  A semi-Peano algebra is an algebra for which each operation is injective, and
the images of the operations are pairwise disjoint. The most straightforward
non-trivial kind of finitely presented semi-Peano algebra are algebras with a
single unary operation. There are two possible directions of generalization:
algebras with a single operation of any arity, and algebras with several unary
operations. The former can be solved easily by adapting results on
equidecomposable groupoids from [2]. However, the second way is somewhat
different. We will show that a finitely presented multi-unary semi-Peano
algebra is the free product of cyclic semi-Peano algebras and that a unique
relation defines such cyclic algebras. In addition, we will characterize each
cyclic algebra up to isomorphism.
