diff --git a/.github/workflows/examples.yml b/.github/workflows/examples.yml
index de83333..991d947 100644
--- a/.github/workflows/examples.yml
+++ b/.github/workflows/examples.yml
@@ -30,3 +30,7 @@ jobs:
       - name: Run Compile And Run
         run: |-
           uv run python/examples/mlir/compile_and_run.py
+
+      - name: Run apply basic schedule to basic payload
+        run: |-
+          uv run python/examples/schedule/transform_a_payload_according_to_a_schedule.py
diff --git a/python/examples/mlir/compile_and_run.py b/python/examples/mlir/compile_and_run.py
index d0529f6..009d9d5 100644
--- a/python/examples/mlir/compile_and_run.py
+++ b/python/examples/mlir/compile_and_run.py
@@ -4,7 +4,6 @@
 from mlir import ir
 from mlir.dialects import transform
 from mlir.dialects.transform import structured
-from mlir.dialects.transform import interpreter
 from mlir.execution_engine import ExecutionEngine
 from mlir.passmanager import PassManager
 
@@ -89,22 +88,6 @@ def create_schedule(ctx: ir.Context) -> ir.Module:
     return schedule
 
 
-def apply_schedule(kernel: ir.Module, schedule: ir.Module) -> None:
-    """
-    Apply transformation schedule to a kernel module.
-    The kernel is modified in-place.
-
-    Args:
-        kernel: A module with payload function.
-        schedule: A module with transform schedule.
-    """
-    interpreter.apply_named_sequence(
-        payload_root=kernel,
-        transform_root=schedule.body.operations[0],
-        transform_module=schedule,
-    )
-
-
 def create_pass_pipeline(ctx: ir.Context) -> PassManager:
     """
     Create an MLIR pass pipeline.
@@ -141,9 +124,11 @@ def main(args):
     ctx = ir.Context()
     kernel = create_kernel(ctx)
 
-    # Create a transform schedule and apply initial lowering.
-    schedule = create_schedule(ctx)
-    apply_schedule(kernel, schedule)
+    # Create a transform schedule and apply initial lowering to kernel.
+    # The kernel is modified in-place.
+    schedule_module = create_schedule(ctx)
+    named_seq: transform.NamedSequenceOp = schedule_module.body.operations[0]
+    named_seq.apply(kernel)
 
     # Create a pass pipeline and lower the kernel to LLVM dialect.
     pm = create_pass_pipeline(ctx)
diff --git a/python/examples/schedule/transform_a_payload_according_to_a_schedule.py b/python/examples/schedule/transform_a_payload_according_to_a_schedule.py
new file mode 100644
index 0000000..12702ab
--- /dev/null
+++ b/python/examples/schedule/transform_a_payload_according_to_a_schedule.py
@@ -0,0 +1,82 @@
+# Simply demonstrates applying a schedule to a payload.
+# To do so generates a basic payload and a basic schedule, purely as an example.
+
+from mlir.ir import Context, Location, InsertionPoint, Operation, Module
+from mlir.ir import RankedTensorType, F32Type, UnitAttr
+from mlir.dialects import arith, func, linalg, tensor, transform
+from mlir.dialects.transform import structured
+
+
+def example_payload() -> Module:
+    """IR for:
+    Zero = ...
+    X = matmul(..., C=Zero)
+    Y = matmul(..., C=Zero)
+    Res = add(X, Y)
+
+    Can be re-written to:
+    X = matmul(..., C=Zero)
+    Res = matmul(..., C=X)
+    """
+
+    print("NOTE: example payload module:")
+    payload = Module.create()
+    with InsertionPoint(payload.body):
+        matrixType = RankedTensorType.get([16, 16], F32Type.get())
+
+        @func.func(matrixType, matrixType, matrixType)
+        def fold_add_on_two_matmuls(matrixA, matrixB, weights):
+            empty = tensor.empty(matrixType.shape, matrixType.element_type)
+            c0 = arith.constant(F32Type.get(), 0.0)
+            zero_init = linalg.fill(c0, outs=[empty])
+            A_x_weights = linalg.matmul(matrixA, weights, outs=[zero_init])
+            empty2 = tensor.empty(matrixType.shape, matrixType.element_type)
+            zero_init2 = linalg.fill(c0, outs=[empty2])
+            B_x_weights = linalg.matmul(matrixB, weights, outs=[zero_init2])
+            added = linalg.add(A_x_weights, B_x_weights, outs=[empty])
+            return added
+
+    print(payload)
+    return payload
+
+
+def example_schedule() -> Module:
+    """Basic schedule wrapping a single rewrite pattern."""
+
+    print("NOTE: example schedule module:")
+    schedule_module = Module.create()
+    schedule_module.operation.attributes["transform.with_named_sequence"] = (
+        UnitAttr.get()
+    )
+    with InsertionPoint(schedule_module.body):
+        named_seq = transform.named_sequence(
+            "__transform_main",
+            input_types=[transform.any_op_t()],
+            result_types=[],
+            arg_attrs=[{"transform.readonly": UnitAttr.get()}],
+        )
+
+        with InsertionPoint(named_seq.body):
+            func = structured.MatchOp.match_op_names(
+                named_seq.bodyTarget, ["func.func"]
+            )  # TODO: fix syntax upstream
+            with InsertionPoint(transform.apply_patterns(func).patterns):
+                Operation.create(
+                    "transform.apply_patterns.linalg.fold_add_into_dest"
+                )  # TODO: expose dedicated builder upstream
+            transform.yield_([])
+
+    print(schedule_module)
+    return schedule_module
+
+
+with Context(), Location.unknown():
+    payload = example_payload()
+    schedule_module = example_schedule()
+    # Actual schedule is defined by the contained transform.named_sequence:
+    schedule: transform.NamedSequenceOp = schedule_module.body.operations[0]
+
+    schedule.apply(payload)  # The actual transformation happens here.
+
+    print("NOTE: result of applying schedule to payload:")
+    print(payload)