diff --git a/CMakeLists.txt b/CMakeLists.txt
index 5be2f98..6ab4d6f 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -1,5 +1,5 @@
 ## Please modify this file freely to adapt to the production of other
-## executables than convexhull and testrun
+## executables than upperhull and testrun
 
 # Description of the different builds
 # +---------------+--------------+--------------+----------|
@@ -87,18 +87,18 @@ get_property(inc_dirs DIRECTORY PROPERTY INCLUDE_DIRECTORIES)
 message("inc_dirs = ${inc_dirs}")
 
 # Convex Hulls : 8, 16, 32 or 64 bits and the version with extras
-file(GLOB SOURCES "examples/convexhull/convexHull8.cpp")
-add_executable(convexhull8 ${SOURCES})
-file(GLOB SOURCES "examples/convexhull/convexHull16.cpp")
-add_executable(convexhull16 ${SOURCES})
-file(GLOB SOURCES "examples/convexhull/convexHull32.cpp")
-add_executable(convexhull32 ${SOURCES})
-file(GLOB SOURCES "examples/convexhull/convexHull64.cpp")
-add_executable(convexhull64 ${SOURCES})
-file(GLOB SOURCES "examples/convexhull/convexHullExtras.cpp")
-add_executable(convexhullextras ${SOURCES})
-file(GLOB SOURCES "examples/convexhull/generateInputConvexHull.cpp")
-add_executable(generateInputConvexHull ${SOURCES})
+file(GLOB SOURCES "examples/upperhull/upperHull8.cpp")
+add_executable(upperhull8 ${SOURCES})
+file(GLOB SOURCES "examples/upperhull/upperHull16.cpp")
+add_executable(upperhull16 ${SOURCES})
+file(GLOB SOURCES "examples/upperhull/upperHull32.cpp")
+add_executable(upperhull32 ${SOURCES})
+file(GLOB SOURCES "examples/upperhull/upperHull64.cpp")
+add_executable(upperhull64 ${SOURCES})
+file(GLOB SOURCES "examples/upperhull/upperHullExtras.cpp")
+add_executable(upperhullextras ${SOURCES})
+file(GLOB SOURCES "examples/upperhull/generateInputUpperHull.cpp")
+add_executable(generateInputUpperHull ${SOURCES})
 
 
 # Test Run : 8, 16, 32 or 64 bits and the version with extras
diff --git a/README.md b/README.md
index c5b58b4..59985e8 100644
--- a/README.md
+++ b/README.md
@@ -35,7 +35,7 @@ template <class T, class D> void StackAlgo<T, D>::run() {
 }
 ```
 ## Use case
-Concrete examples such as a basic test run and the convex hull problem can be found in the [wiki](https://github.com/Azzaare/CompressedStacks.cpp/wiki).
+Concrete examples such as a basic test run and the upper hull problems can be found in the [wiki](https://github.com/Azzaare/CompressedStacks.cpp/wiki).
 
 ### Abstract example : ```Instance<T,D,I>```
 <p>An instance of a Stack Algorithm is described by a set of templates parameters T, D, and I and a set of methods used in the run function above.</p>
diff --git a/examples/convexhull/generateInputConvexHull.cpp b/examples/upperhull/generateInputUpperHull.cpp
similarity index 97%
rename from examples/convexhull/generateInputConvexHull.cpp
rename to examples/upperhull/generateInputUpperHull.cpp
index cf23c7a..3b24a8c 100644
--- a/examples/convexhull/generateInputConvexHull.cpp
+++ b/examples/upperhull/generateInputUpperHull.cpp
@@ -44,7 +44,7 @@ int main(int argc, char *argv[]) {
   std::uint_least64_t i = 0;
   while (i < n) {
 
-    // create output for the convex hull problem.
+    // create output for the upper hull problem.
     // in this case, max and min stand for the maximum and minimum values of x
     // and y
     // generate a random point in the (min,max)2 range
diff --git a/examples/convexhull/include/point2D.hpp b/examples/upperhull/include/point2D.hpp
similarity index 100%
rename from examples/convexhull/include/point2D.hpp
rename to examples/upperhull/include/point2D.hpp
diff --git a/examples/convexhull/include/convexHull.hpp b/examples/upperhull/include/upperHull.hpp
similarity index 78%
rename from examples/convexhull/include/convexHull.hpp
rename to examples/upperhull/include/upperHull.hpp
index 90fbf2c..608d672 100644
--- a/examples/convexhull/include/convexHull.hpp
+++ b/examples/upperhull/include/upperHull.hpp
@@ -1,6 +1,6 @@
-// ConvexHull : Definition
-#ifndef CONVEXHULL
-#define CONVEXHULL
+// UpperHull : Definition
+#ifndef UPPERHULL
+#define UPPERHULL
 
 /*==============================================================================
   Includes
@@ -20,9 +20,9 @@ class emptyContext {};
   Instantiation of a problem
 ==============================================================================*/
 template <class I>
-class ConvexHull : public StackAlgo<emptyContext, Point2D, I> {
+class UpperHull : public StackAlgo<emptyContext, Point2D, I> {
 public:
-  ConvexHull(std::string filePath)
+  UpperHull(std::string filePath)
       : StackAlgo<emptyContext, Point2D, I>(filePath) {}
 
 private:
@@ -58,7 +58,7 @@ class ConvexHull : public StackAlgo<emptyContext, Point2D, I> {
     * reportStack
 ==============================================================================*/
 template <class I>
-Point2D ConvexHull<I>::readInput(std::vector<std::string> line) {
+Point2D UpperHull<I>::readInput(std::vector<std::string> line) {
   double x = std::stof(line[0]);
   double y = std::stof(line[1]);
 
@@ -68,7 +68,7 @@ Point2D ConvexHull<I>::readInput(std::vector<std::string> line) {
   return p;
 }
 
-template <class I> std::shared_ptr<emptyContext> ConvexHull<I>::initStack() {
+template <class I> std::shared_ptr<emptyContext> UpperHull<I>::initStack() {
 
   std::cout << "going to read two values " << std::endl;
 
@@ -82,7 +82,7 @@ template <class I> std::shared_ptr<emptyContext> ConvexHull<I>::initStack() {
   return context;
 }
 
-template <class I> bool ConvexHull<I>::popCondition(Point2D last) {
+template <class I> bool UpperHull<I>::popCondition(Point2D last) {
   Point2D minus1, minus2;
   total++;
   std::cout << std::endl << last << " <<<< pop condition enter " << std::endl;
@@ -114,26 +114,26 @@ template <class I> bool ConvexHull<I>::popCondition(Point2D last) {
 
   return false;
 }
-template <class I> void ConvexHull<I>::prePop(Point2D data) {}
+template <class I> void UpperHull<I>::prePop(Point2D data) {}
 template <class I>
-void ConvexHull<I>::postPop(Point2D data, Data<emptyContext, Point2D, I> elt) {
+void UpperHull<I>::postPop(Point2D data, Data<emptyContext, Point2D, I> elt) {
   std::cout << elt.getData() << " <<<< (post-)Pop!" << std::endl;
 }
-template <class I> void ConvexHull<I>::noPop(Point2D data) {}
+template <class I> void UpperHull<I>::noPop(Point2D data) {}
 
-template <class I> bool ConvexHull<I>::pushCondition(Point2D data) {
+template <class I> bool UpperHull<I>::pushCondition(Point2D data) {
   std::cout << data << " <<<< push condition returning true " << std::endl;
   return true;
 }
 template <class I>
-void ConvexHull<I>::prePush(Data<emptyContext, Point2D, I> elt) {}
+void UpperHull<I>::prePush(Data<emptyContext, Point2D, I> elt) {}
 template <class I>
-void ConvexHull<I>::postPush(Data<emptyContext, Point2D, I> elt) {
-  std::cout << "ConvexHullStackAlgo::pushAction Nothing to see here "
+void UpperHull<I>::postPush(Data<emptyContext, Point2D, I> elt) {
+  std::cout << "UpperHullStackAlgo::pushAction Nothing to see here "
             << elt.getData() << std::endl;
 }
-template <class I> void ConvexHull<I>::noPush(Point2D data) {}
+template <class I> void UpperHull<I>::noPush(Point2D data) {}
 
-template <class I> void ConvexHull<I>::reportStack() {}
+template <class I> void UpperHull<I>::reportStack() {}
 
-#endif // CONVEXHULL
+#endif // UPPERHULL
diff --git a/examples/convexhull/include/convexHullExtras.hpp b/examples/upperhull/include/upperHullExtras.hpp
similarity index 74%
rename from examples/convexhull/include/convexHullExtras.hpp
rename to examples/upperhull/include/upperHullExtras.hpp
index 01c7966..1de1233 100644
--- a/examples/convexhull/include/convexHullExtras.hpp
+++ b/examples/upperhull/include/upperHullExtras.hpp
@@ -1,6 +1,6 @@
-// ConvexHull : Definition
-#ifndef CONVEXHULLEXTRAS
-#define CONVEXHULLEXTRAS
+// UpperHull : Definition
+#ifndef UPPERHULLEXTRAS
+#define UPPERHULLEXTRAS
 
 /*==============================================================================
   Includes
@@ -18,9 +18,9 @@ class emptyContext {};
 ==============================================================================*/
 
 template <class I>
-class ConvexHullExtras : public StackAlgoExtras<emptyContext, Point2D, I> {
+class UpperHullExtras : public StackAlgoExtras<emptyContext, Point2D, I> {
 public:
-  ConvexHullExtras(std::string filePath, bool usecompressed, bool useclassic)
+  UpperHullExtras(std::string filePath, bool usecompressed, bool useclassic)
       : StackAlgoExtras<emptyContext, Point2D, I>(filePath, usecompressed,
                                                   useclassic) {}
 
@@ -57,7 +57,7 @@ class ConvexHullExtras : public StackAlgoExtras<emptyContext, Point2D, I> {
     * reportStack
 ==============================================================================*/
 template <class I>
-Point2D ConvexHullExtras<I>::readInput(std::vector<std::string> line) {
+Point2D UpperHullExtras<I>::readInput(std::vector<std::string> line) {
   double x = std::stof(line[0]);
   double y = std::stof(line[1]);
 
@@ -69,7 +69,7 @@ Point2D ConvexHullExtras<I>::readInput(std::vector<std::string> line) {
 }
 
 template <class I>
-std::shared_ptr<emptyContext> ConvexHullExtras<I>::initStack() {
+std::shared_ptr<emptyContext> UpperHullExtras<I>::initStack() {
   // std::cout << "going to read two values " << std::endl;
 
   // first, read and push two values
@@ -85,7 +85,7 @@ std::shared_ptr<emptyContext> ConvexHullExtras<I>::initStack() {
   return context;
 }
 
-template <class I> bool ConvexHullExtras<I>::popCondition(Point2D last) {
+template <class I> bool UpperHullExtras<I>::popCondition(Point2D last) {
   Point2D minus1, minus2;
   std::cout << std::endl << last << " <<<< pop condition enter " << std::endl;
   StackAlgo<emptyContext, Point2D, I>::println();
@@ -103,27 +103,27 @@ template <class I> bool ConvexHullExtras<I>::popCondition(Point2D last) {
 
   return false;
 }
-template <class I> void ConvexHullExtras<I>::prePop(Point2D data) {}
+template <class I> void UpperHullExtras<I>::prePop(Point2D data) {}
 template <class I>
-void ConvexHullExtras<I>::postPop(Point2D data,
-                                  Data<emptyContext, Point2D, I> elt) {
+void UpperHullExtras<I>::postPop(Point2D data,
+                                 Data<emptyContext, Point2D, I> elt) {
   // std::cout << elt.getData() << " <<<< Pop!" << std::endl;
 }
-template <class I> void ConvexHullExtras<I>::noPop(Point2D data) {}
+template <class I> void UpperHullExtras<I>::noPop(Point2D data) {}
 
-template <class I> bool ConvexHullExtras<I>::pushCondition(Point2D data) {
+template <class I> bool UpperHullExtras<I>::pushCondition(Point2D data) {
   // std::cout << data << " <<<< push condition returning true " << std::endl;
   return true;
 }
 template <class I>
-void ConvexHullExtras<I>::prePush(Data<emptyContext, Point2D, I> elt) {}
+void UpperHullExtras<I>::prePush(Data<emptyContext, Point2D, I> elt) {}
 template <class I>
-void ConvexHullExtras<I>::postPush(Data<emptyContext, Point2D, I> elt) {
-  // std::cout << "ConvexHullStackAlgo::pushAction Nothing to see here " <<
+void UpperHullExtras<I>::postPush(Data<emptyContext, Point2D, I> elt) {
+  // std::cout << "UpperHullStackAlgo::pushAction Nothing to see here " <<
   // elt.getData() << std::endl;
 }
-template <class I> void ConvexHullExtras<I>::noPush(Point2D data) {}
+template <class I> void UpperHullExtras<I>::noPush(Point2D data) {}
 
-template <class I> void ConvexHullExtras<I>::reportStack() {}
+template <class I> void UpperHullExtras<I>::reportStack() {}
 
-#endif // CONVEXHULLEXTRAS
+#endif // UPPERHULLEXTRAS
diff --git a/examples/convexhull/instances/testFileConvexHull1000p50.txt b/examples/upperhull/instances/testFileUpperHull1000p50.txt
similarity index 100%
rename from examples/convexhull/instances/testFileConvexHull1000p50.txt
rename to examples/upperhull/instances/testFileUpperHull1000p50.txt
diff --git a/examples/convexhull/convexHull32.cpp b/examples/upperhull/upperHull16.cpp
similarity index 71%
rename from examples/convexhull/convexHull32.cpp
rename to examples/upperhull/upperHull16.cpp
index fd59c98..16ea05d 100644
--- a/examples/convexhull/convexHull32.cpp
+++ b/examples/upperhull/upperHull16.cpp
@@ -1,19 +1,19 @@
-// ConvexHull : Implementation
+// UpperHull : Implementation
 
 /*==============================================================================
   Includes
 ==============================================================================*/
-#include "include/convexHull.hpp"
+#include "include/upperHull.hpp"
 #include <cstdint>
 
 /*==============================================================================
   Type alias for the different integer size (based on the size of the input)
 ==============================================================================*/
 
-// using ConvexHull8 = ConvexHull<std::uint_least8_t>;
-// using ConvexHull16 = ConvexHull<std::uint_least16_t>;
-using ConvexHull32 = ConvexHull<std::uint_least32_t>;
-// using ConvexHull64 = ConvexHull<std::uint_least64_t>;
+// using UpperHull8 = UpperHull<std::uint_least8_t>;
+using UpperHull16 = UpperHull<std::uint_least16_t>;
+// using UpperHull32 = UpperHull<std::uint_least32_t>;
+// using UpperHull64 = UpperHull<std::uint_least64_t>;
 
 /*==============================================================================
   How to use
@@ -23,7 +23,7 @@ int main(int argc, char *argv[]) {
   // Getting the path of the instance to test
   std::string filepath = argv[1];
 
-  ConvexHull32 stack(filepath);
+  UpperHull16 stack(filepath);
   stack.run();
   // stack.println();
 
diff --git a/examples/convexhull/convexHull8.cpp b/examples/upperhull/upperHull32.cpp
similarity index 69%
rename from examples/convexhull/convexHull8.cpp
rename to examples/upperhull/upperHull32.cpp
index 409d1f6..68bf09f 100644
--- a/examples/convexhull/convexHull8.cpp
+++ b/examples/upperhull/upperHull32.cpp
@@ -1,19 +1,19 @@
-// ConvexHull : Implementation
+// UpperHull : Implementation
 
 /*==============================================================================
   Includes
 ==============================================================================*/
-#include "include/convexHull.hpp"
+#include "include/upperHull.hpp"
 #include <cstdint>
 
 /*==============================================================================
   Type alias for the different integer size (based on the size of the input)
 ==============================================================================*/
 
-using ConvexHull8 = ConvexHull<std::uint_least8_t>;
-// using ConvexHull16 = ConvexHull<std::uint_least16_t>;
-// using ConvexHull32 = ConvexHull<std::uint_least32_t>;
-// using ConvexHull64 = ConvexHull<std::uint_least64_t>;
+// using UpperHull8 = UpperHull<std::uint_least8_t>;
+// using UpperHull16 = UpperHull<std::uint_least16_t>;
+using UpperHull32 = UpperHull<std::uint_least32_t>;
+// using UpperHull64 = UpperHull<std::uint_least64_t>;
 
 /*==============================================================================
   How to use
@@ -23,9 +23,9 @@ int main(int argc, char *argv[]) {
   // Getting the path of the instance to test
   std::string filepath = argv[1];
 
-  ConvexHull8 stack(filepath);
+  UpperHull32 stack(filepath);
   stack.run();
-  //stack.println();
+  // stack.println();
 
   return 0;
 }
diff --git a/examples/convexhull/convexHull16.cpp b/examples/upperhull/upperHull64.cpp
similarity index 69%
rename from examples/convexhull/convexHull16.cpp
rename to examples/upperhull/upperHull64.cpp
index 2a711c4..650a528 100644
--- a/examples/convexhull/convexHull16.cpp
+++ b/examples/upperhull/upperHull64.cpp
@@ -1,19 +1,19 @@
-// ConvexHull : Implementation
+// UpperHull : Implementation
 
 /*==============================================================================
   Includes
 ==============================================================================*/
-#include "include/convexHull.hpp"
+#include "include/upperHull.hpp"
 #include <cstdint>
 
 /*==============================================================================
   Type alias for the different integer size (based on the size of the input)
 ==============================================================================*/
 
-// using ConvexHull8 = ConvexHull<std::uint_least8_t>;
-using ConvexHull16 = ConvexHull<std::uint_least16_t>;
-// using ConvexHull32 = ConvexHull<std::uint_least32_t>;
-// using ConvexHull64 = ConvexHull<std::uint_least64_t>;
+// using UpperHull8 = UpperHull<std::uint_least8_t>;
+// using UpperHull16 = UpperHull<std::uint_least16_t>;
+// using UpperHull32 = UpperHull<std::uint_least32_t>;
+using UpperHull64 = UpperHull<std::uint_least64_t>;
 
 /*==============================================================================
   How to use
@@ -23,9 +23,9 @@ int main(int argc, char *argv[]) {
   // Getting the path of the instance to test
   std::string filepath = argv[1];
 
-  ConvexHull16 stack(filepath);
+  UpperHull64 stack(filepath);
   stack.run();
-  //stack.println();
+  // stack.println();
 
   return 0;
 }
diff --git a/examples/convexhull/convexHull64.cpp b/examples/upperhull/upperHull8.cpp
similarity index 69%
rename from examples/convexhull/convexHull64.cpp
rename to examples/upperhull/upperHull8.cpp
index b61126f..5f35510 100644
--- a/examples/convexhull/convexHull64.cpp
+++ b/examples/upperhull/upperHull8.cpp
@@ -1,19 +1,19 @@
-// ConvexHull : Implementation
+// UpperHull : Implementation
 
 /*==============================================================================
   Includes
 ==============================================================================*/
-#include "include/convexHull.hpp"
+#include "include/upperHull.hpp"
 #include <cstdint>
 
 /*==============================================================================
   Type alias for the different integer size (based on the size of the input)
 ==============================================================================*/
 
-// using ConvexHull8 = ConvexHull<std::uint_least8_t>;
-// using ConvexHull16 = ConvexHull<std::uint_least16_t>;
-// using ConvexHull32 = ConvexHull<std::uint_least32_t>;
-using ConvexHull64 = ConvexHull<std::uint_least64_t>;
+using UpperHull8 = UpperHull<std::uint_least8_t>;
+// using UpperHull16 = UpperHull<std::uint_least16_t>;
+// using UpperHull32 = UpperHull<std::uint_least32_t>;
+// using UpperHull64 = UpperHull<std::uint_least64_t>;
 
 /*==============================================================================
   How to use
@@ -23,9 +23,9 @@ int main(int argc, char *argv[]) {
   // Getting the path of the instance to test
   std::string filepath = argv[1];
 
-  ConvexHull64 stack(filepath);
+  UpperHull8 stack(filepath);
   stack.run();
-  //stack.println();
+  // stack.println();
 
   return 0;
 }
diff --git a/examples/convexhull/convexHullExtras.cpp b/examples/upperhull/upperHullExtras.cpp
similarity index 77%
rename from examples/convexhull/convexHullExtras.cpp
rename to examples/upperhull/upperHullExtras.cpp
index 042772c..4fc342c 100644
--- a/examples/convexhull/convexHullExtras.cpp
+++ b/examples/upperhull/upperHullExtras.cpp
@@ -1,19 +1,19 @@
-// ConvexHull : Implementation
+// UpperHull : Implementation
 
 /*==============================================================================
   Includes
 ==============================================================================*/
-#include "include/convexHullExtras.hpp"
+#include "include/upperHullExtras.hpp"
 #include <cstdint>
 
 /*==============================================================================
   Type alias for the different integer size (based on the size of the input)
 ==============================================================================*/
 
-using ConvexHullExtras8 = ConvexHullExtras<std::uint_least8_t>;
-using ConvexHullExtras16 = ConvexHullExtras<std::uint_least16_t>;
-using ConvexHullExtras32 = ConvexHullExtras<std::uint_least32_t>;
-using ConvexHullExtras64 = ConvexHullExtras<std::uint_least64_t>;
+using UpperHullExtras8 = UpperHullExtras<std::uint_least8_t>;
+using UpperHullExtras16 = UpperHullExtras<std::uint_least16_t>;
+using UpperHullExtras32 = UpperHullExtras<std::uint_least32_t>;
+using UpperHullExtras64 = UpperHullExtras<std::uint_least64_t>;
 
 /*==============================================================================
   How to use
@@ -56,46 +56,46 @@ int main(int argc, char *argv[]) {
 
   switch (atoi(argv[3])) {
   case 8: {
-    ConvexHullExtras8 stack(filepath, usecompressed, useclassic);
+    UpperHullExtras8 stack(filepath, usecompressed, useclassic);
     if (usecompressed && useclassic) {
       stack.runCompare();
       stack.printCompare();
     } else {
       stack.run();
-      //stack.println();
+      // stack.println();
     }
     break;
   }
   case 16: {
-    ConvexHullExtras16 stack(filepath, usecompressed, useclassic);
+    UpperHullExtras16 stack(filepath, usecompressed, useclassic);
     if (usecompressed && useclassic) {
       stack.runCompare();
       stack.printCompare();
     } else {
       stack.run();
-      //stack.println();
+      // stack.println();
     }
     break;
   }
   case 32: {
-    ConvexHullExtras32 stack(filepath, usecompressed, useclassic);
+    UpperHullExtras32 stack(filepath, usecompressed, useclassic);
     if (usecompressed && useclassic) {
       stack.runCompare();
       stack.printCompare();
     } else {
       stack.run();
-      //stack.println();
+      // stack.println();
     }
     break;
   }
   default:
-    ConvexHullExtras64 stack(filepath, usecompressed, useclassic);
+    UpperHullExtras64 stack(filepath, usecompressed, useclassic);
     if (usecompressed && useclassic) {
       stack.runCompare();
       stack.printCompare();
     } else {
       stack.run();
-      //stack.println();
+      // stack.println();
     }
   }
 
diff --git a/include/compressedStack.hpp b/include/compressedStack.hpp
index df73004..a86adce 100644
--- a/include/compressedStack.hpp
+++ b/include/compressedStack.hpp
@@ -82,6 +82,7 @@ class CompressedStack : public Stack<T, D, I> {
   /* Push related */
   void pushExplicit(SPData<T, D, I> elt);
   void pushCompressed(SPData<T, D, I> elt, std::intmax_t lvl, I headIndex);
+  // TODO: Check if compress is used
   void compress(Level<T, D, I> block);
   void resetLevel(Block<T, D, I> block, std::intmax_t lvl);
 
@@ -771,6 +772,7 @@ void CompressedStack<T, D, I>::popBuffer() {
   }
 }
 
+// TODO: erase problem from signature
 template <class T, class D, class I>
 SPData<T, D, I>
 CompressedStack<T, D, I>::popExplicit(StackAlgo<T, D, I> &problem,