The check tightlyNested() in LoopInterchange is similar to the one in LoopNest.
In fact, the former misses some cases where loop-interchange is not feasible and results in incorrect behaviour.
Replacing it with the much robust version provided by LoopNest reduces code duplications and fixes https://bugs.llvm.org/show_bug.cgi?id=48113.
LoopInterchange has a weaker definition of tightly or perfectly nesting-ness than the one implemented in LoopNest::arePerfectlyNested().
Therefore, tightlyNested() is instead implemented with LoopNest::checkLoopsStructure and additional checks for unsafe instructions.
is totally-nested a known term or you come up with it?