{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T22:21:30Z","timestamp":1725488490610},"publisher-location":"Berlin, Heidelberg","reference-count":22,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540638759"},{"type":"electronic","value":"9783540696582"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1997]]},"DOI":"10.1007\/3-540-63875-x_59","type":"book-chapter","created":{"date-parts":[[2007,8,7]],"date-time":"2007-08-07T03:08:01Z","timestamp":1186456081000},"page":"283-296","source":"Crossref","is-referenced-by-count":2,"title":["An analysis of divisibility orderings and recursive path orderings"],"prefix":"10.1007","author":[{"given":"Ryu","family":"Hasegawa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2005,8,1]]},"reference":[{"key":"22_CR1","doi-asserted-by":"crossref","unstructured":"T. Becker and V. Weispfenning, Gr\u00f4bner Bases, Graduate Texts in Mathematics 141, (Springer, 1993).","DOI":"10.1007\/978-1-4612-0913-3_5"},{"key":"22_CR2","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/1385-7258(77)90067-1","volume":"39","author":"D. H. J. Jongh de","year":"1977","unstructured":"D. H. J. de Jongh and R. Parikh, Well-partial orderings and hierarchies, Indagationes Math. 39 (1977) 195\u2013207.","journal-title":"Indagationes Math."},{"key":"22_CR3","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1016\/0304-3975(82)90026-3","volume":"17","author":"N. Dershowitz","year":"1982","unstructured":"N. Dershowitz, Orderings for term-rewriting systems, Theoretical Computer Sci. 17 (1982) 279\u2013301.","journal-title":"Theoretical Computer Sci."},{"key":"22_CR4","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1145\/359138.359142","volume":"22","author":"N. Dershowitz","year":"1979","unstructured":"N. Dershowitz and Z. Manna, Proving termination with multiset orderings, Communications ACM 22 (1979) 465\u2013476.","journal-title":"Communications ACM"},{"key":"22_CR5","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1109\/LICS.1988.5108","volume-title":"Third Annual Symposium on Logic in Computer Science, 1988","author":"N. Dershowitz","year":"1988","unstructured":"N. Dershowitz and M. Okada, Proof theoretic techniques for term rewriting theory, in: Third Annual Symposium on Logic in Computer Science, 1988, Edinburgh, Scotland, (IEEE, 1988) pp. 104\u2013111."},{"key":"22_CR6","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/0003-4843(81)90016-4","volume":"21","author":"J.-Y. Girard","year":"1981","unstructured":"J.-Y. Girard, II 1 2 -logic, part I; dilators, Ann. Math. Logic 21 (1981) 75\u2013219.","journal-title":"Ann. Math. Logic"},{"key":"22_CR7","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/0168-0072(88)90025-5","volume":"37","author":"J.-Y. Girard","year":"1988","unstructured":"J.-Y. Girard, Normal functors, power series and \u03bb-calculus, Ann. Pure Applied Logic 37 (1988) 129\u2013177.","journal-title":"Ann. Pure Applied Logic"},{"key":"22_CR8","doi-asserted-by":"crossref","first-page":"713","DOI":"10.2307\/2274127","volume":"49","author":"J.-Y. Girard","year":"1984","unstructured":"J.-Y. Girard and J. Vauzeilles, Functors and ordinal notations II: A functorial construction of the Bachmann-hierarchy, J. Symbolic Logic 49 (1984) 713\u2013729.","journal-title":"J. Symbolic Logic"},{"key":"22_CR9","doi-asserted-by":"crossref","unstructured":"R. Hasegawa, Well-ordering of algebras and Kruskal's theorem, in: Logic, Language and Computation, Festschrift in Honor of Satoru Takasu, N. D. Jones, M. Hagiya, M. Sato, eds., Lecture Notes in Computer Science 792, (Springer, 1994) pp. 133\u2013172.","DOI":"10.1007\/BFb0032399"},{"key":"22_CR10","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1112\/plms\/s3-2.1.326","volume":"2","author":"G. Higman","year":"1952","unstructured":"G. Higman, Ordering by divisibility in abstract algebras, Proc. London Math. Soc., Third Series 2 (1952) 326\u2013336.","journal-title":"Proc. London Math. Soc., Third Series"},{"key":"22_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0001-8708(81)90052-9","volume":"42","author":"A. Joyal","year":"1981","unstructured":"A. Joyal, Une th\u00e9orie combinatoire des s\u00e9ries formelles, Advances Math. 42 (1981) 1\u201382.","journal-title":"Advances Math."},{"key":"22_CR12","doi-asserted-by":"crossref","unstructured":"A. Joyal, Foncteurs analytiques et esp\u00e8ces de structures, in: Combinatoire Enum\u00e9rative, Proceedings, Montreal, Qu\u00e9bec, Canada, 1985, G. Labelle, P. Leroux, eds., Lecture Notes in Mathematics 1234, (Springer, 1986) pp. 126\u2013159.","DOI":"10.1007\/BFb0072514"},{"key":"22_CR13","first-page":"210","volume":"95","author":"J. B. Kruskal","year":"1960","unstructured":"J. B. Kruskal, Well-quasi-ordering, the tree theorem, and Vazsonyi's conjecture, Transactions American Math. Soc. 95 (1960) 210\u2013225.","journal-title":"Transactions American Math. Soc."},{"key":"22_CR14","unstructured":"P. Lescanne, Uniform termination of term rewriting systems, recursive decomposition ordering with status, in: Ninth Colloquium on Trees in Algebra and Programming, 1984, Bordeaux, France, B. Courcelle ed., (Cambridge University Press, 1984) pp. 181\u2013194."},{"key":"22_CR15","unstructured":"S. Mac Lane and I. Moerdijk, Sheaves in Geometry and Logic, A First Introduction to Topos Theory, (Springer, 1992)."},{"key":"22_CR16","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1109\/LICS.1993.287573","volume-title":"Proc. Eighth Annual IEEE Symposium on Logic in Computer Science, 1992","author":"U. Martin","year":"1993","unstructured":"U. Martin and E. Scott, The order types of termination orderings on monadic terms, strings and multisets, in: Proc. Eighth Annual IEEE Symposium on Logic in Computer Science, 1992, Montreal, Canada, (IEEE, 1993) pp. 356\u2013363."},{"key":"22_CR17","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/S0304-3975(96)00172-7","volume":"175","author":"A. Middeldorp","year":"1997","unstructured":"A. Middeldorp and H. Zantema, Simple termination of rewrite systems, Theoretical Computer Sci., 175 (1997) 127\u2013158.","journal-title":"Theoretical Computer Sci."},{"key":"22_CR18","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1017\/S0305004100003844","volume":"59","author":"C. S. J. A. Nash-Williams","year":"1963","unstructured":"C. St. J. A. Nash-Williams, On well-quasi-ordering finite trees, Proc. Cambridge Philosophical Soc. 59 (1963) 833\u2013835.","journal-title":"Proc. Cambridge Philosophical Soc."},{"key":"22_CR19","unstructured":"K. Sakai, Knuth-Bendix algorithm for Thue system based on kachinuki ordering, ICOT Technical Memorandum: TM-0087, ICOT, Institute for New Generation Computer Technology, Dec. 1984."},{"key":"22_CR20","doi-asserted-by":"crossref","unstructured":"S. G. Simpson, Nonprovability of certain combinatorial properties of finite trees, in: Harvey Friedman's research on the foundations of mathematics, L. A. Harrington, M. D. Morley, A. Scedrov, S. G. Simpson, eds., (North-Holland, 1985) pp. 87\u2013117.","DOI":"10.1016\/S0049-237X(09)70156-9"},{"key":"22_CR21","unstructured":"G. Takeuti, Proof Theory, Studies in Logic and the Foundations of Mathematics, Vol. 81, (North-Holland, 1975)."},{"key":"22_CR22","doi-asserted-by":"crossref","first-page":"945","DOI":"10.2307\/2275919","volume":"59","author":"A. Weiermann","year":"1994","unstructured":"A. Weiermann, A functorial property of the Aczel-Buchholz-Feferman function, J. Symbolic Logic, 59 (1994) 945\u2013955.","journal-title":"J. Symbolic Logic"}],"container-title":["Lecture Notes in Computer Science","Advances in Computing Science \u2014 ASIAN'97"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-63875-X_59","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T16:10:38Z","timestamp":1556727038000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-63875-X_59"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997]]},"ISBN":["9783540638759","9783540696582"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/3-540-63875-x_59","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[1997]]}}}