GROWTH AND EXISTENCE OF IDENTITIES IN A CLASS OF FINITELY PRESENTED INVERSE SEMIGROUPS WITH ZERO
L. M. Shneerson, David Easdown · International Journal of Algebra and Computation · 1996
We prove that a finitely presented Rees quotient of a free inverse semigroup has polynomial or exponential growth, and that the type of growth is algorithmically recognizable. We prove that such a semigroup has polynomial growth if and only if it satisfies a certain semigroup identity. However we give an example of such a semigroup which has exponential growth and satisfies some nontrivial identity in signature with involution.