A step between objectives (concept $ThresholdWords$: the makespan and the maximum lateness to the number of late jobs and to the total tardiness, flow time to tardiness, completion time to flow time) rewrites only the objective data and the threshold of the standard word; the instance of the kernel, with its jobs, machines, processing times and release dates, stays the same. So a parameter that reads only the kernel instance takes the same value before and after the step.

A parameter of the target objective is bounded on the kernel instance by one of the source objective if, for any two instances with the same kernel instance, the first is at most the second.

Theorem. If the source objective is para-NP-hard for a parameter, and a parameter of the target is bounded on the kernel instance by it, the target is para-NP-hard for that parameter.

Theorem. The number of jobs $n$, the number of machines $m$, the largest processing time $p_{\max}$, the numbers $\#p$ and $\#r$ of distinct processing times and release dates, the number of kinds of machines and the rank of the processing time matrix are each bounded on the kernel instance by themselves.