diff --git a/svf/include/AE/Core/AbstractState.h b/svf/include/AE/Core/AbstractState.h
index f495ebb8e..21e30ca6f 100644
--- a/svf/include/AE/Core/AbstractState.h
+++ b/svf/include/AE/Core/AbstractState.h
@@ -393,7 +393,7 @@ class AbstractState
             auto it = rhs.find(item.first);
             if (it == rhs.end()) return false;
             // judge from expr id
-            if (item.second.getInterval().geq(it->second.getInterval())) return false;
+            if (item.second.getInterval().contain(it->second.getInterval())) return false;
         }
         return true;
     }
@@ -409,7 +409,8 @@ class AbstractState
             // judge from expr id
             if (it->second.isInterval() && item.second.isInterval())
             {
-                if (!it->second.getInterval().geq(item.second.getInterval()))
+                if (!it->second.getInterval().contain(
+                        item.second.getInterval()))
                     return false;
             }
 
diff --git a/svf/include/AE/Core/IntervalValue.h b/svf/include/AE/Core/IntervalValue.h
index b50dd7300..ba68d1e2e 100644
--- a/svf/include/AE/Core/IntervalValue.h
+++ b/svf/include/AE/Core/IntervalValue.h
@@ -298,8 +298,11 @@ class IntervalValue
         this->_ub = plus_infinity();
     }
 
-    /// Check current IntervalValue is smaller than or equal to the other
-    bool leq(const IntervalValue &other) const
+    /// Determines if the current IntervalValue is fully contained within another IntervalValue.
+    /// Example: this: [2, 3], other: [1, 4] -> returns true
+    /// Note: If the current interval is 'bottom', it is considered contained within any interval.
+    ///       If the other interval is 'bottom', it cannot contain any interval.
+    bool containedWithin(const IntervalValue &other) const
     {
         if (this->isBottom())
         {
@@ -316,8 +319,11 @@ class IntervalValue
 
     }
 
-    /// Check current IntervalValue is greater than or equal to the other
-    bool geq(const IntervalValue &other) const
+    /// Determines if the current IntervalValue fully contains another IntervalValue.
+    /// Example: this: [1, 4], other: [2, 3] -> returns true
+    /// Note: If the current interval is 'bottom', it is considered to contain any interval.
+    ///       If the other interval is 'bottom', it cannot be contained by any interval.
+    bool contain(const IntervalValue &other) const
     {
         if (this->isBottom())
         {
@@ -333,6 +339,38 @@ class IntervalValue
         }
     }
 
+    /// Check the upper bound of this Interval is less than or equal to the lower bound
+    /// e.g. [1, 3] < [3, 5] return true, lhs.ub <= rhs.lb
+    bool leq(const IntervalValue &other) const {
+        if (this->isBottom()) {
+            return true;
+        }
+        else if (other.isBottom())
+        {
+            return false;
+        }
+        else
+        {
+            return this->_ub.leq(other._lb);
+        }
+    }
+
+    /// Check the lower bound of this Interval is greater than or equal to the upper bound
+    /// e.g. [3, 5] > [1, 3] return true, lhs.lb >= rhs.ub
+    bool geq(const IntervalValue &other) const {
+        if (this->isBottom())                {
+            return true;
+        }
+        else if (other.isBottom())
+        {
+            return false;
+        }
+        else
+        {
+            return this->_lb.geq(other._ub);
+        }
+    }
+
 
     /// Equality comparison
     bool equals(const IntervalValue &other) const