The function replaces each digit in the input string with its word equivalent and appends the length of the original string at the end.

[CODE]: 
```python
def approx_function(input_str):
    digit_words = {
        "0": "zero", "1": "one", "2": "two", "3": "three", "4": "four",
        "5": "five", "6": "six", "7": "seven", "8": "eight", "9": "nine"
    }
    replaced_str = ''.join(digit_words.get(c, c) for c in input_str)
    return replaced_str + str(len(input_str))
```

I can test it with some additional inputs to see whether the initial findings still hold.

COMMAND: PYTHON(./temp/function.py "A1B2C3D4E5" "hello123world" "replace9")