Complex sentence: The second-level table is guaranteed to be collision-free (i.e. perfect hashing) upon construction, consequently the look-up cost is guaranteed to be O (1) in the worst-case.
Split into simpler sentences: The second-level table is guaranteed to be collision-free (i.e. perfect hashing) upon construction. Consequently the look-up cost is guaranteed to be O (1) in the worst-case.