Let B be a semigroup with the additional relation
B is called aband or anidempotent semigroup .
It is shown in this paper that the replacement rules (rewrites) resulting from the axiom of idempotence:
can be replaced by theNoetherian, confluent, conditional rewrites (i. e. a terminating replacement system having the Church-Rosser-Property):
These rewrites are used to obtain a unique normal form for words in B and hence are the basis for a decision procedure for word equality in B.
The proof techniques are based uponterm rewriting systems  rather than the usual algebraic approach. Alternative and simpler proofs of a result reported earlier by Green and Rees  and Gerhardt  have been obtained.
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Communicated by K. Keimel
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Siekmann, J., Szabó, P. A Noetherian and confluent rewrite system for idempotent semigroups. Semigroup Forum 25, 83–110 (1982). https://doi.org/10.1007/BF02573590
- Relative Length
- Equational Theory
- Unification Algorithm
- Replacement Rule
- Abstract Data Type