{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T03:53:58Z","timestamp":1781927638903,"version":"3.54.5"},"publisher-location":"Berlin, Heidelberg","reference-count":24,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540252368","type":"print"},{"value":"9783540322757","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2005]]},"DOI":"10.1007\/978-3-540-32275-7_21","type":"book-chapter","created":{"date-parts":[[2010,12,20]],"date-time":"2010-12-20T21:14:41Z","timestamp":1292879681000},"page":"301-331","source":"Crossref","is-referenced-by-count":85,"title":["The Dependency Pair Framework: Combining Techniques for Automated Termination Proofs"],"prefix":"10.1007","author":[{"given":"J\u00fcrgen","family":"Giesl","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ren\u00e9","family":"Thiemann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Schneider-Kamp","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"21_CR1","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/S0304-3975(99)00207-8","volume":"236","author":"T. Arts","year":"2000","unstructured":"Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical Computer Science\u00a0236, 133\u2013178 (2000)","journal-title":"Theoretical Computer Science"},{"key":"21_CR2","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139172752","volume-title":"Term Rewriting and All That","author":"F. Baader","year":"1998","unstructured":"Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)"},{"key":"21_CR3","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/S0747-7171(87)80022-6","volume":"3","author":"N. Dershowitz","year":"1987","unstructured":"Dershowitz, N.: Termination of rewriting. J. Symb. Computation\u00a03, 69\u2013116 (1987)","journal-title":"J. Symb. Computation"},{"key":"21_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-540-27775-0_1","volume-title":"Logic Programming","author":"N. Dershowitz","year":"2004","unstructured":"Dershowitz, N.: Termination by abstraction. In: Demoen, B., Lifschitz, V. (eds.) ICLP 2004. LNCS, vol.\u00a03132, pp. 1\u201318. Springer, Heidelberg (2004)"},{"key":"21_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1007\/978-3-540-45138-9_39","volume-title":"Mathematical Foundations of Computer Science 2003","author":"A. Geser","year":"2003","unstructured":"Geser, A., Hofbauer, D., Waldmann, J.: Match-bounded string rewriting systems. In: Rovan, B., Vojt\u00e1\u0161, P. (eds.) MFCS 2003. LNCS, vol.\u00a02747, pp. 449\u2013459. Springer, Heidelberg (2003)"},{"issue":"1,2","key":"21_CR6","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/s002000100063","volume":"12","author":"J. Giesl","year":"2001","unstructured":"Giesl, J., Arts, T.: Verification of Erlang processes by dependency pairs. Appl. Algebra in Engineering, Communication and Computing\u00a012(1,2), 39\u201372 (2001)","journal-title":"Appl. Algebra in Engineering, Communication and Computing"},{"issue":"1","key":"21_CR7","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1006\/jsco.2002.0541","volume":"34","author":"J. Giesl","year":"2002","unstructured":"Giesl, J., Arts, T., Ohlebusch, E.: Modular termination proofs for rewriting using dependency pairs. Journal of Symbolic Computation\u00a034(1), 21\u201358 (2002)","journal-title":"Journal of Symbolic Computation"},{"key":"21_CR8","series-title":"Lecture Notes in Computer Science","first-page":"165","volume-title":"Logic for Programming, Artificial Intelligence, and Reasoning","author":"J. Giesl","year":"2003","unstructured":"Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Improving dependency pairs. In: Y. Vardi, M., Voronkov, A. (eds.) LPAR 2003. LNCS, vol.\u00a02850, pp. 165\u2013179. Springer, Heidelberg (2003)"},{"key":"21_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1007\/978-3-540-25979-4_15","volume-title":"Rewriting Techniques and Applications","author":"J. Giesl","year":"2004","unstructured":"Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Automated termination proofs with AProVE. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol.\u00a03091, pp. 210\u2013220. Springer, Heidelberg (2004)"},{"key":"21_CR10","doi-asserted-by":"crossref","first-page":"3","DOI":"10.3233\/FI-1995-24121","volume":"24","author":"B. Gramlich","year":"1995","unstructured":"Gramlich, B.: Abstract relations between restricted termination and confluence properties of rewrite systems. Fundamenta Informaticae\u00a024, 3\u201323 (1995)","journal-title":"Fundamenta Informaticae"},{"key":"21_CR11","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1007\/978-3-540-45085-6_4","volume-title":"Automated Deduction \u2013 CADE-19","author":"N. Hirokawa","year":"2003","unstructured":"Hirokawa, N., Middeldorp, A.: Automating the dependency pair method. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol.\u00a02741, pp. 32\u201346. Springer, Heidelberg (2003); Full version to appear in Information and Computation"},{"key":"21_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/978-3-540-25979-4_18","volume-title":"Rewriting Techniques and Applications","author":"N. Hirokawa","year":"2004","unstructured":"Hirokawa, N., Middeldorp, A.: Dependency pairs revisited. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol.\u00a03091, pp. 249\u2013268. Springer, Heidelberg (2004)"},{"key":"21_CR13","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/978-3-540-30210-0_16","volume-title":"Artificial Intelligence and Symbolic Computation","author":"N. Hirokawa","year":"2004","unstructured":"Hirokawa, N., Middeldorp, A.: Polynomial interpretations with negative coefficients. In: Buchberger, B., Campbell, J. (eds.) AISC 2004. LNCS (LNAI), vol.\u00a03249, pp. 185\u2013198. Springer, Heidelberg (2004)"},{"key":"21_CR14","unstructured":"Kamin, S., L\u00e9vy, J.J.: Two generalizations of the recursive path ordering. Unpublished Manuscript, University of Illinois, IL, USA (1980)"},{"key":"21_CR15","doi-asserted-by":"crossref","unstructured":"Knuth, D., Bendix, P.: Simple word problems in universal algebras. In: Leech, J. (ed.) Computational Problems in Abstract Algebra, pp. 263\u2013297 (1970)","DOI":"10.1016\/B978-0-08-012975-4.50028-X"},{"key":"21_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1007\/10704567_3","volume-title":"Principles and Practice of Declarative Programming","author":"K. Kusakari","year":"1999","unstructured":"Kusakari, K., Nakamura, M., Toyama, Y.: Argument filtering transformation. In: Nadathur, G. (ed.) PPDP 1999. LNCS, vol.\u00a01702, pp. 48\u201362. Springer, Heidelberg (1999)"},{"key":"21_CR17","unstructured":"Lankford, D.: On proving term rewriting systems are Noetherian. Technical Report MTP-3, Louisiana Technical University, Ruston, LA, USA (1979)"},{"key":"21_CR18","unstructured":"Middeldorp, A.: A simple proof to a result of Bernhard Gramlich. Presented at the 5th Japanese Term Rewriting Meeting, Tsukuba (1994), Available from http:\/\/informatik.uibk.ac.at\/users\/ami\/research\/papers\/bg.pdf"},{"key":"21_CR19","doi-asserted-by":"crossref","first-page":"47","DOI":"10.3233\/FI-1995-24123","volume":"24","author":"J. Steinbach","year":"1995","unstructured":"Steinbach, J.: Simplification orderings: History of results. Fundamenta Informaticae\u00a024, 47\u201387 (1995)","journal-title":"Fundamenta Informaticae"},{"key":"21_CR20","unstructured":"Termination Problem Data Base (TPDB), Available from http:\/\/www.lri.fr\/~marche\/wst2004-competition\/tpdb.html"},{"key":"21_CR21","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/978-3-540-25984-8_4","volume-title":"Automated Reasoning","author":"R. Thiemann","year":"2004","unstructured":"Thiemann, R., Giesl, J., Schneider-Kamp, P.: Improved modular termination proofs using dependency pairs. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol.\u00a03097, pp. 75\u201390. Springer, Heidelberg (2004)"},{"key":"21_CR22","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/0020-0190(87)90122-0","volume":"25","author":"Y. Toyama","year":"1987","unstructured":"Toyama, Y.: Counterexamples to the termination for the direct sum of term rewriting systems. Information Processing Letters\u00a025, 141\u2013143 (1987)","journal-title":"Information Processing Letters"},{"issue":"4","key":"21_CR23","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/BF03177743","volume":"32","author":"X. Urbain","year":"2004","unstructured":"Urbain, X.: Modular and incremental automated termination proofs. Journal of Automated Reasoning\u00a032(4), 315\u2013355 (2004)","journal-title":"Journal of Automated Reasoning"},{"key":"21_CR24","doi-asserted-by":"crossref","first-page":"89","DOI":"10.3233\/FI-1995-24124","volume":"24","author":"H. Zantema","year":"1995","unstructured":"Zantema, H.: Termination of term rewriting by semantic labelling. Fundamenta Informaticae\u00a024, 89\u2013105 (1995)","journal-title":"Fundamenta Informaticae"}],"container-title":["Lecture Notes in Computer Science","Logic for Programming, Artificial Intelligence, and Reasoning"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-32275-7_21.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,3]],"date-time":"2021-05-03T03:46:55Z","timestamp":1620013615000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-32275-7_21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005]]},"ISBN":["9783540252368","9783540322757"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-32275-7_21","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005]]}}}