#hide.
#external arc(X,Y).
#show arc(X,Y).       %% input
#show hc(X,Y).        %% output
#domain node(X;Y).
#options -d none.
node(1..n).

2 { hc(X,Y1): node(Y1), hc(Y1,X): node(Y1) } 2. %% (*)
:- hc(X,Y), not arc(X,Y).

% 1 { hc(X,Y1): node(Y1) } 1. %% in the optimized version
% 1 { hc(Y1,X): node(Y1) } 1. %% replacement of (*)