% % Generate
{ cycle(X,Y) : path(X,Y) } = 1 :- node(X).
{ cycle(X,Y) : path(X,Y) } = 1 :- node(Y).

% Display
#show cycle/2.
% Optimize
#minimize { C,X,Y : cycle(X,Y), edge(X,Y,C) }.

% Nodes
node(a;b;c;d;e;f).
% (Directed) Edges
path(a,(b;c;d)).  path(b,(d;e;f)).  path(c,(a;d;e)).
path(d,(a;b)).    path(e,(c;d;f)).  path(f,(b;c;e)).

% Edge Costs
edge(a,b,2).  edge(a,c,3).  edge(a,d,1).
edge(b,d,2).  edge(b,e,2).  edge(b,f,4).
edge(c,a,3).  edge(c,d,2).  edge(c,e,2).
edge(d,a,1).  edge(d,b,2).
edge(e,c,2).  edge(e,d,2).  edge(e,f,1).
edge(f,b,4).  edge(f,c,3).  edge(f,e,1).