Derivational Complexity and Context-Sensitive Rewriting

Abstract Context-sensitive rewriting is a restriction of where reduction steps are allowed on specific arguments $$\mu (f)\subseteq \{1,\ldots ,k\}$$ μ ( f ) ⊆ { 1 , … k } k -ary function symbols f only. Terms which cannot be further rewritten in this way called $$ -normal forms. For left-linear term systems (TRSs), the so-called normalization via - procedure provides systematic to obtain normal forms by stepwise computation and combination intermediate In paper, we show how bounds derivational complexity computations using context-sensitive rewriting. Two main applications envisaged: Normalization -normalization can used with non-terminating TRSs still terminates; other hand, it improve terminating as discards many rewritings.