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, ordered(cons(?x,cons(s(?x),nil))) -> true, ordered(cons(s(?x),cons(?x,nil))) -> false ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ and(leList(?x,cons(s(?x),nil)),ordered(cons(s(?x),nil))) = true, and(leList(s(?x_9),cons(?x_9,nil)),ordered(cons(?x_9,nil))) = false, true = true, true = true, true = true ] Overlay, check Innermost Termination... Innermost Terminating (hence Terminating), not WCR Knuth & Bendix Direct Methods: not CR Final result: not CR new/ordered.trs: Success(not CR) (23 msec.)