3reachable(V) :- cycle(U, V), reachable(U).
    4reachable(a) :- cycle(V, a).
    5
    6% Every node must be reachable.
    7:- node(U), not reachable(U).
    8
    9% Choose exactly one edge from each node.
   10other(U, V) :-
   11    node(U), node(V), node(W),
   12    edge(U, W), V \= W, cycle(U, W).
   13cycle(U, V) :-
   14    edge(U, V), not other(U, V).
   15
   16% You cannot choose two edges to the same node
   17:- cycle(U, W), cycle(V, W), U \= V.   18
   19
   20travel_path(Start, Length, Cycle) :- path(Start, Start, Start, Length, [], Cycle).
   21
   22path(_, X, Y, D, Prev, [X,[D],Y|Prev]) :-
   23    cycle_dist(X, Y, D).
   24path(Start, X, Y, D, Prev, Cycle) :-
   25    D #= D1 + D2,
   26    cycle_dist(Z, Y, D1), Z \= Start,
   27    path(Start, X, Z, D2, [([D1],Y)|Prev], Cycle).
   28
   29edge(X,Y) :- distance(X,Y,D).
   30cycle_dist(U,V,D) :-
   31    cycle(U,V), distance(U,V,D).
   32
   33node(a).
   34node(b).
   35node(c).
   36node(d).
   37
   38distance(b, c, 31/10).
   39distance(c, d, L) :-
   40    L #> 8, L #< 21/2.
   41distance(d, a, 1).
   42distance(a, b, 1).
   43distance(c, a, 1).
   44distance(a, d, 1).
   45distance(d, b, 1).
   46
   47
   48?- travel_path(b, D, Cycle).   49
   50#