## On Operational Termination of Deterministic Conditional Rewrite Systems (2007)

### BibTeX

@MISC{Schernhammer07onoperational,

author = {Felix Schernhammer and Bernhard Gramlich},

title = {On Operational Termination of Deterministic Conditional Rewrite Systems},

year = {2007}

}

### OpenURL

### Abstract

We characterize the practically important notion of operational termination of deterministic conditional term rewriting systems (DCTRSs) by context-sensitive termination of a transformed TRS on original terms. Experimental evaluations show that this new approach yields more power when verifying operational termination than existing ones. Moreover, it allows us to disprove operational termination of DCTRSs.

### Citations

940 |
Term Rewriting and All That
- Baader, Nipkow
- 1998
(Show Context)
Citation Context ...tive (unconditional) TRS on original terms. In the following, we assume familiarity with the basic concepts and notations of (context-free, context-sensitive and conditional) term rewriting (cf. e.g. =-=[2]-=-, [6], [9]). In this work we are exclusively concerned with deterministic conditional term rewrite systems (DCTRSs). 2 Proving operational termination of DCTRSs via context-sensitive quasi-reductivity... |

75 |
Advanced topics in term rewriting
- Ohlebusch
- 2002
(Show Context)
Citation Context ... of context-sensitive quasi-reductivity ([6]), that will be proved to be equivalent to operational termination of DCTRSs. Furthermore, we use a simple modification of unraveling transformations ([7], =-=[9]-=-) that allows us to completely characterize the new property of context-sensitive quasi-reductivity of a DCTRS by means of termination of a context-sensitive (unconditional) TRS on original terms. In ... |

69 | Context-sensitive computations in functional and functional logic programs
- Lucas
- 1998
(Show Context)
Citation Context ...t. operationally terminating DCTRSs always terminate (which is indeed not true for other similar notions like effective termination [5]). We propose the notion of context-sensitive quasi-reductivity (=-=[6]-=-), that will be proved to be equivalent to operational termination of DCTRSs. Furthermore, we use a simple modification of unraveling transformations ([7], [9]) that allows us to completely characteri... |

66 | Mechanizing and improving dependency pairs
- Giesl, Thiemann, et al.
(Show Context)
Citation Context ...it is now sufficient to prove termination on original terms. In order to exploit this relaxation of the termination property, we developed a dedicated method based on the dependency pair framework of =-=[3]-=- and [1], that allows us to prove termination of CSRSs obtained by the proposed transformation on original terms. First experimental results with a prototype implementation are promising. In particula... |

29 |
Termination proofs of well-moded logic programs via conditional rewrite systems
- Ganzinger, Waldmann
- 1993
(Show Context)
Citation Context ...variables in conditions (corresponding to let-constructs or where-clauses in other functional-(logic) languages) and has been used for instance in proofs of termination of (well-moded) logic programs =-=[4]-=-. When analyzing the termination behaviour of conditional TRSs, it turns out that the proof-theoretic notion of operational termination is more adequate than ordinary termination in the sense that pra... |

26 | Unravelings and ultra-properties
- Marchiori
- 1996
(Show Context)
Citation Context ...otion of context-sensitive quasi-reductivity ([6]), that will be proved to be equivalent to operational termination of DCTRSs. Furthermore, we use a simple modification of unraveling transformations (=-=[7]-=-, [9]) that allows us to completely characterize the new property of context-sensitive quasi-reductivity of a DCTRS by means of termination of a context-sensitive (unconditional) TRS on original terms... |

21 | Proving operational termination of membership equational programs
- Durán, Lucas, et al.
(Show Context)
Citation Context ...ation of the resulting CSRS (on original terms). We have shown that the proposed transformation, which has already been discussed in [8] regarding simulation soundness and completeness and briefly in =-=[10]-=- regarding termination analysis, yields operational termination of strictly more DCTRSs than Ohlebusch’s context-free transformation. Furthermore, we developed methods for the termination analysis tha... |

12 |
Operational termination of conditional term rewriting systems
- Lucas, Marché, et al.
- 2005
(Show Context)
Citation Context ...an ordinary termination in the sense that practical evaluations w.r.t. operationally terminating DCTRSs always terminate (which is indeed not true for other similar notions like effective termination =-=[5]-=-). We propose the notion of context-sensitive quasi-reductivity ([6]), that will be proved to be equivalent to operational termination of DCTRSs. Furthermore, we use a simple modification of unravelin... |

11 | Partial inversion of constructor term rewriting systems
- Nishida, Sakai, et al.
- 2005
(Show Context)
Citation Context ...Furthermore, cs-quasi-reductivity can be verified by proving termination of the resulting CSRS (on original terms). We have shown that the proposed transformation, which has already been discussed in =-=[8]-=- regarding simulation soundness and completeness and briefly in [10] regarding termination analysis, yields operational termination of strictly more DCTRSs than Ohlebusch’s context-free transformation... |

8 | Improving context-sensitive dependency pairs
- Alarcón, Emmes, et al.
- 2008
(Show Context)
Citation Context ...w sufficient to prove termination on original terms. In order to exploit this relaxation of the termination property, we developed a dedicated method based on the dependency pair framework of [3] and =-=[1]-=-, that allows us to prove termination of CSRSs obtained by the proposed transformation on original terms. First experimental results with a prototype implementation are promising. In particular, we we... |