The Magic-Set Transformed rules for the project are:

<h2>Bill of Materials Problem</h2>

<PRE>
query(X,Y) :- basic_comp_bff(engine,X,Y).
basic_comp_bff(P,B,sum(&lt;Q&gt;)) :- look_for_bff(P,B,Q), magic_basic_comp_bff(P).
look_for_bff(P,B,Q) :- sub_part_bffb(P,B,Q,b), magic_look_for_bff(P).

sub_part_bffb(X,Y,Q,T) :- comp(X,Y,Q,T), magic_sub_part_bffb(X,T).
sub_part_bffb(X,Y,Q,T) :- comp(Z,Y,Q2,T), sub_part_bbff(X,Z,Q1,T1),
                          Q is Q1 * Q2, magic_sub_part_bffb(X,T).

sub_part_bbff(X,Y,Q,T) :- comp(X,Y,Q,T), magic_sub_part_bbff(X,Y).
sub_part_bbff(X,Y,Q,T) :- comp(Z,Y,Q2,T), sub_part_bbff(X,Z,Q1,T1),
                          Q is Q1 * Q2, magic_sub_part_bbff(X,Y).

magic_basic_comp_bff(engine).
magic_look_for_bff(P) :- magic_basic_comp_bff(P).
magic_sub_part_bffb(P,b) :- magic_look_for_bff(P).

magic_sub_part_bbff(X,Z) :- comp(Z,Y,Q2,T), magic_sub_part_bffb(X,T).
magic_sub_part_bbff(X,Z) :- comp(Z,Y,Q2,T), magic_sub_part_bbff(X,Y).

temp_cost_bf(P,X) :- basic_comp_bff(P,B,Q), price(B,C), X is Q * C.
cost_bf(P,sum(&lt;C&gt;)) :- temp_cost_bf(P,C).
</PRE>



<h2>Anti-Trust Problem</h2>

<PRE>
query(X) :- market_bbf(violet,toys,X).
market_bbf(Comp1,Mrkt,Qty) :- company(Comp1,Mrkt,Qty),
                              magic_market_bbf(Comp1,Mrkt).
market_bbf(Comp1,Mrkt,Qty) :- has_shares(Comp1,Comp2,N), N > 50,
                              market_bbf(Comp2,Mrkt,Qty),
                              magic_market_bbf(Comp1,Mrkt).
magic_market_bbf(violet,toys).
magic_market_bbf(C,M) :- has_shares(C1,C,N), N > 50, 
                         magic_market_bbf(C1,M).

inquire(Comp,Mrkt,sum(&lt;Quota&gt;)) :- market(Comp,Mrkt,Quota).

find_trust(Mrkt,Comp,Total) :- trust_limit(Mrkt,Threshold),
                               inquire(Comp,Mrkt,Total),
                               Total > Threshold.
</PRE>

<h2>Siblings-Cousins-Related Problem</h2>

<PRE>
query(X) :- cousin_bf(h,X).
cousin_bf(X,Y) :- parent(X,Xp), parent(Y,Yp), sibling_bf(Xp,Yp),
                  magic_cousin_bf(X).
cousin_bf(X,Y) :- parent(X,Xp), parent(Y,Yp), cousin_bf(Xp,Yp),
                  magic_cousin_bf(X).
sibling_bf(X,Y) :- parent(X,Z), parent(Y,Z), X <> Y,
                   magic_sibling_bf(X).
magic_cousin_bf(h).
magic_cousin_bf(Xp) :- parent(X,Xp), magic_cousin_bf(X).
magic_sibling_bf(Xp) :- parent(X,Xp), magic_cousin_bf(X).
</PRE>

<h2>Trip Problem</h2>

<PRE>
trip(L,S,E):-leg(L,S,E).
trip(L,S,E):-leg(L,S,I), trip(L,I,E).
trip(L,S,E):-interchange(I,L,M), trip(L,S,I), trip(M,I,E).
query(X):-trip(blue, suwanee, X).

Adorned Set of Rules:

query_f(X):-trip_bbf(blue,suwanee,X).
trip_bbf(L,S,E):-leg(L,S,E).
trip_bbf(L,S,E):-leg(L,S,I), trip_bbf(L,I,E).
trip_bbf(L,S,E):-interchange(I,L,M), trip_bbb(L,S,I), trip_bbf(M,I,E).
trip_bbb(L,S,E):-leg(L,S,E).
trip_bbb(L,S,E):-leg(L,S,I), trip_bbb(L,I,E).
trip_bbb(L,S,E):-interchange(I,L,M), trip_bbb(L,S,I), trip_bbb(M,I,E).


Magic-set of Rules:

magic_trip_bbf(blue,suwanee).
magic_trip_bbf(L,I):-leg(L,S,I),magic_trip_bbf(L,S).
magic_trip_bbb(L,S,I):-interchange(I,L,M),magic_trip_bbf(L,S).
magic_trip_bbf(M,I):-interchange(I,L,M),magic_trip_bbf(L,S).
magic_trip_bbb(L,I,E):-leg(L,S,I),trip_bbb(L,S,E).
magic_trip_bbb(L,S,I):-interchange(I,L,M),magic_trip_bbb(L,S,E).
magic_trip_bbb(M,I,E):-interchange(I,L,M),magic_trip_bbb(L,S,E).


Modified Adorned Set of Rules:

query_f(X):-trip_bbf(blue,suwanee,X).
trip_bbf(L,S,E):-leg(L,S,E),magic_trip_bbf(L,S).
trip_bbf(L,S,E):-leg(L,S,I), trip_bbf(L,I,E),magic_trip_bbf(L,S).
trip_bbf(L,S,E):-interchange(I,L,M), trip_bbb(L,S,I), trip_bbf(M,I,E),magic_trip_bbf(L,S).
trip_bbb(L,S,E):-leg(L,S,E),magic_trip_bbb(L,S,E).
trip_bbb(L,S,E):-leg(L,S,I), trip_bbb(L,I,E),magic_trip_bbb(L,S,E).
trip_bbb(L,S,E):-interchange(I,L,M), trip_bbb(L,S,I), trip_bbb(M,I,E),magic_trip_bbb(L,S,E).


Output: Magic-set of Rules + Modified Adorned Set of Rules
</PRE>