no. 2
A normal form for restricted exponential functions
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 23 (1989) no. 2, pp. 217-231 
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     author = {Degano, Pierpaolo and Gianni, Patrizia},
     title = {A normal form for restricted exponential functions},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {217--231},
     year = {1989},
     publisher = {EDP Sciences},
     volume = {23},
     number = {2},
     mrnumber = {1001727},
     zbl = {0665.03018},
     language = {en},
     url = {https://www.numdam.org/item/ITA_1989__23_2_217_0/}
}
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Degano, Pierpaolo; Gianni, Patrizia. A normal form for restricted exponential functions. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 23 (1989) no. 2, pp. 217-231. https://www.numdam.org/item/ITA_1989__23_2_217_0/

1. G. H. Hardy, Orders of infinity, Cambridge Tracts in Math. Phys., 12, Cambridge University Press 1910, Reprint Hafner, New York. | JFM

2. C. W. Henson and L. A. Rubel, Some Applications of Nevalinna Theory to Mathematical Logic: Identities of Exponential Functions, Trans. of the American Math. Soc., Vol. 282, No. 1, 1984, pp. 1-32. | Zbl | MR

3. G. Huet and D. C. Oppen, Equations and Rewrite Rules: A Survey. In: Formal Languages Theory: Perspectives and Open Problems, R. BOOK Ed., Academic Press, New York, 1980, pp. 349-405.

4. D. Lankford, On Proving Term Rewriting Systems are Noetherian, Rep. MTP-3, Louisiana Tech. Univ., 1979.

5. H. Levitz, An Ordered Set of Arithmetic Functions Representing the Least ε-Number, Z. Math. Logik Grundlag. Math., Vol. 21, 1975, pp. 115-120. | Zbl | MR

6. A. Macintyre, The Laws of Exponentiation. In: Model Theory and Arithmetic, C. BERLINE, K. MCALOON and J.-P. RESSAYRE Eds., Lecture Notes in Mathematics, No. 890, Springer-Verlag, Berlin, 1981, pp. 185-197. | Zbl | MR

7. C. Martin, Equational Theories of Natural Numbers and Transfinite Ordinals, Ph. D. Thesis, Univ. of California, Berkley, 1973.

8. G. E. Peterson and M. E. Stickel, Complete Sets of Reductions for Some Equational Theories, J. of the A.C.M., Vol. 28, 1981, pp. 233-264. | Zbl | MR

9. A. Tarski, Equational Logic and Equational Theories of Algebras. In: Contributions to Mathematical Logic, H. A. SCHMIDT, K. SHUTTE and H. J. THIELE Eds., North-Holland, Amsterdam, 1968, pp. 275-288. | Zbl | MR

10. A. J. Wilkie, On Exponentiation - A Solution to Tarskfs High School Algebra Problem. Unpublished Manuscript, quoted in Assoc. of Automated Reasoning Newsletter, Vol. 3, 1984, p. 6.