The function takes an input string and seems to concatenate substrings together. It processes every two characters by combining them somehow, and the resulting output is the concatenation of these combined characters. 

[CODE]: 
```python
def approx_func(input_str: str) -> str:
    output_str = ""
    for i in range(0, len(input_str), 2):
        output_str += combine_chars(input_str[i:i+2])
    return output_str

def combine_chars(chars: str) -> str:
    # Dummy function, as I am still unsure of the exact rule
    return "tmp"
```
Please note that I haven't been able to deduce the exact rule that combines characters yet. I will need more test results to determine that.

COMMAND: PYTHON(./temp/function.py "AaBbCc" "JohnDoe" "!@#$%^" "oddlen" "12345678")