%% Append Program Finder
/**
%%o([a,b,c],[d,e,f],[[a,d],[b,e],[c,f]]).
o(A,B,C) :-
o(A,B,[],C).
o([],[],C,C).
o(A,B,C,C1):-
A=[A1|As],B=[B1|Bs],
append([A1],[B1],AB),
append(C,[AB],C3),
o(As,Bs,C3,C1).
**/

%% apf1([[1,2,3],[4,5,6],[7,8,9]],[[1,4,7],[2,5,8],[3,6,9]],Program)

apf1(Input,Output,Program) :-
apf(Input,Output,[],Indices),
list_checker1(Indices),
Program=[[o(v(a),v(b),v(c)),
o(v(a),v(b),[],v(c))],
[o([],[],v(c),v(c))],
[o(v(a),v(b),v(c),v(c1)),
v(a)=[v(a1)|v(as)],v(b)=[v(b1)|v(bs)],
append([v(a1)],[v(b1)],v(ab)),
append(v(c),[v(ab)],v(c3)),
o(v(as),v(bs),v(c3),v(c1))]].

apf(_Input, [], Indices, Indices).
apf(Input, Output, Indices1,Indices2) :-
	Output = [Item1 | Items2],
	findindex1(Item1, Input, Index),
	append(Indices1,[Index],Indices3),
	apf(Input,Items2,Indices3,Indices2).
findindex1([], _Input, _Index).
findindex1(Item, Input, Index) :-
	Item = [Value1 | Values],
	findindexa(Value1, Input, 1, Index),
	findindex1(Values, Input, Index).
findindexa(_Value,[],Index,Index).
findindexa(Value,Input,Index1,Index2) :-
	Input = [Item1 | Items],
	length(Item1,Length1),Length2 is Length1 + 1,
	findindex2(Value,Item1,Index1,Index3),
	findindexb(Value,Items,Index3,Index2,Length2).
findindexb(Value,Item,Length,Index1,Length) :-
	%%ifindindex2(Value,Item,1,Index2),
	%%findindexa(Value,Item,Index2,Index1).
        findindexa(Value,Item,1,Index1),!.
findindexb(Value,_Item,Index1,Index2,_Length) :-
        findindexa(Value,[],Index1,Index2).
findindex2(Value, Input, Index, Index) :-
	Input = [Value | _Values], !.
findindex2(_Value, [], Index, Index).
findindex2(Value1, Input, CurrIndex1, Index) :-
        Input = [Value2 | Values],
	not(Value1 = Value2),
	CurrIndex2 is CurrIndex1 + 1,
	findindex2(Value1, Values, CurrIndex2, Index).

list_checker1(List) :-
	List = [Item | Items],
	list_checker2(Item, Items).
list_checker2(_Item, []).
list_checker2(Item1, List) :-
	List = [Item2 | Items],
	Item2 is Item1 + 1,
	list_checker2(Item2, Items).