Geodesic
Coset Enumeration in a Finitely Presented Semigroup
Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 37-46

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The enumeration method for finite groups, the so-called Todd-Coxeter process, has been described in [2], [3]. Leech [4] and Trotter [5] carried out the process of coset enumeration for groups on a computer. However Mendelsohn [1] was the first to present a formal proof of the fact that this process ends after a finite number of steps and that it actually enumerates cosets in a group. Dietze and Schaps [7] used Todd-Coxeter′s method to find all subgroups of a given finite index in a finitely presented group. B. H. Neumann [8] modified Todd-Coxeter′s method to enumerate cosets in a semigroup, giving however no proofs of the effectiveness of this method nor that it actually enumerates cosets in a semigroup. 
Jura, Andrzej. Coset Enumeration in a Finitely Presented Semigroup. Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 37-46. doi: 10.4153/CMB-1978-007-x
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     title = {Coset {Enumeration} in a {Finitely} {Presented} {Semigroup}},
     journal = {Canadian mathematical bulletin},
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     year = {1978},
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     number = {1},
     doi = {10.4153/CMB-1978-007-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-007-x/}
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