play(1,1).
play(1,2).
play(1,4).
play(1,6).
play(1,7).
play(1,9).
play(2,1).
play(2,2).
play(2,4).
play(2,5).
play(2,6).
play(2,8).
play(3,1).
play(3,2).
play(3,7).
play(3,8).
play(4,1).
play(4,5).
play(4,6).
play(4,9).
play(5,3).
play(5,5).
play(5,6).
play(5,7).
play(5,8).
duration(1,2).
duration(2,4).
duration(3,1).
duration(4,3).
duration(5,3).
duration(6,2).
duration(7,5).
duration(8,7).
duration(9,6).
solve6_3(MinWaiting):-
                        length(Concert,9),
                        domain(Concert,1,9),
                        all_distinct(Concert),
                        getWaiting(1,Concert,0,0,0,L1),
                        getWaiting(2,Concert,0,0,0,L2),
                        getWaiting(3,Concert,0,0,0,L3),
                        getWaiting(4,Concert,0,0,0,L4),
                        getWaiting(5,Concert,0,0,0,L5),
                        MinWaiting #= L1+L2+L3+L4+L5,
                        append(Concert,[MinWaiting],Var),
                        minimize(labeling([],Var),MinWaiting).

getWaiting(_,[],_,_,Res,Res).
getWaiting(Player,[Play|Rest],Played,Pending,SoFar,Res):-
                                                play(Player,Play),
                                                NewPlayed #= Played+1,
                                                NewSoFar #= SoFar + Pending,
                                                getWaiting(Player,Rest,NewPlayed,0,NewSoFar,Res).
getWaiting(Player,[Play|Rest],Played,Pending,SoFar,Res):-
                                                Played #> 0,
                                                \+play(Player,Play),
                                                duration(Play,D),
                                                NewPending #= Pending + D,
                                                getWaiting(Player,Rest,Played,NewPending,SoFar,Res).
getWaiting(Player,[Play|Rest],0,Pending,SoFar,Res):-
                                                \+play(Player,Play),
                                                getWaiting(Player,Rest,0,Pending,SoFar,Res).