Rewriting sistems and semigroups

The one of the studies on computer sciences is automoto theory and rewriting systems. Rewriting systems are used in some theories in algebra and also algebra is used in some thesis in rewriting systems. For example, the theories of rewriting systems are quite often used in solutions of some finiteness conditional algebraical problems such as solubility of word problems and in some monoids homology measurement. More especially, group and semigroup presentations on algebra are one within rewriting systems on computer sciences. Every algebraical structure has a presentation. Especially, having a finite presentation is more important in terms of finite rewriting systems. In this thesis we are going to compile some important studies which researches relation between finite presentable semigroups and finite complete rewriting systems.