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
@@ -128,6 +128,11 @@
   /// If there are locals, they will be merged.
   IntegerRelation intersect(IntegerRelation other) const;
 
+  /// Return the intersection of the two relations by directly adding the
+  /// current relation's constraint to the other relation. This specialized
+  /// version does not perform additional checks or modifications.
+  IntegerRelation intersectAddConstraint(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/include/mlir/Analysis/Presburger/PresburgerRelation.h b/mlir/include/mlir/Analysis/Presburger/PresburgerRelation.h
--- a/mlir/include/mlir/Analysis/Presburger/PresburgerRelation.h
+++ b/mlir/include/mlir/Analysis/Presburger/PresburgerRelation.h
@@ -110,6 +110,13 @@
   /// false otherwise.
   bool isIntegerEmpty() const;
 
+  /// Return true if the set is known to be the universe set, false otherwise.
+  bool isUniverse() const;
+
+  /// Return true if the set is consist of a single disjunct, without any local
+  /// variables, false otherwise.
+  bool isConvexNoLocals() const;
+
   /// Find an integer sample from the given set. This should not be called if
   /// any of the disjuncts in the union are unbounded.
   bool findIntegerSample(SmallVectorImpl<MPInt> &sample);
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
@@ -75,6 +75,13 @@
   return result;
 }
 
+IntegerRelation
+IntegerRelation::intersectAddConstraint(IntegerRelation other) const {
+  IntegerRelation result = *this;
+  result.append(other);
+  return result;
+}
+
 bool IntegerRelation::isEqual(const IntegerRelation &other) const {
   assert(space.isCompatible(other.getSpace()) && "Spaces must be compatible.");
   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
@@ -97,6 +97,27 @@
 PresburgerRelation::intersect(const PresburgerRelation &set) const {
   assert(space.isCompatible(set.getSpace()) && "Spaces should match");
 
+  if ((getNumDisjuncts() == 0 || set.isUniverse()) &&
+      space.isEqual(set.getSpace()))
+    return *this;
+
+  if ((set.getNumDisjuncts() == 0 || isUniverse()) &&
+      space.isEqual(set.getSpace()))
+    return set;
+
+  // Special case, where both relation are convex, without any divs and such
+  // that either one of it contains a single constraint. Simply add constraint
+  // to the other relation.
+  if (isConvexNoLocals() && set.isConvexNoLocals() &&
+      space.isEqual(set.getSpace()) &&
+      (getDisjunct(0).getNumConstraints() == 1 ||
+       set.getDisjunct(0).getNumConstraints() == 1)) {
+    PresburgerRelation result(getSpace());
+    result.unionInPlace(getDisjunct(0));
+    result.getDisjunct(0).intersectAddConstraint(set.getDisjunct(0));
+    return result;
+  }
+
   PresburgerRelation result(getSpace());
   for (const IntegerRelation &csA : disjuncts) {
     for (const IntegerRelation &csB : set.disjuncts) {
@@ -453,6 +474,24 @@
   return this->isSubsetOf(set) && set.isSubsetOf(*this);
 }
 
+/// Return true if the Presburger relation is known to represent the universe
+/// set, false otherwise. A Presburger relation is considered to be the universe
+/// set if it contains at least one disjunct that is unconstrained, i.e., it
+/// does not have any constraints or conditions.
+bool PresburgerRelation::isUniverse() const {
+  for (auto &disjunct : getAllDisjuncts()) {
+    if (disjunct.getNumConstraints() == 0)
+      return true;
+  }
+  return false;
+}
+
+bool PresburgerRelation::isConvexNoLocals() const {
+  if (getNumDisjuncts() == 1 && getSpace().getNumLocalVars() == 0)
+    return true;
+  return false;
+}
+
 /// Return true if all the sets in the union are known to be integer empty,
 /// false otherwise.
 bool PresburgerRelation::isIntegerEmpty() const {