  Kristiansen and Murwanashyaka recently proved that Robinson arithmetic Q is
interpretable in an elementary theory of full binary trees, T. We prove that,
conversely, T is interpretable in Q by producing a formal interpretation of T
in an elementary concatenation theory, thereby also establishing mutual
interpretability of T with several well-known weak essentially undecidable
theories of numbers, strings and sets. We also in introduce a "hybrid"
elementary theory of strings and trees and establish its mutual
interpretability with Robinson's weak arithmetic R, the weak theory of binary
trees WT of Kristiansen and Murwanashyaka and a weak concatenation theory of
Higuchi and Hirohata.
