@. A. Lastly, is an overlapping branching, let us write (A, B) = (f 1 uA 1 v 1 g, f 1 uB 1 v 1 g), where (A 1 , B 1 ) is a critical pair. Let A 1 , B 1 and ? 1 be the cells associated with (A 1 , B 1 ). We then define A := f 1 uA 1 v 1 g

J. Bénabou, Introduction to bicategories, Reports of the Midwest Category Seminar, pp.1-77, 1967.
DOI : 10.1007/BF01451367

A. Burroni, Higher-dimensional word problems with applications to equational logic. Theoretical computer science, pp.43-62, 1993.

P. Dehornoy, THE SUBWORD REVERSING METHOD, International Journal of Algebra and Computation, vol.21, issue.01n02, pp.71-118, 2011.
DOI : 10.1142/S0218196711006091

URL : https://hal.archives-ouvertes.fr/hal-00442274

S. Gaussent, Y. Guiraud, and P. Malbos, Coherent presentations of Artin monoids, Compositio Mathematica, vol.22, issue.05, pp.957-998, 2015.
DOI : 10.1090/pspum/056.2/1278735

URL : https://hal.archives-ouvertes.fr/hal-00682233

Y. Guiraud and P. Malbos, Higher-dimensional categories with finite derivation type, Theory and Applications of Categories, vol.22, issue.18, pp.420-478, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00326974

Y. Guiraud and P. Malbos, Coherence in monoidal track categories, Mathematical Structures in Computer Science, vol.26, issue.06, pp.931-969, 2012.
DOI : 10.1090/S0002-9904-1965-11234-4

URL : https://hal.archives-ouvertes.fr/hal-00470795

Y. Guiraud and P. Malbos, Higher-dimensional normalisation strategies for acyclicity, Advances in Mathematics, vol.231, issue.3-4, pp.2294-2351, 2012.
DOI : 10.1016/j.aim.2012.05.010

URL : https://hal.archives-ouvertes.fr/hal-00531242

G. Maxwell and . Kelly, Coherence theorems for lax algebras and for distributive laws, Category seminar, pp.281-375, 1974.

G. Maxwell, S. Kelly, and . Maclane, Closed coherence for a natural transformation, Coherence in categories, pp.1-28, 1972.

C. Roger, . Lyndon, E. Paul, and . Schupp, Combinatorial group theory, 2015.

S. Mac and L. , Natural associativity and commutativity, Rice University Studies, vol.49, issue.4, pp.28-46, 1963.

S. Mac, L. , and R. Paré, Coherence for bicategories and indexed categories, Journal of Pure and Applied Algebra, vol.37, issue.1, pp.59-80, 1985.

F. Métayer, Cofibrant objects among higher-dimensional categories. Homology, Homotopy and Applications, pp.181-203, 2008.

A. Power, A general coherence result, Journal of Pure and Applied Algebra, vol.57, issue.2, pp.165-173, 1989.
DOI : 10.1016/0022-4049(89)90113-8

C. Craig, F. Squier, Y. Otto, and . Kobayashi, A finiteness condition for rewriting systems, Theoretical Computer Science, vol.131, issue.2, pp.271-294, 1994.

R. Street, Limits indexed by category-valued 2-functors, Journal of Pure and Applied Algebra, vol.8, issue.2, pp.149-181, 1976.
DOI : 10.1016/0022-4049(76)90013-X

R. Street, The algebra of oriented simplexes, Journal of Pure and Applied Algebra, vol.49, issue.3, pp.283-335, 1987.
DOI : 10.1016/0022-4049(87)90137-X

R. Street, Categorical structures. Handbook of algebra, pp.529-577, 1996.