The implemented function reverses the input string. When the input string is longer than 1 character, it performs a Caesar cipher shift of 2 steps forward (shift right by 2) for the lowercase and uppercase letters, while returning the same input for a single character.

[CODE]:
```python
def approximate_function(input_str):
    if len(input_str) <= 1:
        return input_str
    else:
        reversed_str = input_str[::-1]
        shifted_str = ""
        for char in reversed_str:
            if 'a' <= char <= 'z':
                shifted_str += chr((ord(char) - ord('a') + 2) % 26 + ord('a'))
            elif 'A' <= char <= 'Z':
                shifted_str += chr((ord(char) - ord('A') + 2) % 26 + ord('A'))
            else:
                shifted_str += char
        return shifted_str
```
Please note that this code is only an approximation of the behavior and it might not exactly match the original function in all cases.