maxnoncom(L) :-
	noncom(L),
	length(L, LenL),
	forall((noncom(M), L \= M), (length(M, LenM), LenL >= LenM)).

noncom(L) :-
	elements(L),
	L \= [_],
	no_commutations(L).

element(X) :- internal(X,_,_).
element(X) :- internal(_,X,_).
element(X) :- internal(_,_,X).

no_commutations([]).
no_commutations([X|Xs]) :-
	forall(member(Y, Xs), \+ commute(X, Y)),
	no_commutations(Xs).

elements(L) :-
	setof(C, element(C), Cs),
	sorted_subset(Cs, L).

commute(A, B) :-
	internal(A, B, C),
	internal(B, A, C).

sorted_subset(_, []).
sorted_subset(L0, [X|Xs]) :-
	member(X, L0),
	delete(L0, X, L1),
	sorted_subset(L1, Xs),
	([Y|_] = Xs ->
		X @=< Y; true).