Function calls at frozen positions in termination of context-sensitive rewriting

Abstract

Context-sensitive rewriting (CSR) is a variant of rewriting where only selected arguments of function symbols can be rewritten. Consequently, the subterm positions of a term are classified as either active, i.e., positions of subterms that can be rewritten; or frozen, i.e., positions that cannot. Frozen positions can be used to denote subexpressions whose evaluation is delayed or just forbidden. A typical example is the if-then-else operator whose second and third arguments are not evaluated until the evaluation of the first argument yields either true or false. Imposing replacement restrictions can improve the termination behavior of rewriting-based computational systems. Termination of CSR has been investigated by several authors and a number of automatic tools are able to prove it. In this paper, we analyze how frozen subterms affect termination of CSR. This analysis helps us to improve our Context- Sensitive Dependency Pair (CS-DP) framework for automatically proving termination of CSR. We have implemented these improvements in our tool mu-term. The experiments show the power of the improvements in practice.