{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,22]],"date-time":"2025-04-22T00:29:24Z","timestamp":1745281764896},"publisher-location":"Berlin, Heidelberg","reference-count":30,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642029585"},{"type":"electronic","value":"9783642029592"}],"license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-3-642-02959-2_22","type":"book-chapter","created":{"date-parts":[[2009,7,25]],"date-time":"2009-07-25T01:02:22Z","timestamp":1248483742000},"page":"277-293","source":"Crossref","is-referenced-by-count":15,"title":["A Term Rewriting Approach to the Automated Termination Analysis of Imperative Programs"],"prefix":"10.1007","author":[{"given":"Stephan","family":"Falke","sequence":"first","affiliation":[]},{"given":"Deepak","family":"Kapur","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"22_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. TCS\u00a0236, 133\u2013178 (2000)","journal-title":"TCS"},{"key":"22_CR2","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. Bradley","year":"2005","unstructured":"Bradley, A., Manna, Z., Sipma, H.: Linear ranking with reachability. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol.\u00a03576, pp. 491\u2013504. Springer, Heidelberg (2005)"},{"key":"22_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/978-3-540-30579-8_8","volume-title":"Verification, Model Checking, and Abstract Interpretation","author":"A. Bradley","year":"2005","unstructured":"Bradley, A., Manna, Z., Sipma, H.: Termination of polynomial programs. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol.\u00a03385, pp. 113\u2013129. Springer, Heidelberg (2005)"},{"key":"22_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1007\/978-3-540-78739-6_13","volume-title":"Programming Languages and Systems","author":"A. Chawdhary","year":"2008","unstructured":"Chawdhary, A., Cook, B., Gulwani, S., Sagiv, M., Yang, H.: Ranking abstractions. In: Drossopoulou, S. (ed.) ESOP 2008. LNCS, vol.\u00a04960, pp. 148\u2013162. Springer, Heidelberg (2008)"},{"key":"22_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/3-540-45319-9_6","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"M. Col\u00f3n","year":"2001","unstructured":"Col\u00f3n, M., Sipma, H.: Synthesis of linear ranking functions. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol.\u00a02031, pp. 67\u201381. Springer, Heidelberg (2001)"},{"key":"22_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"442","DOI":"10.1007\/3-540-45657-0_36","volume-title":"Computer Aided Verification","author":"M. Col\u00f3n","year":"2002","unstructured":"Col\u00f3n, M., Sipma, H.: Practical methods for proving program termination. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol.\u00a02404, pp. 442\u2013454. Springer, Heidelberg (2002)"},{"key":"22_CR7","unstructured":"Conchon, S., Filli\u00e2tre, J.-C., Signoles, J.: Designing a generic graph library using ML functors. In: TFP 2007, pp. 124\u2013140 (2008)"},{"key":"22_CR8","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1007\/s10817-005-9022-x","volume":"34","author":"E. Contejean","year":"2005","unstructured":"Contejean, E., March\u00e9, C., Tom\u00e1s, A.P., Urbain, X.: Mechanically proving termination using polynomial interpretations. JAR\u00a034, 325\u2013363 (2005)","journal-title":"JAR"},{"key":"22_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/11547662_8","volume-title":"Static Analysis","author":"B. Cook","year":"2005","unstructured":"Cook, B., Podelski, A., Rybalchenko, A.: Abstraction refinement for termination. In: Hankin, C., Siveroni, I. (eds.) SAS 2005. LNCS, vol.\u00a03672, pp. 87\u2013101. Springer, Heidelberg (2005)"},{"key":"22_CR10","doi-asserted-by":"crossref","unstructured":"Cook, B., Podelski, A., Rybalchenko, A.: Termination proofs for systems code. In: PLDI 2006, pp. 415\u2013426 (2006)","DOI":"10.1145\/1133981.1134029"},{"key":"22_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1007\/11817963_37","volume-title":"Computer Aided Verification","author":"B. Cook","year":"2006","unstructured":"Cook, B., Podelski, A., Rybalchenko, A.: Terminator: Beyond safety. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol.\u00a04144, pp. 415\u2013418. Springer, Heidelberg (2006)"},{"key":"22_CR12","doi-asserted-by":"crossref","unstructured":"Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: POPL 1978, pp. 84\u201396 (1978)","DOI":"10.1145\/512760.512770"},{"key":"22_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1007\/11817963_11","volume-title":"Computer Aided Verification","author":"B. Dutertre","year":"2006","unstructured":"Dutertre, B., de Moura, L.: A fast linear-arithmetic solver for DPLL(T). In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol.\u00a04144, pp. 81\u201394. Springer, Heidelberg (2006)"},{"key":"22_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1007\/978-3-540-70590-1_7","volume-title":"Rewriting Techniques and Applications","author":"S. Falke","year":"2008","unstructured":"Falke, S., Kapur, D.: Dependency pairs for rewriting with built-in numbers and semantic data structures. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol.\u00a05117, pp. 94\u2013109. Springer, Heidelberg (2008)"},{"key":"22_CR15","doi-asserted-by":"crossref","unstructured":"Falke, S., Kapur, D.: A term rewriting approach to the automated termination analysis of imperative programs. Technical Report TR-CS-2009-02, Department of Computer Science, University of New Mexico (2009), http:\/\/www.cs.unm.edu\/research\/tech-reports\/","DOI":"10.1007\/978-3-642-02959-2_22"},{"key":"22_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1007\/978-3-540-72788-0_33","volume-title":"Theory and Applications of Satisfiability Testing \u2013 SAT 2007","author":"C. Fuhs","year":"2007","unstructured":"Fuhs, C., Giesl, J., Middeldorp, A., Schneider-Kamp, P., Thiemann, R., Zankl, H.: SAT solving for termination analysis with polynomial interpretations. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol.\u00a04501, pp. 340\u2013354. Springer, Heidelberg (2007)"},{"key":"22_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1007\/978-3-642-02348-4_3","volume-title":"RTA 2009","author":"C. Fuhs","year":"2009","unstructured":"Fuhs, C., Giesl, J., Pl\u00fccker, M., Schneider-Kamp, P., Falke, S.: Proving termination of integer term rewriting. In: Treinen, R. (ed.) RTA 2009. LNCS, vol.\u00a05595, pp. 32\u201347. Springer, Heidelberg (2009)"},{"key":"22_CR18","series-title":"LNAI","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)"},{"key":"22_CR19","series-title":"LNAI","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/978-3-540-32275-7_21","volume-title":"Logic for Programming, Artificial Intelligence, and Reasoning","author":"J. Giesl","year":"2005","unstructured":"Giesl, J., Thiemann, R., Schneider-Kamp, P.: The dependency pair framework: Combining techniques for automated termination proofs. In: Baader, F., Voronkov, A. (eds.) LPAR 2004. LNCS (LNAI), vol.\u00a03452, pp. 301\u2013331. Springer, Heidelberg (2005)"},{"key":"22_CR20","series-title":"LNAI","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1007\/978-3-540-73595-3_33","volume-title":"Automated Deduction \u2013 CADE-21","author":"J. Giesl","year":"2007","unstructured":"Giesl, J., Thiemann, R., Swiderski, S., Schneider-Kamp, P.: Proving termination by bounded increase. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol.\u00a04603, pp. 443\u2013459. Springer, Heidelberg (2007)"},{"key":"22_CR21","first-page":"474","volume":"205","author":"N. Hirokawa","year":"2007","unstructured":"Hirokawa, N., Middeldorp, A.: Tyrolean Termination Tool: Techniques and features. IC\u00a0205, 474\u2013511 (2007)","journal-title":"IC"},{"key":"22_CR22","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1023\/A:1005983105493","volume":"21","author":"H. Hong","year":"1998","unstructured":"Hong, H., Jaku\u0161, D.: Testing positiveness of polynomials. JAR\u00a021, 23\u201338 (1998)","journal-title":"JAR"},{"key":"22_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/978-3-642-02348-4_21","volume-title":"RTA 2009","author":"M. Korp","year":"2009","unstructured":"Korp, M., Sternagel, C., Zankl, H., Middeldorp, A.: Tyrolean Termination Tool 2. In: Treinen, R. (ed.) RTA 2009. LNCS, vol.\u00a05595, pp. 295\u2013304. Springer, Heidelberg (2009)"},{"key":"22_CR24","unstructured":"Lankford, D.: On proving term rewriting systems are Noetherian. Memo MTP-3, Mathematics Department, Louisiana Tech. University, Ruston (1979)"},{"issue":"4","key":"22_CR25","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1145\/367177.367199","volume":"3","author":"J. McCarthy","year":"1960","unstructured":"McCarthy, J.: Recursive functions of symbolic expressions and their computation by machine, part I. CACM\u00a03(4), 184\u2013195 (1960)","journal-title":"CACM"},{"key":"22_CR26","unstructured":"Min\u00e9, A.: Weakly Relational Numerical Abstract Domains. PhD thesis, \u00c9cole Polytechnique, Palaiseau, France (2004)"},{"key":"22_CR27","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":"22_CR28","doi-asserted-by":"crossref","unstructured":"Podelski, A., Rybalchenko, A.: Transition invariants. In: LICS 2004, pp. 32\u201341 (2004)","DOI":"10.1109\/LICS.2004.1319598"},{"key":"22_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1007\/978-3-540-27813-9_6","volume-title":"Computer Aided Verification","author":"A. Tiwari","year":"2004","unstructured":"Tiwari, A.: Termination of linear programs. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol.\u00a03114, pp. 70\u201382. Springer, Heidelberg (2004)"},{"key":"22_CR30","volume-title":"Term Rewriting Systems, ch. 6","author":"H. Zantema","year":"2003","unstructured":"Zantema, H.: Termination. In: TeReSe (ed.) Term Rewriting Systems, ch. 6. Cambridge University Press, Cambridge (2003)"}],"container-title":["Lecture Notes in Computer Science","Automated Deduction \u2013 CADE-22"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-02959-2_22","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,21]],"date-time":"2019-05-21T13:52:06Z","timestamp":1558446726000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-02959-2_22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9783642029585","9783642029592"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-02959-2_22","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2009]]}}}