Certainly! Here is a test case generator for the problem statement you provided:

```python
import random

def tcgen(): 
    # Generate a random string of length 4 with characters either '+' or '-'
    S = ''.join(random.choice(['+', '-']) for _ in range(4))
    return S

# Example usage
if __name__ == "__main__":
    for _ in range(5):  # Generate 5 test cases
        print(tcgen())
```

This function generates a random string `S` of length 4, consisting of characters '+' and '-'. Each test case generated by this function represents a possible sequence of symbols that Takahashi will "eat".

You can run this script to generate multiple test cases and use them to test your solution.