This book examines when a semigroup or monoid can be peeled apart from its own equations, using the Church-Rosser property and other rewriting concepts to probe decidability and complexity.

The study starts with core definitions of Thue systems, reduction, and normal forms, then explores how cancellativity behaves under different system constraints. It reveals surprising boundaries: left- or right-cancellativity can be undecidable in general, yet become decidable in specific monadic or commutative settings. The work also connects these ideas to known results about word problems, embeddings, and connections to automata and arithmetic hierarchies.

How Church-Rosser and reduced systems influence normal forms and uniqueness of representations.
Undecidability results for cancellativity in general Thue systems and their monadic extensions.
Decidability conclusions for cancellativity in commutative Thue systems and the role of abelianizations.
Links to broader topics like word problems, automata, and complexity classes.

Ideal for readers of formal language theory, algebra, and theoretical computer science who want a rigorous, model-driven look at when cancellation properties can be algorithmically determined.

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