We present the first method to disprove innermost termination of term rewrite systems automatically. To this end, we first develop a suitable notion of an innermost loop. Second, we show how to detect innermost loops: One can start with any technique amenable to find loops. Then our novel procedure can be applied to decide whether a given loop is an innermost loop. We implemented and successful...

The dependency pair approach is one of the most powerful techniques for automated (innermost) termination proofs of term rewrite systems (TRSs). For any TRS, it generates inequality constraints that have to be satisfied by well-founded orders. However, proving innermost termination is considerably easier than termination, since the constraints for innermost termination are a subset of those for...

Context-sensitive rewriting is a restriction of term rewriting used to model evaluation strategies in functional programming and in programming languages like OBJ. For example, under certain conditions termination of an OBJ program is equivalent to innermost termination of the corresponding contextsensitive rewrite system [25]. To prove termination of context-sensitive rewriting, several method...

Recently, several loop buffer designs have been proposed to reduce instruction fetch energy due to size and location advantage of loop buffer. Nevertheless, on design complexity dictates most loop buffer designs to store only innermost loops without forward branch or instructions within innermost loops before a forward branch. While program modeling shows that typical programs can best be repre...

We consider the problem of inferring a grammar describing the output of a functional program given a grammar describing its input. Solutions to this problem are helpful for detecting bugs or proving safety properties of functional programs, and several rewriting tools exist for solving this problem. However, known grammar inference techniques are not able to take evaluation strategies of the pr...

The reachability problem for given an initial term, a goal term, and a term rewriting system (TRS) is to decide whether the initial one is reachable to the goal one by the TRS or not. A term is shallow if each variable in the term occurs at depth 0 or 1. Innermost reduction is a strategy that rewrites innermost redexes, and context-sensitive reduction is a strategy in which rewritable positions...

The reachability problem for an initial term, a goal term, and a rewrite system is to decide whether the initial term is reachable to goal one by the rewrite system or not. The innermost reachability problem is to decide whether the initial term is reachable to goal one by innermost reductions of the rewrite system or not. A context-sensitive term rewriting system (CS-TRS) is a pair of a term r...