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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)

- 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, 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 wrap-around behavior caused by under-and overflows in bitvector arithmetic operations. This is… (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 in-ductive 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)

- Marc Brockschmidt, Fabian Emmes, Stephan Falke, Carsten Fuhs, Jürgen Giesl
- ACM Trans. Program. Lang. Syst.
- 2016

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

- Carsten Sinz, Stephan Falke, Florian Merz
- SSV
- 2010

—Formalizing the semantics of programming languages like C or C++ for bounded model checking can be cumbersome if complete coverage of all language features is to be achieved. On the other hand, low-level languages that occur during translation (compilation) have a much simpler semantics since they are closer to the machine level. It thus makes sense to use… (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.