diff --git a/mlir/include/mlir/Analysis/AffineStructures.h b/mlir/include/mlir/Analysis/AffineStructures.h
--- a/mlir/include/mlir/Analysis/AffineStructures.h
+++ b/mlir/include/mlir/Analysis/AffineStructures.h
@@ -432,7 +432,8 @@
 
   /// Merge local ids of `this` and `other`. This is done by appending local ids
   /// of `other` to `this` and inserting local ids of `this` to `other` at start
-  /// of its local ids.
+  /// of its local ids. Number of dimension and symbol ids should match in
+  /// `this` and `other`.
   void mergeLocalIds(FlatAffineConstraints &other);
 
   /// Removes all equalities and inequalities.
diff --git a/mlir/lib/Analysis/AffineAnalysis.cpp b/mlir/lib/Analysis/AffineAnalysis.cpp
--- a/mlir/lib/Analysis/AffineAnalysis.cpp
+++ b/mlir/lib/Analysis/AffineAnalysis.cpp
@@ -455,8 +455,8 @@
 
   // Append domain constraints to `ret`.
   domainRel.appendRangeId(rel.getNumRangeDims());
-  domainRel.mergeLocalIds(rel);
   domainRel.mergeSymbolIds(rel);
+  domainRel.mergeLocalIds(rel);
   rel.append(domainRel);
 
   return success();
diff --git a/mlir/lib/Analysis/AffineStructures.cpp b/mlir/lib/Analysis/AffineStructures.cpp
--- a/mlir/lib/Analysis/AffineStructures.cpp
+++ b/mlir/lib/Analysis/AffineStructures.cpp
@@ -512,9 +512,6 @@
                      b->getMaybeValues().begin() + b->getNumDimAndSymbolIds(),
                      [](Optional<Value> id) { return id.hasValue(); }));
 
-  // Bring A and B to common local space
-  a->mergeLocalIds(*b);
-
   SmallVector<Value, 4> aDimValues;
   a->getValues(offset, a->getNumDimIds(), &aDimValues);
 
@@ -543,6 +540,8 @@
 
   // Merge and align symbols of A and B
   a->mergeSymbolIds(*b);
+  // Merge and align local ids of A and B
+  a->mergeLocalIds(*b);
 
   assert(areIdsAligned(*a, *b) && "IDs expected to be aligned");
 }
@@ -1875,8 +1874,13 @@
 
 /// Merge local ids of `this` and `other`. This is done by appending local ids
 /// of `other` to `this` and inserting local ids of `this` to `other` at start
-/// of its local ids.
+/// of its local ids. Number of dimension and symbol ids should match in
+/// `this` and `other`.
 void FlatAffineConstraints::mergeLocalIds(FlatAffineConstraints &other) {
+  assert(getNumDimIds() == other.getNumDimIds() &&
+         "Number of dimension ids should match");
+  assert(getNumSymbolIds() == other.getNumSymbolIds() &&
+         "Number of symbol ids should match");
   unsigned initLocals = getNumLocalIds();
   insertLocalId(getNumLocalIds(), other.getNumLocalIds());
   other.insertLocalId(0, initLocals);
@@ -3665,15 +3669,32 @@
          "Domain of this and range of other do not match");
 
   FlatAffineRelation rel = other;
+
+  // Convert `rel` from
+  //    [otherDomain] -> [otherRange]
+  // to
+  //    [otherDomain] -> [otherRange thisRange]
+  // and `this` from
+  //    [thisDomain] -> [thisRange]
+  // to
+  //    [otherDomain thisDomain] -> [thisRange].
+  unsigned removeDims = rel.getNumRangeDims();
+  insertDomainId(0, rel.getNumDomainDims());
+  rel.appendRangeId(getNumRangeDims());
+
+  // Merge symbol and local identifiers.
   mergeSymbolIds(rel);
   mergeLocalIds(rel);
 
-  // Convert domain of `this` and range of `rel` to local identifiers.
-  convertDimToLocal(0, getNumDomainDims());
-  rel.convertDimToLocal(rel.getNumDomainDims(), rel.getNumDimIds());
-  // Add dimensions such that both relations become `domainRel -> rangeThis`.
-  appendDomainId(rel.getNumDomainDims());
-  rel.appendRangeId(getNumRangeDims());
+  // Convert `rel` from [otherDomain] -> [otherRange thisRange] to
+  // [otherDomain] -> [thisRange] by converting first otherRange range ids
+  // to local ids.
+  rel.convertDimToLocal(rel.getNumDomainDims(),
+                        rel.getNumDomainDims() + removeDims);
+  // Convert `this` from [otherDomain thisDomain] -> [thisRange] to
+  // [otherDomain] -> [thisRange] by converting last thisDomain domain ids
+  // to local ids.
+  convertDimToLocal(getNumDomainDims() - removeDims, getNumDomainDims());
 
   auto thisMaybeValues = getMaybeDimValues();
   auto relMaybeValues = rel.getMaybeDimValues();