Simple generators with a complex Gröbner basis It's known that finding a Gröbner basis of a polynomial ideal has a worst-case space complexity of $O(2^{2^{c\cdot n}})$, where c is constant and n is the number of variables $k[x_1,\ldots,x_n]$.

However, in practice it seems that most ideals have a simple Gröbner basis.

Can anyone give some concrete examples of small generators whose ideal has a large Gröbner basis?
How would I go about searching for such examples (besides a brute-force approach of trying random ideals)?
I just found the following example, from this paper:

GroebnerBasis[{x^5 + y^5 + z^5 - 1, x^3 + y^3 + z^2 - 1}, {x, y, z}] (* Is long *)
$$ (x5+y5+z5−1x3+y3+z2−1)(xyz)
=(x5+y5+z5+−x3+y3+z2+−1)(xyz)
=(x5)(xyz)+(y5)(xyz)+(z5)(xyz)+(−x3)(xyz)+(y3)(xyz)+(z2)(xyz)+(−1)(xyz)
=x6yz+xy6z+xyz6−x4yz+xy4z+xyz3−xyz
=x6yz+xy6z+xyz6−x4yz+xy4z+xyz3−xyz $$