diff --git a/paddle/ir/dialect/shape/ir/shape_op.cc b/paddle/ir/dialect/shape/ir/shape_op.cc
index 3681aafa36520bea1665d3b1d068853f2a44fa8e..776503ea269e3bbcc0dd8047720b8da87a7e63f9 100644
--- a/paddle/ir/dialect/shape/ir/shape_op.cc
+++ b/paddle/ir/dialect/shape/ir/shape_op.cc
@@ -112,6 +112,7 @@ bool SymbolicDim::merge(SymbolicDim other) {
   if (!isDynamic() && !other.isDynamic() && getValue() != other.getValue())
     return false;
   if (isDynamic() && !other.isDynamic()) updateValue(other.getValue());
+  if (!isDynamic() && other.isDynamic()) other.updateValue(getValue());
 
   bool knownNonNegativeFlag =
       getKnownNonNegative() || other.getKnownNonNegative();
diff --git a/paddle/ir/dialect/shape/utils/shape_utils.cc b/paddle/ir/dialect/shape/utils/shape_utils.cc
index 182d335f71c3d4cf3f845ff92b53f78d216625c6..f9d78a63184cb3514014b1f4ad765bda597749d3 100644
--- a/paddle/ir/dialect/shape/utils/shape_utils.cc
+++ b/paddle/ir/dialect/shape/utils/shape_utils.cc
@@ -46,6 +46,154 @@ const std::string SymbolTable::insert(ir::Operation* symbol) {
   return name;
 }
 
+bool SymbolicDimMgr::load() {
+  for (auto op_it = m_.block()->begin(); op_it != m_.block()->end(); op_it++) {
+    symbolTable_.insert(*op_it);
+    SymbolicDim op = (*op_it)->dyn_cast<SymbolicDim>();
+    if (!op) continue;
+    symbolDimUnionSet_[op] = op;
+    symbolNameSet_.insert(op.getSymName());
+  }
+  return loadShapeConstraintGraph();
+}
+
+bool SymbolicDimMgr::loadShapeConstraintGraph() {
+  // TODO(liujinnan): add more constraint function. currently, only support
+  // tie_product_equal.
+  auto constraint_vec =
+      symbolTable_.lookup<ir::dialect::TieProductEqualOp>("tie_product_equal");
+
+  if (!constraint_vec.size()) return true;
+
+  auto build_sym_product = [&](std::vector<ir::Value> range,
+                               SymbolicDimProduct& product) {
+    for (Value v : range) {
+      auto definingOp = v.GetDefiningOp();
+      if (auto constOp = definingOp->dyn_cast<ir::ConstantOp>()) {
+        product.factor *= constOp.value().dyn_cast<ir::Int32Attribute>().data();
+        continue;
+      } else if (auto dimOp = definingOp->dyn_cast<ir::dialect::DimOp>()) {
+        auto sym = symbolTable_.lookup<SymbolicDim>(dimOp.getName());
+        if (!sym) return false;
+        product.symbols.push_back(sym);
+        continue;
+      }
+      return false;
+    }
+    return true;
+  };
+  for (auto op : constraint_vec) {
+    SymbolicDimProduct lhs, rhs;
+    if (!build_sym_product(op.getLhs(), lhs) ||
+        !build_sym_product(op.getRhs(), rhs) ||
+        !mapSymbolicDimProductEqual(lhs, rhs))
+      return false;
+  }
+  return true;
+}
+
+int64_t gcd(int64_t m, int64_t n) {
+  if (!m) return n;
+  if (!n) return m;
+  return (m < n) ? gcd(m, n % m) : gcd(m % n, n);
+}
+
+bool SymbolicDimMgr::mapSymbolicDimProductEqual(const SymbolicDimProduct& lhs,
+                                                const SymbolicDimProduct& rhs) {
+  SymbolicDimProduct newLhs, newRhs;
+  std::tie(newLhs, newRhs) = simplifySymbolicDimProductPair(lhs, rhs);
+
+  // early return for identity case.
+  if (newLhs == newRhs) return true;
+
+  if (newLhs.factor == newRhs.factor && newLhs.symbols.size() == 1 &&
+      newRhs.symbols.size() == 1) {
+    return mapSymbolicDimEqual(newLhs.symbols[0], newRhs.symbols[0]);
+  } else if (newLhs.symbols.size() == 0 && newRhs.symbols.size() == 1 &&
+             newRhs.factor == 1) {
+    return mapSymbolicDimEqual(newConstantSymbolicDim(newLhs.factor),
+                               newRhs.symbols[0]);
+  } else if (newRhs.symbols.size() == 0 && newLhs.symbols.size() == 1 &&
+             newLhs.factor == 1) {
+    return mapSymbolicDimEqual(newConstantSymbolicDim(newRhs.factor),
+                               newLhs.symbols[0]);
+  }
+
+  productEqualityMap_[newLhs][newRhs] = productEqualityMap_[newRhs][newLhs] =
+      true;
+
+  productEqualityMapUpdated_ = false;
+  return true;
+}
+
+std::pair<SymbolicDimProduct, SymbolicDimProduct>
+SymbolicDimMgr::simplifySymbolicDimProductPair(const SymbolicDimProduct& x,
+                                               const SymbolicDimProduct& y) {
+  auto lhs = simplifySymbolicDimProduct(x);
+  auto rhs = simplifySymbolicDimProduct(y);
+
+  SymbolicDimProduct newLhs, newRhs;
+  int64_t gcdFactor = gcd(std::abs(lhs.factor), std::abs(rhs.factor));
+  if (!gcdFactor) return std::make_pair(std::move(newLhs), std::move(newRhs));
+  if (std::abs(lhs.factor) < std::abs(rhs.factor)) {
+    if (lhs.factor < 0) gcdFactor = -gcdFactor;
+  } else {
+    if (rhs.factor < 0) gcdFactor = -gcdFactor;
+  }
+
+  newLhs.factor = lhs.factor / gcdFactor;
+  newRhs.factor = rhs.factor / gcdFactor;
+
+  std::unordered_map<SymbolicDim, int, SymDimHasher> lhsSymbolMap;
+  std::unordered_map<SymbolicDim, int, SymDimHasher> rhsSymbolMap;
+  for (SymbolicDim op : lhs.symbols) ++lhsSymbolMap[op];
+  for (SymbolicDim op : rhs.symbols) ++rhsSymbolMap[op];
+
+  for (SymbolicDim op : lhs.symbols) {
+    auto it = rhsSymbolMap.find(op);
+    if (it != rhsSymbolMap.end() && op.getKnownNonSizeZero()) {
+      if (--it->second == 0) rhsSymbolMap.erase(it);
+      continue;
+    }
+    newLhs.symbols.push_back(op);
+  }
+
+  for (SymbolicDim op : rhs.symbols) {
+    auto it = lhsSymbolMap.find(op);
+    if (it != lhsSymbolMap.end() && op.getKnownNonSizeZero()) {
+      if (--it->second == 0) lhsSymbolMap.erase(it);
+      continue;
+    }
+    newRhs.symbols.push_back(op);
+  }
+
+  if (!newLhs.factor) newLhs.symbols.clear();
+  if (!newRhs.factor) newRhs.symbols.clear();
+
+  return std::make_pair(std::move(newLhs), std::move(newRhs));
+}
+
+SymbolicDimProduct SymbolicDimMgr::simplifySymbolicDimProduct(
+    const SymbolicDimProduct& x) {
+  std::vector<SymbolicDim> copied;
+  copied.reserve(x.symbols.size());
+  for (SymbolicDim op : x.symbols) copied.push_back(getRootSymbolicDim(op));
+
+  sort(copied.begin(), copied.end(), [&](SymbolicDim lhs, SymbolicDim rhs) {
+    return compareSymbolicDimNames(lhs.getSymName(), rhs.getSymName());
+  });
+  SymbolicDimProduct newX;
+  newX.factor = x.factor;
+  for (SymbolicDim op : copied) {
+    if (!op.isDynamic()) {
+      newX.factor *= op.getValue();
+    } else {
+      newX.symbols.push_back(op);
+    }
+  }
+  return newX;
+}
+
 const std::string SymbolicDimMgr::getNextName() {
   std::string name;
   do {
@@ -123,4 +271,154 @@ bool SymbolicDimMgr::mapSymbolicDimEqual(SymbolicDim lhs, SymbolicDim rhs) {
   return true;
 }
 
+SymbolicDimProduct* SymbolicDimMgr::symbolicDimProductDivide(
+    const SymbolicDimProduct& lhs, const SymbolicDimProduct& rhs) {
+  SymbolicDimProduct newLhs, newRhs;
+  std::tie(newLhs, newRhs) = simplifySymbolicDimProductPair(lhs, rhs);
+
+  if (newLhs.factor == 0 || newRhs.factor == 0) return nullptr;
+  if (newLhs.factor % newRhs.factor != 0) return nullptr;
+  if (newLhs.symbols.size() < newRhs.symbols.size()) return nullptr;
+
+  SymbolicDimProduct* result = new SymbolicDimProduct();
+  result->factor = newLhs.factor / newRhs.factor;
+
+  std::unordered_map<SymbolicDim, int, SymDimHasher> symProcMap;
+  for (SymbolicDim sym : newRhs.symbols) ++symProcMap[sym];
+
+  for (SymbolicDim sym : newLhs.symbols) {
+    auto it = symProcMap.find(sym);
+    if (it == symProcMap.end()) {
+      result->symbols.push_back(sym);
+      continue;
+    }
+    if (--it->second == 0) {
+      symProcMap.erase(it);
+      continue;
+    }
+  }
+
+  if (!symProcMap.empty()) return nullptr;
+  return result;
+}
+
+bool SymbolicDimMgr::isMultipleOfKnownSymbolicDimProductEqualPair(
+    const SymbolicDimProduct& lhs, const SymbolicDimProduct& rhs) {
+  for (auto& pairOutter : productEqualityMap_) {
+    const SymbolicDimProduct& x = pairOutter.first;
+    auto factorX = symbolicDimProductDivide(lhs, x);
+    if (!factorX) continue;
+    for (auto& pairInner : pairOutter.second) {
+      if (!pairInner.second) continue;
+      const SymbolicDimProduct& y = pairInner.first;
+      auto factorY = symbolicDimProductDivide(rhs, y);
+      if (!factorY || (*factorX) != (*factorY)) continue;
+      return true;
+    }
+  }
+
+  return false;
+}
+
+bool SymbolicDimMgr::updateProductEqualityMap() {
+  // early return if nothing is updated.
+  if (productEqualityMapUpdated_) return true;
+
+  SymbolicDimProductMap newMap;
+  std::unordered_set<SymbolicDimProduct, SymProductHasher> productSet;
+  for (auto& pairOutter : productEqualityMap_) {
+    const SymbolicDimProduct& x = pairOutter.first;
+    for (auto& pairInner : pairOutter.second) {
+      if (!pairInner.second) continue;
+      const SymbolicDimProduct& y = pairInner.first;
+      SymbolicDimProduct newX, newY;
+      std::tie(newX, newY) = simplifySymbolicDimProductPair(x, y);
+      if (newX == newY) continue;
+      newMap[newX][newY] = newMap[newY][newX] = true;
+      productSet.insert(newX);
+      productSet.insert(newY);
+    }
+  }
+  // hash function of SymbolicDimProduct is expensive, thus we map it to integer
+  // domain first.
+  std::unordered_map<const SymbolicDimProduct*, size_t> symProd2Idx;
+  std::vector<const SymbolicDimProduct*> idx2SymProd(productSet.size());
+  std::vector<size_t> idx2root(productSet.size());
+  for (auto& x : productSet) {
+    size_t idx = symProd2Idx.size();
+    symProd2Idx[&x] = idx;
+    idx2SymProd[idx] = &x;
+    idx2root[idx] = idx;
+  }
+
+  auto getRootIdx = [&](size_t root) {
+    std::vector<size_t> path;
+    while (idx2root[root] != root) {
+      path.push_back(root);
+      root = idx2root[root];
+    }
+    for (size_t idx : path) idx2root[idx] = root;
+    return root;
+  };
+
+  for (size_t x = 0; x < symProd2Idx.size(); ++x) {
+    auto& xProd = *idx2SymProd[x];
+    auto& rowMap = newMap[xProd];
+    size_t xRoot = getRootIdx(x);
+    for (size_t y = x; y < symProd2Idx.size(); ++y) {
+      auto& yProd = *idx2SymProd[y];
+      if (!rowMap[yProd]) continue;
+      idx2root[getRootIdx(y)] = xRoot;
+    }
+  }
+
+  for (size_t x = 0; x < symProd2Idx.size(); ++x)
+    for (size_t y = x; y < symProd2Idx.size(); ++y) {
+      if (getRootIdx(x) != getRootIdx(y)) continue;
+      auto& xSymProd = *idx2SymProd[x];
+      auto& ySymProd = *idx2SymProd[y];
+
+      newMap[xSymProd][ySymProd] = newMap[ySymProd][xSymProd] = true;
+    }
+
+  productEqualityMap_ = std::move(newMap);
+
+  for (auto& x : productSet)
+    for (auto& y : productSet) {
+      if (!productEqualityMap_[x][y]) continue;
+      productEqualityMap_[x][y] = productEqualityMap_[y][x] = false;
+      if (!isMultipleOfKnownSymbolicDimProductEqualPair(x, y)) {
+        productEqualityMap_[x][y] = productEqualityMap_[y][x] = true;
+      }
+    }
+
+  std::unordered_set<SymbolicDimProduct, SymProductHasher> toRemove;
+  for (auto& x : productSet) {
+    if (std::all_of(productSet.begin(),
+                    productSet.end(),
+                    [&](const SymbolicDimProduct& y) {
+                      return !productEqualityMap_[x][y];
+                    })) {
+      toRemove.insert(x);
+    }
+  }
+
+  for (auto& x : toRemove) {
+    productEqualityMap_.erase(x);
+  }
+
+  productEqualityMapUpdated_ = true;
+  return true;
+}
+
+bool SymbolicDimMgr::isSymbolicDimProductEqual(const SymbolicDimProduct& lhs,
+                                               const SymbolicDimProduct& rhs) {
+  SymbolicDimProduct newLhs, newRhs;
+  std::tie(newLhs, newRhs) = simplifySymbolicDimProductPair(lhs, rhs);
+
+  // early return for identity case.
+  if (newLhs == newRhs) return true;
+  IR_ENFORCE(updateProductEqualityMap(), "Update product equality map failed.");
+  return isMultipleOfKnownSymbolicDimProductEqualPair(newLhs, newRhs);
+}
 }  // namespace ir
diff --git a/paddle/ir/dialect/shape/utils/shape_utils.h b/paddle/ir/dialect/shape/utils/shape_utils.h
index 70f2a16c4481e8c30564983249f59210410291e4..8d5fab1a1c811a6978dfcdc8ec4413a7a4bc3b31 100644
--- a/paddle/ir/dialect/shape/utils/shape_utils.h
+++ b/paddle/ir/dialect/shape/utils/shape_utils.h
@@ -18,6 +18,7 @@
 #include <type_traits>
 #include <unordered_map>
 #include <unordered_set>
+#include "paddle/ir/core/builtin_attribute.h"
 #include "paddle/ir/core/builtin_op.h"
 #include "paddle/ir/core/utils.h"
 #include "paddle/ir/dialect/shape/ir/shape_op.h"
@@ -45,7 +46,6 @@ class SymbolTable {
  public:
   explicit SymbolTable(ir::Operation* symbolTableOp)
       : symbolTableOp_(symbolTableOp) {}
-
   template <typename T>
   typename std::enable_if<std::is_same<T, SymbolicDim>::value,
                           SymbolicDim>::type
@@ -97,6 +97,7 @@ struct SymProductHasher {
 class SymbolicDimMgr {
  public:
   explicit SymbolicDimMgr(ir::ModuleOp m);
+  bool load();
   SymbolicDim newSymbolicDim(const std::string& name = {});
   SymbolicDim newConstantSymbolicDim(int64_t val);
   std::vector<SymbolicDim> createSymbolicDimsForRankedValue(Value value);
@@ -104,9 +105,28 @@ class SymbolicDimMgr {
   bool isSymbolicDimEqual(SymbolicDim lhs, SymbolicDim rhs);
   SymbolTable& symbolTable() { return symbolTable_; }
   bool mapSymbolicDimEqual(SymbolicDim lhs, SymbolicDim rhs);
+  SymbolicDimProduct simplifySymbolicDimProduct(const SymbolicDimProduct& x);
+  std::pair<SymbolicDimProduct, SymbolicDimProduct>
+  simplifySymbolicDimProductPair(const SymbolicDimProduct& x,
+                                 const SymbolicDimProduct& y);
+  SymbolicDimProduct* symbolicDimProductDivide(const SymbolicDimProduct& x,
+                                               const SymbolicDimProduct& y);
+
+  bool save();  // TODO(liujinnan): load constraint func
+
+  bool isSymbolicDimProductEqual(const SymbolicDimProduct& lhs,
+                                 const SymbolicDimProduct& rhs);
+  bool mapSymbolicDimProductEqual(const SymbolicDimProduct& lhs,
+                                  const SymbolicDimProduct& rhs);
 
  private:
   const std::string getNextName();
+  bool updateProductEqualityMap();
+  bool isMultipleOfKnownSymbolicDimProductEqualPair(
+      const SymbolicDimProduct& lhs, const SymbolicDimProduct& rhs);
+  bool saveShapeConstraintGraph();  // TODO(liujinnan): load & save
+                                    // shape_constraint_func
+  bool loadShapeConstraintGraph();
 
  private:
   ir::ModuleOp m_;
@@ -127,6 +147,6 @@ class SymbolicDimMgr {
       std::unordered_map<SymbolicDimProduct, bool, SymProductHasher>,
       SymProductHasher>;
   SymbolicDimProductMap productEqualityMap_;
+  bool productEqualityMapUpdated_ = true;
 };
-
 }  // namespace ir
diff --git a/test/cpp/ir/shape_dialect/symbolic_op_test.cc b/test/cpp/ir/shape_dialect/symbolic_op_test.cc
index 7b0751d17ac138666947f353f6e6dbbea5b6536f..138e5e5b0d8c9a3faac8c57ac241d48590e6f135 100644
--- a/test/cpp/ir/shape_dialect/symbolic_op_test.cc
+++ b/test/cpp/ir/shape_dialect/symbolic_op_test.cc
@@ -93,7 +93,10 @@ TEST(assist_struct_test, symbolic_dim_table) {
   EXPECT_FALSE(symbolTable.lookup<ir::dialect::SymbolicDim>("S1"));
 }
 
-TEST(assist_struct_test, symbolic_dim_mgr) {
+TEST(assist_struct_test, symbolic_dim_mgr_simple) {
+  /******************************************************/
+  /* Mgr simple version, only SymbolicDim related func. */
+  /******************************************************/
   ir::IrContext *ctx = ir::IrContext::Instance();
   ir::Program program(ctx);
   ctx->GetOrRegisterDialect<ir::dialect::ShapeDialect>();
@@ -141,6 +144,175 @@ TEST(assist_struct_test, symbolic_dim_mgr) {
   EXPECT_FALSE(symDimMgr.isSymbolicDimEqual(symDimS0, symDimC10));
 }
 
+TEST(assist_struct_test, symbolic_dim_mgr_complex) {
+  /***************************************************************/
+  /* Mgr with constraintOp, and SymbolicDimProduct related func. */
+  /***************************************************************/
+  ir::IrContext *ctx = ir::IrContext::Instance();
+  ir::Program program(ctx);
+  ctx->GetOrRegisterDialect<ir::dialect::ShapeDialect>();
+  ctx->GetOrRegisterDialect<paddle::dialect::PaddleDialect>();
+  ir::Builder builder = ir::Builder(ctx, program.block());
+
+  ir::dialect::SymbolicDim symDimS0 = builder.Build<ir::dialect::SymbolicDim>(
+      "S0", -100000, false, false, true, true);
+  ir::dialect::SymbolicDim symDimS1 = builder.Build<ir::dialect::SymbolicDim>(
+      "S1", -100000, false, false, true, true);
+  ir::dialect::SymbolicDim symDimS2 = builder.Build<ir::dialect::SymbolicDim>(
+      "S2", -100000, false, false, true, true);
+  ir::dialect::SymbolicDim symDimS3 = builder.Build<ir::dialect::SymbolicDim>(
+      "S3", -100000, false, false, true, true);
+  ir::dialect::SymbolicDim symDimS4 = builder.Build<ir::dialect::SymbolicDim>(
+      "S4", -100000, false, false, true, true);
+  ir::dialect::SymbolicDim symDimS5 = builder.Build<ir::dialect::SymbolicDim>(
+      "S5", -100000, false, false, true, true);
+  ir::dialect::SymbolicDim symDimS6 = builder.Build<ir::dialect::SymbolicDim>(
+      "S6", -100000, false, false, true, true);
+  ir::dialect::SymbolicDim symDimS7 = builder.Build<ir::dialect::SymbolicDim>(
+      "S7", -100000, false, false, true, true);
+  ir::dialect::SymbolicDim symDimS8 = builder.Build<ir::dialect::SymbolicDim>(
+      "S8", -100000, false, false, true, true);
+  ir::dialect::SymbolicDim symDimS9 = builder.Build<ir::dialect::SymbolicDim>(
+      "S9", -100000, false, false, true, true);
+  ir::dialect::SymbolicDim symDimS10 = builder.Build<ir::dialect::SymbolicDim>(
+      "S10", -100000, false, false, true, true);
+  ir::dialect::SymbolicDim symDimS11 = builder.Build<ir::dialect::SymbolicDim>(
+      "S11", -100000, false, false, true, true);
+  ir::dialect::SymbolicDim symDimS12 = builder.Build<ir::dialect::SymbolicDim>(
+      "S12", -100000, false, false, true, false);
+  ir::dialect::SymbolicDim symDimC10 = builder.Build<ir::dialect::SymbolicDim>(
+      "C10", 10, true, false, true, true);
+  ir::dialect::SymbolicDim symDimC20 = builder.Build<ir::dialect::SymbolicDim>(
+      "C20", 20, true, false, true, true);
+
+  ir::OpResult dimOpS0 = builder.Build<ir::dialect::DimOp>("S0").out();
+  ir::OpResult dimOpS1 = builder.Build<ir::dialect::DimOp>("S1").out();
+  ir::OpResult dimOpS2 = builder.Build<ir::dialect::DimOp>("S2").out();
+  ir::OpResult dimOpS3 = builder.Build<ir::dialect::DimOp>("S3").out();
+  ir::OpResult dimOpS4 = builder.Build<ir::dialect::DimOp>("S4").out();
+  ir::OpResult dimOpS5 = builder.Build<ir::dialect::DimOp>("S5").out();
+  ir::OpResult dimOpS6 = builder.Build<ir::dialect::DimOp>("S6").out();
+  ir::OpResult dimOpS7 = builder.Build<ir::dialect::DimOp>("S7").out();
+  ir::OpResult dimOpS8 = builder.Build<ir::dialect::DimOp>("S8").out();
+  ir::OpResult dimOpS9 = builder.Build<ir::dialect::DimOp>("S9").out();
+  ir::OpResult dimOpS10 = builder.Build<ir::dialect::DimOp>("S10").out();
+  ir::OpResult dimOpS11 = builder.Build<ir::dialect::DimOp>("S11").out();
+  ir::OpResult dimOpC10 = builder.Build<ir::dialect::DimOp>("C10").out();
+  ir::OpResult dimOpC20 = builder.Build<ir::dialect::DimOp>("C20").out();
+  ir::OpResult constant =
+      builder
+          .Build<ir::ConstantOp>(ir::Int32Attribute::get(ctx, 2),
+                                 ir::Int32Type::get(ctx))
+          ->result(0);
+
+  // Mark S1 == S2.
+  builder.Build<ir::dialect::TieProductEqualOp>(
+      2, 2, std::vector<ir::OpResult>{constant, dimOpS1, dimOpS2, constant});
+  // Mark S0 * S1 == S2 * S3, For check S0 == S3.
+  builder.Build<ir::dialect::TieProductEqualOp>(
+      2, 2, std::vector<ir::OpResult>{dimOpS0, dimOpS1, dimOpS2, dimOpS3});
+  // Mark S4 * S0 * S1 == S2 * S3 * S5, For check S4 == S5.
+  builder.Build<ir::dialect::TieProductEqualOp>(
+      3,
+      3,
+      std::vector<ir::OpResult>{
+          dimOpS4, dimOpS0, dimOpS1, dimOpS2, dimOpS3, dimOpS5});
+  // For check S6 == C10 * C20.
+  builder.Build<ir::dialect::TieProductEqualOp>(
+      1, 2, std::vector<ir::OpResult>{dimOpS6, dimOpC10, dimOpC20});
+  // Mark C10 * S0 * S1 == S2 * S3 * S7, for check C10 == S7.
+  builder.Build<ir::dialect::TieProductEqualOp>(
+      3,
+      3,
+      std::vector<ir::OpResult>{
+          dimOpC10, dimOpS0, dimOpS1, dimOpS2, dimOpS3, dimOpS7});
+
+  // Mark S8 * S9 == S10 * S11, for unsimplify product case
+  builder.Build<ir::dialect::TieProductEqualOp>(
+      2, 2, std::vector<ir::OpResult>{dimOpS8, dimOpS9, dimOpS10, dimOpS11});
+
+  ir::SymbolicDimMgr symDimMgr(program.module_op());
+
+  symDimMgr.load();
+
+  // For check indirect equality: S1 * S4 == S2 * S5
+  ir::SymbolicDimProduct symDimProductLhs;
+  ir::SymbolicDimProduct symDimProductRhs;
+
+  symDimProductLhs.symbols.push_back(symDimS1);
+  symDimProductLhs.symbols.push_back(symDimS4);
+
+  symDimProductRhs.symbols.push_back(symDimS2);
+  symDimProductRhs.symbols.push_back(symDimS5);
+
+  // For uncompletely simplied product check: S8 * S9 * S12 == S10 * S11 * S12
+  ir::SymbolicDimProduct symDimProductLhs_;
+  ir::SymbolicDimProduct symDimProductRhs_;
+
+  symDimProductLhs_.symbols.push_back(symDimS8);
+  symDimProductLhs_.symbols.push_back(symDimS9);
+  symDimProductLhs_.symbols.push_back(symDimS12);
+
+  symDimProductRhs_.symbols.push_back(symDimS10);
+  symDimProductRhs_.symbols.push_back(symDimS11);
+  symDimProductRhs_.symbols.push_back(symDimS12);
+
+  // For check simplifySymbolicDimProduct, {factor = 1, Sym = {S7}} => {factor =
+  // 10}
+  ir::SymbolicDimProduct symDimProductS7;
+  symDimProductS7.symbols.push_back(symDimS7);
+  ir::SymbolicDimProduct simplifiedProductS7 =
+      symDimMgr.simplifySymbolicDimProduct(symDimProductS7);
+
+  // For check simplifySymbolicDimProductPair, X * Y * Y, Y * Y * Z => X, Z
+  ir::SymbolicDimProduct symDimProductPairLhs;
+  ir::SymbolicDimProduct symDimProductPairRhs;
+  ir::SymbolicDimProduct newLhs, newRhs;
+  symDimProductPairLhs.symbols.push_back(symDimS4);
+  symDimProductPairLhs.symbols.push_back(symDimS1);
+  symDimProductPairLhs.symbols.push_back(symDimS2);
+  symDimProductPairRhs.symbols.push_back(symDimS1);
+  symDimProductPairRhs.symbols.push_back(symDimS2);
+  symDimProductPairRhs.symbols.push_back(symDimS3);
+
+  std::tie(newLhs, newRhs) = symDimMgr.simplifySymbolicDimProductPair(
+      symDimProductPairLhs, symDimProductPairRhs);
+
+  // For check symbolicDimProductDivide, {S4 * S1 * C20} / {S1 * C10} => {factor
+  // = 2 Sym = {S4}}
+  ir::SymbolicDimProduct symDimProductDivLhs;
+  ir::SymbolicDimProduct symDimProductDivRhs;
+  symDimProductDivLhs.symbols.push_back(symDimS4);
+  symDimProductDivLhs.symbols.push_back(symDimS1);
+  symDimProductDivLhs.symbols.push_back(symDimC20);
+  symDimProductDivRhs.symbols.push_back(symDimS1);
+  symDimProductDivRhs.symbols.push_back(symDimC10);
+
+  ir::SymbolicDimProduct *divRes = symDimMgr.symbolicDimProductDivide(
+      symDimProductDivLhs, symDimProductDivRhs);
+
+  EXPECT_TRUE(symDimMgr.isSymbolicDimEqual(symDimS1, symDimS2));
+  EXPECT_TRUE(symDimMgr.isSymbolicDimEqual(symDimS0, symDimS3));
+  EXPECT_TRUE(symDimMgr.isSymbolicDimEqual(symDimS4, symDimS5));
+  EXPECT_EQ(symDimS6.getValue(), 200);
+  EXPECT_EQ(symDimMgr.symbolTable().lookup<ir::dialect::SymbolicDim>("C20"),
+            symDimC20);
+  EXPECT_EQ(symDimS7.getValue(), symDimC10.getValue());
+  EXPECT_EQ(simplifiedProductS7.factor, 10);
+  EXPECT_EQ(simplifiedProductS7.symbols.size(), static_cast<size_t>(0));
+  EXPECT_EQ(newLhs.symbols.size(), static_cast<size_t>(1));
+  EXPECT_EQ(newRhs.symbols.size(), static_cast<size_t>(1));
+  EXPECT_EQ(newLhs.symbols[0], symDimMgr.getRootSymbolicDim(symDimS4));
+  EXPECT_EQ(newRhs.symbols[0], symDimMgr.getRootSymbolicDim(symDimS3));
+  EXPECT_EQ(divRes->factor, 2);
+  EXPECT_EQ(divRes->symbols.size(), static_cast<size_t>(1));
+  EXPECT_EQ(divRes->symbols[0], symDimMgr.getRootSymbolicDim(symDimS4));
+  EXPECT_TRUE(
+      symDimMgr.isSymbolicDimProductEqual(symDimProductLhs, symDimProductRhs));
+  EXPECT_TRUE(symDimMgr.isSymbolicDimProductEqual(symDimProductLhs_,
+                                                  symDimProductRhs_));
+}
+
 TEST(assist_struct_test, dim) {
   ir::IrContext *ctx = ir::IrContext::Instance();
   ir::Program program(ctx);