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B. Gramlich. On termination and confluence properties of disjoint and constructorsharing conditional rewrite systems. Theoretical Computer Science, 165(1):97--131, 1996.

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Applying Rewriting Techniques to the Verification of Erlang.. - Arts, Giesl   (Correct)

....s n = t n may be added to rewrite rules l r. In this paper, we restrict ourselves to CTRSs where all variables in the conditions s i ; t i also occur in l. Depending on the interpretation of the equality sign in the conditions, different rewrite relations can be associated with a CTRS, cf. e.g. [Kap84,BK86,DOS88,BG89,DO90,Mid93,Gra94,SMI95,Gra96a, Gra96b]. In our verification example, we transformed the problem into an oriented CTRS [SMI95] where the equality signs in conditions of rewrite rules are interpreted as reachability ( Thus, we denote rewrite rules by s 1 t 1 ; s n t n j l r: 3) In fact, we even have a normal ....

....reduction of C[loe] to C[roe] with rule (3) is only possible if s i oe reduces to t i oe for all 1 i n. Formally, the rewrite relation R of a CTRS R can be defined as R= S j0 R j , where R 0 = and R j 1 = floe roe j s i oe R j t i oe for all 1 i n and some rule (3) in Rg, cf. e.g. [Mid93,Gra96b]. A CTRS R is terminating iff R is well founded. But termination is not enough to ensure that every evaluation with a CTRS is finite. For example, assume that evaluation of the condition leq(m; length(store) in our CTRS would require the reduction of process(store; m) Then evaluation of ....

B. Gramlich, On termination and confluence properties of disjoint and constructor-sharing conditional rewrite systems. TCS, 165:97--131, 1996.


Optimizatizing the Performance of Schema Evolution.. - Claypool, Natarajan.. (1999)   (Correct)

....sequence. The problem with these heuristic selection criteria is however the cost associated with the search space. One important result of our work addresses this limitation and finds that all complete function orderings conform to the confluence property as defined in term rewriting systems [Gra98] i.e. all complete function orderings converge to one unique minimal sequence. Theorem 1 [Confluence Theorem] Given an input schema evolution sequence, Sigma in , all complete function orderings f i produce minimal resultant sequences Sigma i that are all exactly the same. Proof Proof by ....

B. Gramlich. On Termination and Confluence Properties of Disjoint and Constructor-Sharing Conditional Rewrite Systems. Theoritical Computer Science, 165(1):97--131, 1998.


Integration and Optimization of Rule-based Constraint Solvers - Abdennadher, Frühwirth (2004)   (Correct)

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B. Gramlich. On termination and confluence properties of disjoint and constructorsharing conditional rewrite systems. Theoretical Computer Science, 165(1):97--131, 1996.


Combining Theories Sharing Dense Orders - Calogero Zarba Zohar (2003)   (Correct)

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Bernhard Gramlich. On termination and confluence properties of disjoint and constructor-sharing conditional rewrite systems. Theoretical Computer Science, 165(1):97--131, 1996.

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