qsort nil nil qsort cons x xs append qsort filterlow last cons x xs cons x xs cons last cons x xs qsort filterhigh last cons x xs cons x xs filterlow n nil nil filterlow n cons x xs if1 ge n x n x xs if1 true n x xs filterlow n xs if1 false n x xs cons x filterlow n xs filterhigh n nil nil filterhigh n cons x xs if2 ge x n n x xs if2 true n x xs filterhigh n xs if2 false n x xs cons x filterhigh n xs ge x 0 true ge 0 s x false ge s x s y ge x y append nil ys ys append cons x xs ys cons x append xs ys last nil 0 last cons x nil x last cons x cons y xs last cons y xs qsort 1 nil 0 cons 2 append 2 filterlow 2 last 1 filterhigh 2 if1 4 ge 2 true 0 false 0 if2 4 0 0 s 1 ys 0 FULL ./AProVE_09_Inductive/qsortlast.trs