Enno Ohlebusch. Termination is not modular for confluent variable-preserving term rewriting systems. Information Processing Letters, 53:223--228, March 1995. Home/Search Document Details and Download
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Innocuous Constructor-Sharing Combinations - Dershowitz (1997) (4 citations) (Correct)
.... x; y) y g(x; y; y) x f(x; y; x; y; z) f(a; b; z; z; z) a 0 b 0 (F) Drosten [9] composed the following nonterminating combination of confluent systems, only one of which is not left linear: g(x; x; y) y g(x; y; y) x f(a; b; x) f(x; x; x) f(x; y; z) 0 a 0 b 0 (G) Ohlebusch [20] has shown that termination is also not preserved for confluent non erasing systems. An erasing system has variables on the left that do not appear on the right. 3 The Pentagon Property Before turning to rewrite relations, we look at some abstract properties relating two binary relations R and ....
Enno Ohlebusch. Termination is not modular for confluent variable-preserving term rewriting systems.
On the Modularity of Termination of Term Rewriting Systems - Ohlebusch (1993) (37 citations) Self-citation (Ohlebusch) (Correct)
.... (f0; 1; Fg; fF (0; 1; x) F (x; x; x)g) and (F 2 ; R 2 ) fgg; fg(x; y) x; g(x; y) yg) are evidently terminating but their disjoint union is not terminating, for there is the cyclic rewrite derivation t j F (0; 1; g(0; 1) R 1 F (g(0; 1) g(0; 1) g(0; 1) R 2 F (0; g(0; 1) g(0; 1) R 2 t In [Ohl93b] an example is given which shows that R 1 ]R 2 may be non terminating even if R 1 and R 2 are terminating, confluent, irreducible, and variable preserving. Naturally the question arises what restrictions have to be imposed on the constituent TRSs so that their disjoint union is again terminating. ....
E. Ohlebusch. Termination is not Modular for Confluent Variable-Preserving Term Rewriting Systems. Submitted for Publication, 1993.
Modular Properties of Composable Term Rewriting Systems - Ohlebusch (1995) (40 citations) Self-citation (Ohlebusch) (Correct)
....j 1 ) C b f Phi D b (s 1 ) Phi D b (s l Gamma1 ) Phi D b (u 1 ) Phi D b (u p ) Phi D b (s l 1 ) Phi D b (s m )g, where C b f; g = C b [ C b f; g; Now it is a consequence of s 0 l 2 Delta D b (s l ) 22 E. Ohlebusch that Phi D b (s 0 l ) occurs in the term Phi D b (s l ) and hence Phi D b (s l ) Sort(f Phi D b (u) j u 2 Delta D b (s l )g) h: Phi D b (s 0 l ) i CE Phi D b (s 0 l ) C b f Phi D b (u 1 ) Phi D b (u p )g: All in all, Phi D b (t j ) CE Phi D b (t ....
Ohlebusch, E. (1995b). Termination is not modular for confluent variable-preserving term rewriting systems. Information Processing Letters 53, 223--228.
On the Modularity of Confluence of Constructor-Sharing Term.. - Ohlebusch (1994) (7 citations) Self-citation (Ohlebusch) (Correct)
....first proved by Toyama [Toy87b] and is by now referred to as Toyama s Theorem. Not long ago a simplified proof of Toyama s Theorem was given by Klop et al. KMTV91] In contrast to this encouraging result, termination and completeness turned out to lack a modular behavior (see [Toy87a] and also [Ohl93b]) Thus several sufficient criteria ensuring their modularity have been given (for an overview see e.g. Mid90, Gra93, Ohl93a] In order to prove modularity of completeness, one can of course use the confluence of the combined system to show its termination. For example the deep theorem that ....
E. Ohlebusch. Termination is not Modular for Confluent VariablePreserving Term Rewriting Systems. Submitted, 1993.
On the Modularity of Termination of Term Rewriting Systems - Ohlebusch (1993) (37 citations) Self-citation (Ohlebusch) (Correct)
....nor duplicating rules. 5 Concluding Remarks First of all, we point out that normalization is also a modular property of constructor sharing TRSs (the proof for disjoint unions given in [16] can be carried over) The same holds for semi completeness (confluence plus normalization) see [23] for details. Second, we expect that Theorem 3.16 is also true for join conditional term rewriting systems (CTRSs) This, however, does not seem to lead to practically relevant results. In contrast to the unconditional case, the class of C E terminating CTRSs comprises neither the class of ....
E. Ohlebusch. Termination is not Modular for Confluent Variable-Preserving Term Rewriting Systems, 1993. To appear in Information Processing Letters.
WST'04 7th International Workshop on Termination - Codish, Middeldorp (2004) (Correct)
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Enno Ohlebusch. Termination is not modular for confluent variable-preserving term rewriting systems. Information Processing Letters, 53:223--228, March 1995.
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