{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T07:31:57Z","timestamp":1768289517023,"version":"3.49.0"},"publisher-location":"Berlin, Heidelberg","reference-count":39,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642397981","type":"print"},{"value":"9783642397998","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-39799-8_28","type":"book-chapter","created":{"date-parts":[[2013,7,10]],"date-time":"2013-07-10T23:13:06Z","timestamp":1373497986000},"page":"413-429","source":"Crossref","is-referenced-by-count":53,"title":["Better Termination Proving through Cooperation"],"prefix":"10.1007","author":[{"given":"Marc","family":"Brockschmidt","sequence":"first","affiliation":[]},{"given":"Byron","family":"Cook","sequence":"additional","affiliation":[]},{"given":"Carsten","family":"Fuhs","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"28_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/978-3-642-27940-9_4","volume-title":"Verification, Model Checking, and Abstract Interpretation","author":"A. Albarghouthi","year":"2012","unstructured":"Albarghouthi, A., Gurfinkel, A., Chechik, M.: whale: An interpolation-based algorithm for inter-procedural verification. In: Kuncak, V., Rybalchenko, A. (eds.) VMCAI 2012. LNCS, vol.\u00a07148, pp. 39\u201355. Springer, Heidelberg (2012)"},{"key":"28_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/978-3-642-15769-1_8","volume-title":"Static Analysis","author":"C. Alias","year":"2010","unstructured":"Alias, C., Darte, A., Feautrier, P., Gonnord, L.: Multi-dimensional rankings, program termination, and complexity bounds of flowchart programs. In: Cousot, R., Martel, M. (eds.) SAS 2010. LNCS, vol.\u00a06337, pp. 117\u2013133. Springer, Heidelberg (2010)"},{"key":"28_CR3","doi-asserted-by":"crossref","unstructured":"Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical Computer Science\u00a0236(1-2) (2000)","DOI":"10.1016\/S0304-3975(99)00207-8"},{"key":"28_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1007\/3-540-44585-4_25","volume-title":"Computer Aided Verification","author":"T. Ball","year":"2001","unstructured":"Ball, T., Rajamani, S.K.: The SLAM toolkit. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol.\u00a02102, pp. 260\u2013264. Springer, Heidelberg (2001)"},{"key":"28_CR5","doi-asserted-by":"crossref","unstructured":"Berdine, J., Chawdhary, A., Cook, B., Distefano, D., O\u2019Hearn, P.: Variance analyses from invariance analyses. In: Proc. POPL 2007 (2007)","DOI":"10.1145\/1190216.1190249"},{"key":"28_CR6","doi-asserted-by":"crossref","unstructured":"Biere, A., Artho, C., Schuppan, V.: Liveness checking as safety checking. In: Proc. FMICS 2002 (2002)","DOI":"10.1016\/S1571-0661(04)80410-9"},{"key":"28_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1007\/11513988_48","volume-title":"Computer Aided Verification","author":"A.R. Bradley","year":"2005","unstructured":"Bradley, A.R., Manna, Z., Sipma, H.B.: Linear ranking with reachability. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol.\u00a03576, pp. 491\u2013504. Springer, Heidelberg (2005)"},{"key":"28_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1349","DOI":"10.1007\/11523468_109","volume-title":"Automata, Languages and Programming","author":"A.R. Bradley","year":"2005","unstructured":"Bradley, A.R., Manna, Z., Sipma, H.B.: The polyranking principle. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol.\u00a03580, pp. 1349\u20131361. Springer, Heidelberg (2005)"},{"key":"28_CR9","doi-asserted-by":"crossref","unstructured":"Brockschmidt, M., Cook, B., Fuhs, C.: Better termination proving through cooperation. Technical Report AIB 2013-06, RWTH Aachen University, http:\/\/aib.informatik.rwth-aachen.de","DOI":"10.1007\/978-3-642-39799-8_28"},{"key":"28_CR10","doi-asserted-by":"crossref","unstructured":"Bruynooghe, M., Codish, M., Gallagher, J.P., Genaim, S., Vanhoof, W.: Termination analysis of logic programs through combination of type-based norms. ACM Trans. Program. Lang. Syst.\u00a029(2) (2007)","DOI":"10.1145\/1216374.1216378"},{"key":"28_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"570","DOI":"10.1007\/978-3-540-31980-1_40","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"E. Clarke","year":"2005","unstructured":"Clarke, E., Kroning, D., Sharygina, N., Yorav, K.: SATABS: SAT-Based Predicate Abstraction for ANSI-C. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol.\u00a03440, pp. 570\u2013574. Springer, Heidelberg (2005)"},{"key":"28_CR12","doi-asserted-by":"crossref","unstructured":"Codish, M., Gonopolskiy, I., Ben-Amram, A.M., Fuhs, C., Giesl, J.: SAT-based termination analysis using monotonicity constraints over the integers. Theory and Practice of Logic Programming\u00a011(4-5) (2011)","DOI":"10.1017\/S1471068411000147"},{"key":"28_CR13","doi-asserted-by":"crossref","unstructured":"Cook, B., Koskinen, E.: Making prophecies with decision predicates. In: Proc. POPL 2011 (2011)","DOI":"10.1145\/1926385.1926431"},{"key":"28_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/978-3-642-22110-1_26","volume-title":"Computer Aided Verification","author":"B. Cook","year":"2011","unstructured":"Cook, B., Koskinen, E., Vardi, M.: Temporal property verification as a program analysis task. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol.\u00a06806, pp. 333\u2013348. Springer, Heidelberg (2011)"},{"key":"28_CR15","doi-asserted-by":"crossref","unstructured":"Cook, B., Podelski, A., Rybalchenko, A.: Termination proofs for systems code. In: Proc. PLDI 2006 (2006)","DOI":"10.1145\/1133981.1134029"},{"key":"28_CR16","doi-asserted-by":"crossref","unstructured":"Cook, B., See, A., Zuleger, F.: Ramsey vs. lexicographic termination proving. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol.\u00a07795, pp. 47\u201361. Springer, Heidelberg (2013)","DOI":"10.1007\/978-3-642-36742-7_4"},{"key":"28_CR17","doi-asserted-by":"crossref","unstructured":"Dershowitz, N.: Termination of rewriting. J. Symb. Comput. 3(1-2) (1987)","DOI":"10.1016\/S0747-7171(87)80022-6"},{"key":"28_CR18","unstructured":"Falke, S., Kapur, D., Sinz, C.: Termination analysis of C programs using compiler intermediate languages. In: Proc. RTA 2011 (2011)"},{"key":"28_CR19","doi-asserted-by":"crossref","unstructured":"Floyd, R.W.: Assigning meaning to programs. In: Proc. of Symposia in Applied Mathematics. Mathematical Aspects of Computer Science. American Mathematical Society (1967)","DOI":"10.1090\/psapm\/019\/0235771"},{"key":"28_CR20","unstructured":"Geser, A.: Relative Termination. PhD thesis, Universit\u00e4t Passau, Germany (1990)"},{"key":"28_CR21","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/11814771_24","volume-title":"Automated Reasoning","author":"J. Giesl","year":"2006","unstructured":"Giesl, J., Schneider-Kamp, P., Thiemann, R.: aProVE 1.2: automatic termination proofs in the dependency pair framework. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol.\u00a04130, pp. 281\u2013286. Springer, Heidelberg (2006)"},{"issue":"3","key":"28_CR22","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/s10817-006-9057-7","volume":"37","author":"J. Giesl","year":"2006","unstructured":"Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Mechanizing and improving dependency pairs. J. Autom. Reasoning\u00a037(3), 155\u2013203 (2006)","journal-title":"J. Autom. Reasoning"},{"key":"28_CR23","doi-asserted-by":"crossref","unstructured":"Grebenshchikov, S., Lopes, N.P., Popeea, C., Rybalchenko, A.: Synthesizing software verifiers from proof rules. In: Proc. PLDI 2012 (2012)","DOI":"10.1145\/2254064.2254112"},{"key":"28_CR24","doi-asserted-by":"crossref","unstructured":"Gupta, A., Henzinger, T.A., Majumdar, R., Rybalchenko, A., Xu, R.-G.: Proving non-termination. In: Proc. POPL 2008 (2008)","DOI":"10.1145\/1328438.1328459"},{"key":"28_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"304","DOI":"10.1007\/978-3-642-15769-1_19","volume-title":"Static Analysis","author":"W.R. Harris","year":"2010","unstructured":"Harris, W.R., Lal, A., Nori, A.V., Rajamani, S.K.: Alternation for termination. In: Cousot, R., Martel, M. (eds.) SAS 2010. LNCS, vol.\u00a06337, pp. 304\u2013319. Springer, Heidelberg (2010)"},{"key":"28_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/3-540-44829-2_17","volume-title":"Model Checking Software","author":"T.A. Henzinger","year":"2003","unstructured":"Henzinger, T.A., Jhala, R., Majumdar, R., Sutre, G.: Software verification with BLAST. In: Ball, T., Rajamani, S.K. (eds.) SPIN 2003. LNCS, vol.\u00a02648, pp. 235\u2013239. Springer, Heidelberg (2003)"},{"key":"28_CR27","doi-asserted-by":"crossref","unstructured":"Hirokawa, N., Middeldorp, A.: Automating the dependency pair method. Information and Computation\u00a0199(1,2) (2005)","DOI":"10.1016\/j.ic.2004.10.004"},{"key":"28_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1007\/978-3-642-02658-4_52","volume-title":"Computer Aided Verification","author":"B. Jeannet","year":"2009","unstructured":"Jeannet, B., Min\u00e9, A.: apron: A library of numerical abstract domains for static analysis. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol.\u00a05643, pp. 661\u2013667. Springer, Heidelberg (2009)"},{"key":"28_CR29","doi-asserted-by":"crossref","unstructured":"Lee, C.S., Jones, N.D., Ben-Amram, A.M.: The size-change principle for program termination. In: Proc. POPL 2001 (2001)","DOI":"10.1145\/360204.360210"},{"key":"28_CR30","doi-asserted-by":"crossref","unstructured":"Magill, S., Tsai, M.-H., Lee, P., Tsay, Y.-K.: Automatic numeric abstractions for heap-manipulating programs. In: Proc. POPL 2010 (2010)","DOI":"10.1145\/1706299.1706326"},{"key":"28_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/11817963_14","volume-title":"Computer Aided Verification","author":"K.L. McMillan","year":"2006","unstructured":"McMillan, K.L.: Lazy abstraction with interpolants. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol.\u00a04144, pp. 123\u2013136. Springer, Heidelberg (2006)"},{"key":"28_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1007\/978-3-642-27705-4_12","volume-title":"Verified Software: Theories, Tools, Experiments","author":"F. Merz","year":"2012","unstructured":"Merz, F., Falke, S., Sinz, C.: LLBMC: Bounded model checking of C and C++ programs using a compiler IR. In: Joshi, R., M\u00fcller, P., Podelski, A. (eds.) VSTTE 2012. LNCS, vol.\u00a07152, pp. 146\u2013161. Springer, Heidelberg (2012)"},{"key":"28_CR33","doi-asserted-by":"crossref","unstructured":"Min\u00e9, A.: The octagon abstract domain. Higher-Order and Symbolic Computation 19(1) (2006)","DOI":"10.1007\/s10990-006-8609-1"},{"key":"28_CR34","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1007\/978-3-540-69611-7_16","volume-title":"Practical Aspects of Declarative Languages","author":"A. Podelski","year":"2007","unstructured":"Podelski, A., Rybalchenko, A.: ARMC: the logical choice for software model checking with abstraction refinement. In: Hanus, M. (ed.) PADL 2007. LNCS, vol.\u00a04354, pp. 245\u2013259. Springer, Heidelberg (2007)"},{"key":"28_CR35","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1007\/978-3-540-24622-0_20","volume-title":"Verification, Model Checking, and Abstract Interpretation","author":"A. Podelski","year":"2004","unstructured":"Podelski, A., Rybalchenko, A.: A complete method for the synthesis of linear ranking functions. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol.\u00a02937, pp. 239\u2013251. Springer, Heidelberg (2004)"},{"key":"28_CR36","doi-asserted-by":"crossref","unstructured":"Podelski, A., Rybalchenko, A.: Transition invariants. In: Proc. LICS 2004 (2004)","DOI":"10.1109\/LICS.2004.1319598"},{"key":"28_CR37","unstructured":"Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes: The Art of Scientific Computing (1989)"},{"key":"28_CR38","unstructured":"Rybalchenko, A.: Private communication (2013)"},{"key":"28_CR39","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1007\/978-3-642-19835-9_9","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"A. Tsitovich","year":"2011","unstructured":"Tsitovich, A., Sharygina, N., Wintersteiger, C.M., Kroening, D.: Loop summarization and termination analysis. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol.\u00a06605, pp. 81\u201395. Springer, Heidelberg (2011)"}],"container-title":["Lecture Notes in Computer Science","Computer Aided Verification"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-39799-8_28","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,28]],"date-time":"2022-02-28T09:19:23Z","timestamp":1646039963000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-39799-8_28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642397981","9783642397998"],"references-count":39,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-39799-8_28","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}