diff --git a/mlir/include/mlir/Support/CyclicReplacerCache.h b/mlir/include/mlir/Support/CyclicReplacerCache.h
new file mode 100644
index 00000000000000..42428c1507ffb5
--- /dev/null
+++ b/mlir/include/mlir/Support/CyclicReplacerCache.h
@@ -0,0 +1,280 @@
+//===- CyclicReplacerCache.h ------------------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+//
+// This file contains helper classes for caching replacer-like functions that
+// map values between two domains. They are able to handle replacer logic that
+// contains self-recursion.
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef MLIR_SUPPORT_CYCLICREPLACERCACHE_H
+#define MLIR_SUPPORT_CYCLICREPLACERCACHE_H
+
+#include "mlir/IR/Visitors.h"
+#include "llvm/ADT/DenseSet.h"
+#include "llvm/ADT/MapVector.h"
+#include <set>
+
+namespace mlir {
+
+//===----------------------------------------------------------------------===//
+// CyclicReplacerCache
+//===----------------------------------------------------------------------===//
+
+/// A cache for replacer-like functions that map values between two domains. The
+/// difference compared to just using a map to cache in-out pairs is that this
+/// class is able to handle replacer logic that is self-recursive (and thus may
+/// cause infinite recursion in the naive case).
+///
+/// This class provides a hook for the user to perform cycle pruning when a
+/// cycle is identified, and is able to perform context-sensitive caching so
+/// that the replacement result for an input that is part of a pruned cycle can
+/// be distinct from the replacement result for the same input when it is not
+/// part of a cycle.
+///
+/// In addition, this class allows deferring cycle pruning until specific inputs
+/// are repeated. This is useful for cases where not all elements in a cycle can
+/// perform pruning. The user still must guarantee that at least one element in
+/// any given cycle can perform pruning. Even if not, an assertion will
+/// eventually be tripped instead of infinite recursion (the run-time is
+/// linearly bounded by the maximum cycle length of its input).
+///
+/// WARNING: This class works best with InT & OutT that are trivial scalar
+/// types. The input/output elements will be frequently copied and hashed.
+template <typename InT, typename OutT>
+class CyclicReplacerCache {
+public:
+  /// User-provided replacement function & cycle-breaking functions.
+  /// The cycle-breaking function must not make any more recursive invocations
+  /// to this cached replacer.
+  using CycleBreakerFn = std::function<std::optional<OutT>(InT)>;
+
+  CyclicReplacerCache() = delete;
+  CyclicReplacerCache(CycleBreakerFn cycleBreaker)
+      : cycleBreaker(std::move(cycleBreaker)) {}
+
+  /// A possibly unresolved cache entry.
+  /// If unresolved, the entry must be resolved before it goes out of scope.
+  struct CacheEntry {
+  public:
+    ~CacheEntry() { assert(result && "unresovled cache entry"); }
+
+    /// Check whether this node was repeated during recursive replacements.
+    /// This only makes sense to be called after all recursive replacements are
+    /// completed and the current element has resurfaced to the top of the
+    /// replacement stack.
+    bool wasRepeated() const {
+      // If the top frame includes itself as a dependency, then it must have
+      // been repeated.
+      ReplacementFrame &currFrame = cache.replacementStack.back();
+      size_t currFrameIndex = cache.replacementStack.size() - 1;
+      return currFrame.dependentFrames.count(currFrameIndex);
+    }
+
+    /// Resolve an unresolved cache entry by providing the result to be stored
+    /// in the cache.
+    void resolve(OutT result) {
+      assert(!this->result && "cache entry already resolved");
+      cache.finalizeReplacement(element, result);
+      this->result = std::move(result);
+    }
+
+    /// Get the resolved result if one exists.
+    const std::optional<OutT> &get() const { return result; }
+
+  private:
+    friend class CyclicReplacerCache;
+    CacheEntry() = delete;
+    CacheEntry(CyclicReplacerCache<InT, OutT> &cache, InT element,
+               std::optional<OutT> result = std::nullopt)
+        : cache(cache), element(std::move(element)), result(result) {}
+
+    CyclicReplacerCache<InT, OutT> &cache;
+    InT element;
+    std::optional<OutT> result;
+  };
+
+  /// Lookup the cache for a pre-calculated replacement for `element`.
+  /// If one exists, a resolved CacheEntry will be returned. Otherwise, an
+  /// unresolved CacheEntry will be returned, and the caller must resolve it
+  /// with the calculated replacement so it can be registered in the cache for
+  /// future use.
+  /// Multiple unresolved CacheEntries may be retrieved. However, any unresolved
+  /// CacheEntries that are returned must be resolved in reverse order of
+  /// retrieval, i.e. the last retrieved CacheEntry must be resolved first, and
+  /// the first retrieved CacheEntry must be resolved last. This should be
+  /// natural when used as a stack / inside recursion.
+  CacheEntry lookupOrInit(InT element);
+
+private:
+  /// Register the replacement in the cache and update the replacementStack.
+  void finalizeReplacement(InT element, OutT result);
+
+  CycleBreakerFn cycleBreaker;
+  DenseMap<InT, OutT> standaloneCache;
+
+  struct DependentReplacement {
+    OutT replacement;
+    /// The highest replacement frame index that this cache entry is dependent
+    /// on.
+    size_t highestDependentFrame;
+  };
+  DenseMap<InT, DependentReplacement> dependentCache;
+
+  struct ReplacementFrame {
+    /// The set of elements that is only legal while under this current frame.
+    /// They need to be removed from the cache when this frame is popped off the
+    /// replacement stack.
+    DenseSet<InT> dependingReplacements;
+    /// The set of frame indices that this current frame's replacement is
+    /// dependent on, ordered from highest to lowest.
+    std::set<size_t, std::greater<size_t>> dependentFrames;
+  };
+  /// Every element currently in the progress of being replaced pushes a frame
+  /// onto this stack.
+  SmallVector<ReplacementFrame> replacementStack;
+  /// Maps from each input element to its indices on the replacement stack.
+  DenseMap<InT, SmallVector<size_t, 2>> cyclicElementFrame;
+  /// If set to true, we are currently asking an element to break a cycle. No
+  /// more recursive invocations is allowed while this is true (the replacement
+  /// stack can no longer grow).
+  bool resolvingCycle = false;
+};
+
+template <typename InT, typename OutT>
+typename CyclicReplacerCache<InT, OutT>::CacheEntry
+CyclicReplacerCache<InT, OutT>::lookupOrInit(InT element) {
+  assert(!resolvingCycle &&
+         "illegal recursive invocation while breaking cycle");
+
+  if (auto it = standaloneCache.find(element); it != standaloneCache.end())
+    return CacheEntry(*this, element, it->second);
+
+  if (auto it = dependentCache.find(element); it != dependentCache.end()) {
+    // Update the current top frame (the element that invoked this current
+    // replacement) to include any dependencies the cache entry had.
+    ReplacementFrame &currFrame = replacementStack.back();
+    currFrame.dependentFrames.insert(it->second.highestDependentFrame);
+    return CacheEntry(*this, element, it->second.replacement);
+  }
+
+  auto [it, inserted] = cyclicElementFrame.try_emplace(element);
+  if (!inserted) {
+    // This is a repeat of a known element. Try to break cycle here.
+    resolvingCycle = true;
+    std::optional<OutT> result = cycleBreaker(element);
+    resolvingCycle = false;
+    if (result) {
+      // Cycle was broken.
+      size_t dependentFrame = it->second.back();
+      dependentCache[element] = {*result, dependentFrame};
+      ReplacementFrame &currFrame = replacementStack.back();
+      // If this is a repeat, there is no replacement frame to pop. Mark the top
+      // frame as being dependent on this element.
+      currFrame.dependentFrames.insert(dependentFrame);
+
+      return CacheEntry(*this, element, *result);
+    }
+
+    // Cycle could not be broken.
+    // A legal setup must ensure at least one element of each cycle can break
+    // cycles. Under this setup, each element can be seen at most twice before
+    // the cycle is broken. If we see an element more than twice, we know this
+    // is an illegal setup.
+    assert(it->second.size() <= 2 && "illegal 3rd repeat of input");
+  }
+
+  // Otherwise, either this is the first time we see this element, or this
+  // element could not break this cycle.
+  it->second.push_back(replacementStack.size());
+  replacementStack.emplace_back();
+
+  return CacheEntry(*this, element);
+}
+
+template <typename InT, typename OutT>
+void CyclicReplacerCache<InT, OutT>::finalizeReplacement(InT element,
+                                                         OutT result) {
+  ReplacementFrame &currFrame = replacementStack.back();
+  // With the conclusion of this replacement frame, the current element is no
+  // longer a dependent element.
+  currFrame.dependentFrames.erase(replacementStack.size() - 1);
+
+  auto prevLayerIter = ++replacementStack.rbegin();
+  if (prevLayerIter == replacementStack.rend()) {
+    // If this is the last frame, there should be zero dependents.
+    assert(currFrame.dependentFrames.empty() &&
+           "internal error: top-level dependent replacement");
+    // Cache standalone result.
+    standaloneCache[element] = result;
+  } else if (currFrame.dependentFrames.empty()) {
+    // Cache standalone result.
+    standaloneCache[element] = result;
+  } else {
+    // Cache dependent result.
+    size_t highestDependentFrame = *currFrame.dependentFrames.begin();
+    dependentCache[element] = {result, highestDependentFrame};
+
+    // Otherwise, the previous frame inherits the same dependent frames.
+    prevLayerIter->dependentFrames.insert(currFrame.dependentFrames.begin(),
+                                          currFrame.dependentFrames.end());
+
+    // Mark this current replacement as a depending replacement on the closest
+    // dependent frame.
+    replacementStack[highestDependentFrame].dependingReplacements.insert(
+        element);
+  }
+
+  // All depending replacements in the cache must be purged.
+  for (InT key : currFrame.dependingReplacements)
+    dependentCache.erase(key);
+
+  replacementStack.pop_back();
+  auto it = cyclicElementFrame.find(element);
+  it->second.pop_back();
+  if (it->second.empty())
+    cyclicElementFrame.erase(it);
+}
+
+//===----------------------------------------------------------------------===//
+// CachedCyclicReplacer
+//===----------------------------------------------------------------------===//
+
+/// A helper class for cases where the input/output types of the replacer
+/// function is identical to the types stored in the cache. This class wraps
+/// the user-provided replacer function, and can be used in place of the user
+/// function.
+template <typename InT, typename OutT>
+class CachedCyclicReplacer {
+public:
+  using ReplacerFn = std::function<OutT(InT)>;
+  using CycleBreakerFn =
+      typename CyclicReplacerCache<InT, OutT>::CycleBreakerFn;
+
+  CachedCyclicReplacer() = delete;
+  CachedCyclicReplacer(ReplacerFn replacer, CycleBreakerFn cycleBreaker)
+      : replacer(std::move(replacer)), cache(std::move(cycleBreaker)) {}
+
+  OutT operator()(InT element) {
+    auto cacheEntry = cache.lookupOrInit(element);
+    if (std::optional<OutT> result = cacheEntry.get())
+      return *result;
+
+    OutT result = replacer(element);
+    cacheEntry.resolve(result);
+    return result;
+  }
+
+private:
+  ReplacerFn replacer;
+  CyclicReplacerCache<InT, OutT> cache;
+};
+
+} // namespace mlir
+
+#endif // MLIR_SUPPORT_CYCLICREPLACERCACHE_H
diff --git a/mlir/unittests/Support/CMakeLists.txt b/mlir/unittests/Support/CMakeLists.txt
index 1dbf072bcbbfd1..ec79a1c6409092 100644
--- a/mlir/unittests/Support/CMakeLists.txt
+++ b/mlir/unittests/Support/CMakeLists.txt
@@ -1,4 +1,5 @@
 add_mlir_unittest(MLIRSupportTests
+  CyclicReplacerCacheTest.cpp
   IndentedOstreamTest.cpp
   StorageUniquerTest.cpp
 )
diff --git a/mlir/unittests/Support/CyclicReplacerCacheTest.cpp b/mlir/unittests/Support/CyclicReplacerCacheTest.cpp
new file mode 100644
index 00000000000000..ca02a3d692b2a8
--- /dev/null
+++ b/mlir/unittests/Support/CyclicReplacerCacheTest.cpp
@@ -0,0 +1,478 @@
+//===- CyclicReplacerCacheTest.cpp ----------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "mlir/Support/CyclicReplacerCache.h"
+#include "llvm/ADT/SetVector.h"
+#include "gmock/gmock.h"
+#include <map>
+#include <set>
+
+using namespace mlir;
+
+TEST(CachedCyclicReplacerTest, testNoRecursion) {
+  CachedCyclicReplacer<int, bool> replacer(
+      /*replacer=*/[](int n) { return static_cast<bool>(n); },
+      /*cycleBreaker=*/[](int n) { return std::nullopt; });
+
+  EXPECT_EQ(replacer(3), true);
+  EXPECT_EQ(replacer(0), false);
+}
+
+TEST(CachedCyclicReplacerTest, testInPlaceRecursionPruneAnywhere) {
+  // Replacer cycles through ints 0 -> 1 -> 2 -> 0 -> ...
+  CachedCyclicReplacer<int, int> replacer(
+      /*replacer=*/[&](int n) { return replacer((n + 1) % 3); },
+      /*cycleBreaker=*/[&](int n) { return -1; });
+
+  // Starting at 0.
+  EXPECT_EQ(replacer(0), -1);
+  // Starting at 2.
+  EXPECT_EQ(replacer(2), -1);
+}
+
+//===----------------------------------------------------------------------===//
+// CachedCyclicReplacer: ChainRecursion
+//===----------------------------------------------------------------------===//
+
+/// This set of tests uses a replacer function that maps ints into vectors of
+/// ints.
+///
+/// The replacement result for input `n` is the replacement result of `(n+1)%3`
+/// appended with an element `42`. Theoretically, this will produce an
+/// infinitely long vector. The cycle-breaker function prunes this infinite
+/// recursion in the replacer logic by returning an empty vector upon the first
+/// re-occurrence of an input value.
+namespace {
+class CachedCyclicReplacerChainRecursionPruningTest : public ::testing::Test {
+public:
+  // N ==> (N+1) % 3
+  // This will create a chain of infinite length without recursion pruning.
+  CachedCyclicReplacerChainRecursionPruningTest()
+      : replacer(
+            [&](int n) {
+              ++invokeCount;
+              std::vector<int> result = replacer((n + 1) % 3);
+              result.push_back(42);
+              return result;
+            },
+            [&](int n) -> std::optional<std::vector<int>> {
+              return baseCase.value_or(n) == n
+                         ? std::make_optional(std::vector<int>{})
+                         : std::nullopt;
+            }) {}
+
+  std::vector<int> getChain(unsigned N) { return std::vector<int>(N, 42); };
+
+  CachedCyclicReplacer<int, std::vector<int>> replacer;
+  int invokeCount = 0;
+  std::optional<int> baseCase = std::nullopt;
+};
+} // namespace
+
+TEST_F(CachedCyclicReplacerChainRecursionPruningTest, testPruneAnywhere0) {
+  // Starting at 0. Cycle length is 3.
+  EXPECT_EQ(replacer(0), getChain(3));
+  EXPECT_EQ(invokeCount, 3);
+
+  // Starting at 1. Cycle length is 5 now because of a cached replacement at 0.
+  invokeCount = 0;
+  EXPECT_EQ(replacer(1), getChain(5));
+  EXPECT_EQ(invokeCount, 2);
+
+  // Starting at 2. Cycle length is 4. Entire result is cached.
+  invokeCount = 0;
+  EXPECT_EQ(replacer(2), getChain(4));
+  EXPECT_EQ(invokeCount, 0);
+}
+
+TEST_F(CachedCyclicReplacerChainRecursionPruningTest, testPruneAnywhere1) {
+  // Starting at 1. Cycle length is 3.
+  EXPECT_EQ(replacer(1), getChain(3));
+  EXPECT_EQ(invokeCount, 3);
+}
+
+TEST_F(CachedCyclicReplacerChainRecursionPruningTest, testPruneSpecific0) {
+  baseCase = 0;
+
+  // Starting at 0. Cycle length is 3.
+  EXPECT_EQ(replacer(0), getChain(3));
+  EXPECT_EQ(invokeCount, 3);
+}
+
+TEST_F(CachedCyclicReplacerChainRecursionPruningTest, testPruneSpecific1) {
+  baseCase = 0;
+
+  // Starting at 1. Cycle length is 5 (1 -> 2 -> 0 -> 1 -> 2 -> Prune).
+  EXPECT_EQ(replacer(1), getChain(5));
+  EXPECT_EQ(invokeCount, 5);
+
+  // Starting at 0. Cycle length is 3. Entire result is cached.
+  invokeCount = 0;
+  EXPECT_EQ(replacer(0), getChain(3));
+  EXPECT_EQ(invokeCount, 0);
+}
+
+//===----------------------------------------------------------------------===//
+// CachedCyclicReplacer: GraphReplacement
+//===----------------------------------------------------------------------===//
+
+/// This set of tests uses a replacer function that maps from cyclic graphs to
+/// trees, pruning out cycles in the process.
+///
+/// It consists of two helper classes:
+/// - Graph
+///   - A directed graph where nodes are non-negative integers.
+/// - PrunedGraph
+///   - A Graph where edges that used to cause cycles are now represented with
+///     an indirection (a recursionId).
+namespace {
+class CachedCyclicReplacerGraphReplacement : public ::testing::Test {
+public:
+  /// A directed graph where nodes are non-negative integers.
+  struct Graph {
+    using Node = int64_t;
+
+    /// Use ordered containers for deterministic output.
+    /// Nodes without outgoing edges are considered nonexistent.
+    std::map<Node, std::set<Node>> edges;
+
+    void addEdge(Node src, Node sink) { edges[src].insert(sink); }
+
+    bool isCyclic() const {
+      DenseSet<Node> visited;
+      for (Node root : llvm::make_first_range(edges)) {
+        if (visited.contains(root))
+          continue;
+
+        SetVector<Node> path;
+        SmallVector<Node> workstack;
+        workstack.push_back(root);
+        while (!workstack.empty()) {
+          Node curr = workstack.back();
+          workstack.pop_back();
+
+          if (curr < 0) {
+            // A negative node signals the end of processing all of this node's
+            // children. Remove self from path.
+            assert(path.back() == -curr && "internal inconsistency");
+            path.pop_back();
+            continue;
+          }
+
+          if (path.contains(curr))
+            return true;
+
+          visited.insert(curr);
+          auto edgesIter = edges.find(curr);
+          if (edgesIter == edges.end() || edgesIter->second.empty())
+            continue;
+
+          path.insert(curr);
+          // Push negative node to signify recursion return.
+          workstack.push_back(-curr);
+          workstack.insert(workstack.end(), edgesIter->second.begin(),
+                           edgesIter->second.end());
+        }
+      }
+      return false;
+    }
+
+    /// Deterministic output for testing.
+    std::string serialize() const {
+      std::ostringstream oss;
+      for (const auto &[src, neighbors] : edges) {
+        oss << src << ":";
+        for (Graph::Node neighbor : neighbors)
+          oss << " " << neighbor;
+        oss << "\n";
+      }
+      return oss.str();
+    }
+  };
+
+  /// A Graph where edges that used to cause cycles (back-edges) are now
+  /// represented with an indirection (a recursionId).
+  ///
+  /// In addition to each node having an integer ID, each node also tracks the
+  /// original integer ID it had in the original graph. This way for every
+  /// back-edge, we can represent it as pointing to a new instance of the
+  /// original node. Then we mark the original node and the new instance with
+  /// a new unique recursionId to indicate that they're supposed to be the same
+  /// node.
+  struct PrunedGraph {
+    using Node = Graph::Node;
+    struct NodeInfo {
+      Graph::Node originalId;
+      /// A negative recursive index means not recursive. Otherwise nodes with
+      /// the same originalId & recursionId are the same node in the original
+      /// graph.
+      int64_t recursionId;
+    };
+
+    /// Add a regular non-recursive-self node.
+    Node addNode(Graph::Node originalId, int64_t recursionIndex = -1) {
+      Node id = nextConnectionId++;
+      info[id] = {originalId, recursionIndex};
+      return id;
+    }
+    /// Add a recursive-self-node, i.e. a duplicate of the original node that is
+    /// meant to represent an indirection to it.
+    std::pair<Node, int64_t> addRecursiveSelfNode(Graph::Node originalId) {
+      return {addNode(originalId, nextRecursionId), nextRecursionId++};
+    }
+    void addEdge(Node src, Node sink) { connections.addEdge(src, sink); }
+
+    /// Deterministic output for testing.
+    std::string serialize() const {
+      std::ostringstream oss;
+      oss << "nodes\n";
+      for (const auto &[nodeId, nodeInfo] : info) {
+        oss << nodeId << ": n" << nodeInfo.originalId;
+        if (nodeInfo.recursionId >= 0)
+          oss << '<' << nodeInfo.recursionId << '>';
+        oss << "\n";
+      }
+      oss << "edges\n";
+      oss << connections.serialize();
+      return oss.str();
+    }
+
+    bool isCyclic() const { return connections.isCyclic(); }
+
+  private:
+    Graph connections;
+    int64_t nextRecursionId = 0;
+    int64_t nextConnectionId = 0;
+    /// Use ordered map for deterministic output.
+    std::map<Graph::Node, NodeInfo> info;
+  };
+
+  PrunedGraph breakCycles(const Graph &input) {
+    assert(input.isCyclic() && "input graph is not cyclic");
+
+    PrunedGraph output;
+
+    DenseMap<Graph::Node, int64_t> recMap;
+    auto cycleBreaker = [&](Graph::Node inNode) -> std::optional<Graph::Node> {
+      auto [node, recId] = output.addRecursiveSelfNode(inNode);
+      recMap[inNode] = recId;
+      return node;
+    };
+
+    CyclicReplacerCache<Graph::Node, Graph::Node> cache(cycleBreaker);
+
+    std::function<Graph::Node(Graph::Node)> replaceNode =
+        [&](Graph::Node inNode) {
+          auto cacheEntry = cache.lookupOrInit(inNode);
+          if (std::optional<Graph::Node> result = cacheEntry.get())
+            return *result;
+
+          // Recursively replace its neighbors.
+          SmallVector<Graph::Node> neighbors;
+          if (auto it = input.edges.find(inNode); it != input.edges.end())
+            neighbors = SmallVector<Graph::Node>(
+                llvm::map_range(it->second, replaceNode));
+
+          // Create a new node in the output graph.
+          int64_t recursionIndex =
+              cacheEntry.wasRepeated() ? recMap.lookup(inNode) : -1;
+          Graph::Node result = output.addNode(inNode, recursionIndex);
+
+          for (Graph::Node neighbor : neighbors)
+            output.addEdge(result, neighbor);
+
+          cacheEntry.resolve(result);
+          return result;
+        };
+
+    /// Translate starting from each node.
+    for (Graph::Node root : llvm::make_first_range(input.edges))
+      replaceNode(root);
+
+    return output;
+  }
+
+  /// Helper for serialization tests that allow putting comments in the
+  /// serialized format. Every line that begins with a `;` is considered a
+  /// comment. The entire line, incl. the terminating `\n` is removed.
+  std::string trimComments(StringRef input) {
+    std::ostringstream oss;
+    bool isNewLine = false;
+    bool isComment = false;
+    for (char c : input) {
+      // Lines beginning with ';' are comments.
+      if (isNewLine && c == ';')
+        isComment = true;
+
+      if (!isComment)
+        oss << c;
+
+      if (c == '\n') {
+        isNewLine = true;
+        isComment = false;
+      }
+    }
+    return oss.str();
+  }
+};
+} // namespace
+
+TEST_F(CachedCyclicReplacerGraphReplacement, testSingleLoop) {
+  // 0 -> 1 -> 2
+  // ^         |
+  // +---------+
+  Graph input = {{{0, {1}}, {1, {2}}, {2, {0}}}};
+  PrunedGraph output = breakCycles(input);
+  ASSERT_FALSE(output.isCyclic()) << output.serialize();
+  EXPECT_EQ(output.serialize(), trimComments(R"(nodes
+; root 0
+0: n0<0>
+1: n2
+2: n1
+3: n0<0>
+; root 1
+4: n2
+; root 2
+5: n1
+edges
+1: 0
+2: 1
+3: 2
+4: 3
+5: 4
+)"));
+}
+
+TEST_F(CachedCyclicReplacerGraphReplacement, testDualLoop) {
+  // +----> 1 -----+
+  // |             v
+  // 0 <---------- 3
+  // |             ^
+  // +----> 2 -----+
+  //
+  // Two loops:
+  // 0 -> 1 -> 3 -> 0
+  // 0 -> 2 -> 3 -> 0
+  Graph input = {{{0, {1, 2}}, {1, {3}}, {2, {3}}, {3, {0}}}};
+  PrunedGraph output = breakCycles(input);
+  ASSERT_FALSE(output.isCyclic()) << output.serialize();
+  EXPECT_EQ(output.serialize(), trimComments(R"(nodes
+; root 0
+0: n0<0>
+1: n3
+2: n1
+3: n2
+4: n0<0>
+; root 1
+5: n3
+6: n1
+; root 2
+7: n2
+edges
+1: 0
+2: 1
+3: 1
+4: 2 3
+5: 4
+6: 5
+7: 5
+)"));
+}
+
+TEST_F(CachedCyclicReplacerGraphReplacement, testNestedLoops) {
+  // +----> 1 -----+
+  // |      ^      v
+  // 0 <----+----- 2
+  //
+  // Two nested loops:
+  // 0 -> 1 -> 2 -> 0
+  //      1 -> 2 -> 1
+  Graph input = {{{0, {1}}, {1, {2}}, {2, {0, 1}}}};
+  PrunedGraph output = breakCycles(input);
+  ASSERT_FALSE(output.isCyclic()) << output.serialize();
+  EXPECT_EQ(output.serialize(), trimComments(R"(nodes
+; root 0
+0: n0<0>
+1: n1<1>
+2: n2
+3: n1<1>
+4: n0<0>
+; root 1
+5: n1<2>
+6: n2
+7: n1<2>
+; root 2
+8: n2
+edges
+2: 0 1
+3: 2
+4: 3
+6: 4 5
+7: 6
+8: 4 7
+)"));
+}
+
+TEST_F(CachedCyclicReplacerGraphReplacement, testDualNestedLoops) {
+  // +----> 1 -----+
+  // |      ^      v
+  // 0 <----+----- 3
+  // |      v      ^
+  // +----> 2 -----+
+  //
+  // Two sets of nested loops:
+  // 0 -> 1 -> 3 -> 0
+  //      1 -> 3 -> 1
+  // 0 -> 2 -> 3 -> 0
+  //      2 -> 3 -> 2
+  Graph input = {{{0, {1, 2}}, {1, {3}}, {2, {3}}, {3, {0, 1, 2}}}};
+  PrunedGraph output = breakCycles(input);
+  ASSERT_FALSE(output.isCyclic()) << output.serialize();
+  EXPECT_EQ(output.serialize(), trimComments(R"(nodes
+; root 0
+0: n0<0>
+1: n1<1>
+2: n3<2>
+3: n2
+4: n3<2>
+5: n1<1>
+6: n2<3>
+7: n3
+8: n2<3>
+9: n0<0>
+; root 1
+10: n1<4>
+11: n3<5>
+12: n2
+13: n3<5>
+14: n1<4>
+; root 2
+15: n2<6>
+16: n3
+17: n2<6>
+; root 3
+18: n3
+edges
+; root 0
+3: 2
+4: 0 1 3
+5: 4
+7: 0 5 6
+8: 7
+9: 5 8
+; root 1
+12: 11
+13: 9 10 12
+14: 13
+; root 2
+16: 9 14 15
+17: 16
+; root 3
+18: 9 14 17
+)"));
+}