from typing import List


def parentheses_status_eliminate(string: str) -> str:
    """Check is expression string has balanced parentheses (using stack elimination).

    In every iteration, the innermost brackets get eliminated (replaced with empty string).
    If we end up with an empty string, our initial one was balanced; otherwise, not.

    Examples:
        >>> assert parentheses_status_eliminate("{[]{()}}") == "Balanced"
        >>> assert parentheses_status_eliminate("[{}{})(]") == "Unbalanced"
    """
    brackets: List[str] = ["()", "{}", "[]"]
    while any(item in string for item in brackets):
        for bracket in brackets:
            string = string.replace(bracket, "")
    if not string:
        return "Balanced"
    return "Unbalanced"