Complexity of Conditional Term Rewriting

Abstract

We propose a notion of complexity for oriented conditional rewrite systems satisfying certain restrictions. This notion is realistic in the sense that it measures not only successful computations, but also partial computations that result in a failed rule application. A transformation to unconditional context-sensitive rewrite systems is presented which reflects this complexity notion, as well as a technique to derive runtime and derivational complexity bounds for the result of this transformation.

An Inversion Tool for Conditional Term Rewriting Systems - A Case Study of Ackermann Inversion

“…The number of required rewrite steps is used in the complexity of conditional term rewriting systems [8], and the number of function/predicate calls is used in the complexity analysis of functional and logic programs [9,11]. Here, function calls correspond to the number of function-rooted terms that must be rewritten to reach normal form.…”