J. David and . Anick, On the homology of associative algebras, Trans. Amer. Math. Soc, vol.296, issue.2, pp.641-659, 1986.

R. Berger, Weakly confluent quadratic algebras, Algebras and Representation Theory, vol.1, issue.3, pp.189-213, 1998.
DOI : 10.1023/A:1009918131382

R. Berger, Confluence and quantum Yang-Baxter equation, Journal of Pure and Applied Algebra, vol.145, issue.3, pp.267-283, 2000.
DOI : 10.1016/S0022-4049(98)00102-9
URL : https://doi.org/10.1016/s0022-4049(98)00102-9

R. Berger, Koszulity for Nonquadratic Algebras, Journal of Algebra, vol.239, issue.2, pp.705-734, 2001.
DOI : 10.1006/jabr.2000.8703
URL : https://doi.org/10.1006/jabr.2000.8703

G. M. Bergman, The diamond lemma for ring theory, Advances in Mathematics, vol.29, issue.2, pp.178-218, 1978.
DOI : 10.1016/0001-8708(78)90010-5

C. Chenavier, Reduction operators and completion of rewriting systems, Journal of Symbolic Computation, vol.84, 2017.
DOI : 10.1016/j.jsc.2017.03.002
URL : https://hal.archives-ouvertes.fr/hal-01325907

S. Chouhy and A. Solotar, Projective resolutions of associative algebras and ambiguities, Journal of Algebra, vol.432, pp.22-61, 2015.
DOI : 10.1016/j.jalgebra.2015.02.019

V. Dotsenko and A. Khoroshkin, Gröbner bases for operads. Duke Math, J, vol.153, issue.2, pp.363-396, 2010.

C. Eder, Signature-based algorithms to compute standard bases, 2012.
DOI : 10.1145/1993886.1993906

J. Faugère, A new efficient algorithm for computing Gr??bner bases (F4), Journal of Pure and Applied Algebra, vol.139, issue.1-3, pp.61-88, 1998.
DOI : 10.1016/S0022-4049(99)00005-5

J. Faugère, A new efficient algorithm for computing Gröbner bases without reduction to zero (F 5 ), Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, pp.75-83, 2002.

J. Faugère and S. Rahmany, Solving systems of polynomial equations with symmetries using SAGBI-Gröbner bases, ISSAC 2009?Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, pp.151-158, 2009.

R. Gebauer and H. M. Möller, On an installation of Buchberger's algorithm, Journal of Symbolic Computation, vol.6, issue.2-3, pp.275-286, 1988.
DOI : 10.1016/S0747-7171(88)80048-8

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

Y. Guiraud and P. Malbos, Identities among relations for higher-dimensional rewriting systems, OPERADS 2009, pp.145-161, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00426228

Y. Kobayashi, Complete rewriting systems and homology of monoid algebras, Journal of Pure and Applied Algebra, vol.65, issue.3, pp.263-275, 1990.
DOI : 10.1016/0022-4049(90)90106-R

J. Koszul, Homologie et cohomologie des alg??bres de Lie, Bulletin de la Société mathématique de France, vol.2, pp.65-127, 1950.
DOI : 10.24033/bsmf.1410
URL : http://www.numdam.org/article/BSMF_1950__78__65_0.pdf

D. Lazard, Gr??bner bases, Gaussian elimination and resolution of systems of algebraic equations, Computer algebra, pp.146-156, 1983.
DOI : 10.1007/3-540-12868-9_99

H. , M. Möller, and F. Mora, New constructive methods in classical ideal theory, J. Algebra, vol.100, issue.1, pp.138-178, 1986.

H. Möller, T. Mora, and C. Traverso, Gröbner bases computation using syzygies, Papers from the international symposium on Symbolic and algebraic computation, pp.320-328, 1992.

T. Mora, An introduction to commutative and noncommutative Gr??bner bases, Second International Colloquium on Words, Languages and Combinatorics, pp.131-173, 1992.
DOI : 10.1016/0304-3975(94)90283-6
URL : https://doi.org/10.1016/0304-3975(94)90283-6

B. Stewart and . Priddy, Koszul resolutions, Trans. Amer. Math. Soc, vol.152, pp.39-60, 1970.

F. Schreyer, Die berechnung von syzygien mit dem verallgemeinerten weierstraßschen divisionssatz und eine anwendung auf analytische cohen-macaulay stellenalgebren minimaler multiplizität, 1980.

J. Tate, Homology of Noetherian rings and local rings, Illinois J. Math, vol.1, pp.14-27, 1957.

T. Vaccon and K. Yokoyama, A tropical F5 algorithm. arXiv preprint, 2017.
DOI : 10.1145/3087604.3087630
URL : https://hal.archives-ouvertes.fr/hal-01521865

X. Xiu, Non-commutative Gröbner bases and applications, 2012.