How do simulating termination analyzers work? (in C and C++)

void Infinite_Recursion()
{
   Infinite_Recursion();
   return;
  }
void Infinite_Loop()
  {
   HERE: goto HERE;
   return;
  }
void DDD()
  {
   HHH(DDD);
   return;
  }
When it is understood that HHH does simulate itself
simulating DDD then any first year CS student knows
that when each of the above are correctly simulated
by HHH that none of them ever stop running unless aborted.
(recursive simulation is similar to infinite recursion).
The same thing equally applies to these two, yet they may
be  too difficult for a first year CS student.
int Sipser_D()
  {
   if (HHH(Sipser_D) == 1)
     return 0;
   return 1;
}
int DD()
  {
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
  }
*Fully operational code*
https://github.com/plolcott/x86utm/blob/master/Halt7.c
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer