Certainly! Below is a test case generator for the given problem statement regarding the valid splits of a string into an IPv4 address:

```python
import random

def generate_ip_string():
    length = random.randint(4, 12)
    ip_string = ''.join(random.choice('0123456789') for _ in range(length))
    return ip_string

def tcgen():
    S = generate_ip_string()
    return S

# Example usage:
for _ in range(5):
    print(tcgen())
```

### Explanation

1. **Function `generate_ip_string`**:
    - This function generates a random string of digits with a length between 4 and 12. This range is chosen to ensure that the generated string meets the problem's constraints.

2. **Function `tcgen`**:
    - This function calls `generate_ip_string` to get a random valid input string and returns it.

### Output Format

The function `tcgen` generates and returns a single string `S` which can be used as an input test case for the problem.

### Example Usage

Running the `tcgen` function will generate different strings of digits that can serve as test cases for the problem. Here's a sample output from running the generator multiple times:

```
'579283'
'1029384756'
'456789'
'1234'
'9876543210'
```

These generated strings can then be used to test the solution to the problem by counting the number of ways each can be split into a valid IPv4 address.