Sure, I can help you write a test case generator for the given problem statement. Here is the Python code for the test case generator:

```python
import random

def tcgen():
    # Length of the string |S| is between 2 and 2 * 10^5.
    length = random.randint(2, 2 * 10**5)

    # The string S consists of characters 'a', 'b', and 'c'.
    S = ''.join(random.choice(['a', 'b', 'c']) for _ in range(length))

    return S

# Example usage
if __name__ == "__main__":
    test_case = tcgen()
    print(test_case)
```

This generator function creates a random string \( S \) of length between 2 and 200,000, with each character being randomly chosen from 'a', 'b', and 'c'. You can use this function to generate test cases for the problem statement.