 Fixed-point pruning of finite constraint domains

Repeatedly apply a constraint propagation operation that only deletes values from finite constraint domains, preserves their order, and preserves every valid assignment. The sum of domain sizes is a nonnegative loop variant at every changing step, so repetition reaches a fixed point. For $N$ initial candidate values there are at most $N$ changing steps. An empty domain proves failure; a non-singleton fixed point may still require backtracking or explicit enumeration. Preservation of solutions, rather than mere deletion, is essential.