[. Atig, A. Bouajjani, S. Burckhardt, and M. Musuvathi, On the verification problem for weak memory models, POPL, pp.7-18, 2010.

A. [. Abdulla, B. Bouajjani, and . Jonsson, On-the-fly analysis of systems with unbounded, lossy FIFO channels, Proc. 10th Int. Conf. Computer Aided Verification (CAV '98), pp.305-318, 1998.
DOI : 10.1007/BFb0028754

N. [. Abdulla, A. Bertrand, P. Rabinovich, and . Schnoebelen, Verification of probabilistic systems with faulty communication, Information and Computation, vol.202, issue.2, pp.141-165, 2005.
DOI : 10.1016/j.ic.2005.05.008

A. Annichini, A. Bouajjani, and M. Sighireanu, TReX: A Tool for Reachability Analysis of Complex Systems, CAV, pp.368-372, 2001.
DOI : 10.1007/3-540-44585-4_34

URL : https://hal.archives-ouvertes.fr/hal-00110460

A. [. Abdulla, A. Collomb-annichini, B. Bouajjani, and . Jonsson, Using Forward Reachability Analysis for Verification of Lossy Channel Systems, Formal Methods in System Design, vol.25, issue.1, pp.39-65, 2004.
DOI : 10.1023/B:FORM.0000033962.51898.1a

. A. Ado-+-08-]-p, J. Abdulla, J. Deneux, K. Ouaknine, J. Quaas et al., Universality analysis for one-clock timed automata, Fundamenta Informaticae, vol.89, issue.4, pp.419-450, 2008.

B. [. Abdulla and . Jonsson, Verifying programs with unreliable channels, Proc. 8th IEEE Symp. Logic in Computer Science (LICS '93), pp.160-170, 1993.

]. P. Aj96a, B. Abdulla, and . Jonsson, Undecidable verification problems for programs with unreliable channels, Information and Computation, vol.130, issue.1, pp.71-90, 1996.

]. P. Aj96b, B. Abdulla, and . Jonsson, Verifying programs with unreliable channels, Information and Computation, vol.127, issue.2, pp.91-101, 1996.

[. Abdulla and M. Kindahl, Decidability of simulation and bisimulation between lossy channel systems and finite state systems (extended abstract), In CONCUR, pp.333-347, 1995.

N. [. Baier, P. Bertrand, and . Schnoebelen, On Computing Fixpoints in Well-Structured Regular Model Checking, with Applications to Lossy Channel Systems, Proc. LPAR 2006, pp.347-361, 2006.
DOI : 10.1007/11916277_24

URL : https://hal.archives-ouvertes.fr/inria-00424346

N. [. Baier, P. Bertrand, and . Schnoebelen, Verifying nondeterministic probabilistic channel systems against ?-regular lineartime properties, ACM Transactions on Computational Logic, vol.9, issue.1, 2007.
DOI : 10.1145/1297658.1297663

URL : https://hal.archives-ouvertes.fr/inria-00424516

. [. Bertrand, . Ph, and . Schnoebelen, Model Checking Lossy Channels Systems Is Probably Decidable, Proc. 6th Int. Conf. Foundations of Software Science and Computation Structures Zafiropulo. On communicating finite-state machines, pp.120-135323, 1983.
DOI : 10.1007/3-540-36576-1_8

URL : https://hal.archives-ouvertes.fr/inria-00424339

A. [. Cécé, S. Finkel, and . Iyer, Unreliable Channels Are Easier to Verify Than Perfect Channels, Information and Computation, vol.124, issue.1, pp.20-31, 1996.
DOI : 10.1006/inco.1996.0003

]. P. Clo86 and . Clote, On the finite containment problem for Petri nets, Theoretical Computer Science, vol.43, issue.1, pp.99-105, 1986.

. [. Chambart, . Ph, and . Schnoebelen, Toward a Compositional Theory of Leftist Grammars and Transformations, Proc. FOSSACS 2010, pp.237-251, 2010.
DOI : 10.1007/978-3-642-12032-9_17

E. [. Cichon and . Bittar, Ordinal recursive bounds for Higman's theorem, Theoretical Computer Science, vol.201, issue.1-2, pp.63-84, 1998.
DOI : 10.1016/S0304-3975(97)00009-1

]. D. De-jongh and R. Parikh, Well-partial orderings and hierarchies, Indagationes Mathematicae (Proceedings), vol.80, issue.3, pp.195-207, 1977.
DOI : 10.1016/1385-7258(77)90067-1

Z. [. Dershowitz and . Manna, Proving termination with multiset orderings, Communications of the ACM, vol.22, issue.8, pp.465-476, 1979.
DOI : 10.1145/359138.359142

[. Figueira, S. Figueira, S. Schmitz, and P. Schnoebelen, Ackermann and primitiverecursive bounds with Dickson's lemma, Computing Research Repository, 2010.

A. Finkel and J. Goubault-larrecq, Forward analysis for WSTS, part I: Completions, Proceedings of the 26th Annual Symposium on Theoretical Aspects of Computer Science (STACS'09), volume 3 of Leibniz International Proceedings in Informatics Leibniz- Zentrum für Informatik, pp.433-444, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00359699

A. Finkel and J. Goubault-larrecq, Forward Analysis for WSTS, Part??II: Complete WSTS, Proceedings of the 36th International Colloquium on Automata , Languages and Programming, pp.188-199, 2009.
DOI : 10.1007/978-3-642-02930-1_16

]. A. Fin85 and . Finkel, Une généralisation des théorèmes de Higman et de Simon aux mots infinis, Theoretical Computer Science, vol.38, issue.1, pp.137-142, 1985.

A. Finkel, A generalization of the procedure of karp and miller to well structured transition systems, Proceedings of the 14th International Colloquium on Automata , Languages and Programming (ICALP'87), pp.499-508, 1987.
DOI : 10.1007/3-540-18088-5_43

]. A. Fin94 and . Finkel, Decidability of the termination problem for completely specificied protocols, Distributed Computing, pp.129-135, 1994.

. [. Finkel, . Ph, and . Schnoebelen, Well-structured transition systems everywhere! Theoretical Computer Science, pp.63-92, 2001.

S. [. Fairtlough and . Wainer, Hierarchies of Provably Recursive Functions, Handbook of Proof Theory, pp.149-207, 1998.
DOI : 10.1016/S0049-237X(98)80018-9

H. [. Greenlaw, W. L. Hoover, and . Ruzzo, Limits to Parallel Computation: P-Completeness Theory, 1995.

A. [. Gabelaia, F. Kurucz, M. Wolter, and . Zakharyaschev, Nonprimitive recursive decidability of products of modal logics with expanding domains, Annals of Pure and Applied Logic, vol.142, pp.1-3245, 2006.

]. L. Hai69 and . Haines, On free monoids partially ordered by embedding

]. G. Hig52 and . Higman, Ordering by divisibility in abstract algebras, In London Math. Soc, issue.2, pp.326-336, 1952.

. G. Hmk-+-05-]-j, M. Henriksen, K. N. Mukund, M. A. Kumar, P. S. Sohoni et al., A theory of regular MSC languages, Information and Computation, vol.202, issue.1, pp.1-38, 2005.

[. Jancar, Nonprimitive recursive complexity and undecidability for Petri net equivalences, Theoretical Computer Science, vol.256, issue.1-2, pp.23-30, 2001.
DOI : 10.1016/S0304-3975(00)00100-6

]. T. Jur08 and . Jurdzi´nskijurdzi´nski, Leftist grammars are nonprimitive recursive, Proc. ICALP, pp.51-62, 2008.

]. G. Kre52 and . Kreisel, On the interpretation of the nonfinitist proofs, ii. The Journal of Symbolic Logic, pp.43-58, 1952.

J. B. Kruskal, The theory of well-quasi-ordering: A frequently discovered concept, Journal of Combinatorial Theory, Series A, vol.13, issue.3, pp.297-305, 1972.
DOI : 10.1016/0097-3165(72)90063-5

]. J. Lee78 and . Van-leeuwen, Effective constructions in well-partially-ordered free monoids, Discrete Mathematics, vol.21, issue.3, pp.237-252, 1978.

A. [. Lohrey and . Muscholl, Bounded MSC communication, Information and Computation, vol.189, issue.2, pp.160-181, 2004.
DOI : 10.1016/j.ic.2003.10.002

URL : https://hal.archives-ouvertes.fr/hal-00306245

. Lno-+-08-]-r, T. Lazi´clazi´c, J. Newcomb, A. W. Ouaknine, J. Roscoe et al., Nets with tokens which carry data, Fundamenta Informaticae, vol.88, issue.3, pp.251-274, 2008.

]. R. May03a and . Mayr, Undecidable problems in unreliable computations, Theoretical Computer Science, vol.297, issue.13, pp.337-354, 2003.

]. R. May03b and . Mayr, Undecidable problems in unreliable computations, Theoretical Computer Science, vol.297, issue.13, pp.337-354, 2003.

]. K. Mca84 and . Mcaloon, Petri nets and large finite sets, Theoretical Computer Science, vol.32, issue.12, pp.173-183, 1984.

W. Ernst, A. R. Mayr, and . Meyer, The complexity of the finite containment problem for petri nets, J. ACM, vol.28, issue.3, pp.561-576, 1981.

]. H. Mül85 and . Müller, Weak Petri net computers for Ackermann functions, Elektronische Informationsverarbeitung und Kybernetik, vol.21, issue.45, pp.236-246, 1985.

]. P. Odi92 and . Odifreddi, Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers (Studies in Logic and the Foundations of Mathematics), 1992.

J. [. Ouaknine and . Worrell, On the decidability and complexity of Metric Temporal Logic over finite words. Logical Methods in Comp, Science, vol.3, issue.1, pp.1-27, 2007.

. [. Péter, Konstruktion nichtrekursiver Funktionen, Mathematische Annalen, vol.110, issue.1, pp.42-60, 1935.
DOI : 10.1007/BF01472200

]. J. [-rob65 and . Robbin, Subrecursive hierarchies, 1965.

]. H. Ros84 and . Rose, Subrecursion: Functions and Hierarchies, volume 9 of Oxford Logic Guides, 1984.

]. H. Tou97 and . Touzet, Propriétés combinatoires pour la terminaison de systèmes des réécriture, Thèse de doctorat, 1997.

]. H. Tou02 and . Touzet, A characterisation of multiply recursive functions with higman's lemma. Information and Computation, pp.534-544, 2002.

]. S. Wai70 and . Wainer, A classification of the ordinal recursive functions, Arch. math. Logik Grundlag, vol.13, pp.3-4136, 1970.

]. S. Wai72 and . Wainer, Ordinal recursion, and a refinement of the extended grzegorczyk hierarchy, The Journal of Symbolic Logic, vol.37, issue.2, pp.281-292, 1972.