Termination Proofs for Ground Rewrite Systems – Interpretations and Derivational Complexity

Abstract.

It is shown that finite terminating ground term rewrite systems have linearly bounded derivational complexity. This is proven via some suitable interpretation into the natural numbers. Terminating ground systems are not necessarily totally terminating, i.e., a strictly monotone interpretation into a well-order might not exist. We show, however, that those systems are almostω-terminating in the sense that such an interpretation into the sum of a finite partial order and the natural numbers always effectively exists. Finally, we show that for ground systems total termination is equivalent to ω-termination, and that this is a decidable property.