diff --git a/testcases/web/demos/001_Tutorial-Max.scala b/testcases/web/demos/001_Tutorial-Max.scala
index 75ac1a0b6b8fa29a77b1a0b5ca62360cbe71b764..ba1aaca110227613b4a4e8a792f666e61119f440 100644
--- a/testcases/web/demos/001_Tutorial-Max.scala
+++ b/testcases/web/demos/001_Tutorial-Max.scala
@@ -1,4 +1,3 @@
-import leon.lang._
 import leon.lang.synthesis._
 import leon.annotation._
 object Max {
@@ -42,7 +41,8 @@ object Max {
     max(x,y) == max(y,x) &&
     max(x,max(y,z)) == max(max(x,y), z) &&
     max(x,y) + z == max(x + z, y + z)
-  } holds
+  } ensuring(_ == true)
+  // holds
 */
 
 /*
@@ -54,4 +54,10 @@ object Max {
   } ensuring (res =>
     x <= res && y <= res && (res == x || res == y))
 */
+
+/*
+  def max(x: BigInt, y: BigInt): BigInt = {
+    ???[BigInt]
+  } ensuring(res => (res == x || res == y) &&  x <= res && y <= res)
+*/
 }
diff --git a/testcases/web/demos/003_Tutorial-Sort.scala b/testcases/web/demos/003_Tutorial-Sort.scala
index f665aecc5df5f2fccfd61b6823d639d9bf4c6280..aa5629f9b676f63c968972fb0a0b61b0696df1fa 100644
--- a/testcases/web/demos/003_Tutorial-Sort.scala
+++ b/testcases/web/demos/003_Tutorial-Sort.scala
@@ -1,18 +1,10 @@
-import leon.lang._
+import leon.lang.Set
 import leon.lang.synthesis._
-import leon.annotation._
 object Sort {
   sealed abstract class List
   case object Nil extends List
   case class Cons(head: BigInt, tail: List) extends List
 
-  def size(l: List): BigInt = (l match {
-      case Nil => 0
-      case Cons(x, rest) => x + size(rest)
-  }) ensuring(res =>  res > 0)
-
-  def s1 = size(Cons(10, Cons(1000, Nil)))
-
   def content(l: List): Set[BigInt] = l match {
     case Nil => Set()
     case Cons(i, t) => Set(i) ++ content(t)
@@ -53,7 +45,6 @@ object Sort {
     }
   } ensuring {(res:List) => 
      isSorted(res) && content(res) == content(l) ++ Set(x)}
-   // size(res) == size(l) + 1
 */
 
   // We can also synthesize the body of sInsert interactively