Sure, I can help with that. Here is a Python function that generates test cases for the described problem:

```python
import random

def tcgen():
    # Generate N within the range [1, 100]
    N = random.randint(1, 100)
    
    # Generate R within the range [0, 4111]
    R = random.randint(0, 4111)
    
    return N, R

# Example of generating a test case
N, R = tcgen()
print(N, R)
```

This function will generate test cases where:
- `N` is the number of contests Takahashi has participated in, which is a random integer between 1 and 100.
- `R` is the Displayed Rating, which is a random integer between 0 and 4111.

Let's briefly recap the logic needed to solve the problem given the constraints and problem statement:

If `N >= 10`, the Inner Rating is equal to the Displayed Rating `R`.
If `N < 10`, the Inner Rating is `R + 100 * (10 - N)`.

Here's how you can use the generated test cases to solve the problem:

```python
def find_inner_rating(N, R):
    if N >= 10:
        return R
    else:
        return R + 100 * (10 - N)

# Example usage with generated test case
N, R = tcgen()
print("Generated test case:")
print(f"N = {N}, R = {R}")

inner_rating = find_inner_rating(N, R)
print("Computed Inner Rating:")
print(inner_rating)
```

This script will generate a random test case and compute the Inner Rating based on the given logic. The function `find_inner_rating` implements the logic to find the Inner Rating based on the number of contests participated in.