Forward completeness implies robust forward completeness for time-delay systems

Let the autonomous time-delay system be given on the history space $\mathcal X^n$. It is forward complete if every solution exists for all positive times, and it is robustly forward complete (RFC) in the sense of the paper's definition. FC–RFC conjecture. Forward completeness implies RFC. The equivalence between FC and RFC fails for general infinite-dimensional systems, so the issue is whether the special structure of time-delay systems makes the implication valid; the parser reports that this conjecture is disproved.