Semantic labeling is a powerful transformation technique for proving termination of term rewrite systems. The semantic part is given by a model or a quasi-model of the rewrite rules. A variant of semantic labeling is predictive labeling where the quasi-model condition is only required for the usable rules. In this paper we investigate how semantic and predictive labeling can be used to prove in...

A new adaptive finite element method for solving the Stokes equations is developed, which is shown to converge with the best possible rate. The method consists of 3 nested loops. The outermost loop consists of an adaptive finite element method for solving the pressure from the (elliptic) Schur complement system that arises by eliminating the velocity. Each of the arising finite element problems...

This paper is concerned with the complexity analysis of constructor term rewrite systems and its ramification in implicit computational complexity. We introduce a path order with multiset status, the polynomial path order POP, that is applicable in two related, but distinct contexts. On the one hand POP induces polynomial innermost runtime complexity and hence may serve as a syntactic, and full...

Context . AU Mic is a young and nearby M-dwarf star harbouring circumstellar debris disc one recently discovered planet on an eight-day orbit. Large-scale structures within the were also are moving outwards at high velocity. Aims We aim to study this system with highest spatial resolution in order probe innermost regions search for additional low-mass companions or set detection limits. Methods...