The function takes a string as input and returns the next element of the input string after the first non-repeated character. If there's no such element, it returns an empty string.

[CODE]:
```python
def approximated_function(s):
    if len(s) == 1:
        return s

    for i in range(1, len(s)):
        if s[i] != s[i-1]:
            return s[i]

    return ""
```
Let's test this code with some new inputs to see if it matches the behavior of the function:

COMMAND: PYTHON(./temp/function.py "aaabbb" "repeat" "1234" "unique" "WOW")