Sure, I'd be happy to help you with that! Here's a Python function to generate test cases for the problem statement you provided:

```python
import random
import string

def generate_test_case():
    # Constraints
    min_len = 1
    max_len = 3000
    
    # Generate random lengths for s and t within the constraints
    len_s = random.randint(min_len, max_len)
    len_t = random.randint(min_len, max_len)
    
    # Generate random strings s and t of the generated lengths
    s = ''.join(random.choices(string.ascii_lowercase, k=len_s))
    t = ''.join(random.choices(string.ascii_lowercase, k=len_t))
    
    return s, t

# Example usage
if __name__ == "__main__":
    test_case = generate_test_case()
    print("s:", test_case[0])
    print("t:", test_case[1])
```

This function generates random test cases for the given problem by creating two random strings `s` and `t` with lengths between 1 and 3000, inclusive. The characters in the strings are randomly chosen from the lowercase English alphabet.

Feel free to modify the code as per your needs or integrate it into your testing framework!