We define a new theory of concatenation WTC which is much weaker than Grzegorczyk's well-known theory TC. We prove that WTC is mutually interpretable with the weak theory of arithmetic R. The latter is, in a technical sense, much weaker than Robinson's arithmetic Q, but still essentially undecidable. Hence, as a corollary, WTC is also essentially undecidable.
"Weak Theories of Concatenation and Arithmetic." Notre Dame J. Formal Logic 53 (2) 203 - 222, 2012. https://doi.org/10.1215/00294527-1715698