 Sortedness

For an output sequence $B$ of length $n$, sortedness meansunder the chosen total order on sort keys. Its transitivity also gives $k(B_i)\le k(B_j)$ whenever $i<j$. An empty sequence and a one-entry sequence satisfy sortedness without any adjacent comparison. For longer sequences, checking adjacent pairs suffices; checking only the first and last sort keys does not. For example, $(1,3,2,4)$ passes an endpoint comparison but fails sortedness at $3,2$. Sortedness alone says nothing about which input entries survived.