P. A. Abdulla, K. Cer¯-ans, B. Jonsson, and Y. Tsay, Algorithmic Analysis of Programs with Well Quasi-ordered Domains, Information and Computation, vol.160, issue.1-2, p.160
DOI : 10.1006/inco.1999.2843

M. Blondin, A. Finkel, and P. Mckenzie, Handling Infinitely Branching WSTS, Proc. ICALP 2014, pp.13-25, 2014.
DOI : 10.1007/978-3-662-43951-7_2

R. Bonnet, On the cardinality of the set of initial intervals of a partially ordered set, Infinite and finite sets, pp.189-198, 1975.

L. Bozzelli and P. Ganty, Complexity Analysis of the Backward Coverability Algorithm for VASS, Proc. RP 2011, pp.96-109, 2011.
DOI : 10.1007/978-3-642-24288-5_10

P. Chambart, . Ph, and . Schnoebelen, The Ordinal Recursive Complexity of Lossy Channel Systems, 2008 23rd Annual IEEE Symposium on Logic in Computer Science, pp.205-216, 2008.
DOI : 10.1109/LICS.2008.47

E. A. Cicho´ncicho´n and E. T. 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

N. Decker and D. Thoma, On Freeze LTL with Ordered Attributes, Proc. FoSSaCS 2016, pp.269-284, 2016.
DOI : 10.1007/978-3-642-15155-2_54

D. Figueira, S. Figueira, S. Schmitz, and P. Schnoebelen, Ackermannian and Primitive-Recursive Bounds with Dickson's Lemma, 2011 IEEE 26th Annual Symposium on Logic in Computer Science, pp.269-278, 2011.
DOI : 10.1109/LICS.2011.39

A. Finkel and J. Goubault-larrecq, Forward analysis for WSTS, part I: Completions, Proc. STACS 2009, pp.433-444, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00359699

A. Finkel, . Ph, and . Schnoebelen, Well-structured transition systems everywhere ! Theor, Comput. Sci, vol.256, issue.12, pp.63-92, 2001.

A. Finkel, P. Mckenzie, and C. Picaronny, A well-structured framework for analysing petri net extensions, Information and Computation, vol.195, issue.1-2, pp.1-29, 2004.
DOI : 10.1016/j.ic.2004.01.005

J. Goubault-larrecq, P. Karandikar, K. Narayan-kumar, and P. Schnoebelen, The ideal approach to computing closed subsets in well-quasi-orderings, 2016.

S. Haase, P. Schmitz, and . Schnoebelen, The power of priority channel systems, Logic. Meth. in Comput. Sci, vol.10, issue.44, pp.1-39
URL : https://hal.archives-ouvertes.fr/hal-00793809

S. Haddad, P. Schmitz, and . Schnoebelen, The Ordinal-Recursive Complexity of Timed-arc Petri Nets, Data Nets, and Other Enriched Nets, 2012 27th Annual IEEE Symposium on Logic in Computer Science, pp.355-364, 2012.
DOI : 10.1109/LICS.2012.46
URL : https://hal.archives-ouvertes.fr/hal-00793811

G. Higman, Ordering by Divisibility in Abstract Algebras, Proceedings of the London Mathematical Society, vol.3, issue.1, pp.326-336, 1952.
DOI : 10.1112/plms/s3-2.1.326

S. Lazi´clazi´c and . Schmitz, The ideal view on Rackoff's coverability technique, Proc. RP 2015, pp.1-13, 2015.

T. Lazi´clazi´c, J. Newcomb, A. Ouaknine, J. Roscoe, and . Worrell, Nets with tokens which carry data, Fund. Inform, vol.88, issue.3, pp.251-274, 2008.

J. Lazi´clazi´c, J. Ouaknine, and . Worrell, Zeno, Hercules, and the Hydra: Safety metric temporal logic is Ackermann-complete, ACM Trans. Comput. Logic, issue.3, pp.17-2016

R. Lipton, The reachability problem requires exponential space, 1976.

. Meyer, On Boundedness in Depth in the ??-Calculus, Proc. IFIP TCS, pp.477-489, 2008.
DOI : 10.1007/978-0-387-09680-3_32

M. Montali and A. Rivkin, Model checking Petri nets with names using data-centric dynamic systems, Formal Aspects of Computing, vol.71, issue.2-3, 2016.
DOI : 10.1007/s00165-016-0370-6

. Rackoff, The covering and boundedness problems for vector addition systems, Theoretical Computer Science, vol.6, issue.2, pp.223-231, 1978.
DOI : 10.1016/0304-3975(78)90036-1

F. Rosa-velardo, Ordinal recursive complexity of Unordered Data Nets, Information and Computation, 2014.
DOI : 10.1016/j.ic.2017.02.002

D. Rosa-velardo and . De-frutos-escrig, Name Creation vs. Replication in Petri Net Systems, Fund. Inform, vol.88, issue.3, pp.329-356, 2008.
DOI : 10.1007/978-3-540-73094-1_24

D. Rosa-velardo and . De-frutos-escrig, Decidability and complexity of Petri nets with unordered data, Theoretical Computer Science, vol.412, issue.34, pp.4439-4451, 2011.
DOI : 10.1016/j.tcs.2011.05.007

M. Rosa-velardo and . Martos-salgado, Multiset rewriting for the verification of depth-bounded processes with name binding, Information and Computation, vol.215, pp.68-87, 2012.
DOI : 10.1016/j.ic.2012.03.004

. Schmitz, Complexity Hierarchies beyond Elementary, ACM Transactions on Computation Theory, vol.8, issue.1, pp.1-36, 2016.
DOI : 10.1145/2858784
URL : https://hal.archives-ouvertes.fr/hal-01267354

S. Schmitz, . Ph, and . Schnoebelen, Multiply-Recursive Upper Bounds with Higman???s Lemma, Proc. ICALP 2011, pp.441-452, 2011.
DOI : 10.1006/jsco.1994.1059

S. Schmitz, . Ph, and . Schnoebelen, Algorithmic aspects of WQO theory. Lecture notes, 2012. URL http://cel.archives-ouvertes
URL : https://hal.archives-ouvertes.fr/cel-00727025

S. Schmitz, . Ph, and . Schnoebelen, The Power of Well-Structured Systems, Proc. Concur 2013, pp.5-24, 2013.
DOI : 10.1007/978-3-642-40184-8_2
URL : https://hal.archives-ouvertes.fr/hal-00907964

. Ph and . Schnoebelen, Revisiting Ackermann-hardness for lossy counter machines and reset Petri nets, Proc. MFCS 2010, pp.616-628, 2010.

S. S. Wainer, A classification of the ordinal recursive functions, Archiv f??r Mathematische Logik und Grundlagenforschung, vol.24, issue.No. 3, pp.136-153, 1970.
DOI : 10.1007/BF01973619