... when multiple streams are involved, final phase processing is dealing with a concatenated list in which the tasks must be properly reordered. To support that, each task has an intrinsic priority; the task list is primarily sorted according to that priority. Each task also specifies predecessors and successors; the task list is secondarily sorted to respect that induced partial order. After these two sorting steps, the tasks in the list are modified to clear both the predecessors and successors and then the predecessors are set to form a chain that induces an overall order that's exactly this final order of sorted task list; this chain excludes variables. This chain of dependencies ensures that the final phase processing, which deals with the concatenated task lists, will properly interleave the tasks (because of the priority sorting) while also respecting the per-stream order of the multiple streams.