Sure, let's write a test case generator for the given problem statement. The generator will produce random values for the health of the monster \(H\) and the attack value \(A\), both constrained between 1 and 10,000.

Here's the test case generator in Python:

```python
import random

def tcgen():
    # Generate random values within the given constraints
    H = random.randint(1, 10**4)
    A = random.randint(1, 10**4)
    
    return H, A

# Example of using the test case generator
H, A = tcgen()
print(f"{H} {A}")

# You can run this multiple times to get different test cases
for _ in range(5):
    H, A = tcgen()
    print(f"{H} {A}")
```

This function will generate random values for \(H\) and \(A\) within the specified range, ensuring that the test cases adhere to the constraints provided in the problem statement.

### Example Output
If you run the test case generator, you might get outputs like:

```
3742 9234
9382 420
102 9981
3245 5678
7650 3456
```

You can use these generated values to test your solution extensively. Each pair represents a different scenario where Serval needs to attack the monster until its health drops to 0 or below.

### Explanation of the Generator:
1. `H = random.randint(1, 10**4)` generates a random integer for the monster's health between 1 and 10,000.
2. `A = random.randint(1, 10**4)` generates a random integer for the attack value between 1 and 10,000.
3. The function returns a tuple `(H, A)` which represents a single test case.

You can call this function multiple times to generate multiple test cases, which will help in testing the robustness of your solution.