diff --git a/lib/Dialect/CGGI/Transforms/ExpandLUT.cpp b/lib/Dialect/CGGI/Transforms/ExpandLUT.cpp
index 066c1ecd1..06f113389 100644
--- a/lib/Dialect/CGGI/Transforms/ExpandLUT.cpp
+++ b/lib/Dialect/CGGI/Transforms/ExpandLUT.cpp
@@ -68,7 +68,9 @@ struct ExpandLUT : impl::ExpandLUTBase<ExpandLUT> {
     alignment::populateWithGenerated(patterns);
     patterns.add<ExpandLutLinComb>(context);
 
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns));
   }
 };
 
diff --git a/lib/Dialect/LinAlg/Conversions/LinalgToTensorExt/LinalgToTensorExt.cpp b/lib/Dialect/LinAlg/Conversions/LinalgToTensorExt/LinalgToTensorExt.cpp
index 2ee92a798..4f151ea43 100644
--- a/lib/Dialect/LinAlg/Conversions/LinalgToTensorExt/LinalgToTensorExt.cpp
+++ b/lib/Dialect/LinAlg/Conversions/LinalgToTensorExt/LinalgToTensorExt.cpp
@@ -360,7 +360,9 @@ struct LinalgToTensorExt
     patterns.add<ConvertLinalgMatmul>(&solver, context);
 
     // Run pattern matching and conversion
-    if (failed(applyPatternsAndFoldGreedily(module, std::move(patterns)))) {
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    if (failed(applyPatternsGreedily(module, std::move(patterns)))) {
       return signalPassFailure();
     }
   }
diff --git a/lib/Dialect/ModArith/Transforms/ConvertToMac.cpp b/lib/Dialect/ModArith/Transforms/ConvertToMac.cpp
index 5aebf02d7..296b8909f 100644
--- a/lib/Dialect/ModArith/Transforms/ConvertToMac.cpp
+++ b/lib/Dialect/ModArith/Transforms/ConvertToMac.cpp
@@ -59,7 +59,9 @@ struct ConvertToMac : impl::ConvertToMacBase<ConvertToMac> {
 
     patterns.add<FindMac>(context);
 
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns));
   }
 };
 
diff --git a/lib/Dialect/Polynomial/Transforms/NTTRewrites.cpp b/lib/Dialect/Polynomial/Transforms/NTTRewrites.cpp
index dd839314c..1fef82122 100644
--- a/lib/Dialect/Polynomial/Transforms/NTTRewrites.cpp
+++ b/lib/Dialect/Polynomial/Transforms/NTTRewrites.cpp
@@ -23,7 +23,9 @@ struct PolyMulToNTT : impl::PolyMulToNTTBase<PolyMulToNTT> {
     RewritePatternSet patterns(context);
     // TODO(#1095): migrate to mod arith type
     // patterns.add<rewrites::NTTRewritePolyMul>(patterns.getContext());
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns));
   }
 };
 
diff --git a/lib/Dialect/Secret/Conversions/SecretToCGGI/SecretToCGGI.cpp b/lib/Dialect/Secret/Conversions/SecretToCGGI/SecretToCGGI.cpp
index f7b44b883..55cbab0a2 100644
--- a/lib/Dialect/Secret/Conversions/SecretToCGGI/SecretToCGGI.cpp
+++ b/lib/Dialect/Secret/Conversions/SecretToCGGI/SecretToCGGI.cpp
@@ -713,8 +713,9 @@ struct SecretToCGGI : public impl::SecretToCGGIBase<SecretToCGGI> {
 
     RewritePatternSet cleanupPatterns(context);
     patterns.add<ResolveUnrealizedConversionCast>(context);
-    if (failed(
-            applyPatternsAndFoldGreedily(module, std::move(cleanupPatterns)))) {
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    if (failed(applyPatternsGreedily(module, std::move(cleanupPatterns)))) {
       return signalPassFailure();
     }
   }
diff --git a/lib/Dialect/Secret/Transforms/CaptureGenericAmbientScope.cpp b/lib/Dialect/Secret/Transforms/CaptureGenericAmbientScope.cpp
index cb003c639..04a6bd006 100644
--- a/lib/Dialect/Secret/Transforms/CaptureGenericAmbientScope.cpp
+++ b/lib/Dialect/Secret/Transforms/CaptureGenericAmbientScope.cpp
@@ -24,7 +24,9 @@ struct CaptureGenericAmbientScope
     mlir::RewritePatternSet patterns(context);
 
     patterns.add<CaptureAmbientScope>(context);
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns));
   }
 };
 
diff --git a/lib/Dialect/Secret/Transforms/DistributeGeneric.cpp b/lib/Dialect/Secret/Transforms/DistributeGeneric.cpp
index 529f2577b..d0f3e9834 100644
--- a/lib/Dialect/Secret/Transforms/DistributeGeneric.cpp
+++ b/lib/Dialect/Secret/Transforms/DistributeGeneric.cpp
@@ -660,7 +660,9 @@ struct DistributeGeneric
     // These patterns are shared with canonicalization
     patterns.add<FoldSecretSeparators, CollapseSecretlessGeneric,
                  RemoveUnusedGenericArgs, RemoveNonSecretGenericArgs>(context);
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns));
 
     // used by secret-to-<scheme> lowering
     moveMgmtAttrAnnotationFromInnerToOuter(getOperation());
diff --git a/lib/Dialect/Secret/Transforms/MergeAdjacentGenerics.cpp b/lib/Dialect/Secret/Transforms/MergeAdjacentGenerics.cpp
index a3f544917..15891c876 100644
--- a/lib/Dialect/Secret/Transforms/MergeAdjacentGenerics.cpp
+++ b/lib/Dialect/Secret/Transforms/MergeAdjacentGenerics.cpp
@@ -23,7 +23,9 @@ struct MergeAdjacentGenericsPass
     mlir::RewritePatternSet patterns(context);
 
     patterns.add<MergeAdjacentGenerics>(context);
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns));
   }
 };
 
diff --git a/lib/Dialect/TOSA/Conversions/TosaToSecretArith/TosaToSecretArith.cpp b/lib/Dialect/TOSA/Conversions/TosaToSecretArith/TosaToSecretArith.cpp
index a87f4164b..aa66403f3 100644
--- a/lib/Dialect/TOSA/Conversions/TosaToSecretArith/TosaToSecretArith.cpp
+++ b/lib/Dialect/TOSA/Conversions/TosaToSecretArith/TosaToSecretArith.cpp
@@ -141,7 +141,9 @@ struct TosaToSecretArith
     patterns.add<ConvertTosaSigmoid>(&solver, context);
 
     // Run pattern matching and conversion
-    if (failed(applyPatternsAndFoldGreedily(module, std::move(patterns)))) {
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    if (failed(applyPatternsGreedily(module, std::move(patterns)))) {
       return signalPassFailure();
     }
   }
diff --git a/lib/Dialect/TensorExt/Transforms/CollapseInsertionChains.cpp b/lib/Dialect/TensorExt/Transforms/CollapseInsertionChains.cpp
index 952d9d1ea..5f9471ad5 100644
--- a/lib/Dialect/TensorExt/Transforms/CollapseInsertionChains.cpp
+++ b/lib/Dialect/TensorExt/Transforms/CollapseInsertionChains.cpp
@@ -181,7 +181,9 @@ struct CollapseInsertionChains
     RewritePatternSet patterns(context);
 
     patterns.add<ConvertAlignedExtractInsertToRotate>(context);
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns));
   }
 };
 
diff --git a/lib/Dialect/TensorExt/Transforms/InsertRotate.cpp b/lib/Dialect/TensorExt/Transforms/InsertRotate.cpp
index 4e10eb9db..fe0c68797 100644
--- a/lib/Dialect/TensorExt/Transforms/InsertRotate.cpp
+++ b/lib/Dialect/TensorExt/Transforms/InsertRotate.cpp
@@ -91,7 +91,9 @@ struct InsertRotate : impl::InsertRotateBase<InsertRotate> {
 
     alignment::populateWithGenerated(patterns);
     canonicalization::populateWithGenerated(patterns);
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns));
   }
 };
 
diff --git a/lib/Transforms/ApplyFolders/ApplyFolders.cpp b/lib/Transforms/ApplyFolders/ApplyFolders.cpp
index f98d54474..1dd1ebcce 100644
--- a/lib/Transforms/ApplyFolders/ApplyFolders.cpp
+++ b/lib/Transforms/ApplyFolders/ApplyFolders.cpp
@@ -24,7 +24,9 @@ struct ApplyFolders : impl::ApplyFoldersBase<ApplyFolders> {
         [](tensor::ExtractSliceOp op) { return true; };
     tensor::populateFoldConstantExtractSlicePatterns(patterns, controlFn);
     // Use the greedy pattern driver to apply folders.
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns));
   }
 };
 
diff --git a/lib/Transforms/ConvertIfToSelect/ConvertIfToSelect.cpp b/lib/Transforms/ConvertIfToSelect/ConvertIfToSelect.cpp
index 09c4ffc68..cae4c695c 100644
--- a/lib/Transforms/ConvertIfToSelect/ConvertIfToSelect.cpp
+++ b/lib/Transforms/ConvertIfToSelect/ConvertIfToSelect.cpp
@@ -125,7 +125,9 @@ struct ConvertIfToSelect : impl::ConvertIfToSelectBase<ConvertIfToSelect> {
     }
 
     patterns.add<IfToSelectConversion>(getOperation(), &solver, context);
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns));
 
     LLVM_DEBUG({ annotateSecretness(getOperation(), &solver); });
   }
diff --git a/lib/Transforms/ConvertSecretExtractToStaticExtract/ConvertSecretExtractToStaticExtract.cpp b/lib/Transforms/ConvertSecretExtractToStaticExtract/ConvertSecretExtractToStaticExtract.cpp
index 6a8111042..ab7e0db49 100644
--- a/lib/Transforms/ConvertSecretExtractToStaticExtract/ConvertSecretExtractToStaticExtract.cpp
+++ b/lib/Transforms/ConvertSecretExtractToStaticExtract/ConvertSecretExtractToStaticExtract.cpp
@@ -185,7 +185,9 @@ struct ConvertSecretExtractToStaticExtract
 
     patterns.add<SecretExtractToStaticExtractConversion>(getOperation(),
                                                          &solver, context);
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns));
 
     LLVM_DEBUG({ annotateSecretness(getOperation(), &solver); });
   }
diff --git a/lib/Transforms/ConvertSecretForToStaticFor/ConvertSecretForToStaticFor.cpp b/lib/Transforms/ConvertSecretForToStaticFor/ConvertSecretForToStaticFor.cpp
index 141118daa..4f9c81e06 100644
--- a/lib/Transforms/ConvertSecretForToStaticFor/ConvertSecretForToStaticFor.cpp
+++ b/lib/Transforms/ConvertSecretForToStaticFor/ConvertSecretForToStaticFor.cpp
@@ -193,7 +193,9 @@ struct ConvertSecretForToStaticFor
     }
 
     patterns.add<SecretForToStaticForConversion>(&solver, context);
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns));
   }
 };
 
diff --git a/lib/Transforms/ConvertSecretInsertToStaticInsert/ConvertSecretInsertToStaticInsert.cpp b/lib/Transforms/ConvertSecretInsertToStaticInsert/ConvertSecretInsertToStaticInsert.cpp
index 514fe5b01..b7b07815c 100644
--- a/lib/Transforms/ConvertSecretInsertToStaticInsert/ConvertSecretInsertToStaticInsert.cpp
+++ b/lib/Transforms/ConvertSecretInsertToStaticInsert/ConvertSecretInsertToStaticInsert.cpp
@@ -170,7 +170,9 @@ struct ConvertSecretInsertToStaticInsert
 
     patterns.add<SecretInsertToStaticInsertConversion>(getOperation(), &solver,
                                                        context);
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns));
 
     LLVM_DEBUG({ annotateSecretness(getOperation(), &solver); });
   }
diff --git a/lib/Transforms/ConvertSecretWhileToStaticFor/ConvertSecretWhileToStaticFor.cpp b/lib/Transforms/ConvertSecretWhileToStaticFor/ConvertSecretWhileToStaticFor.cpp
index 79e6baf40..bd04586d1 100644
--- a/lib/Transforms/ConvertSecretWhileToStaticFor/ConvertSecretWhileToStaticFor.cpp
+++ b/lib/Transforms/ConvertSecretWhileToStaticFor/ConvertSecretWhileToStaticFor.cpp
@@ -177,7 +177,9 @@ struct ConvertSecretWhileToStaticFor
     }
 
     patterns.add<SecretWhileToStaticForConversion>(&solver, context);
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns));
   }
 };
 
diff --git a/lib/Transforms/ForwardInsertToExtract/ForwardInsertToExtract.cpp b/lib/Transforms/ForwardInsertToExtract/ForwardInsertToExtract.cpp
index 432b14fd2..ab1bbc243 100644
--- a/lib/Transforms/ForwardInsertToExtract/ForwardInsertToExtract.cpp
+++ b/lib/Transforms/ForwardInsertToExtract/ForwardInsertToExtract.cpp
@@ -122,7 +122,9 @@ struct ForwardInsertToExtract
     RewritePatternSet patterns(context);
     DominanceInfo dom(getOperation());
     patterns.add<ForwardSingleInsertToExtract>(context, dom);
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns));
   }
 };
 
diff --git a/lib/Transforms/ForwardStoreToLoad/ForwardStoreToLoad.cpp b/lib/Transforms/ForwardStoreToLoad/ForwardStoreToLoad.cpp
index f89f44e32..e348e5557 100644
--- a/lib/Transforms/ForwardStoreToLoad/ForwardStoreToLoad.cpp
+++ b/lib/Transforms/ForwardStoreToLoad/ForwardStoreToLoad.cpp
@@ -235,7 +235,9 @@ struct ForwardStoreToLoad : impl::ForwardStoreToLoadBase<ForwardStoreToLoad> {
     DominanceInfo dom(getOperation());
     patterns.add<AffineLoadLowering, AffineStoreLowering>(context);
     patterns.add<ForwardSingleStoreToLoad, RemoveUnusedStore>(context, dom);
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns));
   }
 };
 
diff --git a/lib/Transforms/LinalgCanonicalizations/LinalgCanonicalizations.cpp b/lib/Transforms/LinalgCanonicalizations/LinalgCanonicalizations.cpp
index 327a3b80c..a86d328d6 100644
--- a/lib/Transforms/LinalgCanonicalizations/LinalgCanonicalizations.cpp
+++ b/lib/Transforms/LinalgCanonicalizations/LinalgCanonicalizations.cpp
@@ -175,7 +175,9 @@ struct LinalgCanonicalizations
     patterns.add<FoldConstantLinalgTranspose>(context);
 
     // Run pattern matching and conversion
-    if (failed(applyPatternsAndFoldGreedily(module, std::move(patterns)))) {
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    if (failed(applyPatternsGreedily(module, std::move(patterns)))) {
       return signalPassFailure();
     }
   }
diff --git a/lib/Transforms/MemrefToArith/ExpandCopy.cpp b/lib/Transforms/MemrefToArith/ExpandCopy.cpp
index 627af1e6c..56121a967 100644
--- a/lib/Transforms/MemrefToArith/ExpandCopy.cpp
+++ b/lib/Transforms/MemrefToArith/ExpandCopy.cpp
@@ -104,8 +104,9 @@ struct ExpandCopyPass : impl::ExpandCopyPassBase<ExpandCopyPass> {
     mlir::RewritePatternSet patterns(&getContext());
     patterns.add<MemrefCopyExpansionPattern>(&getContext(), disableAffineLoop);
 
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns),
-                                       config);
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns), config);
   }
 };
 
diff --git a/lib/Transforms/TensorToScalars/TensorToScalars.cpp b/lib/Transforms/TensorToScalars/TensorToScalars.cpp
index 273f176c0..2e7e91d11 100644
--- a/lib/Transforms/TensorToScalars/TensorToScalars.cpp
+++ b/lib/Transforms/TensorToScalars/TensorToScalars.cpp
@@ -150,8 +150,9 @@ struct TensorToScalars : impl::TensorToScalarsBase<TensorToScalars> {
 
     // Empty PatternSet = only run folders (should never fail)
     RewritePatternSet emptyPatterns(context);
-    (void)applyPatternsAndFoldGreedily(getOperation(),
-                                       std::move(emptyPatterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(emptyPatterns));
   }
 };
 
diff --git a/lib/Transforms/UnusedMemRef/UnusedMemRef.cpp b/lib/Transforms/UnusedMemRef/UnusedMemRef.cpp
index 2fdcc322f..e4edc9857 100644
--- a/lib/Transforms/UnusedMemRef/UnusedMemRef.cpp
+++ b/lib/Transforms/UnusedMemRef/UnusedMemRef.cpp
@@ -43,7 +43,9 @@ struct RemoveUnusedMemRef
     MLIRContext* context = &getContext();
     RewritePatternSet patterns(context);
     patterns.add<RemoveUnusedMemrefPattern>(context);
-    (void)applyPatternsAndFoldGreedily(getOperation(), std::move(patterns));
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    (void)applyPatternsGreedily(getOperation(), std::move(patterns));
   }
 };
 
diff --git a/lib/Transforms/YosysOptimizer/YosysOptimizer.cpp b/lib/Transforms/YosysOptimizer/YosysOptimizer.cpp
index 90ee1c405..30e1f039a 100644
--- a/lib/Transforms/YosysOptimizer/YosysOptimizer.cpp
+++ b/lib/Transforms/YosysOptimizer/YosysOptimizer.cpp
@@ -385,7 +385,9 @@ LogicalResult unrollAndMergeGenerics(Operation *op, int unrollFactor,
         mlir::RewritePatternSet patterns(op->getContext());
         patterns.add<FrontloadAffineApply, secret::MergeAdjacentGenerics>(
             op->getContext(), innerMostLoop);
-        if (failed(applyPatternsAndFoldGreedily(op, std::move(patterns)))) {
+        // TODO (#1221): Investigate whether folding (default: on) can be
+        // skipped here.
+        if (failed(applyPatternsGreedily(op, std::move(patterns)))) {
           return WalkResult::interrupt();
         }
 
@@ -589,7 +591,9 @@ void YosysOptimizer::runOnOperation() {
   }
 
   secret::populateGenericCanonicalizers(cleanupPatterns, ctx);
-  if (failed(applyPatternsAndFoldGreedily(op, std::move(cleanupPatterns)))) {
+  // TODO (#1221): Investigate whether folding (default: on) can be skipped
+  // here.
+  if (failed(applyPatternsGreedily(op, std::move(cleanupPatterns)))) {
     signalPassFailure();
     getOperation()->emitError() << "Failed to cleanup generic ops";
     return;
@@ -601,7 +605,9 @@ void YosysOptimizer::runOnOperation() {
   // generic inputs is an easy way to do that.
   mlir::RewritePatternSet patterns(ctx);
   patterns.add<secret::CaptureAmbientScope, secret::YieldStoredMemrefs>(ctx);
-  if (failed(applyPatternsAndFoldGreedily(op, std::move(patterns)))) {
+  // TODO (#1221): Investigate whether folding (default: on) can be skipped
+  // here.
+  if (failed(applyPatternsGreedily(op, std::move(patterns)))) {
     signalPassFailure();
     getOperation()->emitError()
         << "Failed to preprocess generic ops before yosys optimizer";
@@ -636,7 +642,9 @@ void YosysOptimizer::runOnOperation() {
     // Merge generics after the function bodies are extracted.
     mlir::RewritePatternSet mergePatterns(ctx);
     mergePatterns.add<secret::MergeAdjacentGenerics>(ctx);
-    if (failed(applyPatternsAndFoldGreedily(op, std::move(mergePatterns)))) {
+    // TODO (#1221): Investigate whether folding (default: on) can be skipped
+    // here.
+    if (failed(applyPatternsGreedily(op, std::move(mergePatterns)))) {
       signalPassFailure();
       getOperation()->emitError()
           << "Failed to merge generic ops before yosys optimizer";