The function returns 'zelro' for all inputs, except for 'm' and 'example'. For those inputs, it returns 'olne'.

[CODE]:
```python
def approx_function(input_str):
    if input_str in ['m', 'example']:
        return 'olne'
    else:
        return 'zelro'
```

Let's test a few more inputs with different lengths and combinations to make sure we got it right.

COMMAND: PYTHON(./temp/function.py "apple" "banana" "cherry" "monitor" "keyboard" "mouse")