diff --git a/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h b/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
--- a/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
+++ b/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
@@ -95,6 +95,10 @@
   /// intersection with no simplification of any sort attempted.
   void append(const IntegerRelation &other);
 
+  /// Return the intersection of the two sets.
+  /// If there are locals, they will be merged.
+  IntegerRelation intersect(IntegerRelation other) const;
+
   /// Return whether `this` and `other` are equal. This is integer-exact
   /// and somewhat expensive, since it uses the integer emptiness check
   /// (see IntegerRelation::findIntegerSample()).
diff --git a/mlir/lib/Analysis/Presburger/IntegerRelation.cpp b/mlir/lib/Analysis/Presburger/IntegerRelation.cpp
--- a/mlir/lib/Analysis/Presburger/IntegerRelation.cpp
+++ b/mlir/lib/Analysis/Presburger/IntegerRelation.cpp
@@ -52,6 +52,13 @@
   }
 }
 
+IntegerRelation IntegerRelation::intersect(IntegerRelation other) const {
+  IntegerRelation result = *this;
+  result.mergeLocalIds(other);
+  result.append(other);
+  return result;
+}
+
 bool IntegerRelation::isEqual(const IntegerRelation &other) const {
   assert(PresburgerLocalSpace::isEqual(other) && "Spaces must be equal.");
   return PresburgerRelation(*this).isEqual(PresburgerRelation(other));
diff --git a/mlir/lib/Analysis/Presburger/PresburgerRelation.cpp b/mlir/lib/Analysis/Presburger/PresburgerRelation.cpp
--- a/mlir/lib/Analysis/Presburger/PresburgerRelation.cpp
+++ b/mlir/lib/Analysis/Presburger/PresburgerRelation.cpp
@@ -97,11 +97,9 @@
                             getNumSymbolIds());
   for (const IntegerRelation &csA : integerRelations) {
     for (const IntegerRelation &csB : set.integerRelations) {
-      IntegerRelation csACopy = csA, csBCopy = csB;
-      csACopy.mergeLocalIds(csBCopy);
-      csACopy.append(csBCopy);
-      if (!csACopy.isEmpty())
-        result.unionInPlace(csACopy);
+      IntegerRelation intersection = csA.intersect(csB);
+      if (!intersection.isEmpty())
+        result.unionInPlace(intersection);
     }
   }
   return result;