Abstract
It is shown that a termination proof for a term rewriting system using multiset path orderings (i.e. recursive path orderings with multiset status only) yields a primitive recursive bound on the length of derivations, measured in the size of the starting term, confirming a conjecture of Plaisted [Pla78]. This result holds for a great variety of path orderings including path of subterms ordering, recursive decomposition ordering, and the path ordering of Kapur, Narendran, Sivakumar if lexicographic status is not incorporated. The result is essentially optimal as such derivation lengths can be found in each level of the Grzegorczyk hierarchy, even for string rewriting systems.
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Hofbauer, D. (1990). Termination proofs by multiset path orderings imply primitive recursive derivation lengths. In: Kirchner, H., Wechler, W. (eds) Algebraic and Logic Programming. ALP 1990. Lecture Notes in Computer Science, vol 463. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53162-9_50
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DOI: https://doi.org/10.1007/3-540-53162-9_50
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