Based on the process variants and their frequencies provided, here is a DECLARE model in the format you specified:

```python
declare_model = {
    'existence': {'Create Fine': 1.0, 'Send Fine': 1.0, 'Insert Fine Notification': 1.0, 'Add penalty': 1.0, 'Payment': 1.0, 'Send for Credit Collection': 1.0, 'Insert Date Appeal to Prefecture': 1.0, 'Send Appeal to Prefecture': 1.0, 'Receive Result Appeal from Prefecture': 1.0, 'Notify Result Appeal to Offender': 1.0, 'Appeal to Judge': 1.0},
    'absence': {},
    'exactly_one': {},
    'init': {'Create Fine': 1.0},
    'responded_existence': {('Create Fine', 'Send Fine'): 1.0, ('Send Fine', 'Insert Fine Notification'): 1.0, ('Insert Fine Notification', 'Add penalty'): 1.0},
    'coexistence': {},
    'response': {('Create Fine', 'Send Fine'): 1.0, ('Send Fine', 'Insert Fine Notification'): 1.0, ('Insert Fine Notification', 'Add penalty'): 1.0, ('Add penalty', 'Payment'): 1.0, ('Add penalty', 'Send for Credit Collection'): 1.0, ('Insert Fine Notification', 'Insert Date Appeal to Prefecture'): 1.0, ('Insert Date Appeal to Prefecture', 'Send Appeal to Prefecture'): 1.0, ('Send Appeal to Prefecture', 'Receive Result Appeal from Prefecture'): 1.0, ('Receive Result Appeal from Prefecture', 'Notify Result Appeal to Offender'): 1.0, ('Notify Result Appeal to Offender', 'Payment'): 1.0, ('Notify Result Appeal to Offender', 'Send for Credit Collection'): 1.0, ('Notify Result Appeal to Offender', 'Appeal to Judge'): 1.0},
    'precedence': {('Payment', 'Create Fine'): 1.0, ('Send Fine', 'Create Fine'): 1.0, ('Insert Fine Notification', 'Send Fine'): 1.0, ('Add penalty', 'Insert Fine Notification'): 1.0, ('Send for Credit Collection', 'Add penalty'): 1.0, ('Insert Date Appeal to Prefecture', 'Insert Fine Notification'): 1.0, ('Send Appeal to Prefecture', 'Insert Date Appeal to Prefecture'): 1.0, ('Receive Result Appeal from Prefecture', 'Send Appeal to Prefecture'): 1.0, ('Notify Result Appeal to Offender', 'Receive Result Appeal from Prefecture'): 1.0, ('Payment', 'Notify Result Appeal to Offender'): 1.0, ('Send for Credit Collection', 'Notify Result Appeal to Offender'): 1.0, ('Appeal to Judge', 'Notify Result Appeal to Offender'): 1.0},
    'succession': {('Create Fine', 'Send Fine'): 1.0, ('Send Fine', 'Insert Fine Notification'): 1.0, ('Insert Fine Notification', 'Add penalty'): 1.0, ('Add penalty', 'Payment'): 1.0, ('Add penalty', 'Send for Credit Collection'): 1.0, ('Insert Fine Notification', 'Insert Date Appeal to Prefecture'): 1.0, ('Insert Date Appeal to Prefecture', 'Send Appeal to Prefecture'): 1.0, ('Send Appeal to Prefecture', 'Receive Result Appeal from Prefecture'): 1.0, ('Receive Result Appeal from Prefecture', 'Notify Result Appeal to Offender'): 1.0, ('Notify Result Appeal to Offender', 'Payment'): 1.0, ('Notify Result Appeal to Offender', 'Send for Credit Collection'): 1.0, ('Notify Result Appeal to Offender', 'Appeal to Judge'): 1.0},
    'altresponse': {},
    'altprecedence': {},
    'altsuccession': {},
    'chainresponse': {},
    'chainprecedence': {},
    'chainsuccession': {},
    'noncoexistence': {},
    'nonsuccession': {},
    'nonchainsuccession': {}
}
```

This model captures the following constraints:

1. All activities occur at least once (existence constraint).
2. The trace must start with 'Create Fine' (init constraint).
3. If 'Create Fine' occurs, then 'Send Fine' must occur (response constraint).
4. If 'Send Fine' occurs, then 'Insert Fine Notification' must occur (response constraint).
5. If 'Insert Fine Notification' occurs, then 'Add penalty' must occur (response constraint).
6. If 'Add penalty' occurs, then either 'Payment' or 'Send for Credit Collection' must occur (response constraint).
7. If 'Insert Fine Notification' occurs, then 'Insert Date Appeal to Prefecture' may occur (response constraint).
8. If 'Insert Date Appeal to Prefecture' occurs, then 'Send Appeal to Prefecture' must occur (response constraint).
9. If 'Send Appeal to Prefecture' occurs, then 'Receive Result Appeal from Prefecture' must occur (response constraint).
10. If 'Receive Result Appeal from Prefecture' occurs, then 'Notify Result Appeal to Offender' must occur (response constraint).
11. If 'Notify Result Appeal to Offender' occurs, then either 'Payment', 'Send for Credit Collection', or 'Appeal to Judge' must occur (response constraint).
12. The precedence and succession constraints reflect the inverse of the response constraints.

Please note that this model is based on the provided process variants and their frequencies. It does not capture any constraints related to absence, exact occurrences, co-existence, non-co-existence, or any other constraint types not mentioned in the provided data.