diff --git a/yellow-paper/docs/rollup-circuits/index.md b/yellow-paper/docs/rollup-circuits/index.md
index 29bbf7caddf..f093cbed596 100644
--- a/yellow-paper/docs/rollup-circuits/index.md
+++ b/yellow-paper/docs/rollup-circuits/index.md
@@ -308,17 +308,19 @@ class MergeRollupInputs {
 MergeRollupInputs *-- ChildRollupData: left
 MergeRollupInputs *-- ChildRollupData: right
 
+
 class RootRollupInputs { 
-    l1_to_l2_msgs_tree: Snapshot
     l1_to_l2_msgs: List~Fr~
     l1_to_l2_msgs_sibling_path: List~Fr~
-
+    parent: Header,
+    parent_sibling_path: List~Fr~
     archive_sibling_path: List~Fr~
     left: ChildRollupData
     right: ChildRollupData
 }
 RootRollupInputs *-- ChildRollupData: left
 RootRollupInputs *-- ChildRollupData: right
+RootRollupInputs *-- Header : parent
 
 
 class RootRollupPublicInputs {
@@ -428,7 +430,7 @@ graph BT
     K2[l2_to_l1_msgs 1.0]
     K3[l2_to_l1_msgs 1.1]
     K4[l2_to_l1_msgs 2.0]
-    K5[TxEffect 2.1]
+    K5[l2_to_l1_msgs 2.1]
     K6[l2_to_l1_msgs 3.0]
     K7[l2_to_l1_msgs 3.1]
 
diff --git a/yellow-paper/docs/rollup-circuits/merge_rollup.md b/yellow-paper/docs/rollup-circuits/merge_rollup.md
index 84b59358d33..e375cffde12 100644
--- a/yellow-paper/docs/rollup-circuits/merge_rollup.md
+++ b/yellow-paper/docs/rollup-circuits/merge_rollup.md
@@ -76,22 +76,22 @@ def MergeRollupCircuit(
     left: ChildRollupData, 
     right: ChildRollupData
 ) -> BaseOrMergeRollupPublicInputs:
-    assert left.proof.is_valid(left.inputs)
-    assert right.proof.is_valid(right.inputs)
+    assert left.proof.is_valid(left.public_inputs)
+    assert right.proof.is_valid(right.public_inputs)
 
-    assert left.inputs.constants == right.inputs.constants
-    assert right.inputs.start == left.inputs.end
-    assert left.inputs.type == right.inputs.type
-    assert left.inputs.height_in_block_tree == right.inputs.height_in_block_tree
+    assert left.public_inputs.constants == right.public_inputs.constants
+    assert left.public_inputs.end == right.public_inputs.start
+    assert left.public_inputs.type == right.public_inputs.type
+    assert left.public_inputs.height_in_block_tree == right.public_inputs.height_in_block_tree
 
     return BaseOrMergeRollupPublicInputs(
         type=1,
-        height_in_block_tree=left.inputs.height_in_block_tree + 1,
+        height_in_block_tree=left.public_inputs.height_in_block_tree + 1,
         aggregation_object=AggregationObject(left.proof, right.proof),
-        txs_hash=SHA256(left.inputs.txs_hash | right.inputs.txs_hash),
-        out_hash=SHA256(left.inputs.out_hash | right.inputs.out_hash),
-        start=left.inputs.start,
-        end=right.inputs.end,
-        constants=left.inputs.constants
+        txs_hash=SHA256(left.public_inputs.txs_hash | right.public_inputs.txs_hash),
+        out_hash=SHA256(left.public_inputs.out_hash | right.public_inputs.out_hash),
+        start=left.public_inputs.start,
+        end=right.public_inputs.end,
+        constants=left.public_inputs.constants
     )
 ```
\ No newline at end of file
diff --git a/yellow-paper/docs/rollup-circuits/root_rollup.md b/yellow-paper/docs/rollup-circuits/root_rollup.md
index 16bbbb83a92..b24e1f953b6 100644
--- a/yellow-paper/docs/rollup-circuits/root_rollup.md
+++ b/yellow-paper/docs/rollup-circuits/root_rollup.md
@@ -126,14 +126,15 @@ class ChildRollupData {
 ChildRollupData *-- BaseOrMergeRollupPublicInputs: public_inputs
 
 class RootRollupInputs { 
-    l1_to_l2_msgs_tree: Snapshot
     l1_to_l2_msgs: List~Fr~
     l1_to_l2_msgs_sibling_path: List~Fr~
-
+    parent: Header,
+    parent_sibling_path: List~Fr~
     archive_sibling_path: List~Fr~
     left: ChildRollupData
     right: ChildRollupData
 }
+RootRollupInputs *-- Header : parent
 RootRollupInputs *-- ChildRollupData: left
 RootRollupInputs *-- ChildRollupData: right
 
@@ -149,29 +150,33 @@ RootRollupPublicInputs *--Header : header
 
 ```python
 def RootRollupCircuit(
-    left: ChildRollupData, 
-    right: ChildRollupData, 
     l1_to_l2_msgs: List[Fr],
     l1_to_l2_msgs_sibling_path: List[Fr],
     parent: Header,
     parent_sibling_path: List[Fr],
     archive_sibling_path: List[Fr],
+    left: ChildRollupData, 
+    right: ChildRollupData, 
 ) -> RootRollupPublicInputs:
-    assert left.proof.is_valid(left.inputs)
-    assert right.proof.is_valid(right.inputs)
+    assert left.proof.is_valid(left.public_inputs)
+    assert right.proof.is_valid(right.public_inputs)
+
+    assert left.public_inputs.constants == right.public_inputs.constants
+    assert left.public_inputs.end == right.public_inputs.start
+    assert left.public_inputs.type == right.public_inputs.type
+    assert left.public_inputs.height_in_block_tree == right.public_inputs.height_in_block_tree
 
-    assert left.inputs.constants == right.inputs.constants
-    assert right.inputs.start == left.inputs.end
-    assert left.inputs.type == right.inputs.type
-    assert left.inputs.height_in_block_tree == right.inputs.height_in_block_tree
+    assert parent.state.partial == left.public_inputs.start
 
+    # Check that the parent is a valid parent
     assert merkle_inclusion(
         parent.hash(), 
         parent_sibling_path, 
-        left.inputs.constants.global_variables.block_number, 
-        left.inputs.constants.last_archive.root
+        left.public_inputs.constants.global_variables.block_number, 
+        left.public_inputs.constants.last_archive.root
     )
 
+    # Update the l1 to l2 msg tree
     l1_to_l2_msg_subtree = MerkleTree(l1_to_l2_msgs)
     l1_to_l2_msg_tree = merkle_insertion(
         parent.state.l1_to_l2_message_tree, 
@@ -181,17 +186,17 @@ def RootRollupCircuit(
         L1_To_L2_HEIGHT
     )
 
-    txs_hash = SHA256(left.inputs.txs_hash | right.inputs.txs_hash)
-    out_hash = SHA256(left.inputs.txs_hash | right.inputs.out_hash)
+    txs_hash = SHA256(left.public_inputs.txs_hash | right.public_inputs.txs_hash)
+    out_hash = SHA256(left.public_inputs.txs_hash | right.public_inputs.out_hash)
 
     header = Header(
-        last_archive = left.inputs.constants.last_archive,
+        last_archive = left.public_inputs.constants.last_archive,
         body_hash = SHA256(txs_hash | out_hash | SHA256(l1_to_l2_msgs)),
         state = StateReference(
             l1_to_l2_message_tree = l1_to_l2_msg_tree,
-            partial = right.inputs.end,
+            partial = right.public_inputs.end,
         ),
-        global_variables = left.inputs.constants.global_variables,
+        global_variables = left.public_inputs.constants.global_variables,
     )
 
     archive = merkle_insertion(
@@ -203,7 +208,9 @@ def RootRollupCircuit(
     )
 
     return RootRollupPublicInputs(
-        aggregation_object = left.inputs.aggregation_object + right.inputs.aggregation_object,
+        aggregation_object = 
+            left.public_inputs.aggregation_object + 
+            right.public_inputs.aggregation_object,
         archive = archive,
         header: Header,
     )