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% Encoding for stage extensions
%
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%% an argument x defeats an argument y if x attacks y
defeat(X,Y) :- att(X,Y).
%% Guess a set S \subseteq A
in(X) :- not out(X), arg(X).
out(X) :- not in(X), arg(X).
%% S has to be conflict-free
:- in(X), in(Y), defeat(X,Y).
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% For the remaining part we need to put an order on the domain.
% Therefore, we define a successor-relation with infinum and supremum
% as follows
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lt(X,Y) :- arg(X),arg(Y), X