The computability path ordering: the end of a quest
  In this paper, we first briefly survey automated termination proof methods for higher-order calculi. We then concentrate on the higher-order recursive path ordering, for which we provide an improved definition, the Computability Path Ordering. This new definition appears indeed to capture the essence of computability arguments \`a la Tait and Girard, therefore explaining the name of the improved ordering. 
Fr\'ed\'eric Blanqui (INRIA Lorraine - LORIA), Jean-Pierre Jouannaud   (LIX, INRIA Saclay Ile de France), Albert Rubio