, Competition on software verification (SV-COMP), 2018.

, Proceedings of 9th International Conference on Formal Methods in Computer-Aided Design, 2009.

R. Bagnara, P. M. Hill, E. Ricci, and E. Zaffanella, Precise widening operators for convex polyhedra, Sci. Comput. Program, vol.58, issue.1-2, pp.28-56, 2005.

R. Bagnara, P. M. Hill, and E. Zaffanella, Widening operators for powerset domains, STTT, vol.9, issue.3-4, pp.413-414, 2007.

A. Bakhirkin, HCAI, a path focusing abstract interpreter for Horn clauses, 2018.

A. Bakhirkin and D. Monniaux, Combining forward and backward abstract interpretation of Horn clauses, pp.23-45
URL : https://hal.archives-ouvertes.fr/hal-01551447

F. Benoy, A. King, and F. Mesnard, Computing convex hulls with a linear solver, TPLP, vol.5, issue.1-2, pp.259-271, 2005.

D. Beyer, A. Cimatti, A. Griggio, M. E. Keremoglu, and R. Sebastiani, Software model checking via large-block encoding, Proceedings of 9th International Conference on Formal Methods in Computer-Aided Design, pp.25-32, 2009.

N. Bjørner, A. Gurfinkel, K. L. Mcmillan, A. Rybalchenko, L. D. Beklemishev et al., Horn clause solvers for program verification, Fields of Logic and Computation II-Essays Dedicated to Yuri Gurevich on the Occasion of His 75th Birthday, vol.9300, pp.24-51, 2015.

S. Chaki, A. Gurfinkel, and O. Strichman, Decision diagrams for linear arithmetic, Proceedings of 9th International Conference on Formal Methods in Computer-Aided Design, pp.53-60, 2009.

J. Chen and P. Cousot, A binary decision tree abstract domain functor, Static Analysis-22nd International Symposium, vol.2015, pp.36-53, 2015.

P. Cousot and N. Halbwachs, Automatic discovery of linear restraints among variables of a program, Conference Record of the Fifth Annual ACM Symposium on Principles of Programming Languages, pp.84-96, 1978.

A. Fouilhé, Revisiting the abstract domain of polyhedra : constraints-only representation and formal proof. (Le domaine abstrait des polyèdres revisité : représentation par contraintes et preuve formelle), 2015.

J. Fourier, Histoire de l'Académie pour 1824, vol.2, pp.325-328, 1890.

A. Gurfinkel and S. Chaki, Boxes: A symbolic abstract domain of boxes, Static Analysis-17th International Symposium, vol.6337, pp.287-303, 2010.

A. Gurfinkel, T. Kahsai, A. Komuravelli, and J. A. Navas, The seahorn verification framework, Computer Aided Verification (CAV), vol.9206, pp.343-361, 2015.

N. Halbwachs, Détermination automatique de relations linéaires vérifiées par les variables d'un programme, 1979.

J. Imbert, Fourier's elimination: Which to choose? In: PPCP, pp.117-129, 1993.

B. Jeannet, , 2018.

D. Kohler, Projections of convex polyhedral sets, 1967.

A. Maréchal, New Algorithmics for Polyhedral Calculus via Parametric Linear Programming. (Nouvelle Algorithmique pour le Calcul Polyédral via Programmation Linéaire Paramétrique), 2017.

A. Maréchal, D. Monniaux, and M. Périn, Scalable minimizing-operators on polyhedra via parametric linear programming, pp.212-231

A. Maréchal and M. Périn, Efficient elimination of redundancies in polyhedra by raytracing, Verification, Model Checking, and Abstract Interpretation-18th International Conference, vol.10145, pp.367-385, 2017.

A. Maréchal and M. Périn, Efficient elimination of redundancies in polyhedra by raytracing, Verification, Model Checking, and Abstract Interpretation-18th International Conference, vol.10145, pp.367-385, 2017.

P. Mcmullen, The maximum numbers of faces of a convex polytope, Mathematika, vol.17, pp.179-184, 1970.

D. Monniaux and F. Alberti, A simple abstraction of arrays and maps by program translation, Static analysis (SAS), vol.9291, pp.217-234, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01162795

D. Monniaux and L. Gonnord, Using bounded model checking to focus fixpoint iterations, Static Analysis-18th International Symposium, vol.6887, pp.369-385, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00600087

D. Monniaux and L. Gonnord, Cell morphing: From array programs to array-free Horn clauses, Static analysis, vol.9837, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01206882

D. Monniaux and L. Gonnord, Cell morphing: From array programs to array-free Horn clauses, Static Analysis-23rd International Symposium, vol.9837, pp.361-382, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01206882

T. S. Motzkin, Beiträge zur Theorie der Linearen Ungleichungen, 1936.

F. Ranzato, Static Analysis-24th International Symposium, vol.10422, 2017.

X. Rival and L. Mauborgne, The trace partitioning abstract domain, ACM Trans. Program. Lang. Syst, vol.29, issue.5, p.26, 2007.

A. Simon and A. King, rule ( verifier. error false false false ) ) ( rule ( verifier. error false true true ) ) ( rule ( verifier. error true false true ) ) ( rule ( verifier. error true true true ) ) ( rule main@entry ) ( rule (= > ( and main@entry true (= > main@_bb_0 ( and main@_bb_0 main@entry_0 ) ) main@_bb_0 (= > ( and main@_bb_0 main@entry_0, Static Analysis, 12th International Symposium, vol.3672, pp.336-351, 2005.

, = > ( and main@_bb_0 main@entry_0 ) (= main@ % x .0. i1_0 0) )

, = > ( and main@_bb_0 main@entry_0 ) (= main@ % y .0. i2_1 main@ % y .0. i2_0 )

, = main@ % x .0. i1_1 main@ % x .0. i1_0 ) ) ) > ( and ( main@_bb main@ % x .0. i1_0 main@ % y .0. i2_0 ) true (= main@ % _1_0, vol.0

, > main@_bb_1 ( and main@_bb_1 main@_bb_0 ) ) main@_bb_1 (= > ( and main@_bb_1 main@_bb_0 ) main@ % _3_0 ) (= > ( and main@_bb_1 main@_bb_0 ) (= main@ % y .0. i2_1 main@ % _2_0

, > ( and main@_bb_1 main@_bb_0 ) (= main@ % x .0. i1_1 main@ % _1_0 ) )

, > ( and main@_bb_1 main@_bb_0 ) (= main@ % y .0. i2_2 main@ % y .0. i2_1 ) )

, = main@ % x .0. i1_2 main@ % x .0. i1_1 ) ) ) ( let (( a !1 ( and ( main@_bb main@ % x .0. i1_0 main@ % y .0. i2_0 ) true (= main@ % _1_0, vol.1

, = > main@verifier. error_0 ( and main@verifier. error_0 main@_bb_0 ) )

, = > ( and main@verifier. error_0 main@_bb_0 ) ( not main@ % _3_0 ) )

=. and M. , main@_bb_0 ) (= main@ %. lcssa5_0 main@ % _2_0 ) ), vol.0

=. and M. , main@_bb_0 ) (= main@ %. lcssa_0 main@ % _1_0 ) ), vol.0

=. and M. , main@_bb_0 ) (= main@ %. lcssa5_1 main@ %. lcssa5_0 ) ), vol.0

(. and M. , main@_bb_0 ) (= main@ %. lcssa_1 main@ %. lcssa_0 ) ), vol.0

=. Main@verifier,

=. Main@verifier,

=. Main@verifier, error_0 (= main@ % or. cond. i_0 ( and main@ % _4_0 main@ % _5_0 ) ) )

=. Main@verifier, , vol.0

=. Main@verifier, error. split_0 ( and main@verifier. error. split_0 main@verifier. error_0 ) )

, System of Horn clauses produced by SeaHorn for the program in Fig, vol.6