Albert Rubio (UPC, Barcelona) PRESENT AND FUTURE OF PROVING TERMINATION OF REWRITING ---------------------------------------------------------------------- We give an overview of the state of the art in termination of first-order and higher-order rewriting, showing how termination analysis has evolved in the last years and which are the current needs of improvement. We will discuss how to keep the research on termination of rewriting progressing and devise some new challenges for the forthcoming years.