J. David and . Anick, On the homology of associative algebras, Trans. Amer. Math. Soc, vol.296, issue.2, p.641659, 1986.

G. M. Bergman, The diamond lemma for ring theory, Advances in Mathematics, vol.29, issue.2, p.178218, 1978.
DOI : 10.1016/0001-8708(78)90010-5

A. M. Bigatti, M. Caboara, and L. Robbiano, Computing inhomogeneous Gröbner bases, J. Symbolic Comput, vol.46, issue.5, p.498510, 2011.

A. Miguel, M. Borges-trenard, T. Borges-quintana, and . Mora, Computing Gröbner bases by FGLM techniques in a non-commutative setting, J. Symbolic Comput, vol.30, issue.4, pp.429-449, 2000.

B. Buchberger, A criterion for detecting unnecessary reductions in the construction of Gröbner-bases, Symbolic and algebraic computation (EUROSAM '79, Internat. Sympos., Marseille, p.321, 1979.

M. Caboara, M. Kreuzer, and L. Robbiano, Eciently computing minimal sets of critical pairs, J. Symbolic Comput, vol.38, issue.4, p.11691190, 2004.

C. Chenavier, Reduction operators and completion of rewriting systems, Journal of Symbolic Computation, vol.84, p.5783, 2018.
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, p.2261, 2015.
DOI : 10.1016/j.jalgebra.2015.02.019

J. Faugère, A new ecient algorithm for computing Gröbner bases (F 4 ) Eective methods in algebraic geometry, J. Pure Appl. Algebra, vol.139, issue.1-3, p.6188, 1998.

J. Faugère, A new ecient algorithm for computing Gröbner bases without reduction to zero (F 5 ), Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, p.7583, 2002.

J. Faugère, P. Gianni, D. Lazard, and T. Mora, Ecient computation of zero-dimensional Gröbner bases by change of ordering, J. Symbolic Comput, vol.16, issue.4, p.329344, 1993.

Y. Guiraud, E. Hobeck, and P. Malbos, Convergent presentations and polygraphic resolutions of associative algebras. 65 pages, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01006220

Y. Kobayashi, Gröbner bases of associative algebras and the Hochschild cohomology, Trans. Amer. Math. Soc, vol.357, issue.3, p.10951124, 2005.

M. Kreuzer and L. Robbiano, Computational commutative algebra. 2, 2005.
DOI : 10.1007/978-3-540-70628-1

M. Kreuzer and L. Robbiano, Computational commutative algebra 1, 2008.
DOI : 10.1007/978-3-540-70628-1

T. Mora, An introduction to commutative and noncommutative Gröbner bases, Second International Colloquium on Words, Languages and Combinatorics, p.131173, 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, p.3960, 1970.

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