Let $F_A$ be the free group generated by the finite set $A$ and let $\phi\colon F_A \to F_A$ be a group-automorphism. It is known [1] that $$ \mathrm{Fix}(\phi) = \{g \in F_A : \phi(g) = g\} $$ is (freely) finitely generated. Moreover, if $\phi$ is positive, that is, if $\phi(a)$ is a product of the generators for all $a \in A$, then there is an algorithm for computing $\mathrm{Fix}(\phi)$ [2]. My question is whether someone knows an implementation of this algorithm. I tried the usual sources (SageMath, Mathematica) without success. Even if there is an implementation that works for particular cases, it'd be useful for me.
[1] D. Coope. Automorphisms of Free Groups Have Finitely Generated Fixed Point Sets, 1987.
[2] M. Marshall & M. Lustig. On the dynamics and the fixed subgroup of a free group automorphism.