{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T03:53:59Z","timestamp":1781927639273,"version":"3.54.5"},"publisher-location":"Berlin, Heidelberg","reference-count":30,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540223450","type":"print"},{"value":"9783540259848","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2004]]},"DOI":"10.1007\/978-3-540-25984-8_4","type":"book-chapter","created":{"date-parts":[[2010,9,11]],"date-time":"2010-09-11T02:31:38Z","timestamp":1284172298000},"page":"75-90","source":"Crossref","is-referenced-by-count":24,"title":["Improved Modular Termination Proofs Using Dependency Pairs"],"prefix":"10.1007","author":[{"given":"Ren\u00e9","family":"Thiemann","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00fcrgen","family":"Giesl","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":"4_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1007\/10721975_18","volume-title":"Rewriting Techniques and Applications","author":"T. Arts","year":"2000","unstructured":"Arts, T.: System description: The dependency pair method. In: Bachmair, L. (ed.) RTA 2000. LNCS, vol.\u00a01833, pp. 261\u2013264. Springer, Heidelberg (2000)"},{"key":"4_CR2","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":"4_CR3","unstructured":"Arts, T., Giesl, J.: A collection of examples for termination of term rewriting using dependency pairs. Technical Report AIB-2001-0912, RWTH Aachen (2001)"},{"key":"4_CR4","doi-asserted-by":"crossref","unstructured":"Baader, F., Nipkow, T.: Term Rewriting and All That, Cambridge (1998)","DOI":"10.1017\/CBO9781139172752"},{"key":"4_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/10721959_27","volume-title":"Automated Deduction - CADE-17","author":"C. Borralleras","year":"2000","unstructured":"Borralleras, C., Ferreira, M., Rubio, A.: Complete monotonic semantic path orderings. In: McAllester, D. (ed.) CADE 2000. LNCS, vol.\u00a01831, Springer, Heidelberg (2000)"},{"key":"4_CR6","unstructured":"Contejean, E., March\u00e9, C., Monate, B., Urbain, X.: CiME, http:\/\/cime.lri.fr"},{"key":"4_CR7","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. Comp.\u00a03, 69\u2013116 (1987)","journal-title":"J. Symb. Comp."},{"key":"4_CR8","doi-asserted-by":"crossref","unstructured":"Dershowitz, N.: 33 examples of termination. In: Proc. French Spring School of Theoretical Computer Science, Font Romeux. LNCS, vol.\u00a0909, pp. 16\u201326 (1995)","DOI":"10.1007\/3-540-59340-3_2"},{"key":"4_CR9","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1145\/571157.571164","volume-title":"Proc. 4th PPDP","author":"O. Fissore","year":"2002","unstructured":"Fissore, O., Gnaedig, I., Kirchner, H.: Cariboo: An induction based proof tool for termination with strategies. In: Kirchner, C. (ed.) Proc. 4th PPDP, Pittsburgh, PA, USA, pp. 62\u201373. ACM Press, New York (2002)"},{"issue":"1,2","key":"4_CR10","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":"4_CR11","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":"4_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1007\/978-3-540-39813-4_11","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":"4_CR13","doi-asserted-by":"crossref","unstructured":"Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Mechanizing dependency pairs. Technical Report AIB-2003-0812, RWTH Aachen, Germany (2003)","DOI":"10.1007\/978-3-540-39813-4_11"},{"key":"4_CR14","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":"4_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/3-540-44881-0_23","volume-title":"Rewriting Techniques and Applications","author":"J. Giesl","year":"2003","unstructured":"Giesl, J., Zantema, H.: Liveness in rewriting. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol.\u00a02706, pp. 321\u2013336. Springer, Heidelberg (2003)"},{"key":"4_CR16","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1007\/BF01190827","volume":"5","author":"B. Gramlich","year":"1994","unstructured":"Gramlich, B.: Generalized sufficient conditions for modular termination of rewriting. Appl. Algebra in Engineering, Communication & Computing\u00a05, 131\u2013158 (1994)","journal-title":"Appl. Algebra in Engineering, Communication & Computing"},{"key":"4_CR17","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":"4_CR18","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)"},{"key":"4_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/3-540-44881-0_22","volume-title":"Rewriting Techniques and Applications","author":"N. Hirokawa","year":"2003","unstructured":"Hirokawa, N., Middeldorp, A.: Tsukuba termination tool. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol.\u00a02706, pp. 311\u2013320. Springer, Heidelberg (2003)"},{"key":"4_CR20","volume-title":"Two generalizations of the recursive path ordering","author":"S. Kamin","year":"1980","unstructured":"Kamin, S., L\u00e9vy, J.J.: Two generalizations of the recursive path ordering. University of Illinois, IL (1980) (unpublished Manuscript)"},{"key":"4_CR21","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":"4_CR22","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":"4_CR23","unstructured":"Lankford, D.: On proving term rewriting systems are Noetherian. Technical Report MTP-3, Louisiana Technical University, Ruston, LA, USA (1979)"},{"key":"4_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3661-8","volume-title":"Advanced Topics in Term Rewriting","author":"E. Ohlebusch","year":"2002","unstructured":"Ohlebusch, E.: Advanced Topics in Term Rewriting. Springer, Heidelberg (2002)"},{"key":"4_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/3-540-59200-8_44","volume-title":"Rewriting Techniques and Applications","author":"J. Steinbach","year":"1995","unstructured":"Steinbach, J.: Automatic termination proofs with transformation orderings. In: Hsiang, J. (ed.) RTA 1995. LNCS, vol.\u00a0914, pp. 11\u201325. Springer, Heidelberg (1995); Full version in Technical Report SR-92-23, Universit\u00e4t Kaiserslautern"},{"key":"4_CR26","first-page":"47","volume":"24","author":"J. Steinbach","year":"1995","unstructured":"Steinbach, J.: Simplification orderings: History of results. Fund. I.\u00a024, 47\u201387 (1995)","journal-title":"Fund. I."},{"key":"4_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1007\/3-540-44881-0_19","volume-title":"Rewriting Techniques and Applications","author":"R. Thiemann","year":"2003","unstructured":"Thiemann, R., Giesl, J.: Size-change termination for term rewriting. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol.\u00a02706, pp. 264\u2013278. Springer, Heidelberg (2003)"},{"key":"4_CR28","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"},{"key":"4_CR29","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1007\/3-540-45744-5_42","volume-title":"Automated Reasoning","author":"X. Urbain","year":"2001","unstructured":"Urbain, X.: Automated incremental termination proofs for hierarchically defined term rewriting systems. In: Gor\u00e9, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol.\u00a02083, pp. 485\u2013498. Springer, Heidelberg (2001)"},{"key":"4_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/978-3-540-25979-4_7","volume-title":"Rewriting Techniques and Applications","author":"H. Zantema","year":"2004","unstructured":"Zantema, H.: TORPA: Termination of rewriting proved automatically. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol.\u00a03091, pp. 95\u2013104. Springer, Heidelberg (2004); Full version in TU\/e CS-Report 03-14, TU Eindhoven"}],"container-title":["Lecture Notes in Computer Science","Automated Reasoning"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-25984-8_4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,3]],"date-time":"2023-06-03T07:31:07Z","timestamp":1685777467000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-25984-8_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004]]},"ISBN":["9783540223450","9783540259848"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-25984-8_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004]]}}}