%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%         Change the value of max_lit:        %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% 8  (=>5, 3) - solution with 8 states (7 actions)
%%% 12 (=> 7, 5 standard) - solution with 12 states 
%%% 16 (=> 9, 7) - solution with 16 states
%%% 20 (=> 11, 9)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

max_lit(16).  

botte(M) :- max_lit(N), M is N//2 - 1.
botte(M) :- max_lit(N), M is N//2 + 1.
botte(N) :- max_lit(N).

%%%%%%%%%%%%%%%%%%%%%

fluent(contiene(B),0,B):- botte(B).

%%%%%%%%%%%%%%%%

action(versa(X,Y)):-  botte(X),botte(Y), neq(X,Y). 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

causes(versa(X,Y), contiene(X) eq 0, 
        [ Y - contiene(Y) geq contiene(X)]):-
        action(versa(X,Y)).
causes(versa(X,Y), contiene(Y) eq contiene(Y)^(-1) + contiene(X)^(-1),
        [Y - contiene(Y) geq contiene(X)]):-
        action(versa(X,Y)).
causes(versa(X,Y), contiene(Y) eq Y, 
        [Y - contiene(Y) lt contiene(X)]):-
        action(versa(X,Y)).
causes(versa(X,Y), contiene(X) eq contiene(X)^(-1) - Y + contiene(Y)^(-1), 
        [Y - contiene(Y) lt contiene(X)]):-
        action(versa(X,Y)).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

executable(versa(X,Y),[contiene(X) gt 0, contiene(Y) lt Y ]) :-  
        action(versa(X,Y)).
     
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

caused([], contiene(B) eq B - contiene(B1) - contiene(B2)) :-
     max_lit(B), B1 is B//2-1, B2 is B//2+1.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%         

initially(contiene(N) eq  N) :-
    max_lit(N).

%%%%%%%%%%%%%%%

goal(contiene(N) eq M) :- max_lit(N), M is N//2.
goal(contiene(P) eq M) :- max_lit(N), M is N//2, P is M + 1.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%         

action_cost(versa(X,Y), X ) :- action(versa(X,Y)). 
plan_cost(plan leq 170).