CoCoA » CoCoA-5

Andraschko reported the following by email:
Consider the following code which computes the minimal polynomial of sqrt(2)+sqrt³(3)+sqrt⁵(5):

S ::= QQ[x,t1,t2,t3];
Use S;
L := [x-(t1+t2+t3), t1^2-2, t2^3-3, t3^5-5];
I := ideal(S,L);
J := elim([t1,t2,t3],I);
f := gens(J)[1]; -- some ugly poly of deg 30 that is in I

Now let's just compute for fun NR. This should be 0 since f is in I and L is a Gröbner basis by the coprime LT criterion.
It does and it is very fast (not even a second). Now if we do the same with DivAlg, it is VERY slow - although it should normally do the same and just store some information on its way.
Why is it so slow? It took 16 minutes on my system until it was finished.