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- Jürgen Giesl, René Thiemann, Peter Schneider-Kamp, Stephan Falke
- Journal of Automated Reasoning
- 2006

The dependency pair technique is a powerful method for automated termination and innermost termination proofs of term rewrite systems (TRSs). For any TRS, it generates inequality constraints that have to be satisfied by well-founded orders. We improve the dependency pair technique by considerably reducing the number of constraints produced for (innermost)… (More)

We describe the system AProVE, an automated prover to verify (innermost) termination of term rewrite systems (TRSs). For this system, we have developed and implemented efficient algorithms based on classical simplification orders, dependency pairs, and the size-change principle. In particular, it contains many new improvements of the dependency pair… (More)

- Florian Merz, Stephan Falke, Carsten Sinz
- VSTTE
- 2012

Bounded model checking (BMC) of C and C++ programs is challenging due to the complex and intricate syntax and semantics of these programming languages. The BMC tool LLBMC presented in this paper thus uses the LLVM compiler framework in order to translate C and C++ programs into LLVM’s intermediate representation. The resulting code is then converted into a… (More)

- Marc Brockschmidt, Fabian Emmes, Stephan Falke, Carsten Fuhs, Jürgen Giesl
- TACAS
- 2014

We present a modular approach to automatic complexity analysis. Based on a novel alternation between finding symbolic time bounds for program parts and using these to infer size bounds on program variables, we can restrict each analysis step to a small part of the program while maintaining a high level of precision. Extensive experiments with the… (More)

- Stephan Falke, Deepak Kapur
- IJCAR
- 2012

This paper presents new results on the decidability of inductive validity of conjectures. For this, a class of term rewrite systems (TRSs) with built-in linear integer arithmetic is introduced and it is shown how these TRSs can be used in the context of inductive theorem proving. The proof method developed for this couples (implicit) inductive reasoning… (More)

- Stephan Falke, Deepak Kapur, Carsten Sinz
- RTA
- 2011

Modeling the semantics of programming languages like C for the automated termination analysis of programs is a challenge if complete coverage of all language features should be achieved. On the other hand, low-level intermediate languages that occur during the compilation of C programs to machine code have a much simpler semantics since most of the… (More)

- Stephan Falke, Deepak Kapur
- CADE
- 2009

An approach based on term rewriting techniques for the automated termination analysis of imperative programs operating on integers is presented. An imperative program is transformed into rewrite rules with constraints from quantifier-free Presburger arithmetic. Any computation in the imperative program corresponds to a rewrite sequence, and termination of… (More)

When using rewrite techniques for termination analysis of programs, a main problem are pre-defined data types like integers. We extend term rewriting by built-in integers and adapt the dependency pair framework to prove termination of integer term rewriting automatically.

- Stephan Falke, Deepak Kapur, Carsten Sinz
- VSTTE
- 2012

Currently, nearly all methods for proving termination of imperative programs apply an unsound and incomplete abstraction by treating bitvectors and bitvector arithmetic as (unbounded) integers and integer arithmetic, respectively. This abstraction ignores the wraparound behavior caused by underand overflows in bitvector arithmetic operations. This is… (More)

- Stephan Falke, Deepak Kapur
- RTA
- 2008

Rewrite systems on free data structures have limited expressive power since semantic data structures like sets or multisets cannot be modeled elegantly. In this work we define a class of rewrite systems that allows the use of semantic data structures. Additionally, built-in natural numbers, including (dis)equality, ordering, and divisibility constraints,… (More)