# Automated Termination Proofs with Measure Functions

@inproceedings{Giesl1995AutomatedTP, title={Automated Termination Proofs with Measure Functions}, author={J{\"u}rgen Giesl}, booktitle={KI}, year={1995} }

This paper deals with the automation of termination proofs for recursively defined algorithms (i.e. algorithms in a pure functional language). Previously developed methods for their termination proofs either had a low degree of automation or they were restricted to one single fixed measure function to compare data objects. To overcome these drawbacks we introduce a calculus for automated termination proofs which is able to handle arbitrary measure functions based on polynomial norms.

## 26 Citations

### On Formalised Proofs of Termination of Recursive Functions

- Computer Science, MathematicsPPDP
- 1999

In proof checkers and theorem provers, recursive definitions of functions are shown to terminate automatically in standard non-formalised termination proofs of recursive functions, using a decreasing measure.

### Termination Analysis for Partial Functions

- Computer ScienceSAS
- 1996

This paper deals with automated termination analysis for partial functional programs, i.e. for functional programs which do not terminate for each input, and presents a method to determine their domains automatically automatically.

### Termination Analysis for Partial Functions ?

- Computer Science
- 1996

This paper deals with automated termination analysis for partial functional programs, i.e. for functional programs which do not terminate for each input, and presents a method to determine their domains automatically automatically.

### Induction Proofs with Partial Functions

- Computer Science, Mathematics
- 1998

By slightly restricting the application of most well-known techniques developed for (explicit) induction theorem proving, it is possible to develop a calculus for automated induction proofs with partial functions.

### Termination Analysis for Functional Programs using Term Orderings

- Computer ScienceSAS
- 1995

This paper presents a procedure for automated termination proofs of functional programs in contrast to previously presented methods a suited well-founded ordering does not have to be fixed in advance by the user, but can be synthesized automatically.

### Termination of String Rewriting Proved Automatically

- Computer ScienceJournal of Automated Reasoning
- 2005

A combination of polynomial interpretations, recursive path order, RFC match-bounds, the dependency pair method, and semantic labelling can be used for automatically proving termination of an extensive class of string rewriting systems.

### Approximating the Domains of Functional and Imperative Programs

- Computer Science
- 1999

A method is presented to determine domains of functional programs automatically and for each functional program a termination predicate algorithm is synthesized that only returns true for inputs where the program is terminating.

### Towards Automated Termination Proofs through "Freezing"

- Computer ScienceRTA
- 1998

It is proved that applying the freezing technique to a left-linear term rewriting system always terminates, and it is shown that many interesting TRSs in the literature can be handled with the help of freezing while they elude a lot of other approaches aiming for generating termination proofs automatically for term rewriting systems.

### Termination Analysis for Functional Programs Using Term Orderings ?

- Computer Science
- 1995

This paper presents a procedure for automated termination proofs of functional programs using a suited well-founded ordering that does not have to be xed in advance by the user, but can be synthesized automatically.

### Proving and Disproving Termination of Higher-Order Functions

- Computer Science, MathematicsFroCoS
- 2005

The dependency pair technique is extended to handle (untyped) applicative TRSs and a method to prove non-termination with dependency pairs is introduced, while up to now dependency pairs were only used to verify termination.

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