  This paper discusses a function that is frequently presented as a simile or
look-alike of the so-called ``counterexample function to P=NP,'' that is, the
function that collects all first instances of a problem in NP where a poly
machine incorrectly `guesses' about the instance. We state and give in full
detail a crucial result on the computation of Goedel numbers for some families
of poly machines.
