A Dependency Pair Framework for Innermost Complexity Analysis of Term Rewrite Systems

Abstract

Abstract. We present a modular framework to analyze the innermost runtime complexity of term rewrite systems automatically. Our method is based on the dependency pair framework for termination analysis. In contrast to previous work, we developed a direct adaptation of successful termination techniques from the dependency pair framework in order to use them for complexity analysis. By extensive experimental results, we demonstrate the power of our method compared to existing techniques.

Analysing the complexity of functional programs: higher-order meets first-order

“…In order to achieve composability of the analysis, the given system is typically split into smaller parts (see for example [9]), and each of them is analysed separately. Furthermore, contextualisation (aka path analysis [30]) and a suitable form of flow graph analysis (or dependency pair analysis [29,40]) is performed. However, at the end of the day, syntactic and semantic basic techniques, like path orders or interpretations [50,Chapter 6] are employed.…”

Analyzing Innermost Runtime Complexity of Term Rewriting by Dependency Pairs

“…To evaluate the usefulness of the rhs simplification processor and the unreachable DT processor (which are new compared to the preliminary version of the current paper in [27]), we also tested the full version of AProVE against a variant where we disabled these two processors. As shown in the table of Fig.…”

“…A preliminary version of this paper appeared in [27]. The current paper extends [27] substantially, e.g., by including proofs for all theorems, by two new processors for complexity analysis (Thm.…”

“…The current paper extends [27] substantially, e.g., by including proofs for all theorems, by two new processors for complexity analysis (Thm. 32 and 34) and experiments to justify their significance, by detailed information on the impact of the different processors in Sect.…”

Symbolic Evaluation Graphs and Term Rewriting — A General Methodology for Analyzing Logic Programs

“…In general, for any R ′ ⊆ R, the function irc R ′ ,R maps any n ∈ N to the maximal number of i → R ′ -steps that occur in any sequence of i → R -steps starting with a basic term t where |t| ≤ n. Related notions of "relative" complexity for TRSs were used in, e.g., [4,20,31,41]. Most existing automated complexity provers can also approximate irc R ′ ,R asymptotically.…”