diff --git a/polly/lib/Analysis/ScopInfo.cpp b/polly/lib/Analysis/ScopInfo.cpp
index 951dfc79a4d2..3074a947d37c 100644
--- a/polly/lib/Analysis/ScopInfo.cpp
+++ b/polly/lib/Analysis/ScopInfo.cpp
@@ -747,8 +747,7 @@ void MemoryAccess::dump() const { print(errs()); }
 //
 static isl_map *getEqualAndLarger(isl_space *setDomain) {
   isl_space *Space = isl_space_map_from_set(setDomain);
-  isl_map *Map = isl_map_universe(isl_space_copy(Space));
-  isl_local_space *MapLocalSpace = isl_local_space_from_space(Space);
+  isl_map *Map = isl_map_universe(Space);
   unsigned lastDimension = isl_map_dim(Map, isl_dim_in) - 1;
 
   // Set all but the last dimension to be equal for the input and output
@@ -762,20 +761,8 @@ static isl_map *getEqualAndLarger(isl_space *setDomain) {
   // last dimension of the output.
   //
   //   input[?,?,?,...,iX] -> output[?,?,?,...,oX] : iX < oX
-  //
-  isl_val *v;
-  isl_ctx *Ctx = isl_map_get_ctx(Map);
-  isl_constraint *c = isl_inequality_alloc(isl_local_space_copy(MapLocalSpace));
-  v = isl_val_int_from_si(Ctx, -1);
-  c = isl_constraint_set_coefficient_val(c, isl_dim_in, lastDimension, v);
-  v = isl_val_int_from_si(Ctx, 1);
-  c = isl_constraint_set_coefficient_val(c, isl_dim_out, lastDimension, v);
-  v = isl_val_int_from_si(Ctx, -1);
-  c = isl_constraint_set_constant_val(c, v);
-
-  Map = isl_map_add_constraint(Map, c);
-
-  isl_local_space_free(MapLocalSpace);
+  Map = isl_map_order_lt(Map, isl_dim_in, lastDimension, isl_dim_out,
+                         lastDimension);
   return Map;
 }
 
diff --git a/polly/lib/Transform/ScheduleOptimizer.cpp b/polly/lib/Transform/ScheduleOptimizer.cpp
index f00f431d5909..6bf6718b5f7e 100644
--- a/polly/lib/Transform/ScheduleOptimizer.cpp
+++ b/polly/lib/Transform/ScheduleOptimizer.cpp
@@ -213,17 +213,12 @@ IslScheduleOptimizer::getPrevectorMap(isl_ctx *ctx, int DimToVectorize,
 
   // Create an identity map for everything except DimToVectorize and map
   // DimToVectorize to the point loop at the innermost dimension.
-  for (int i = 0; i < ScheduleDimensions; i++) {
-    c = isl_equality_alloc(isl_local_space_copy(LocalSpace));
-    c = isl_constraint_set_coefficient_si(c, isl_dim_in, i, -1);
-
+  for (int i = 0; i < ScheduleDimensions; i++)
     if (i == DimToVectorize)
-      c = isl_constraint_set_coefficient_si(c, isl_dim_out, PointDimension, 1);
+      TilingMap =
+          isl_map_equate(TilingMap, isl_dim_in, i, isl_dim_out, PointDimension);
     else
-      c = isl_constraint_set_coefficient_si(c, isl_dim_out, i, 1);
-
-    TilingMap = isl_map_add_constraint(TilingMap, c);
-  }
+      TilingMap = isl_map_equate(TilingMap, isl_dim_in, i, isl_dim_out, i);
 
   // it % 'VectorWidth' = 0
   LocalSpaceRange = isl_local_space_range(isl_local_space_copy(LocalSpace));
@@ -236,10 +231,8 @@ IslScheduleOptimizer::getPrevectorMap(isl_ctx *ctx, int DimToVectorize,
   TilingMap = isl_map_intersect_range(TilingMap, Modulo);
 
   // it <= ip
-  c = isl_inequality_alloc(isl_local_space_copy(LocalSpace));
-  isl_constraint_set_coefficient_si(c, isl_dim_out, TileDimension, -1);
-  isl_constraint_set_coefficient_si(c, isl_dim_out, PointDimension, 1);
-  TilingMap = isl_map_add_constraint(TilingMap, c);
+  TilingMap = isl_map_order_le(TilingMap, isl_dim_out, TileDimension,
+                               isl_dim_out, PointDimension);
 
   // ip <= it + ('VectorWidth' - 1)
   c = isl_inequality_alloc(LocalSpace);