  Signature-based algorithms are a popular kind of algorithms for computing
Groebner basis, including the famous F5 algorithm, F5C, extended F5, G2V and
the GVW algorithm. In this paper, an efficient method is proposed to solve the
detachability problem. The new method only uses the outputs of signature-based
algorithms, and no extra Groebner basis computations are needed. When a
Groebner basis is obtained by signature-based algorithms, the detachability
problem can be settled in polynomial time.
