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
@@ -128,11 +128,6 @@
   /// 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 +110,9 @@
   /// false otherwise.
   bool isIntegerEmpty() const;
 
+  /// Return true if there is no disjunct, false otherwise.
+  bool isPlainEmpty() const;
+
   /// Return true if the set is known to be the universe set, false otherwise.
   bool isUniverse() const;
 
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
@@ -75,13 +75,6 @@
   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
@@ -97,27 +97,14 @@
 PresburgerRelation::intersect(const PresburgerRelation &set) const {
   assert(space.isCompatible(set.getSpace()) && "Spaces should match");
 
-  if ((getNumDisjuncts() == 0 || set.isUniverse()) &&
-      space.isEqual(set.getSpace()))
+  // When there exists a set that is an empty set or a universe set, just
+  // directly returns another set
+  if (isPlainEmpty() || set.isUniverse())
     return *this;
 
-  if ((set.getNumDisjuncts() == 0 || isUniverse()) &&
-      space.isEqual(set.getSpace()))
+  if (set.isPlainEmpty() || isUniverse())
     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) {
@@ -492,6 +479,9 @@
   return false;
 }
 
+/// Return true if there is no disjunct, false otherwise.
+bool PresburgerRelation::isPlainEmpty() const { return getNumDisjuncts() == 0; }
+
 /// Return true if all the sets in the union are known to be integer empty,
 /// false otherwise.
 bool PresburgerRelation::isIntegerEmpty() const {