Under an R-alignment restriction on morphisms to finite semigroups, every morphism into forest algebras admits bounded-depth factorizations of forests, with a counterexample showing the condition is necessary.
Observe that by Definition 10.1, a context C ∈ Contexts(A) has exactly one address labeled□, so this is well defined
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A Factorization Theorem for Forest Algebras
Under an R-alignment restriction on morphisms to finite semigroups, every morphism into forest algebras admits bounded-depth factorizations of forests, with a counterexample showing the condition is necessary.