Geodesic
On identical transformations in commutative semigroups
Diskretnaya Matematika, Tome 19 (2007) no. 4, pp. 139-149
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It is proved that in any commutative semigroup the complexity of transformation of equal terms of length at most $n$ into each other is of order $n\log n$. 
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D. M. Motin. On identical transformations in commutative semigroups. Diskretnaya Matematika, Tome 19 (2007) no. 4, pp. 139-149. http://geodesic.mathdoc.fr/item/DM_2007_19_4_a9/

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[2] Lyndon R. C., “Identities in two-valued calculi”, Trans. Amer. Math. Soc., 71:3 (1951), 457–465 | DOI | MR | Zbl

[3] Yablonskii S. V., Gavrilov G. P., Kudryavtsev V. B., Funktsii algebry logiki i klassy Posta, Nauka, Moskva, 1966 | MR | Zbl