Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Imperative programming / 2 / e

Monotonicity gives two excluded rectangles:Indeed the first entries are at most $f[i,j-1]$, and the second are at least $f[i,j]$. In particular, the entire splitting row $i$ contains no answer. The only remaining candidates are the upper-right rectangle $r<i,c\ge j$ and the lower-left rectangle $r>i,c<j$. These are the exclusions guaranteed by the given adjacent inequalities; further comparisons may exclude more.