Note on 1-dimensional integrally closed Mori semigroups (Q2719899)

In a paper written in 1971, J. Querré posed the question: is a 1-dimensional integrally closed quasi-local Mori domain always a discrete valuation domain? This query was answered in the negative in a 1983 article by V. Baruci. Matsuda (the second author of this paper) posed the semigroup version of this problem in 1997, namely, must a 1-dimensional integrally closed quasi-local Mori semigroup be a discrete valuation semigroup of rank 1? In this short note, the authors give an example which establishes that the semigroup version of Querré's problem is also false. Here the authors construct a semigroup that is a 1-dimensional integrally closed quasi-local Mori semigroup that is neither a valuation nor a Noetherian semigroup.