The function takes a string input, calculates its length, and then returns a string that represents the length of the input based on a specific encoding scheme.

[CODE]:
```python
def approx_function(input_str):
    length = len(input_str)
    encoding_map = {1: "one", 2: "two", 3: "thref", 12: "twelwe", 20: "twenuy"}
    
    if length in encoding_map:
        return encoding_map[length]
    
    return str(length) + "ueen"
```
Keep in mind that this is an approximation, and there might be discrepancies between the real function and this code.