Relational vs. PICK/Object DBMS

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Sorry for the omissions/errors in the previous post.

I would like to know which model/DBMS perform better (in terms of programmers productivity, system requirements, etc.) on the following problems (stated in terms of relational model) :

 1)Been given the domains {A,A1,A2,...,An}, with large n and the following  database schema:

• for all i in 1..n, Ri(A,Ai) is a base relation
• for all i in 1..n, A is a candidate key for the relation Ri

 answer the questions:

1. for {i1,i2,...,ip} given , find R(A,Ai1,Ai2,...,Aip) with the constraints R(A,Aik) = Rik(A,Aik) for all k in 1..p, R is minimal.
2. for a in A given, find R(A,Ai1,Ai2,...,Aip) with the constraints:
   • R(A=a,Aik) = Rik(A=a,Aik) for all k in 1..p
   • {Ai1,...,Aip} is maximal
   • R is minimal
3. Let P(A) be the power set of domain A for any domain A. Been given the domains {A,B,C} and the database schema R1(P(A),P(B)), R2(P(B),P(C)) answer the question: find R(P(A),P(B),P(C)) with the contstraints:
   • R(P(A),P(B))=R1(P(A),P(B))
   • R(P(B),P(C))=R2(P(B),P(C))
   • R minimal

 Note:

1. No NULLs are allowed
2. R(X1,X2,...,Xp) is the projection of R on the attributes (X1,...,Xp)
3. R(X1=a,X2,...,Xp) is the projection of R on the attributes (X1,...,Xp) followed by the selection upon X1=a (or viceversa)
4. R1(P(A1),P(A2), ..., P(Ap))=R2(P(A1),P(A2),...,P(Ap)) iff
   • for any (X1,...,Xp) in R1, for any (x1,...,xp) in X1xX2,...xXp there is an (Y1,...,Yp) in R2 such that (x1,...,xp) is in Y1xY2x...xYp
   • for any (Y1,...,Yp) in R2, for any (y1,...,yp) in Y1xY2,...xYp there is an (X1,...,Xp) in R1 such that (y1,...,yp) is in X1xX2x...xXp
5. for any R(P(A1),P(A2),...,P(Ap)), for any two distinct (X1,X2,...,Xp) , (Y1,Y2,...,Yp) from R, X1x...xXp /\ Y1x...xYp is void where /\ stands for intersection and x for cartesian product.
6. A maximal (minimal) means A has a maximal (minimal) number of elements.

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