Orbit closures of algebraic group actions

An algorithm is proposed allowing to constructively decide whether one orbit of an algebraic transformation group is contained in the closure of another or not.
In particular, this yields a constructive way to decide whether two such orbits coincide or not. This basic problem arises in a number of theories such as degeneration theory of algebras and modules, classification of some classes of algebraic varieties (e.g., curves, hypersurfaces), geometric complexity theory (Cook's celebrated $P\neq NP$ problem).