  For an ideal I with a positive dimensional real variety, based on moment
relaxations, we study how to compute a Pommaret basis which is simultaneously a
Groebner basis of an ideal J generated by the kernel of a truncated moment
matrix and nesting between I and its real radical ideal. We provide a
certificate consisting of a condition on coranks of moment matrices for
terminating the algorithm. For a generic delta-regular coordinate system, we
prove that the condition is satisfiable in a large enough order of moment
relaxations.
