### Abstract

Automatic termination analysers typically measure the size of terms applying norms which are mappings from terms to the natural numbers. This paper illustrates how to enable the use of size functions defined as tuples of these simpler norm functions. This approach enables us to simplify the problem of deriving automatically a candidate norm with which to prove termination. Instead of deriving a single, complex norm function, it is sufficient to determine a collection of simpler norms, some combination of which, leads to a proof of termination. We propose that a collection of simple norms, one for each of the recursive data-types in the program, is often a suitable choice. We first demonstrate the power of combining norm functions and then the adequacy of combining norms based on regular types.

Translated title of the contribution | Combining Norms to Prove Termination |
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Original language | English |

Title of host publication | Unknown |

Editors | A. Cortesi |

Publisher | Springer Berlin Heidelberg |

Pages | 126 - 138 |

Number of pages | 12 |

ISBN (Print) | 3540436316 |

Publication status | Published - Apr 2002 |

### Bibliographical note

Conference Proceedings/Title of Journal: Verification, Model Checking, and Abstract Interpretation, Third International Workshop, VMCAI 2002.## Cite this

Genaim, S., Codish, M., Gallagher, J., & Lagoon, V. (2002). Combining Norms to Prove Termination. In A. Cortesi (Ed.),

*Unknown*(pp. 126 - 138). Springer Berlin Heidelberg. http://www.cs.bris.ac.uk/Publications/pub_info.jsp?id=1000624