Confluence of right ground term rewriting systems is decidable

Term rewriting systems provide a versatile model of computation. An important property which allows to abstract from potential nondeterminism of parallel execution of the modelled program is confluence. In this paper we prove that confluence of a fairly large class of systems, namely right ground term rewriting systems, is decidable. We introduce a labelling of variables with colours and constrain substitutions according to these colours. We show how right ground rewriting systems can be reduced to simple systems with coloured variables. Such systems can be analysed using reduction-automata techniques which leads to an interesting decision procedure for confluence.