NO Rewrite Rules: [ ordered(nil) -> true, ordered(cons(?x,?ys)) -> and(leList(?x,?ys),ordered(?ys)), leList(?x,nil) -> true, leList(?x,cons(?y,?ys)) -> and(le(?x,?y),leList(?x,?ys)), le(0,?y) -> true, le(s(?x),0) -> false, le(s(?x),s(?y)) -> le(?x,?y), and(true,true) -> true, and(?x,true) -> ?x, and(true,?y) -> ?y, and(false,false) -> false, sort(nil) -> nil, sort(cons(?x,?ys)) -> insert(?x,sort(?ys)), insert(?x,nil) -> cons(?x,nil), insert(?x,cons(?y,?ys)) -> if(le(?x,?y),cons(?x,cons(?y,?ys)),cons(?y,insert(?x,?ys))), if(true,?y,?z) -> ?y, if(false,?y,?z) -> ?z, ordered(sort(?xs)) -> true ] Apply Direct Methods... Inner CPs: [ ordered(nil) = true, ordered(insert(?x_8,sort(?ys_8))) = true ] Outer CPs: [ true = true, true = true, true = true ] not Overlay, check Termination... Terminating, not WCR Knuth & Bendix Direct Methods: not CR Final result: not CR new/insert.trs: Success(not CR) (33 msec.)