## 1,309 Citations

### A Functional Approach to String Rewriting and Gröbner bases

- Mathematics, Computer Science
- 2017

An algebraic formulation of completion is given and it is shown that such a completion exists using the lattice structure and the notions of confluence and of Church-Rosser property are equivalent.

### Confluence and Normalization in Reduction Systems Lecture Notes

- Mathematics
- 2015

We study confluence and normalization in abstract reduction systems and apply the results to combinatory logic and an abstract version of the lambda beta calculus. For both systems we obtain the…

### Introduction to Term Rewriting Systems

- Computer Science
- 1998

The confluence property is introduced, which is certainly one of the most fundamental properties ofterm rewriting theory, and applications of term rewriting systems to the field of automated theorem proving are presented.

### On some slowly terminating term rewriting systems

- Computer Science, Mathematics
- 2015

We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano…

### Term Rewriting

- Computer ScienceCSL
- 1999

This tutorial gives an introduction to term rewriting, which is an important computational model with applications in algebra, software engineering, declarative programming, and theorem proving.

### Joint Spectral Radius Theory for Automated Complexity Analysis of Rewrite Systems

- Computer ScienceCAI
- 2011

This paper strengthens and unifies improvements based on the theory of weighted automata and linear algebra by using joint spectral radius theory on the derivational complexity of (compatible) rewrite systems.

### Semantic Matching for Left-Linear Convergent Rewrite Systems

- Computer ScienceJ. Funct. Log. Program.
- 1999

A calculus for solving the semantic matching problem with respect to left-linear or variable-preserving convergent termrewriting systems is presented and the approach to designing a special calculus for special goals is proposed.

### Relative Undecidability in Term Rewriting: II. The Confluence Hierarchy

- EducationInf. Comput.
- 2002

For a hierarchy of properties of term rewriting systems related to confluence we prove relative undecidability, i.e., for implications X ↠ Y in the hierarchy the property X is undecidable for term…

### Confluence and Termination of Simply Typed Term Rewriting Systems

- Computer ScienceRTA
- 2001

A simple proof method for confluence is studied which employs a characterization of the diamond property of a parallel reduction and a new confluence result is obtained for orthogonal conditional STTRSs.

### A Coinductive Framework for Infinitary Rewriting and Equational Reasoning

- Computer ScienceRTA
- 2015

A coinductive framework for defining infinitary analogues of equational reasoning and rewriting in a uniform way that has neither the need for ordinals nor for metric convergence, making the framework especially suitable for formalizations in theorem provers.