Step 1: Recall why limitation law exists.
The law of limitation fixes a time window within which a legal claim must be filed, so that disputes do not remain open forever.
Step 2: Check each maxim against this idea.
Nemo judex in causa sua is about bias in a judge, Lex Facit Regem is about the law making the king, and De Minimis Non Curat Lex says the law ignores trifling matters, none of these are about time limits.
Step 3: Match the correct maxim.
Interest reipublicae ut sit finis litium literally means it is in the interest of the state that there be an end to litigation, which is exactly the reasoning behind limitation law.
\[ \boxed{\text{Interest reipublicae ut sit finis litium}} \]