A Predicative Harmonization of the Time and Provable Hierarchies
  A decidable transfinite hierarchy is defined by assigning ordinals to the programs of an imperative language. It singles out: the classes TIMEF(n^c) and TIMEF(n_c); the finite Grzegorczyk classes at and above the elementary level, and the \Sigma_k-IND fragments of PA. Limited operators, diagonalization, and majorization functions are not used. 
Salvatore Caporaso