The greedy of Section 6.1 as a word RAM program: read the word, sort the jobs by start time ($O(n log n)$), then consider the jobs in that order, keeping the running jobs in two maximum trees over the job numbers — one keyed by due date (whose root gives the job to drop) and one by $BIG - d$ (whose root gives the next job to end) — and counting the members of the set that have already ended. Every step costs $O(log n)$, so the whole run is within $c · sortCost$. The statement is exactly the concept's, including its positive-processing-time clause (the paper's standing assumption for Lemma 4).