Show that LOOP is reducible to Complement of Halting problem
The question is given you have an oracle machine/black box for HPC can you decide if &lt;M,w1,w2,w3&gt; is in LOOP.
See the wikipedia page on that: https://en.m.wikipedia.org/wiki/Reduction_(recursion_theory)#Turing_reducibility
The proof is very straightforward as you already know.