H. Zantema. Termination of term rewriting. In M.A. Bezem, J.W. Klop, and R.C. de Vrijer, editors, Term Rewriting Systems, chapter 6. Cambridge University Press, 2003 (to appear). Home/Search Document Details and Download
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Two Solutions to Incorporate Zero, Successor and Equality in.. - Badban, Pol (Correct)
....R OBDD. It su#ces to prove termination: We apply TRS rules to a given BDD, until we reach a normal form after a finite number of steps, which is guaranteed by termination. The so derived BDD is the R OBDD. We prove termination by means of a powerful tool, the recursive path ordering (# rpo ) [13, 29]. This is a standard way to extend a (total) well founded order on a set of labels to a (total) well founded order on trees over these labels. To this end, we view guards as labels, ordered by Definition 8, and BDDs are viewed as binary trees, so ITE(g, T 1 , T 2 ) corresponds to the tree g(T 1 , ....
....or S 2 rpo T or . II) f rpo T 1 , T 2 or . III) f rpo T 1 , T 2 and either (S 1 rpo T 1 ) or (S 1 T 1 and S 2 rpo T 2 ) Here x rpo y means: x rpo y or x y, also S rpo T 1 , T 2 means: S rpo T 1 and S rpo T 2 . This definition yields an order, as it is shown in [29]. In order to prove termination, we will show that each rewrite rule (of Definition 9) is indeed a reduction rule regarding rpo . The next lemma will be very helpful to show that this reduction property really holds. y) and g (w) If f g. Proof. v. Then x ....
[Article contains additional citation context not shown here]
H. Zantema. Termination of term rewriting. In M.A. Bezem, J.W. Klop, and R.C. de Vrijer, editors, Term Rewriting Systems, chapter 6. Cambridge University Press, 2003 (to appear).
Two Solutions to Incorporate Zero, Successor and Equality in.. - Badban, Pol (2002) (Correct)
....R OBDD. It su#ces to prove termination: We apply TRS rules to a given BDD, until we reach a normal form after a finite number of steps, which is guaranteed by termination. The so derived BDD is the R OBDD. We prove termination by means of a powerful tool, the recursive path ordering (# rpo ) [13, 29]. This is a standard way to extend a (total) well founded order on a set of labels to a (total) well founded order on trees over these labels. To this end, we view guards as labels, ordered by Definition 8, and BDDs are viewed as binary trees, so ITE(g,T 1 ,T 2 ) corresponds to the tree g(T 1 ,T 2 ....
....rpo T or . II) f gandS# rpo T 1 ,T 2 or . III) gand S# rpo T 1 ,T 2 and either (S 1 rpo T 1 ) or (S T 1 and S 2 rpo T 2 ) Here x rpo y means: x rpo y or y, also S rpo T 1 ,T 2 means: S rpo T 1 and S rpo T 2 . This definition yields an order, as it is shown in [29]. In order to prove termination, we will show that each rewrite rule (of Definition 9) is indeed a reduction rule regarding rpo . The next lemma will be very helpful to show that this reduction property really holds. y) and (w) Iff g. Proof. Case I: y# v. Then ....
[Article contains additional citation context not shown here]
H. Zantema. Termination of term rewriting. In M.A. Bezem, J.W. Klop, and R.C. de Vrijer, editors, Term Rewriting Systems, chapter 6. Cambridge University Press, 2003 (to appear).
Recursively Defined (Quasi) Orders on Terms - Ferreira (1997) (Correct)
....We will consider a definition of weight and of the kbo similar to the one presented in [7] however we extend the precedence to be a quasi order in F and allow for more than one maximum element in F with arity one and weight zero. Other more general possibilities for weight functions do exist. In [27] a general weight function is given using an interpretation of terms in a weakly monotone algebra. In the following we assume lexicographic extension as defined in 2.11. Definition 4.24. A weight function OE : F [ X IN is a function satisfying: OE(f ) is = OE 0 if f 2 X OE 0 if ....
Zantema, H. Termination of term rewriting. Tech. rep., University of Utrecht, 1997. To appear. 45
Recursively Defined (Quasi) Orders on Terms - Ferreira (1997) (Correct)
....We will consider a definition of weight and of the kbo similar to the one presented in [7] however we extend the precedence to be a quasi order in F and allow for more than one maximum element in F with arity one and weight zero. Other more general possibilities for weight functions do exist. In [27] a general weight function is given using an interpretation of terms in a weakly monotone algebra. In the following we assume lexicographic extension as defined in 2.11. Definition 4.24. A weight function OE : F [ X IN is a function satisfying: OE(f ) is 8 : OE 0 if f 2 X OE 0 if ....
Zantema, H. Termination of term rewriting. Tech. rep., University of Utrecht, 1997. To appear.
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