max nil 0 max cons x nil x max cons x cons y xs if1 ge x y x y xs if1 true x y xs max cons x xs if1 false x y xs max cons y xs del x nil nil del x cons y xs if2 eq x y x y xs if2 true x y xs xs if2 false x y xs cons y del x xs eq 0 0 true eq 0 s y false eq s x 0 false eq s x s y eq x y sort xs if3 empty xs xs if3 true xs nil if3 false xs sort del max xs xs empty nil true empty cons x xs false ge x 0 true ge 0 s x false ge s x s y ge x y max 1 nil 0 0 0 cons 2 if1 4 ge 2 true 0 false 0 del 2 if2 4 eq 2 s 1 sort 1 if3 2 empty 1 FULL ./AProVE_09_Inductive/maxsortcondition.trs