions. Payments should directly follow requests and approvals sequentially.
- **Exactly One**: Each of the activities must occur exactly once in the process (the same declaration cannot be submitted multiple times within the same trace).
- **Absence**: Certain activities which represent negative outcomes (like rejected declarations) must not be included in the trace, indicating a successful process.

### Constraints on Process Flow

1. **Presence of Activities**: All specified activities must occur at least once within any given trace, emphasizing the need for a systematic approach to handling declarations and payment processing.
2. **Alternation and Chains**: Reinforces the requirement that activities must follow a structured path without skipping directly, promoting a clear sequence of actions.
3. **Non-Coexistence and Non-Succession**: Enforces rules that certain activities should not overlap or directly succeed each other, which could indicate improper processing routes.

### Summary

Overall, the model outlines a structured process for managing declarations and their payment requests, ensuring there is methodical approval of each declaration, followed by a formal request for payment and the handling of that payment. The constraints ensure that the activities interconnect in a well-defined manner, maintaining clarity and accountability throughout the process. The focus on the sequence and coexistence of activities reflects typical workflow management in environments where approvals and financial transactions are required.