  The word problem is an old and central problem in (computational) group
theory. It is well-known that the word problem is undecidable in general, but
decidable for specific types of presentations. Consistent polycyclic
presentations are an important class of group presentations with solvable word
problem. These presentations play a fundamental role in the algorithmic theory
of polycyclic groups. Problems analogous to the word problem arise when
computing with other algebraic structures. Various aspects of this topic are
considered in the literature. The aim of this paper is to provide a general
approach to the topic including polycyclic groups and nilpotent associative
algebras as examples.
