  In 2009, Ghani, Hancock and Pattinson gave a tree-like representation of
stream processors $A^{\mathbb{N}} \rightarrow B^{\mathbb{N}}$. In 2021, Garner
showed that this representation can be established in terms of algebraic theory
and comodels: the set of infinite streams $A^{\mathbb{N}}$ is the final comodel
of the algebraic theory of $A$-valued input $\mathbb{T}_A$ and the set of
stream processors $\mathit{Top}(A^{\mathbb{N}},B^{\mathbb{N}})$ can be seen as
the final $\mathbb{T}_A$-$\mathbb{T}_B$-bimodel. In this paper, we generalize
Garner's results to the case of free algebraic theories.
