Index: include/polly/DependenceInfo.h
===================================================================
--- include/polly/DependenceInfo.h
+++ include/polly/DependenceInfo.h
@@ -76,20 +76,17 @@
   /// connect all instances of a reduction with each other, they are therefore
   /// cyclic and possibly "reversed".
   enum Type {
-    // Write after read
-    TYPE_WAR = 1 << 0,
-
     // Read after write
-    TYPE_RAW = 1 << 1,
+    TYPE_RAW = 1 << 0,
 
-    // Write after write
-    TYPE_WAW = 1 << 2,
+    // False dependences (write after write / write after read)
+    TYPE_FALSE = 1 << 2,
 
     // Reduction dependences
-    TYPE_RED = 1 << 3,
+    TYPE_RED = 1 << 1,
 
     // Transitive closure of the reduction dependences (& the reverse)
-    TYPE_TC_RED = 1 << 4,
+    TYPE_TC_RED = 1 << 3,
   };
 
   /// Get the dependences of type @p Kinds.
@@ -158,8 +155,8 @@
   /// Create an empty dependences struct.
   explicit Dependences(const std::shared_ptr<isl_ctx> &IslCtx,
                        AnalysisLevel Level)
-      : RAW(nullptr), WAR(nullptr), WAW(nullptr), RED(nullptr), TC_RED(nullptr),
-        IslCtx(IslCtx), Level(Level) {}
+      : RAW(nullptr), WAR(nullptr), WAW(nullptr), False(nullptr), RED(nullptr),
+        TC_RED(nullptr), IslCtx(IslCtx), Level(Level) {}
 
   /// Calculate and add at the privatization dependences.
   void addPrivatizationDependences();
@@ -179,6 +176,7 @@
   isl_union_map *RAW;
   isl_union_map *WAR;
   isl_union_map *WAW;
+  isl_union_map *False;
 
   /// The special reduction dependences.
   isl_union_map *RED;
Index: lib/Analysis/DependenceInfo.cpp
===================================================================
--- lib/Analysis/DependenceInfo.cpp
+++ lib/Analysis/DependenceInfo.cpp
@@ -424,7 +424,7 @@
     isl_union_map_free(RAW);
     isl_union_map_free(WAW);
     isl_union_map_free(WAR);
-    RAW = WAW = WAR = nullptr;
+    RAW = WAW = WAR = False = nullptr;
     isl_ctx_reset_error(IslCtx.get());
   }
 
@@ -435,6 +435,8 @@
     RED = isl_union_map_empty(isl_union_map_get_space(RAW));
     TC_RED = isl_union_map_empty(isl_union_set_get_space(TaggedStmtDomain));
     isl_union_set_free(TaggedStmtDomain);
+    False =
+        isl_union_map_union(isl_union_map_copy(WAW), isl_union_map_copy(WAR));
     return;
   }
 
@@ -569,6 +571,7 @@
   WAR = isl_union_map_coalesce(WAR);
   RED = isl_union_map_coalesce(RED);
   TC_RED = isl_union_map_coalesce(TC_RED);
+  False = isl_union_map_union(isl_union_map_copy(WAW), isl_union_map_copy(WAR));
 
   DEBUG(dump());
 }
@@ -578,7 +581,7 @@
   if (LegalityCheckDisabled)
     return true;
 
-  isl_union_map *Dependences = getDependences(TYPE_RAW | TYPE_WAW | TYPE_WAR);
+  isl_union_map *Dependences = getDependences(TYPE_RAW | TYPE_FALSE);
   isl_space *Space = S.getParamSpace();
   isl_union_map *Schedule = isl_union_map_empty(Space);
 
@@ -698,6 +701,8 @@
   printDependencyMap(OS, RED);
   OS << "\tTransitive closure of reduction dependences:\n\t\t";
   printDependencyMap(OS, TC_RED);
+  OS << "\tFalse dependences:\n\t\t";
+  printDependencyMap(OS, False);
 }
 
 void Dependences::dump() const { print(dbgs()); }
@@ -706,10 +711,11 @@
   isl_union_map_free(RAW);
   isl_union_map_free(WAR);
   isl_union_map_free(WAW);
+  isl_union_map_free(False);
   isl_union_map_free(RED);
   isl_union_map_free(TC_RED);
 
-  RED = RAW = WAR = WAW = TC_RED = nullptr;
+  RED = RAW = WAR = WAW = TC_RED = False = nullptr;
 
   for (auto &ReductionDeps : ReductionDependences)
     isl_map_free(ReductionDeps.second);
@@ -724,11 +730,9 @@
   if (Kinds & TYPE_RAW)
     Deps = isl_union_map_union(Deps, isl_union_map_copy(RAW));
 
-  if (Kinds & TYPE_WAR)
-    Deps = isl_union_map_union(Deps, isl_union_map_copy(WAR));
-
-  if (Kinds & TYPE_WAW)
-    Deps = isl_union_map_union(Deps, isl_union_map_copy(WAW));
+  if (Kinds & TYPE_FALSE) {
+    Deps = isl_union_map_union(Deps, isl_union_map_copy(False));
+  }
 
   if (Kinds & TYPE_RED)
     Deps = isl_union_map_union(Deps, isl_union_map_copy(RED));
Index: lib/Analysis/PolyhedralInfo.cpp
===================================================================
--- lib/Analysis/PolyhedralInfo.cpp
+++ lib/Analysis/PolyhedralInfo.cpp
@@ -81,9 +81,8 @@
     return false;
   DEBUG(dbgs() << "Loop :\t" << L->getHeader()->getName() << ":\n");
 
-  isl_union_map *Deps =
-      D.getDependences(Dependences::TYPE_RAW | Dependences::TYPE_WAW |
-                       Dependences::TYPE_WAR | Dependences::TYPE_RED);
+  isl_union_map *Deps = D.getDependences(
+      Dependences::TYPE_RAW | Dependences::TYPE_FALSE | Dependences::TYPE_RED);
   DEBUG(dbgs() << "Dependences :\t" << stringFromIslObj(Deps) << "\n");
 
   isl_union_map *Schedule = getScheduleForLoop(S, L);
Index: lib/CodeGen/IslAst.cpp
===================================================================
--- lib/CodeGen/IslAst.cpp
+++ lib/CodeGen/IslAst.cpp
@@ -182,8 +182,8 @@
     return false;
 
   isl_union_map *Schedule = isl_ast_build_get_schedule(Build);
-  isl_union_map *Deps = D->getDependences(
-      Dependences::TYPE_RAW | Dependences::TYPE_WAW | Dependences::TYPE_WAR);
+  isl_union_map *Deps =
+      D->getDependences(Dependences::TYPE_RAW | Dependences::TYPE_FALSE);
 
   if (!D->isParallel(Schedule, Deps, &NodeInfo->MinimalDependenceDistance) &&
       !isl_union_map_free(Schedule))
Index: lib/Transform/ScheduleOptimizer.cpp
===================================================================
--- lib/Transform/ScheduleOptimizer.cpp
+++ lib/Transform/ScheduleOptimizer.cpp
@@ -781,13 +781,9 @@
 ///         and false, otherwise.
 static bool containsOnlyMatMulDep(__isl_keep isl_map *Schedule,
                                   const Dependences *D, int &Pos) {
-  auto *WAR = D->getDependences(Dependences::TYPE_WAR);
-  if (!isl_union_map_is_empty(WAR)) {
-    isl_union_map_free(WAR);
-    return false;
-  }
-  isl_union_map_free(WAR);
-  auto *Dep = D->getDependences(Dependences::TYPE_RAW);
+
+  auto *Dep =
+      D->getDependences(Dependences::TYPE_RAW | Dependences::TYPE_FALSE);
   auto *Red = D->getDependences(Dependences::TYPE_RED);
   if (Red)
     Dep = isl_union_map_union(Dep, Red);
@@ -1421,20 +1417,17 @@
   LastSchedule = nullptr;
 
   // Build input data.
-  int ValidityKinds =
-      Dependences::TYPE_RAW | Dependences::TYPE_WAR | Dependences::TYPE_WAW;
+  int ValidityKinds = Dependences::TYPE_RAW | Dependences::TYPE_FALSE;
   int ProximityKinds;
 
   if (OptimizeDeps == "all")
-    ProximityKinds =
-        Dependences::TYPE_RAW | Dependences::TYPE_WAR | Dependences::TYPE_WAW;
+    ProximityKinds = Dependences::TYPE_RAW | Dependences::TYPE_FALSE;
   else if (OptimizeDeps == "raw")
     ProximityKinds = Dependences::TYPE_RAW;
   else {
     errs() << "Do not know how to optimize for '" << OptimizeDeps << "'"
            << " Falling back to optimizing all dependences.\n";
-    ProximityKinds =
-        Dependences::TYPE_RAW | Dependences::TYPE_WAR | Dependences::TYPE_WAW;
+    ProximityKinds = Dependences::TYPE_RAW | Dependences::TYPE_FALSE;
   }
 
   isl_union_set *Domain = S.getDomains();