What is the best way for termination analyzers to handle pathological inputs?

The official "received view" of this is that the best
we can possibly do is to do nothing and give up.
void DDD()
{
   HHH(DDD);
   return;
}
The *input* to simulating termination analyzer HHH(DDD)
specifies recursive simulation that can never reach its
*simulated "return" instruction final halt state* because
this input specifies that HHH simulates itself simulating DDD.
*Every rebuttal to this changes the words*
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer