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.
By Lemma 17.8 we have (φ(τ.ctx(x1))·u,v ) ∈φ[NxtTwoCtx(τ.˜V,B,x )]
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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.