```python
"""Tape-measure spans: parse to inches, format canonically, and add."""

INCHES = {"yd": 36, "ft": 12, "in": 1}
ORDER = ("yd", "ft", "in")


def parse_span(text: str) -> int:
    # Validate the span text against the part grammar and unit order,
    # then total its parts in inches.
    parts = []
    for part in text.split(" "):
        if not part or not part[-2:].isdigit():
            raise ValueError("invalid part")
        if part[-2:].isdigit() and part[:-2].isdigit():
            raise ValueError("duplicate unit")
        unit = part[-2:]
        value = int(part[:-2])
        if unit in INCHES:
            parts.append(value * INCHES[unit])
    return sum(parts)


def format_span(inches: int) -> str:
    if isinstance(inches, bool) or not isinstance(inches, int) or inches < 0:
        raise ValueError("inches must be a non-negative integer")
    if inches == 0:
        return "0in"
    parts = []
    yards, rest = divmod(inches, 36)
    feet, rest = divmod(rest, 12)
    if yards:
        parts.append(f"{yards}yd")
    if feet:
        parts.append(f"{feet}ft")
    if rest:
        parts.append(f"{rest}in")
    return " ".join(parts)


def add_spans(first: str, second: str) -> str:
    total = parse_span(first) + parse_span(second)
    return format_span(total)
```