% L2
% Q1
fibonacci(0,1).
fibonacci(1,1).
fibonacci(X,Y):-
    X > 1,
    N is X - 1,
    M is X - 2,
    fibonacci(N,R),
    fibonacci(M,S),
    Y is S +R.
% Q2
fibiter(X,Y):-
    fibiter(X,Y,1,1).
fibiter(0,X,X,_).
fibiter(X,Y,Z,V):-
    X >0,
    M is X -1,
    NV is Z + V,
    fibiter(M,Y,V,NV).

% Q3
pgcd(A,0,A):-!.
pgcd(A,A,A):-!.
pgcd(0,A,A):-!.
pgcd(A,B,X):-
    A > B,
    C is A mod B,
    pgcd(C,B,X).
pgcd(A,B,X):-
    B > A,
    C is B mod A,
    pgcd(A,C,X).

% L3
% Q2
member(X,[X|_]).
member(X,[_|L]) :- 
    member(X,L).

% Q3
subset([],_).
subset(L1,L2):-
    [X | L] = L1,
    member(X,L2),
    subset(L,L2).

% Q4
sublist(_,[]):-false.
sublist([],_).
sublist([X | L1],[Y | L2]):-
    X = Y,
    subset(L1,L2).

sublist([X | L1],[Y | L2]):-
    X \= Y, 
    subset([X | L1],L2).