P. B. Andrews and E. L. Cohen, Theorem proving in type theory, International Joint Conference on Artificial Intelligence (IJCAI-77), p.566, 1977.

T. Aoto and T. Yamada, Termination of Simply Typed Term Rewriting by Translation and Labelling, Rewriting Techniques and Applications, pp.380-394, 2003.
DOI : 10.1007/3-540-44881-0_27

F. Baader and T. Nipkow, Term Rewriting and All That, 1998.

J. Backes and C. E. Brown, Analytic Tableaux for Higher-Order Logic with Choice, Journal of Automated Reasoning, vol.44, issue.2, pp.451-479, 2011.
DOI : 10.3792/pja/1195521329

J. Banâtre, P. Fradet, and Y. Radenac, Generalised multisets for chemical programming, Mathematical Structures in Computer Science, vol.16, issue.04, pp.557-580, 2006.
DOI : 10.1017/S0960129506005317

H. Becker, J. C. Blanchette, U. Waldmann, and D. Wand, Formalization of Knuth?Bendix orders for lambda-free higher-order terms. Archive of Formal Proofs, 2016.

H. Becker, J. C. Blanchette, U. Waldmann, and D. Wand, A Transfinite Knuth???Bendix Order for Lambda-Free Higher-Order Terms, 2017.
DOI : 10.1016/j.jsc.2014.09.033
URL : https://hal.archives-ouvertes.fr/hal-01592186

M. Beeson, Lambda Logic, International Joint Conference on Automated Reasoning, pp.460-474, 2004.
DOI : 10.1007/978-3-540-25984-8_34

C. Benzmüller and M. Kohlhase, Extensional higher-order resolution, Conference on Automated Deduction (CADE-15), volume 1421 of LNCS, pp.56-71, 1998.
DOI : 10.1007/BFb0054248

C. Benzmüller and D. Miller, Automation of Higher-Order Logic, Computational Logic of Handbook of the History of Logic, pp.215-254, 2014.
DOI : 10.1016/B978-0-444-51624-4.50005-8

J. C. Blanchette, M. Fleury, and D. Traytel, Formalization of nested multisets, hereditary multisets, and syntactic ordinals. Archive of Formal Proofs, 2016.

J. C. Blanchette, J. Hölzl, A. Lochbihler, L. Panny, A. Popescu et al., Truly Modular (Co)datatypes for Isabelle/HOL, Interactive Theorem Proving, 2014.
DOI : 10.1007/978-3-319-08970-6_7

J. C. Blanchette, C. Kaliszyk, L. C. Paulson, and J. Urban, Hammering towards QED, J. Formalized Reasoning, vol.9, issue.1, pp.101-148, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01386988

J. C. Blanchette and T. Nipkow, Nitpick: A Counterexample Generator for Higher-Order Logic Based on a Relational Model Finder, Interactive Theorem Proving, pp.131-146, 2010.
DOI : 10.1007/978-3-642-14052-5_11

J. C. Blanchette, U. Waldmann, and D. Wand, Formalization of recursive path orders for lambda-free higher-order terms. Archive of Formal Proofs, 2016.

J. C. Blanchette, U. Waldmann, and D. Wand, A Lambda-Free Higher-Order Recursive??Path??Order, Foundations of Software Science and Computation Structures volume 10203 of LNCS, pp.461-479, 2017.
DOI : 10.1007/3-540-45127-7_25

F. Blanqui, J. Jouannaud, and A. Rubio, The computability path ordering, Logical Methods in Computer Science, vol.11, issue.4, p.2015
DOI : 10.2168/LMCS-11(4:3)2015
URL : https://hal.archives-ouvertes.fr/hal-01163091

M. Bofill, C. Borralleras, E. Rodríguez-carbonell, and A. Rubio, The recursive path and polynomial ordering for first-order and higher-order terms, Journal of Logic and Computation, vol.23, issue.1, pp.263-305, 2013.
DOI : 10.1093/logcom/exs027

M. Bofill and A. Rubio, Paramodulation with Non-Monotonic Orderings and Simplification, Journal of Automated Reasoning, vol.19, issue.4, pp.51-98, 2013.
DOI : 10.1007/978-3-642-76771-5

N. Dershowitz and Z. Manna, Proving termination with multiset orderings, Communications of the ACM, vol.22, issue.8, pp.465-476, 1979.
DOI : 10.1145/359138.359142
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.145.8728

M. C. Ferreira and H. Zantema, Well-foundedness of term orderings, Conditional and Typed Rewriting Systems (CTRS-94), pp.106-123, 1994.
DOI : 10.1007/3-540-60381-6_7
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.612

J. Giesl, R. Thiemann, and P. Schneider-kamp, Proving and Disproving Termination of Higher-Order Functions, Frontiers of Combining Systems, pp.216-231, 2005.
DOI : 10.1007/11559306_12
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.59.1912

L. Henkin, Completeness in the theory of types, The Journal of Symbolic Logic, vol.14, issue.02, pp.81-91, 1950.
DOI : 10.1007/BF01696781

N. Hirokawa, A. Middeldorp, and H. Zankl, Uncurrying for Termination and Complexity, Journal of Automated Reasoning, vol.50, issue.5, pp.279-315, 2013.
DOI : 10.1007/s00200-007-0046-9
URL : https://link.springer.com/content/pdf/10.1007%2Fs10817-012-9248-3.pdf

G. Huet and D. C. Oppen, Equations and Rewrite Rules: A Survey, Formal Language Theory: Perspectives and Open Problems, pp.349-405, 1980.
DOI : 10.1016/B978-0-12-115350-2.50017-8
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.397.599

G. P. Huet, A mechanization of type theory, International Joint Conference on Artificial Intelligence (IJCAI-73), pp.139-146, 1973.

R. J. Hughes, Super-combinators a new implementation method for applicative languages, Proceedings of the 1982 ACM symposium on LISP and functional programming , LFP '82, pp.1-10, 1982.
DOI : 10.1145/800068.802129
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.472.4622

J. Jouannaud and A. Rubio, Polymorphic higher-order recursive path orderings, Journal of the ACM, vol.54, issue.1, pp.1-2, 2007.
DOI : 10.1145/1206035.1206037
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.78.1121

R. Kennaway, J. W. Klop, M. R. Sleep, and F. De-vries, Comparing Curried and Uncurried Rewriting, Journal of Symbolic Computation, vol.21, issue.1, pp.15-39, 1996.
DOI : 10.1006/jsco.1996.0002

D. E. Knuth and P. B. Bendix, Simple Word Problems in Universal Algebras, Computational Problems in Abstract Algebra, pp.263-297, 1970.
DOI : 10.1007/978-3-642-81955-1_23

C. Kop, Higher Order Termination, 2012.

C. Kop and F. Van-raamsdonk, A Higher-Order Iterative Path Ordering, Logic for Programming, pp.697-711, 2008.
DOI : 10.1007/978-3-540-89439-1_48
URL : http://dare.ubvu.vu.nl/bitstream/1871/34190/1/219615.pdf

L. Kovács, G. Moser, and A. Voronkov, On Transfinite Knuth-Bendix Orders, Conference on Automated Deduction (CADE-23), pp.384-399, 2011.
DOI : 10.1007/s10817-009-9131-z

L. Kovács and A. Voronkov, First-Order Theorem Proving and Vampire, Computer Aided Verification, pp.1-35, 2013.
DOI : 10.1007/978-3-642-39799-8_1

M. Lifantsev and L. Bachmair, An LPO-based termination ordering for higher-order terms without ??-abstraction, Theorem Proving in Higher Order Logics (TPHOLs '98), volume 1479 of LNCS, pp.277-293, 1998.
DOI : 10.1007/BFb0055142

B. Löchner, Things to Know when Implementing KBO, Journal of Automated Reasoning, vol.2, issue.2, pp.289-310, 2006.
DOI : 10.1007/s10817-006-9031-4

M. Ludwig and U. Waldmann, An Extension of the Knuth-Bendix Ordering with LPO-Like Properties, Logic for Programming, pp.348-362, 2007.
DOI : 10.1007/978-3-540-75560-9_26

W. Mccune, Otter 3.3 reference manual, 2003.
DOI : 10.2172/822573

R. Nieuwenhuis and A. Rubio, Paramodulation-Based Theorem Proving, Handbook of Automated Reasoning, pp.371-443, 2001.
DOI : 10.1016/B978-044450813-3/50009-6
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.6344

T. Nipkow, L. C. Paulson, and M. Wenzel, Isabelle/HOL: A Proof Assistant for Higher- Order Logic, LNCS, vol.2283, 2002.
DOI : 10.1007/3-540-45949-9

S. Schulz, System Description: E??1.8, Logic for Programming, Artificial Intelligence, and Reasoning (LPAR-19), pp.735-743, 2013.
DOI : 10.1007/978-3-642-45221-5_49

C. Sternagel and R. Thiemann, Executable multivariate polynomials Archive of Formal Proofs, 2010.

C. Sternagel and R. Thiemann, Generalized and Formalized Uncurrying, Frontiers of Combining Systems, pp.243-258, 2011.
DOI : 10.1007/978-3-642-03359-9_31
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.231.9059

C. Sternagel and R. Thiemann, Formalizing Knuth-Bendix orders and Knuth-Bendix completion, Rewriting Techniques and Applications, pp.287-302, 2013.

N. Sultana, J. C. Blanchette, and L. C. Paulson, LEO-II and Satallax on the Sledgehammer test bench, Journal of Applied Logic, vol.11, issue.1, pp.91-102, 2013.
DOI : 10.1016/j.jal.2012.12.002
URL : http://doi.org/10.1016/j.jal.2012.12.002

Y. Toyama, Termination of S-Expression Rewriting Systems: Lexicographic Path Ordering for Higher-Order Terms, Rewriting Techniques and Applications, pp.40-54, 2004.
DOI : 10.1007/978-3-540-25979-4_3

D. A. Turner, A new implementation technique for applicative languages. Software: Practice and Experience, pp.31-49, 1979.
DOI : 10.1002/spe.4380090105

C. Weidenbach, D. Dimova, A. Fietzke, R. Kumar, M. Suda et al., SPASS Version 3.5, Conference on Automated Deduction (CADE-22), pp.140-145, 2009.
DOI : 10.1007/978-3-540-73595-3_38

M. Wisniewski, A. Steen, K. Kern, and C. Benzmüller, Effective Normalization Techniques for HOL, International Joint Conference on Automated Reasoning, pp.362-370, 2016.
DOI : 10.1007/3-540-61511-3_75

H. Zankl, S. Winkler, and A. Middeldorp, Beyond polynomials and Peano arithmetic???automation of elementary and ordinal interpretations, Journal of Symbolic Computation, vol.69, pp.129-158, 2015.
DOI : 10.1016/j.jsc.2014.09.033