fstsplit 0 x nil fstsplit s n nil nil fstsplit s n cons h t cons h fstsplit n t sndsplit 0 x x sndsplit s n nil nil sndsplit s n cons h t sndsplit n t empty nil true empty cons h t false leq 0 m true leq s n 0 false leq s n s m leq n m length nil 0 length cons h t s length t app nil x x app cons h t x cons h app t x map_f pid nil nil map_f pid cons h t app f pid h map_f pid t head cons h t h tail cons h t t ring st_1 in_2 st_2 in_3 st_3 m if_1 st_1 in_2 st_2 in_3 st_3 m empty fstsplit m st_1 if_1 st_1 in_2 st_2 in_3 st_3 m false ring sndsplit m st_1 cons fstsplit m st_1 in_2 st_2 in_3 st_3 m ring st_1 in_2 st_2 in_3 st_3 m if_2 st_1 in_2 st_2 in_3 st_3 m leq m length st_2 if_2 st_1 in_2 st_2 in_3 st_3 m true if_3 st_1 in_2 st_2 in_3 st_3 m empty fstsplit m st_2 if_3 st_1 in_2 st_2 in_3 st_3 m false ring st_1 in_2 sndsplit m st_2 cons fstsplit m st_2 in_3 st_3 m if_2 st_1 in_2 st_2 in_3 st_3 m false if_4 st_1 in_2 st_2 in_3 st_3 m empty fstsplit m app map_f two head in_2 st_2 if_4 st_1 in_2 st_2 in_3 st_3 m false ring st_1 tail in_2 sndsplit m app map_f two head in_2 st_2 cons fstsplit m app map_f two head in_2 st_2 in_3 st_3 m ring st_1 in_2 st_2 in_3 st_3 m if_5 st_1 in_2 st_2 in_3 st_3 m empty map_f two head in_2 if_5 st_1 in_2 st_2 in_3 st_3 m true ring st_1 tail in_2 st_2 in_3 st_3 m ring st_1 in_2 st_2 in_3 st_3 m if_6 st_1 in_2 st_2 in_3 st_3 m leq m length st_3 if_6 st_1 in_2 st_2 in_3 st_3 m true if_7 st_1 in_2 st_2 in_3 st_3 m empty fstsplit m st_3 if_7 st_1 in_2 st_2 in_3 st_3 m false ring st_1 in_2 st_2 in_3 sndsplit m st_3 m if_6 st_1 in_2 st_2 in_3 st_3 m false if_8 st_1 in_2 st_2 in_3 st_3 m empty fstsplit m app map_f three head in_3 st_3 if_8 st_1 in_2 st_2 in_3 st_3 m false ring st_1 in_2 st_2 tail in_3 sndsplit m app map_f three head in_3 st_3 m ring st_1 in_2 st_2 in_3 st_3 m if_9 st_1 in_2 st_2 in_3 st_3 m empty map_f three head in_3 if_9 st_1 in_2 st_2 in_3 st_3 m true ring st_1 in_2 st_2 tail in_3 st_3 m fstsplit 2 0 0 nil 0 s 1 cons 2 sndsplit 2 empty 1 true 0 false 0 leq 2 length 1 app 2 map_f 2 f 2 head 1 tail 1 ring 6 if_1 7 if_2 7 if_3 7 if_4 7 two 0 if_5 7 if_6 7 if_7 7 if_8 7 three 0 if_9 7 FULL ./TRS/AProVE/AAECC-ring.trs