## On the Modularity of Termination of Term Rewriting Systems (1993)

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Venue: | Theoretical Computer Science |

Citations: | 29 - 3 self |

### BibTeX

@ARTICLE{Ohlebusch93onthe,

author = {Enno Ohlebusch},

title = {On the Modularity of Termination of Term Rewriting Systems},

journal = {Theoretical Computer Science},

year = {1993},

volume = {136}

}

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### Abstract

It is well-known that termination is not a modular property of term rewriting systems, i.e., it is not preserved under disjoint union. The objective of this paper is to provide a "uniform framework" for sufficient conditions which ensure the modularity of termination. We will prove the following result. Whenever the disjoint union of two terminating term rewriting systems is non-terminating, then one of the systems is not C E -terminating (i.e., it looses its termination property when extended with the rules Cons(x; y) ! x and Cons(x; y) ! y) and the other is collapsing. This result has already been achieved by Gramlich [7] for finitely branching term rewriting systems. A more sophisticated approach is necessary, however, to prove it in full generality. Most of the known sufficient criteria for the preservation of termination [24, 15, 13, 7] follow as corollaries from our result, and new criteria are derived. This paper particularly settles the open question whether simple termination ...