Chapter 13: Global Code Motion

Co-authored-by: Thalia Archibald <thalia@archibald.dev>
Co-authored-by: Dibyendu Majumdar <mobile@majumdar.org.uk>
Co-authored-by: Tamás Hadházy <85063808+Hels15@users.noreply.github.com>
Co-authored-by: Hsiang-Ying Fu <66062782+fuhsnn@users.noreply.github.com>
Co-authored-by: tannal <tannal2409@gmail.com>
Co-authored-by: hadha <helsgithub15@gmail.com>
Co-authored-by: fuhsnn <66062782+fuhsnn@users.noreply.github.com>
Co-authored-by: XmiliaH <45106915+XmiliaH@users.noreply.github.com>
Co-authored-by: Symious <14933944+symious@users.noreply.github.com>
Co-authored-by: RobertObkircher <robert.obkircher@gmail.com>
Co-authored-by: Robert Obkircher <robert.obkircher@gmail.com>
Co-authored-by: Claude Opus 5 <noreply@anthropic.com>

30 files changed, 2370 insertions, 0 deletions

diff --git a/docs/chapter13/13-grammar.md b/docs/chapter13/13-grammar.md
new file mode 100644
index 00000000..4e7ae5b4
--- /dev/null
+++ b/docs/chapter13/13-grammar.md
@@ -0,0 +1,130 @@
+# Grammar for Chapter 13
+
+```antlrv4
+grammar SimpleLanguage;
+
+program
+    : statement+ EOF
+    ;
+
+statement
+    : returnStatement
+    | structDeclaration
+    | declStatement
+    | blockStatement
+    | expressionStatement
+    | ifStatement
+    | whileStatement
+    | breakStatement
+    | continueStatement
+    ;
+
+PRIMTYPE
+    : 'int'
+    ;
+
+field
+    : PRIMTYPE IDENTIFIER ';'
+    | structName ('?')? IDENTIFIER ';'
+    ;
+
+fields
+    : field+
+    ;
+
+structDeclaration
+    : 'struct' IDENTIFIER '{' fields '}'
+    ;
+
+whileStatement
+    : 'while' '(' expression ')' statement
+    ;
+
+breakStatement
+    : 'break' ';'
+    ;
+
+continueStatement
+    : 'continue' ';'
+    ;
+
+ifStatement
+    : 'if' '(' expression ')' statement ('else' statement)?
+    ;
+
+
+expressionStatement
+    : IDENTIFIER '=' expression ';'
+    | fieldExpression '=' expression ';'
+    ;
+
+blockStatement
+    : '{' statement+ '}'
+    ;
+
+structName
+    : IDENTIFIER
+    ;
+
+declStatement
+    : PRIMTYPE IDENTIFIER '=' expression ';'
+    | structName ('?')? IDENTIFIER '=' expression ';'
+    ;
+
+returnStatement
+    : 'return' expression ';'
+    ;
+
+expression
+    : comparisonExpression
+    ;
+
+comparisonExpression
+    : additiveExpression (('==' | '!='| '>'| '<'| '>='| '<=') additiveExpression)*
+    ;
+
+additiveExpression
+    : multiplicativeExpression (('+' | '-') multiplicativeExpression)*
+    ;
+
+multiplicativeExpression
+    : unaryExpression (('*' | '/') unaryExpression)*
+    ;
+
+unaryExpression
+    : ('-') unaryExpression
+    | '!' unaryExpression
+    | primaryExpression
+    ;
+
+newExpression
+    : 'new' IDENTIFIER
+    ;
+
+fieldExpression
+    : primaryExpression '.' IDENTIFIER
+    ;
+
+primaryExpression
+    : IDENTIFIER
+    | INTEGER_LITERAL
+    | 'true'
+    | 'false'
+    | 'null'
+    | newExpression
+    | '(' expression ')'
+    | fieldExpression
+    ;
+
+INTEGER_LITERAL
+    : [1-9][0-9]*
+    | [0]
+    ;
+
+IDENTIFIER
+    : NON_DIGIT (NON_DIGIT | DEC_DIGIT)*
+    ;
+
+NON_DIGIT: [a-zA-Z_];
+DEC_DIGIT: [0-9];
+```
diff --git a/docs/chapter13/Makefile b/docs/chapter13/Makefile
new file mode 100644
index 00000000..6fa0f057
--- /dev/null
+++ b/docs/chapter13/Makefile
@@ -0,0 +1 @@
+include ../../graph/docs.mk
diff --git a/docs/chapter13/README.md b/docs/chapter13/README.md
new file mode 100644
index 00000000..b59563d5
--- /dev/null
+++ b/docs/chapter13/README.md
@@ -0,0 +1,371 @@
+# Chapter 13: Global Code Motion
+
+[Previous: Chapter 12](../chapter12/README.md) |
+[Next: Chapter 14](../chapter14/README.md)
+
+This chapter schedules the graphs built in Chapters 10-12, including
+reference fields and lazy memory partitions. It chooses a slot-0 control input
+for movable operations and preserves the ordering of potentially aliasing
+Loads and Stores.
+
+Also in this chapter, we'll be presenting several fairly detailed graph
+algorithms.  You might want to brush up on your graph theory!
+
+# Table of Contents
+
+1. [High Level Overview](#high-level-overview)
+2. [Scheduling Walk Through](#scheduling-walk-through)
+3. [Scheduling a Loop](#scheduling-a-loop)
+4. [Components of the Global Code Motion Algorithm](#components-of-the-global-code-motion-algorithm)
+5. [Identification of Basic Blocks in SoN graph](#identification-of-basic-blocks-in-son-graph)
+6. [Handling Infinite Loops](#handling-infinite-loops)
+7. [Dominators](#dominators)
+8. [Loop depth](#loop-depth)
+9. [Early Schedule](#early-schedule)
+10. [Late Schedule](#late-schedule)
+11. [Inserting Anti Dependencies](#inserting-anti-dependencies)
+12. [Video Walk Through](#video-walk-through)
+
+You can also read [this chapter](https://github.com/SeaOfNodes/Simple/tree/linear-chapter13) in a linear Git revision history on the [linear](https://github.com/SeaOfNodes/Simple/tree/linear) branch and [compare](https://github.com/SeaOfNodes/Simple/compare/linear-chapter12...linear-chapter13) it to the previous chapter.
+
+
+The original input source program defines a sequence in which things happen. As
+we parse the program into Sea of Nodes representation and perform various
+optimizations, this sequence is not fully maintained. The optimized Sea of
+Nodes graph is driven by the dependencies between nodes rather than the
+sequence of instructions in the original source program.
+
+Our goal in this chapter is to look at how we can recover a schedule for executing instructions from an
+optimized Sea of Nodes graph. This schedule needs to preserve the semantics of the original source program,
+but is otherwise allowed to reorder the execution of instructions.
+
+Since the scheduling algorithm works across the implicit Basic Blocks in the SoN Graph,
+we call this a Global Code Motion algorithm; the scheduler can move instructions across Basic Block boundaries.
+
+The primary reference for this algorithm is the GCM GVN paper [^1]. However, the implementation in Simple has some
+differences compared to the version described in the paper.
+
+Since this is a complex topic, we will present a high level summary first and then delve into the details.
+
+## High Level Overview
+
+The Sea of Nodes graph has two virtual graphs within it.
+
+* There is a control flow graph, represented by certain node types, such as Start, If, Region, etc.
+* There is a data graph, primarily driven by Def-Use edges between nodes that produce or consume values or memory.
+
+From a scheduling point of view, the control flow graph is fixed, and immovable.
+However, the nodes that consume or produce data values/memory have some flexibility in terms of when they are executed. The goal of the
+scheduling algorithm is to find the best placement of these nodes so that they are both optimum and correct.
+
+At its core, the scheduling algorithm works in two phases:
+
+* Schedule Early - in this phase, we do an upward DFS walk on the "inputs" of each Node, starting from the bottom (Stop). We schedule each data node to the
+  first control block where they are dominated by their inputs.
+* Schedule Late - in this phase we work backwards from Stop, scheduling uses before definitions, and move data nodes to a block between the first block calculated above,
+  and the last control block where they dominate all their uses. The placement is subject to the condition that it is in the shallowest loop nest possible, and is as control dependent as possible.
+  Additionally, the placement of Load instructions must ensure correct ordering between Loads and Stores of the same memory location.
+
+## Scheduling Walk Through
+
+Before we describe the steps in detail, it is instructive to walk through an example and see the changes that occur to the SoN graph during scheduling.
+
+To motivate the discussion, we will use this example program.
+
+```java
+struct S { int f; }
+S v=new S;
+v.f = 2;
+int i=new S.f;
+i=v.f;
+if (arg) v.f=1;
+return i;
+```
+
+First let's look at the graph before scheduling.
+
+These walkthrough diagrams show the precise `S.f` chain and the final
+MemMerge consumed by Return. The unchanged default memory comes from Start;
+any redundant bulk Phis have folded away. As in Chapters 10 and 11, the diagrams omit
+control-flow context, including Regions and their Phi bindings. Small,
+detached True/False projections remain where they gate a Load or Store.
+Unlike Chapter 10's schematic source gates, these figures show the actual
+scheduling inputs at each stage. Entry-block and Loop bindings are omitted.
+
+![Graph1](./graph1.svg)
+
+Observe that
+
+* Control nodes are immovable. Most are omitted here.
+* New nodes already have control inputs, and Phis are bound to Regions;
+  these bindings remain fixed even though they are not drawn.
+* The load `.f` and store `.f=` nodes are still "floating": they have no
+  control input at this stage, so scheduling must choose their blocks.
+
+Now, let's look at the graph after we run the early schedule.
+
+![Graph2](./graph2.svg)
+
+
+The early schedule puts the load `.f` and stores `.f=` in the first basic
+block, since their inputs are available there. These entry-block control
+bindings are omitted, so the memory view looks unchanged.
+
+The graph below focuses on memory and data dependencies after late scheduling.
+The control-flow scaffold, including the Region, is omitted. Store #22's
+control input remains visible as the red edge to the standalone True
+projection #8; the Store-to-Load anti-dependency and memory Phis are retained.
+
+![Graph3](./graph3.svg)
+
+The snip below shows the main changes in the graph:
+
+![Store ordered after the earlier load](./graph3-snip.svg)
+
+* The store `.f=` now has an anti-dependency on the load `.f`; this ensures that the store is scheduled after the load, as required by program semantics. We discuss anti-dependencies in detail later.
+* Observe also that the store `.f=` is now bound to the True branch of the If node.
+
+## Scheduling a Loop
+
+We show another example, this time involving a loop.
+
+```java
+struct S { int f; }
+S v = new S;
+int i = arg;
+while (arg > 0) {
+    int j = i/3;
+    if (arg == 5)
+        v.f = j;
+    arg = arg - 1;
+}
+return v;
+```
+
+The SoN graph prior to scheduling looks like this:
+
+![Graph4](./graph4.svg)
+
+Following early schedule generation, we get:
+
+![Graph5](./graph5.svg)
+
+The early schedule places Store #31 at the loop header (its control binding
+is omitted). Late scheduling moves it to the True branch #15 of
+`if (arg == 5)`, shown by the red control edge:
+
+![Graph6](./graph6.svg)
+
+The final execution schedule shows that the expression `i/3` can be performed outside the loop because it only depends on the
+original value of `arg`, and hence is loop invariant.
+
+## Components of the Global Code Motion Algorithm
+
+We have already alluded to several components of the GCM algorithm in passing above. Here we list them out as well as others we did not mention:
+
+* The SoN graph has implicit basic blocks in the control flow nodes. For the GCM algo, we need to recognize these nodes more explicitly.
+* When a program has an infinite loop, it poses a problem for the algo, as nodes can be unreachable from the Stop node. To work around this issue, we need to discover
+  infinite loops and create a dummy edge connecting the loop to the Stop node.
+* Loops are already identified in the Simple SoN graph, so we do not need a loop discovery step. However, we need to compute the loop depth associated with each CFG node.
+* In [Chapter 6](../chapter06/README.md) we explained the concept of Dominators. Dominators are key to the GCM algo, and we extend our incremental dominator discovery algo to
+  ensure that it meets the requirements of the algo.
+* We already mentioned the two phases of the algo - the Early Scheduling and the Late Scheduling.
+* In addition, we need to add anti-dependency edges between Loads and Stores in certain scenarios to enforce correct execution order.
+* There are a few changes to our Node hierarchy to help us implement the GCM algo more conveniently. These changes do not conceptually alter the Node hierarchy we inherited from the previous chapters.
+
+## Identification of Basic Blocks in SoN graph
+
+The Sea of Nodes graph already captures the program's control flow graph. This information is implicit in the control nodes and edges from control nodes to other types of nodes.
+
+To recap, Control starts at the Start node, via a projection that is bound to the name `$ctrl`. As the control flows in the program, this name binding gets updated, and control is
+passed around, until it reaches the Stop node.
+
+The Basic Block structure of the CFG can be easily constructed by recognizing that certain control nodes start a Basic Block, whereas certain others end a BB.
+
+Here is the list of all control nodes:
+
+| Node   | Starts a BB                             | Ends a BB |
+|--------|-----------------------------------------|-----------|
+| Start  | Yes but only via the `$ctrl` projection | No        |
+| CProj  | Yes if input control is an If node      | No        |
+| Region | Yes                                     | No        |
+| If     | No                                      | Yes       |
+| Return | No                                      | Yes       |
+| Stop   | Yes                                     | Yes       |
+
+Changes to Node hierarchy in this chapter:
+
+* All control nodes above now extend a base class CFG Node. This allows us to place common functionality of control flow nodes in the base class.
+* The CProj node extends the regular Proj node and is used in following cases:
+  * The `$ctrl` projection off Start
+  * The True and False projections off If.
+* The Never node is a special sub class of If that is used to handle infinite loops as explained later.
+* The XCtrl node represents a dead control.
+
+## Handling Infinite Loops
+
+Here is an example of code that contains an infinite loop:
+
+```java
+while (1) {}
+return 0;
+```
+
+First let's look at the graph resulting from this:
+
+![Graph7](./graph7.svg)
+
+Now, look at the modified graph after we insert an edge from the infinite loop to Stop node.
+
+![Graph8](./graph8.svg)
+
+The implementation is in
+[`LoopNode.forceExit()`](../../src/main/java/com/seaofnodes/simple/node/LoopNode.java#L57).
+It walks the backedge's dominator chain to look for an exit. If none exists,
+it inserts a Never node and a never-taken return path, making the loop
+reachable to the scheduler's backward walk.
+
+## Dominators
+
+In Simple, we compute Dominators incrementally. Our approach relies on the fact that we may delete parts of the graph during peepholes,
+but we never introduce new control structure via peepholes. This allows us to use a simple approach described below.
+
+The CFG node is the base class for all control nodes. It maintains a conservative approximation of dominator depth via `_idepth`. This field is a cached value representing
+the immediate dominator depth. Its initial value is `0`, which signifies that it has not yet been computed. The depth is computed on request.
+
+See [`CFGNode.idepth()`](../../src/main/java/com/seaofnodes/simple/node/CFGNode.java#L51)
+for the default computation and cache. The overrides in
+[`RegionNode`](../../src/main/java/com/seaofnodes/simple/node/RegionNode.java#L94),
+[`LoopNode`](../../src/main/java/com/seaofnodes/simple/node/LoopNode.java#L31),
+[`StartNode`](../../src/main/java/com/seaofnodes/simple/node/StartNode.java#L36), and
+[`StopNode`](../../src/main/java/com/seaofnodes/simple/node/StopNode.java#L58)
+handle merges, loop entries, and the graph's endpoints.
+
+If portions of the control flow graph are deleted, then there will be gaps in the `_idepth`, but it still correctly reflects the
+invariant that the value of `_idepth` increases as we go down the dominator tree.
+
+Alongside the dominator depth, which is cached on first compute, a method is provided to get the immediate Dominator node. This
+value is not cached as it is only valid at a point in time, and is invalidated as the graph changes.
+
+[`CFGNode.idom()` and `domLCA()`](../../src/main/java/com/seaofnodes/simple/node/CFGNode.java#L60)
+provide the default immediate dominator and the walk that finds the least
+common ancestor of two dominators.
+[`RegionNode.idom()`](../../src/main/java/com/seaofnodes/simple/node/RegionNode.java#L103)
+combines the incoming paths; [`LoopNode.idom()`](../../src/main/java/com/seaofnodes/simple/node/LoopNode.java#L33)
+uses the loop entry. Start and Stop have no immediate dominator.
+
+## Loop Depth
+
+Simple's Sea of Nodes graph identifies loops explicitly via Loop nodes. Since the language provides a single way to create a loop, using the `while` statement,
+it is not necessary to implement a generic loop discovery process.
+
+We do however need to compute a loop depth. This is done similarly to how we compute the dominator depth.
+
+[`CFGNode.loopDepth()`](../../src/main/java/com/seaofnodes/simple/node/CFGNode.java#L78)
+inherits depth from its control input, while
+[`RegionNode.loopDepth()`](../../src/main/java/com/seaofnodes/simple/node/RegionNode.java#L116)
+uses an incoming path.
+[`LoopNode.loopDepth()`](../../src/main/java/com/seaofnodes/simple/node/LoopNode.java#L35)
+adds a nesting level and walks the backedge's dominator chain to mark loop exits.
+[`StartNode`](../../src/main/java/com/seaofnodes/simple/node/StartNode.java#L41) and
+[`StopNode`](../../src/main/java/com/seaofnodes/simple/node/StopNode.java#L68)
+establish the outermost depth of 1.
+
+## Early Schedule
+
+The GCM algorithm proper starts with the computation of the early schedule, during which we do an upward DFS walk on the "inputs" of each Node, starting from the bottom (Stop). We schedule each data node to the
+first control block where they are dominated by their inputs.
+
+A pre-condition of this is to ensure that infinite loops have been fixed as described earlier.
+
+The implementation starts in
+[`GlobalCodeMotion.schedEarly()`](../../src/main/java/com/seaofnodes/simple/GlobalCodeMotion.java#L62).
+[`_rpo_cfg()`](../../src/main/java/com/seaofnodes/simple/GlobalCodeMotion.java#L85)
+builds the CFG traversal order, and
+[`_schedEarly()`](../../src/main/java/com/seaofnodes/simple/GlobalCodeMotion.java#L94)
+recursively schedules data inputs. It skips recursion through Phi inputs to
+avoid entering a data cycle before its control has been scheduled.
+
+Existing control and Phi/Proj bindings are preserved. Floating nodes receive
+the deepest input block as their earliest placement. MemMerge follows this
+same rule, ignoring absent entries in its sparse alias table.
+
+## Late Schedule
+
+Late scheduling starts at Stop and uses a worklist to place uses before their
+definitions. CFG nodes, Phis, projections, and allocations provide fixed
+placements. Other nodes wait until their uses have been scheduled; a Load also
+waits for memory users that can overwrite or merge its alias. The chosen block
+lies between the early placement and the common dominator of all uses, favoring
+shallower loops and then deeper control flow.
+
+The implementation is divided into these steps:
+
+* [`schedLate()`](../../src/main/java/com/seaofnodes/simple/GlobalCodeMotion.java#L114)
+  manages the placement tables and installs the final control inputs;
+  [`breadth()`](../../src/main/java/com/seaofnodes/simple/GlobalCodeMotion.java#L129)
+  drives the worklist and wakes definitions and waiting loads as uses finish.
+* [`_doSchedLate()`](../../src/main/java/com/seaofnodes/simple/GlobalCodeMotion.java#L175)
+  finds the common dominator of uses, accounts for load anti-dependencies, and
+  walks toward the early placement. It calls
+  [`better()`](../../src/main/java/com/seaofnodes/simple/GlobalCodeMotion.java#L215)
+  to compare candidate blocks.
+* [`use_block()`](../../src/main/java/com/seaofnodes/simple/GlobalCodeMotion.java#L202)
+  handles Phi uses at their matching incoming control paths, rather than at
+  the merge itself.
+
+## Inserting Anti Dependencies
+
+To ensure that Loads and Stores to the same memory location are correctly
+ordered, we insert an edge from the Store to the Load as described below: the
+Store must wait for the earlier Load.  We call these edges anti-dependencies
+because they do not represent the Def-Use dependency that we normally capture
+in SoN, and are purely present as scheduling constraints.
+
+We compute anti-dependencies DURING running schedule late. This is because we rely on the early-schedule, and the late-schedule of the Load's uses (before scheduling the Load).
+
+Looking backwards from the Load, we follow its memory input to Start's memory
+projection, a memory Phi, or a Store. Optimization has already selected the
+Load's precise slice through any MemMerge. We inspect users of that memory
+definition, keeping only Stores and memory Phis that cover the Load's alias.
+Start's single memory projection may supply many aliases, so sharing a memory
+input alone does not imply an anti-dependency.
+
+MemMerge only packages slices; it does not overwrite any of them. Treating it
+as a write could make a Load wait for an aggregate which itself depends on the
+Load's result. The same alias filter is used both when deciding whether a Load
+is ready to schedule and when computing its anti-dependencies. A completed
+memory user wakes waiting loads even if their shared memory definition has
+already been scheduled.
+
+Since we're in the middle of `schedLate`, we have already computed all the late
+schedules of a Load's users, and we have the Loads *Least Common Ancestor* of
+uses, the LCA or late position.  We inspect the set of mem-defs that might
+impact the Load, and either add an anti-dependency from Store to Load, or raise
+the Loads effective LCA.  For Phi mem-defs, we look at the Phi inputs and place
+an effective use on that block; this will be used to raise the Load's LCA.  For
+stores, we do the same - until/unless we find stores with the SAME block as the
+Load's LCA. Then we add the anti-dependency edge to force ordering within the
+same block.
+
+See [`antiUse()`](../../src/main/java/com/seaofnodes/simple/GlobalCodeMotion.java#L224)
+for the alias filter, and
+[`find_anti_dep()`](../../src/main/java/com/seaofnodes/simple/GlobalCodeMotion.java#L233)
+for marking the Load's candidate blocks and inspecting competing memory users.
+[`anti_dep()`](../../src/main/java/com/seaofnodes/simple/GlobalCodeMotion.java#L260)
+walks the competing operation's dominator interval, raises the Load's LCA,
+and adds a Store-to-Load edge when required. It checks the Store's full interval
+because the evaluator's scheduler may place that Store independently of GCM.
+
+## Video Walk Through
+
+Please watch the following video for a detailed walk through of the implementation.
+
+* [Coffee Compiler Club - 21 June 2024](https://youtu.be/5Po0gxfE7LA?feature=shared).
+* [Coffee Compiler Club - 26 June 2024](https://www.youtube.com/watch?v=HnN2YzmFb-8&t=0s)
+
+[^1]: Cliff Click. (1995).
+  Global Code Motion Global Value Numbering.
+
+Next, [Chapter 14](../chapter14/README.md) adds floating-point arithmetic and
+narrow numeric types to this scheduled compiler.
diff --git a/docs/chapter13/graph1.gv b/docs/chapter13/graph1.gv
new file mode 100644
index 00000000..4d6ee1fe
--- /dev/null
+++ b/docs/chapter13/graph1.gv
@@ -0,0 +1,79 @@
+digraph chapter13 {
+/*
+struct S { int f; }
+S v=new S;
+v.f = 2;
+int i=new S.f;
+i=v.f;
+if (arg) v.f=1;
+return i;
+
+*/
+	rankdir=BT;
+	concentrate="true";
+	compound="true";
+	subgraph cluster_Nodes {
+		Start2 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">Start</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">$ctrl</TD><TD PORT="p1">$mem</TD><TD PORT="p2">arg</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		MemMerge [ shape=box label="MemMerge" ];
+		Stop3 [ shape=box style=filled fillcolor=yellow label="Stop" ];
+		Con_4 [ label="#0" ];
+		new9 [ label="new S" ];
+		Con_11 [ label="#2" ];
+		Store12 [ label=".f =" ];
+		new13 [ label="new S" ];
+		Store14 [ label=".f =" ];
+		Load16 [ label=".f" ];
+		If17 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">If</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">True</TD><TD PORT="p1" BGCOLOR="yellow">False</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Con_21 [ label="#1" ];
+		Store22 [ label=".f =" ];
+		Region23 [ shape=box style=filled fillcolor=yellow label="Region" ];
+		Phi_224 [ style=filled fillcolor=lightyellow label="MemPhi_2" ];
+		Return25 [ shape=box style=filled fillcolor=yellow label="Return" ];
+		{ rank=same; Region23;Phi_224;}
+	}
+	edge [ fontname=Helvetica, fontsize=8 ];
+	Stop3 -> Return25[taillabel=0 color=red];
+	new9 -> Start2:p0[taillabel=0 color=green];
+	Store12 -> Start2:p1[taillabel=1 color=blue];
+	Store12 -> new9[taillabel=2];
+	Store12 -> Con_11[taillabel=3];
+	new13 -> Start2:p0[taillabel=0 color=green];
+	Store14 -> Store12[taillabel=1 color=blue];
+	Store14 -> new13[taillabel=2];
+	Store14 -> Con_4[taillabel=3];
+	Load16 -> Store14[taillabel=1 color=blue];
+	Load16 -> new9[taillabel=2];
+	If17 -> Start2:p0[taillabel=0 color=red];
+	If17 -> Start2:p2[taillabel=1];
+	Store22 -> Store14[taillabel=1 color=blue];
+	Store22 -> new9[taillabel=2];
+	Store22 -> Con_21[taillabel=3];
+	Region23 -> If17:p0[taillabel=1 color=red];
+	Region23 -> If17:p1[taillabel=2 color=red];
+	Phi_224 -> Region23 [style=dotted taillabel=0];
+	Phi_224 -> Store22[taillabel=1 color=blue];
+	Phi_224 -> Store14[taillabel=2 color=blue constraint=false];
+	Return25 -> Region23[taillabel=0 color=red];
+	Return25 -> Load16[taillabel=2];
+	Return25 -> MemMerge[taillabel=1 color=blue];
+	MemMerge -> Start2:p1[taillabel=1 color=blue];
+	MemMerge -> Phi_224[taillabel=2 color=blue];
+}
diff --git a/docs/chapter13/graph1.json b/docs/chapter13/graph1.json
new file mode 100644
index 00000000..aac69ce2
--- /dev/null
+++ b/docs/chapter13/graph1.json
@@ -0,0 +1,25 @@
+{
+  "ver": 1,
+  "comp": "chapter13/docs/graph1.svg",
+  "step": 1,
+  "roots": [25],
+  "scope": 0,
+  "nodes": [
+    {"id": 1, "label": "MemMerge", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "DATA", "label": null}, {"idx": 1, "def": 6, "role": "MEM", "label": null}, {"idx": 2, "def": 224, "role": "MEM", "label": null}], "proj": null},
+    {"id": 2, "label": "Start", "type": null, "kind": "CTRL", "edges": [], "proj": null},
+    {"id": 4, "label": "#0", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 6, "label": "$mem", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 2, "role": "MEM", "label": null}], "proj": {"par": 2, "idx": 1}},
+    {"id": 9, "label": "new S", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}], "proj": null},
+    {"id": 11, "label": "#2", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 12, "label": ".f =", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "DATA", "label": null}, {"idx": 1, "def": 6, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}, {"idx": 3, "def": 11, "role": "DATA", "label": null}], "proj": null},
+    {"id": 13, "label": "new S", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}], "proj": null},
+    {"id": 14, "label": ".f =", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "DATA", "label": null}, {"idx": 1, "def": 12, "role": "MEM", "label": null}, {"idx": 2, "def": 13, "role": "DATA", "label": null}, {"idx": 3, "def": 4, "role": "DATA", "label": null}], "proj": null},
+    {"id": 16, "label": ".f", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "DATA", "label": null}, {"idx": 1, "def": 14, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}], "proj": null},
+    {"id": 21, "label": "#1", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 22, "label": ".f =", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "DATA", "label": null}, {"idx": 1, "def": 14, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}, {"idx": 3, "def": 21, "role": "DATA", "label": null}], "proj": null},
+    {"id": 25, "label": "Return", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 1, "role": "MEM", "label": null}, {"idx": 2, "def": 16, "role": "DATA", "label": null}], "proj": null},
+    {"id": 224, "label": "MemPhi_2", "type": null, "kind": "PHI", "edges": [{"idx": 0, "def": 0, "role": "ASSOC", "label": null}, {"idx": 1, "def": 22, "role": "MEM", "label": null}, {"idx": 2, "def": 14, "role": "MEM", "label": null}], "proj": null}
+  ],
+  "groups": [
+  ]
+}
diff --git a/docs/chapter13/graph1.svg b/docs/chapter13/graph1.svg
new file mode 100644
index 00000000..93a2a03f
--- /dev/null
+++ b/docs/chapter13/graph1.svg
@@ -0,0 +1,123 @@
+<svg aria-label="Compiler graph" width="565" height="766" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 565 766" style="font-family: sans-serif;"><style>
+    html, body { height:100%; margin:0; font-family:sans-serif; }
+    .viewer { height:100%; display:grid; grid-template-rows:auto minmax(0,1fr) auto; }
+    .source { padding:8px; border-bottom:1px solid #ccc; }
+    #program { width:min(600px,80vw); vertical-align:middle; }
+    #status { margin-top:4px; }
+    #graph { min-height:0; overflow:hidden; position:relative; background:#fafbfc; }
+    #elk { width:100%; height:100%; }
+    #graph svg { display:block; }
+    .tools { display:flex; flex-wrap:wrap; align-items:center; gap:14px; margin-top:8px; font-size:12px; }
+    .hint { color:#616c78; }
+    .ctrl { color:#b63838; } .mem { color:#2867b2; } .data { color:#536477; }
+    .edge { fill:none; stroke-width:1.5; }
+    .edge.CTRL { stroke-width:2; }
+    .edge.ASSOC { stroke-dasharray:4 4; }
+    .edge.PARSER { stroke-dasharray:5 4; }
+    .parser rect { fill:#f6f0ff; stroke:#7956a5; stroke-width:1.5; stroke-dasharray:5 4; }
+    .edge.selected { stroke-width:3.5; }
+    .edge.bundle { stroke-width:4; }
+    .edge.bundle.selected { stroke-width:6; }
+    .edge-hit { fill:none; stroke:transparent; stroke-width:12; vector-effect:non-scaling-stroke; pointer-events:stroke; cursor:pointer; }
+    .edge-jump { fill:transparent; pointer-events:all; cursor:pointer; }
+    .node { cursor:pointer; }
+    .box { stroke:#758191; stroke-width:1; }
+    .node.held .box { stroke-dasharray:5 3; }
+    .node.near .box { stroke:#c18221; stroke-width:2; }
+    .node.focus .box { stroke:#9c4900; stroke-width:3; }
+    .node.selected .box { stroke:#1569b9; stroke-width:3; }
+    .node.folded .box { stroke-width:4; }
+    .node.folding .box { fill:#f4ccd7; }
+    .fold-tag { font-size:9px; font-weight:700; fill:#963751; }
+    .peep-area { fill:#fff3d9; fill-opacity:.8; stroke:#c18221; stroke-width:2; pointer-events:none; }
+    .node.peep-edit .box { stroke:#9c4900; stroke-width:3; }
+    .node.error .box { stroke:#b42318; stroke-width:4; }
+    #event.error { color:#b42318; font-weight:600; white-space:pre-wrap; overflow-wrap:anywhere; }
+    .peep-ghosts { pointer-events:none; }
+    .region-box { stroke:#9da9b8; stroke-width:1.5; }
+    .fold-btn { cursor:pointer; }
+    .fold-btn rect { fill:white; stroke:#596674; }
+    .fold-btn text { font-size:14px; fill:#152330; }
+    .fold-btn:focus rect { stroke:#1569b9; stroke-width:2; }
+    .shortcut { cursor:pointer; }
+    .shortcut path { fill:none; stroke-width:1.5; }
+    .shortcut rect { fill:#fff8ec; stroke:#b63838; stroke-dasharray:3 2; }
+    .shortcut text { font-size:11px; fill:#783030; }
+    .shortcut.selected rect, .shortcut:focus rect { stroke-width:2.5; }
+    .label { font-size:12px; fill:#152330; font-weight:600; }
+    .node-id { font-size:10px; fill:#596674; font-weight:400; }
+    .type { font-size:11px; fill:#455768; }
+    .port { stroke:#536477; stroke-width:1; }
+    .row { stroke:#b6afcf; stroke-width:1; }
+    .bind { font-size:12px; fill:#152330; }
+    .slot { font-size:10px; fill:#364352; paint-order:stroke; stroke:#fafbfc; stroke-width:3; }
+    #detail { position:absolute; top:8px; right:8px; margin:0; padding:12px; max-width:320px;
+      max-height:45%; overflow:auto; white-space:pre-wrap; overflow-wrap:anywhere;
+      background:#fffffff2; border:1px solid #bac5d0; border-radius:4px; font-size:12px; }
+    .controls { display:flex; flex-wrap:wrap; justify-content:center; align-items:center; gap:6px; padding:6px; }
+    .button { color:white; background:black; font-size:20px; min-width:30px; }
+    .button:disabled { background:grey; }
+    .count { font-size:20px; min-width:35px; text-align:center; }
+    #N { width:6ch; }
+    #scrub { width:clamp(120px,35vw,600px); }
+  </style><defs><marker id="arrow-CTRL" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#b63838"/></marker><marker id="arrow-DATA" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#536477"/></marker><marker id="arrow-MEM" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#2867b2"/></marker><marker id="arrow-ASSOC" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#9396a3"/></marker><marker id="arrow-PARSER" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#7956a5"/></marker></defs><rect width="100%" height="100%" fill="rgb(250, 251, 252)"/><g><g class="regions" style="opacity: 1;"/><rect class="peep-area" rx="36" style="opacity: 0;"/><g class="edges"><path class="edge MEM" id="e1i1" d="M84,118 L84,536 Q84,544 92,544 L137,544 Q145,544 145,552 L145,582" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#1[1] → #6 · MEM</title></path><path class="edge MEM" id="e1i2" d="M175,534 L175,582" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#1[2] → #224 · MEM</title></path><path class="edge MEM" id="e12i1" d="M84,118 L84,130 Q84,138 92,138 L146,138 Q154,138 154,146 L154,166" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#12[1] → #6 · MEM</title></path><path class="edge DATA" id="e12i2" d="M242,118 L242,123 Q242,128 237,128 L186,128 Q178,128 178,136 L178,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#12[2] → #9 · DATA</title></path><path class="edge DATA" id="e12i3" d="M394,118 L394,130 Q394,138 386,138 L210,138 Q202,138 202,146 L202,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#12[3] → #11 · DATA</title></path><path class="edge MEM" id="e14i1" d="M166,222 L166,227 Q166,232 171,232 L298,232 Q306,232 306,240 L306,270" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#14[1] → #12 · MEM</title></path><path class="edge DATA" id="e14i2" d="M318,222 L318,227 Q318,232 323,232 L324,232 Q330,232 330,238 L330,270" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#14[2] → #13 · DATA</title></path><path class="edge DATA" id="e14i3" d="M470,222 L470,227 Q470,232 465,232 L362,232 Q354,232 354,240 L354,270" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#14[3] → #4 · DATA</title></path><path class="edge MEM" id="e16i1" d="M318,326 L318,374" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#16[1] → #14 · MEM</title></path><path class="edge DATA" id="e16i2" d="M242,118 L242,123 Q242,128 247,128 L532,128 Q540,128 540,136 L540,328 Q540,336 532,336 L356,336 Q348,336 348,344 L348,374" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#16[2] → #9 · DATA</title></path><path class="edge MEM" id="e22i1" d="M318,326 L318,338 Q318,346 310,346 L151,346 Q143,346 143,354 L143,374" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#22[1] → #14 · MEM</title></path><path class="edge DATA" id="e22i2" d="M242,118 L242,123 Q242,128 237,128 L103,128 Q95,128 95,136 L95,348 Q95,356 103,356 L159,356 Q167,356 167,364 L167,374" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#22[2] → #9 · DATA</title></path><path class="edge DATA" id="e22i3" d="M166,326 L166,331 Q166,336 171,336 L183,336 Q191,336 191,344 L191,374" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#22[3] → #21 · DATA</title></path><path class="edge MEM" id="e25i1" d="M145,638 L145,643 Q145,648 150,648 L280,648 Q288,648 288,656 L288,686" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#25[1] → #1 · MEM</title></path><path class="edge DATA" id="e25i2" d="M318,430 L318,686" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#25[2] → #16 · DATA</title></path><path class="edge MEM" id="e224i1" d="M155,430 L155,478" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#224[1] → #22 · MEM</title></path><path class="edge MEM" id="e224i2" d="M318,326 L318,338 Q318,346 310,346 L233,346 Q225,346 225,354 L225,432 Q225,440 217,440 L203,440 Q195,440 195,448 L195,478" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#224[2] → #14 · MEM</title></path></g><g class="edge-hits"/><g class="parser" style="opacity: 1;"/><g class="nodes"><g class="node" id="n1" data-id="1" transform="translate(85,588)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>MemMerge</tspan><tspan class="node-id">  #1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#1 MemMerge
+Type not computed
+
+[0] → —  DATA
+[1] → #6  MEM
+[2] → #224  MEM</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n2" data-id="2" transform="translate(24,24)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Start</tspan><tspan class="node-id">  #2</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#2 Start
+Type not computed
+
+</title></g><g class="node" id="n4" data-id="4" transform="translate(410,172)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#0</tspan><tspan class="node-id">  #4</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#4 #0
+Type not computed
+
+</title></g><g class="node" id="n6" data-id="6" transform="translate(24,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>$mem</tspan><tspan class="node-id">  #6/1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#6 $mem
+Projection 1 of #2
+Type not computed
+
+[0] → #2  MEM</title></g><g class="node" id="n9" data-id="9" transform="translate(182,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>new S</tspan><tspan class="node-id">  #9</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#9 new S
+Type not computed
+
+[0] → —  CTRL</title><circle class="port" cx="60" cy="-3" r="3" fill="white"/><text class="slot" x="60" y="-10" text-anchor="middle">0</text></g><g class="node" id="n11" data-id="11" transform="translate(334,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#2</tspan><tspan class="node-id">  #11</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#11 #2
+Type not computed
+
+</title></g><g class="node" id="n12" data-id="12" transform="translate(106,172)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f =</tspan><tspan class="node-id">  #12</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#12 .f =
+Type not computed
+
+[0] → —  DATA
+[1] → #6  MEM
+[2] → #9  DATA
+[3] → #11  DATA</title><circle class="port" cx="24" cy="-3" r="3" fill="white"/><circle class="port" cx="48" cy="-3" r="3" fill="#536477"/><circle class="port" cx="72" cy="-3" r="3" fill="#536477"/><circle class="port" cx="96" cy="-3" r="3" fill="#536477"/><text class="slot" x="24" y="-10" text-anchor="middle">0</text><text class="slot" x="48" y="-10" text-anchor="middle">1</text><text class="slot" x="72" y="-10" text-anchor="middle">2</text><text class="slot" x="96" y="-10" text-anchor="middle">3</text></g><g class="node" id="n13" data-id="13" transform="translate(258,172)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>new S</tspan><tspan class="node-id">  #13</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#13 new S
+Type not computed
+
+[0] → —  CTRL</title><circle class="port" cx="60" cy="-3" r="3" fill="white"/><text class="slot" x="60" y="-10" text-anchor="middle">0</text></g><g class="node" id="n14" data-id="14" transform="translate(258,276)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f =</tspan><tspan class="node-id">  #14</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#14 .f =
+Type not computed
+
+[0] → —  DATA
+[1] → #12  MEM
+[2] → #13  DATA
+[3] → #4  DATA</title><circle class="port" cx="24" cy="-3" r="3" fill="white"/><circle class="port" cx="48" cy="-3" r="3" fill="#536477"/><circle class="port" cx="72" cy="-3" r="3" fill="#536477"/><circle class="port" cx="96" cy="-3" r="3" fill="#536477"/><text class="slot" x="24" y="-10" text-anchor="middle">0</text><text class="slot" x="48" y="-10" text-anchor="middle">1</text><text class="slot" x="72" y="-10" text-anchor="middle">2</text><text class="slot" x="96" y="-10" text-anchor="middle">3</text></g><g class="node" id="n16" data-id="16" transform="translate(258,380)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f</tspan><tspan class="node-id">  #16</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#16 .f
+Type not computed
+
+[0] → —  DATA
+[1] → #14  MEM
+[2] → #9  DATA</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n21" data-id="21" transform="translate(106,276)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#1</tspan><tspan class="node-id">  #21</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#21 #1
+Type not computed
+
+</title></g><g class="node" id="n22" data-id="22" transform="translate(95,380)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f =</tspan><tspan class="node-id">  #22</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#22 .f =
+Type not computed
+
+[0] → —  DATA
+[1] → #14  MEM
+[2] → #9  DATA
+[3] → #21  DATA</title><circle class="port" cx="24" cy="-3" r="3" fill="white"/><circle class="port" cx="48" cy="-3" r="3" fill="#536477"/><circle class="port" cx="72" cy="-3" r="3" fill="#536477"/><circle class="port" cx="96" cy="-3" r="3" fill="#536477"/><text class="slot" x="24" y="-10" text-anchor="middle">0</text><text class="slot" x="48" y="-10" text-anchor="middle">1</text><text class="slot" x="72" y="-10" text-anchor="middle">2</text><text class="slot" x="96" y="-10" text-anchor="middle">3</text></g><g class="node" id="n25" data-id="25" transform="translate(228,692)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Return</tspan><tspan class="node-id">  #25</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#25 Return
+Type not computed
+
+[0] → —  CTRL
+[1] → #1  MEM
+[2] → #16  DATA</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n224" data-id="224" transform="translate(115,484)" style="opacity: 1;"><path class="box" d="M12,0H108L120,22L108,44H12L0,22Z" fill="#f5e4fa"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>MemPhi_2</tspan><tspan class="node-id">  #224</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#224 MemPhi_2
+Type not computed
+
+[0] → —  ASSOC
+[1] → #22  MEM
+[2] → #14  MEM</title><circle class="port" cx="0" cy="-3" r="3" fill="white"/><circle class="port" cx="40" cy="-3" r="3" fill="#536477"/><circle class="port" cx="80" cy="-3" r="3" fill="#536477"/><text class="slot" x="0" y="-10" text-anchor="middle">0</text><text class="slot" x="40" y="-10" text-anchor="middle">1</text><text class="slot" x="80" y="-10" text-anchor="middle">2</text></g></g><g class="region-heads" style="opacity: 1;"/><g class="shortcuts" style="opacity: 1;"/><g class="peep-ghosts" pointer-events="none"/></g></svg>
diff --git a/docs/chapter13/graph2.gv b/docs/chapter13/graph2.gv
new file mode 100644
index 00000000..94d94dae
--- /dev/null
+++ b/docs/chapter13/graph2.gv
@@ -0,0 +1,84 @@
+digraph chapter13 {
+/*
+struct S { int f; }
+S v=new S;
+v.f = 2;
+int i=new S.f;
+i=v.f;
+if (arg) v.f=1;
+return i;
+
+*/
+	rankdir=BT;
+	concentrate="true";
+	compound="true";
+	subgraph cluster_Nodes {
+		Start2 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">Start</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">$ctrl</TD><TD PORT="p1">$mem</TD><TD PORT="p2">arg</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		MemMerge [ shape=box label="MemMerge" ];
+		Stop3 [ shape=box style=filled fillcolor=yellow label="Stop" ];
+		Con_4 [ label="#0" ];
+		new9 [ label="new S" ];
+		Con_11 [ label="#2" ];
+		Store12 [ label=".f =" ];
+		new13 [ label="new S" ];
+		Store14 [ label=".f =" ];
+		Load16 [ label=".f" ];
+		If17 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">If</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">True</TD><TD PORT="p1" BGCOLOR="yellow">False</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Con_21 [ label="#1" ];
+		Store22 [ label=".f =" ];
+		Region23 [ shape=box style=filled fillcolor=yellow label="Region" ];
+		Phi_224 [ style=filled fillcolor=lightyellow label="MemPhi_2" ];
+		Return25 [ shape=box style=filled fillcolor=yellow label="Return" ];
+		{ rank=same; Region23;Phi_224;}
+	}
+	edge [ fontname=Helvetica, fontsize=8 ];
+	Stop3 -> Return25[taillabel=0 color=red];
+	new9 -> Start2:p0[taillabel=0 color=green];
+	Store12 -> Start2:p0[taillabel=0 color=red];
+	Store12 -> Start2:p1[taillabel=1 color=blue];
+	Store12 -> new9[taillabel=2];
+	Store12 -> Con_11[taillabel=3];
+	new13 -> Start2:p0[taillabel=0 color=green];
+	Store14 -> Start2:p0[taillabel=0 color=red];
+	Store14 -> Store12[taillabel=1 color=blue];
+	Store14 -> new13[taillabel=2];
+	Store14 -> Con_4[taillabel=3];
+	Load16 -> Start2:p0[taillabel=0 color=red];
+	Load16 -> Store14[taillabel=1 color=blue];
+	Load16 -> new9[taillabel=2];
+	If17 -> Start2:p0[taillabel=0 color=red];
+	If17 -> Start2:p2[taillabel=1];
+	Store22 -> Start2:p0[taillabel=0 color=red];
+	Store22 -> Store14[taillabel=1 color=blue];
+	Store22 -> new9[taillabel=2];
+	Store22 -> Con_21[taillabel=3];
+	Region23 -> If17:p0[taillabel=1 color=red];
+	Region23 -> If17:p1[taillabel=2 color=red];
+	Phi_224 -> Region23 [style=dotted taillabel=0];
+	Phi_224 -> Store22[taillabel=1 color=blue];
+	Phi_224 -> Store14[taillabel=2 color=blue constraint=false];
+	Return25 -> Region23[taillabel=0 color=red];
+	Return25 -> Load16[taillabel=2];
+	Return25 -> MemMerge[taillabel=1 color=blue];
+	MemMerge -> Start2:p1[taillabel=1 color=blue];
+	MemMerge -> Phi_224[taillabel=2 color=blue];
+	MemMerge -> Region23[taillabel=0 color=green];
+}
diff --git a/docs/chapter13/graph2.json b/docs/chapter13/graph2.json
new file mode 100644
index 00000000..47689c72
--- /dev/null
+++ b/docs/chapter13/graph2.json
@@ -0,0 +1,25 @@
+{
+  "ver": 1,
+  "comp": "chapter13/docs/graph2.svg",
+  "step": 1,
+  "roots": [25],
+  "scope": 0,
+  "nodes": [
+    {"id": 1, "label": "MemMerge", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 6, "role": "MEM", "label": null}, {"idx": 2, "def": 224, "role": "MEM", "label": null}], "proj": null},
+    {"id": 2, "label": "Start", "type": null, "kind": "CTRL", "edges": [], "proj": null},
+    {"id": 4, "label": "#0", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 6, "label": "$mem", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 2, "role": "MEM", "label": null}], "proj": {"par": 2, "idx": 1}},
+    {"id": 9, "label": "new S", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}], "proj": null},
+    {"id": 11, "label": "#2", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 12, "label": ".f =", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 6, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}, {"idx": 3, "def": 11, "role": "DATA", "label": null}], "proj": null},
+    {"id": 13, "label": "new S", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}], "proj": null},
+    {"id": 14, "label": ".f =", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 12, "role": "MEM", "label": null}, {"idx": 2, "def": 13, "role": "DATA", "label": null}, {"idx": 3, "def": 4, "role": "DATA", "label": null}], "proj": null},
+    {"id": 16, "label": ".f", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 14, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}], "proj": null},
+    {"id": 21, "label": "#1", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 22, "label": ".f =", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 14, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}, {"idx": 3, "def": 21, "role": "DATA", "label": null}], "proj": null},
+    {"id": 25, "label": "Return", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 1, "role": "MEM", "label": null}, {"idx": 2, "def": 16, "role": "DATA", "label": null}], "proj": null},
+    {"id": 224, "label": "MemPhi_2", "type": null, "kind": "PHI", "edges": [{"idx": 0, "def": 0, "role": "ASSOC", "label": null}, {"idx": 1, "def": 22, "role": "MEM", "label": null}, {"idx": 2, "def": 14, "role": "MEM", "label": null}], "proj": null}
+  ],
+  "groups": [
+  ]
+}
diff --git a/docs/chapter13/graph2.svg b/docs/chapter13/graph2.svg
new file mode 100644
index 00000000..05210749
--- /dev/null
+++ b/docs/chapter13/graph2.svg
@@ -0,0 +1,123 @@
+<svg aria-label="Compiler graph" width="565" height="766" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 565 766" style="font-family: sans-serif;"><style>
+    html, body { height:100%; margin:0; font-family:sans-serif; }
+    .viewer { height:100%; display:grid; grid-template-rows:auto minmax(0,1fr) auto; }
+    .source { padding:8px; border-bottom:1px solid #ccc; }
+    #program { width:min(600px,80vw); vertical-align:middle; }
+    #status { margin-top:4px; }
+    #graph { min-height:0; overflow:hidden; position:relative; background:#fafbfc; }
+    #elk { width:100%; height:100%; }
+    #graph svg { display:block; }
+    .tools { display:flex; flex-wrap:wrap; align-items:center; gap:14px; margin-top:8px; font-size:12px; }
+    .hint { color:#616c78; }
+    .ctrl { color:#b63838; } .mem { color:#2867b2; } .data { color:#536477; }
+    .edge { fill:none; stroke-width:1.5; }
+    .edge.CTRL { stroke-width:2; }
+    .edge.ASSOC { stroke-dasharray:4 4; }
+    .edge.PARSER { stroke-dasharray:5 4; }
+    .parser rect { fill:#f6f0ff; stroke:#7956a5; stroke-width:1.5; stroke-dasharray:5 4; }
+    .edge.selected { stroke-width:3.5; }
+    .edge.bundle { stroke-width:4; }
+    .edge.bundle.selected { stroke-width:6; }
+    .edge-hit { fill:none; stroke:transparent; stroke-width:12; vector-effect:non-scaling-stroke; pointer-events:stroke; cursor:pointer; }
+    .edge-jump { fill:transparent; pointer-events:all; cursor:pointer; }
+    .node { cursor:pointer; }
+    .box { stroke:#758191; stroke-width:1; }
+    .node.held .box { stroke-dasharray:5 3; }
+    .node.near .box { stroke:#c18221; stroke-width:2; }
+    .node.focus .box { stroke:#9c4900; stroke-width:3; }
+    .node.selected .box { stroke:#1569b9; stroke-width:3; }
+    .node.folded .box { stroke-width:4; }
+    .node.folding .box { fill:#f4ccd7; }
+    .fold-tag { font-size:9px; font-weight:700; fill:#963751; }
+    .peep-area { fill:#fff3d9; fill-opacity:.8; stroke:#c18221; stroke-width:2; pointer-events:none; }
+    .node.peep-edit .box { stroke:#9c4900; stroke-width:3; }
+    .node.error .box { stroke:#b42318; stroke-width:4; }
+    #event.error { color:#b42318; font-weight:600; white-space:pre-wrap; overflow-wrap:anywhere; }
+    .peep-ghosts { pointer-events:none; }
+    .region-box { stroke:#9da9b8; stroke-width:1.5; }
+    .fold-btn { cursor:pointer; }
+    .fold-btn rect { fill:white; stroke:#596674; }
+    .fold-btn text { font-size:14px; fill:#152330; }
+    .fold-btn:focus rect { stroke:#1569b9; stroke-width:2; }
+    .shortcut { cursor:pointer; }
+    .shortcut path { fill:none; stroke-width:1.5; }
+    .shortcut rect { fill:#fff8ec; stroke:#b63838; stroke-dasharray:3 2; }
+    .shortcut text { font-size:11px; fill:#783030; }
+    .shortcut.selected rect, .shortcut:focus rect { stroke-width:2.5; }
+    .label { font-size:12px; fill:#152330; font-weight:600; }
+    .node-id { font-size:10px; fill:#596674; font-weight:400; }
+    .type { font-size:11px; fill:#455768; }
+    .port { stroke:#536477; stroke-width:1; }
+    .row { stroke:#b6afcf; stroke-width:1; }
+    .bind { font-size:12px; fill:#152330; }
+    .slot { font-size:10px; fill:#364352; paint-order:stroke; stroke:#fafbfc; stroke-width:3; }
+    #detail { position:absolute; top:8px; right:8px; margin:0; padding:12px; max-width:320px;
+      max-height:45%; overflow:auto; white-space:pre-wrap; overflow-wrap:anywhere;
+      background:#fffffff2; border:1px solid #bac5d0; border-radius:4px; font-size:12px; }
+    .controls { display:flex; flex-wrap:wrap; justify-content:center; align-items:center; gap:6px; padding:6px; }
+    .button { color:white; background:black; font-size:20px; min-width:30px; }
+    .button:disabled { background:grey; }
+    .count { font-size:20px; min-width:35px; text-align:center; }
+    #N { width:6ch; }
+    #scrub { width:clamp(120px,35vw,600px); }
+  </style><defs><marker id="arrow-CTRL" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#b63838"/></marker><marker id="arrow-DATA" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#536477"/></marker><marker id="arrow-MEM" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#2867b2"/></marker><marker id="arrow-ASSOC" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#9396a3"/></marker><marker id="arrow-PARSER" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#7956a5"/></marker></defs><rect width="100%" height="100%" fill="rgb(250, 251, 252)"/><g><g class="regions" style="opacity: 1;"/><rect class="peep-area" rx="36" style="opacity: 0;"/><g class="edges"><path class="edge MEM" id="e1i1" d="M84,118 L84,536 Q84,544 92,544 L137,544 Q145,544 145,552 L145,582" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#1[1] → #6 · MEM</title></path><path class="edge MEM" id="e1i2" d="M175,534 L175,582" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#1[2] → #224 · MEM</title></path><path class="edge MEM" id="e12i1" d="M84,118 L84,130 Q84,138 92,138 L146,138 Q154,138 154,146 L154,166" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#12[1] → #6 · MEM</title></path><path class="edge DATA" id="e12i2" d="M242,118 L242,123 Q242,128 237,128 L186,128 Q178,128 178,136 L178,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#12[2] → #9 · DATA</title></path><path class="edge DATA" id="e12i3" d="M394,118 L394,130 Q394,138 386,138 L210,138 Q202,138 202,146 L202,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#12[3] → #11 · DATA</title></path><path class="edge MEM" id="e14i1" d="M166,222 L166,227 Q166,232 171,232 L298,232 Q306,232 306,240 L306,270" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#14[1] → #12 · MEM</title></path><path class="edge DATA" id="e14i2" d="M318,222 L318,227 Q318,232 323,232 L324,232 Q330,232 330,238 L330,270" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#14[2] → #13 · DATA</title></path><path class="edge DATA" id="e14i3" d="M470,222 L470,227 Q470,232 465,232 L362,232 Q354,232 354,240 L354,270" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#14[3] → #4 · DATA</title></path><path class="edge MEM" id="e16i1" d="M318,326 L318,374" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#16[1] → #14 · MEM</title></path><path class="edge DATA" id="e16i2" d="M242,118 L242,123 Q242,128 247,128 L532,128 Q540,128 540,136 L540,328 Q540,336 532,336 L356,336 Q348,336 348,344 L348,374" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#16[2] → #9 · DATA</title></path><path class="edge MEM" id="e22i1" d="M318,326 L318,338 Q318,346 310,346 L151,346 Q143,346 143,354 L143,374" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#22[1] → #14 · MEM</title></path><path class="edge DATA" id="e22i2" d="M242,118 L242,123 Q242,128 237,128 L103,128 Q95,128 95,136 L95,348 Q95,356 103,356 L159,356 Q167,356 167,364 L167,374" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#22[2] → #9 · DATA</title></path><path class="edge DATA" id="e22i3" d="M166,326 L166,331 Q166,336 171,336 L183,336 Q191,336 191,344 L191,374" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#22[3] → #21 · DATA</title></path><path class="edge MEM" id="e25i1" d="M145,638 L145,643 Q145,648 150,648 L280,648 Q288,648 288,656 L288,686" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#25[1] → #1 · MEM</title></path><path class="edge DATA" id="e25i2" d="M318,430 L318,686" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#25[2] → #16 · DATA</title></path><path class="edge MEM" id="e224i1" d="M155,430 L155,478" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#224[1] → #22 · MEM</title></path><path class="edge MEM" id="e224i2" d="M318,326 L318,338 Q318,346 310,346 L233,346 Q225,346 225,354 L225,432 Q225,440 217,440 L203,440 Q195,440 195,448 L195,478" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#224[2] → #14 · MEM</title></path></g><g class="edge-hits"/><g class="parser" style="opacity: 1;"/><g class="nodes"><g class="node" id="n1" data-id="1" transform="translate(85,588)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>MemMerge</tspan><tspan class="node-id">  #1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#1 MemMerge
+Type not computed
+
+[0] → —  CTRL
+[1] → #6  MEM
+[2] → #224  MEM</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n2" data-id="2" transform="translate(24,24)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Start</tspan><tspan class="node-id">  #2</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#2 Start
+Type not computed
+
+</title></g><g class="node" id="n4" data-id="4" transform="translate(410,172)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#0</tspan><tspan class="node-id">  #4</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#4 #0
+Type not computed
+
+</title></g><g class="node" id="n6" data-id="6" transform="translate(24,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>$mem</tspan><tspan class="node-id">  #6/1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#6 $mem
+Projection 1 of #2
+Type not computed
+
+[0] → #2  MEM</title></g><g class="node" id="n9" data-id="9" transform="translate(182,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>new S</tspan><tspan class="node-id">  #9</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#9 new S
+Type not computed
+
+[0] → —  CTRL</title><circle class="port" cx="60" cy="-3" r="3" fill="white"/><text class="slot" x="60" y="-10" text-anchor="middle">0</text></g><g class="node" id="n11" data-id="11" transform="translate(334,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#2</tspan><tspan class="node-id">  #11</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#11 #2
+Type not computed
+
+</title></g><g class="node" id="n12" data-id="12" transform="translate(106,172)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f =</tspan><tspan class="node-id">  #12</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#12 .f =
+Type not computed
+
+[0] → —  CTRL
+[1] → #6  MEM
+[2] → #9  DATA
+[3] → #11  DATA</title><circle class="port" cx="24" cy="-3" r="3" fill="white"/><circle class="port" cx="48" cy="-3" r="3" fill="#536477"/><circle class="port" cx="72" cy="-3" r="3" fill="#536477"/><circle class="port" cx="96" cy="-3" r="3" fill="#536477"/><text class="slot" x="24" y="-10" text-anchor="middle">0</text><text class="slot" x="48" y="-10" text-anchor="middle">1</text><text class="slot" x="72" y="-10" text-anchor="middle">2</text><text class="slot" x="96" y="-10" text-anchor="middle">3</text></g><g class="node" id="n13" data-id="13" transform="translate(258,172)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>new S</tspan><tspan class="node-id">  #13</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#13 new S
+Type not computed
+
+[0] → —  CTRL</title><circle class="port" cx="60" cy="-3" r="3" fill="white"/><text class="slot" x="60" y="-10" text-anchor="middle">0</text></g><g class="node" id="n14" data-id="14" transform="translate(258,276)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f =</tspan><tspan class="node-id">  #14</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#14 .f =
+Type not computed
+
+[0] → —  CTRL
+[1] → #12  MEM
+[2] → #13  DATA
+[3] → #4  DATA</title><circle class="port" cx="24" cy="-3" r="3" fill="white"/><circle class="port" cx="48" cy="-3" r="3" fill="#536477"/><circle class="port" cx="72" cy="-3" r="3" fill="#536477"/><circle class="port" cx="96" cy="-3" r="3" fill="#536477"/><text class="slot" x="24" y="-10" text-anchor="middle">0</text><text class="slot" x="48" y="-10" text-anchor="middle">1</text><text class="slot" x="72" y="-10" text-anchor="middle">2</text><text class="slot" x="96" y="-10" text-anchor="middle">3</text></g><g class="node" id="n16" data-id="16" transform="translate(258,380)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f</tspan><tspan class="node-id">  #16</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#16 .f
+Type not computed
+
+[0] → —  CTRL
+[1] → #14  MEM
+[2] → #9  DATA</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n21" data-id="21" transform="translate(106,276)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#1</tspan><tspan class="node-id">  #21</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#21 #1
+Type not computed
+
+</title></g><g class="node" id="n22" data-id="22" transform="translate(95,380)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f =</tspan><tspan class="node-id">  #22</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#22 .f =
+Type not computed
+
+[0] → —  CTRL
+[1] → #14  MEM
+[2] → #9  DATA
+[3] → #21  DATA</title><circle class="port" cx="24" cy="-3" r="3" fill="white"/><circle class="port" cx="48" cy="-3" r="3" fill="#536477"/><circle class="port" cx="72" cy="-3" r="3" fill="#536477"/><circle class="port" cx="96" cy="-3" r="3" fill="#536477"/><text class="slot" x="24" y="-10" text-anchor="middle">0</text><text class="slot" x="48" y="-10" text-anchor="middle">1</text><text class="slot" x="72" y="-10" text-anchor="middle">2</text><text class="slot" x="96" y="-10" text-anchor="middle">3</text></g><g class="node" id="n25" data-id="25" transform="translate(228,692)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Return</tspan><tspan class="node-id">  #25</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#25 Return
+Type not computed
+
+[0] → —  CTRL
+[1] → #1  MEM
+[2] → #16  DATA</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n224" data-id="224" transform="translate(115,484)" style="opacity: 1;"><path class="box" d="M12,0H108L120,22L108,44H12L0,22Z" fill="#f5e4fa"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>MemPhi_2</tspan><tspan class="node-id">  #224</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#224 MemPhi_2
+Type not computed
+
+[0] → —  ASSOC
+[1] → #22  MEM
+[2] → #14  MEM</title><circle class="port" cx="0" cy="-3" r="3" fill="white"/><circle class="port" cx="40" cy="-3" r="3" fill="#536477"/><circle class="port" cx="80" cy="-3" r="3" fill="#536477"/><text class="slot" x="0" y="-10" text-anchor="middle">0</text><text class="slot" x="40" y="-10" text-anchor="middle">1</text><text class="slot" x="80" y="-10" text-anchor="middle">2</text></g></g><g class="region-heads" style="opacity: 1;"/><g class="shortcuts" style="opacity: 1;"/><g class="peep-ghosts" pointer-events="none"/></g></svg>
diff --git a/docs/chapter13/graph3-snip.jpg b/docs/chapter13/graph3-snip.jpg
new file mode 100644
index 00000000..804a32c4
--- /dev/null
+++ b/docs/chapter13/graph3-snip.jpg
diff --git a/docs/chapter13/graph3-snip.json b/docs/chapter13/graph3-snip.json
new file mode 100644
index 00000000..548dbdf3
--- /dev/null
+++ b/docs/chapter13/graph3-snip.json
@@ -0,0 +1,17 @@
+{
+  "ver": 1,
+  "comp": "chapter13/docs/graph3-snip.svg",
+  "step": 1,
+  "roots": [22],
+  "scope": 0,
+  "nodes": [
+    {"id": 8, "label": "True", "type": null, "kind": "CTRL", "edges": [], "proj": {"par": 0, "idx": 0}},
+    {"id": 9, "label": "new S", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}], "proj": null},
+    {"id": 14, "label": ".f =", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 0, "role": "MEM", "label": null}, {"idx": 2, "def": 0, "role": "DATA", "label": null}, {"idx": 3, "def": 0, "role": "DATA", "label": null}], "proj": null},
+    {"id": 16, "label": ".f", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 14, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}], "proj": null},
+    {"id": 21, "label": "#1", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 22, "label": ".f =", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 8, "role": "CTRL", "label": null}, {"idx": 1, "def": 14, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}, {"idx": 3, "def": 21, "role": "DATA", "label": null}, {"idx": 4, "def": 16, "role": "DATA", "label": null}], "proj": null}
+  ],
+  "groups": [
+  ]
+}
diff --git a/docs/chapter13/graph3-snip.svg b/docs/chapter13/graph3-snip.svg
new file mode 100644
index 00000000..9f5218af
--- /dev/null
+++ b/docs/chapter13/graph3-snip.svg
@@ -0,0 +1,91 @@
+<svg aria-label="Compiler graph" width="427" height="314" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 427 314" style="font-family: sans-serif;"><style>
+    html, body { height:100%; margin:0; font-family:sans-serif; }
+    .viewer { height:100%; display:grid; grid-template-rows:auto minmax(0,1fr) auto; }
+    .source { padding:8px; border-bottom:1px solid #ccc; }
+    #program { width:min(600px,80vw); vertical-align:middle; }
+    #status { margin-top:4px; }
+    #graph { min-height:0; overflow:hidden; position:relative; background:#fafbfc; }
+    #elk { width:100%; height:100%; }
+    #graph svg { display:block; }
+    .tools { display:flex; flex-wrap:wrap; align-items:center; gap:14px; margin-top:8px; font-size:12px; }
+    .hint { color:#616c78; }
+    .ctrl { color:#b63838; } .mem { color:#2867b2; } .data { color:#536477; }
+    .edge { fill:none; stroke-width:1.5; }
+    .edge.CTRL { stroke-width:2; }
+    .edge.ASSOC { stroke-dasharray:4 4; }
+    .edge.PARSER { stroke-dasharray:5 4; }
+    .parser rect { fill:#f6f0ff; stroke:#7956a5; stroke-width:1.5; stroke-dasharray:5 4; }
+    .edge.selected { stroke-width:3.5; }
+    .edge.bundle { stroke-width:4; }
+    .edge.bundle.selected { stroke-width:6; }
+    .edge-hit { fill:none; stroke:transparent; stroke-width:12; vector-effect:non-scaling-stroke; pointer-events:stroke; cursor:pointer; }
+    .edge-jump { fill:transparent; pointer-events:all; cursor:pointer; }
+    .node { cursor:pointer; }
+    .box { stroke:#758191; stroke-width:1; }
+    .node.held .box { stroke-dasharray:5 3; }
+    .node.near .box { stroke:#c18221; stroke-width:2; }
+    .node.focus .box { stroke:#9c4900; stroke-width:3; }
+    .node.selected .box { stroke:#1569b9; stroke-width:3; }
+    .node.folded .box { stroke-width:4; }
+    .node.folding .box { fill:#f4ccd7; }
+    .fold-tag { font-size:9px; font-weight:700; fill:#963751; }
+    .peep-area { fill:#fff3d9; fill-opacity:.8; stroke:#c18221; stroke-width:2; pointer-events:none; }
+    .node.peep-edit .box { stroke:#9c4900; stroke-width:3; }
+    .node.error .box { stroke:#b42318; stroke-width:4; }
+    #event.error { color:#b42318; font-weight:600; white-space:pre-wrap; overflow-wrap:anywhere; }
+    .peep-ghosts { pointer-events:none; }
+    .region-box { stroke:#9da9b8; stroke-width:1.5; }
+    .fold-btn { cursor:pointer; }
+    .fold-btn rect { fill:white; stroke:#596674; }
+    .fold-btn text { font-size:14px; fill:#152330; }
+    .fold-btn:focus rect { stroke:#1569b9; stroke-width:2; }
+    .shortcut { cursor:pointer; }
+    .shortcut path { fill:none; stroke-width:1.5; }
+    .shortcut rect { fill:#fff8ec; stroke:#b63838; stroke-dasharray:3 2; }
+    .shortcut text { font-size:11px; fill:#783030; }
+    .shortcut.selected rect, .shortcut:focus rect { stroke-width:2.5; }
+    .label { font-size:12px; fill:#152330; font-weight:600; }
+    .node-id { font-size:10px; fill:#596674; font-weight:400; }
+    .type { font-size:11px; fill:#455768; }
+    .port { stroke:#536477; stroke-width:1; }
+    .row { stroke:#b6afcf; stroke-width:1; }
+    .bind { font-size:12px; fill:#152330; }
+    .slot { font-size:10px; fill:#364352; paint-order:stroke; stroke:#fafbfc; stroke-width:3; }
+    #detail { position:absolute; top:8px; right:8px; margin:0; padding:12px; max-width:320px;
+      max-height:45%; overflow:auto; white-space:pre-wrap; overflow-wrap:anywhere;
+      background:#fffffff2; border:1px solid #bac5d0; border-radius:4px; font-size:12px; }
+    .controls { display:flex; flex-wrap:wrap; justify-content:center; align-items:center; gap:6px; padding:6px; }
+    .button { color:white; background:black; font-size:20px; min-width:30px; }
+    .button:disabled { background:grey; }
+    .count { font-size:20px; min-width:35px; text-align:center; }
+    #N { width:6ch; }
+    #scrub { width:clamp(120px,35vw,600px); }
+  </style><defs><marker id="arrow-CTRL" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#b63838"/></marker><marker id="arrow-DATA" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#536477"/></marker><marker id="arrow-MEM" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#2867b2"/></marker><marker id="arrow-ASSOC" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#9396a3"/></marker><marker id="arrow-PARSER" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#7956a5"/></marker></defs><rect width="100%" height="100%" fill="rgb(250, 251, 252)"/><g><g class="regions" style="opacity: 1;"/><rect class="peep-area" rx="36" style="opacity: 0;"/><g class="edges"><path class="edge MEM" id="e16i1" d="M109,80 L109,92 Q109,100 117,100 L335,100 Q343,100 343,108 L343,128" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#16[1] → #14 · MEM</title></path><path class="edge DATA" id="e16i2" d="M261,80 L261,85 Q261,90 266,90 L365,90 Q373,90 373,98 L373,128" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#16[2] → #9 · DATA</title></path><path class="edge CTRL" id="e22i0" d="M62,184 L62,234" stroke="#b63838" marker-start="url(#arrow-CTRL)" style="opacity: 1;"><title>#22[0] → #8 · CTRL</title></path><path class="edge MEM" id="e22i1" d="M109,80 L109,186 Q109,194 101,194 L90,194 Q82,194 82,202 L82,234" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#22[1] → #14 · MEM</title></path><path class="edge DATA" id="e22i2" d="M261,80 L261,85 Q261,90 256,90 L128,90 Q120,90 120,98 L120,196 Q120,204 112,204 L110,204 Q102,204 102,212 L102,234" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#22[2] → #9 · DATA</title></path><path class="edge DATA" id="e22i3" d="M191,184 L191,206 Q191,214 183,214 L130,214 Q122,214 122,222 L122,234" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#22[3] → #21 · DATA</title></path><path class="edge DATA" id="e22i4" d="M343,184 L343,216 Q343,224 335,224 L147,224 Q142,224 142,229 L142,234" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#22[4] → #16 · DATA</title></path></g><g class="edge-hits"/><g class="parser" style="opacity: 1;"/><g class="nodes"><g class="node" id="n8" data-id="8" transform="translate(24,152)" style="opacity: 1;"><path class="box" d="M0,0H75V26H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="37.5" y="17"><tspan>True</tspan><tspan class="node-id">  #8/0</tspan></text><text class="type" text-anchor="middle" y="35" x="37.5"/><title>#8 True
+Projection 0 of #0
+Type not computed
+
+</title></g><g class="node" id="n9" data-id="9" transform="translate(201,30)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>new S</tspan><tspan class="node-id">  #9</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#9 new S
+Type not computed
+
+[0] → —  CTRL</title><circle class="port" cx="60" cy="-3" r="3" fill="white"/><text class="slot" x="60" y="-10" text-anchor="middle">0</text></g><g class="node" id="n14" data-id="14" transform="translate(49,30)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f =</tspan><tspan class="node-id">  #14</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#14 .f =
+Type not computed
+
+[0] → —  CTRL
+[1] → —  MEM
+[2] → —  DATA
+[3] → —  DATA</title><circle class="port" cx="24" cy="-3" r="3" fill="white"/><circle class="port" cx="48" cy="-3" r="3" fill="white"/><circle class="port" cx="72" cy="-3" r="3" fill="white"/><circle class="port" cx="96" cy="-3" r="3" fill="white"/><text class="slot" x="24" y="-10" text-anchor="middle">0</text><text class="slot" x="48" y="-10" text-anchor="middle">1</text><text class="slot" x="72" y="-10" text-anchor="middle">2</text><text class="slot" x="96" y="-10" text-anchor="middle">3</text></g><g class="node" id="n16" data-id="16" transform="translate(283,134)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f</tspan><tspan class="node-id">  #16</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#16 .f
+Type not computed
+
+[0] → —  CTRL
+[1] → #14  MEM
+[2] → #9  DATA</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n21" data-id="21" transform="translate(131,134)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#1</tspan><tspan class="node-id">  #21</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#21 #1
+Type not computed
+
+</title></g><g class="node" id="n22" data-id="22" transform="translate(42,240)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f =</tspan><tspan class="node-id">  #22</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#22 .f =
+Type not computed
+
+[0] → #8  CTRL
+[1] → #14  MEM
+[2] → #9  DATA
+[3] → #21  DATA
+[4] → #16  DATA</title><circle class="port" cx="20" cy="-3" r="3" fill="#536477"/><circle class="port" cx="40" cy="-3" r="3" fill="#536477"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="80" cy="-3" r="3" fill="#536477"/><circle class="port" cx="100" cy="-3" r="3" fill="#536477"/><text class="slot" x="20" y="-10" text-anchor="middle">0</text><text class="slot" x="40" y="-10" text-anchor="middle">1</text><text class="slot" x="60" y="-10" text-anchor="middle">2</text><text class="slot" x="80" y="-10" text-anchor="middle">3</text><text class="slot" x="100" y="-10" text-anchor="middle">4</text></g></g><g class="region-heads" style="opacity: 1;"/><g class="shortcuts" style="opacity: 1;"/><g class="peep-ghosts" pointer-events="none"/></g></svg>
diff --git a/docs/chapter13/graph3.gv b/docs/chapter13/graph3.gv
new file mode 100644
index 00000000..53c9aafe
--- /dev/null
+++ b/docs/chapter13/graph3.gv
@@ -0,0 +1,85 @@
+digraph chapter13 {
+/*
+struct S { int f; }
+S v=new S;
+v.f = 2;
+int i=new S.f;
+i=v.f;
+if (arg) v.f=1;
+return i;
+
+*/
+	rankdir=BT;
+	concentrate="true";
+	compound="true";
+	subgraph cluster_Nodes {
+		Start2 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">Start</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">$ctrl</TD><TD PORT="p1">$mem</TD><TD PORT="p2">arg</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		MemMerge [ shape=box label="MemMerge" ];
+		Stop3 [ shape=box style=filled fillcolor=yellow label="Stop" ];
+		Con_4 [ label="#0" ];
+		new9 [ label="new S" ];
+		Con_11 [ label="#2" ];
+		Store12 [ label=".f =" ];
+		new13 [ label="new S" ];
+		Store14 [ label=".f =" ];
+		Load16 [ label=".f" ];
+		If17 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">If</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">True</TD><TD PORT="p1" BGCOLOR="yellow">False</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Con_21 [ label="#1" ];
+		Store22 [ label=".f =" ];
+		Region23 [ shape=box style=filled fillcolor=yellow label="Region" ];
+		Phi_224 [ style=filled fillcolor=lightyellow label="MemPhi_2" ];
+		Return25 [ shape=box style=filled fillcolor=yellow label="Return" ];
+		{ rank=same; Region23;Phi_224;}
+	}
+	edge [ fontname=Helvetica, fontsize=8 ];
+	Stop3 -> Return25[taillabel=0 color=red];
+	new9 -> Start2:p0[taillabel=0 color=green];
+	Store12 -> Start2:p0[taillabel=0 color=red];
+	Store12 -> Start2:p1[taillabel=1 color=blue];
+	Store12 -> new9[taillabel=2];
+	Store12 -> Con_11[taillabel=3];
+	new13 -> Start2:p0[taillabel=0 color=green];
+	Store14 -> Start2:p0[taillabel=0 color=red];
+	Store14 -> Store12[taillabel=1 color=blue];
+	Store14 -> new13[taillabel=2];
+	Store14 -> Con_4[taillabel=3];
+	Load16 -> Start2:p0[taillabel=0 color=red];
+	Load16 -> Store14[taillabel=1 color=blue];
+	Load16 -> new9[taillabel=2];
+	If17 -> Start2:p0[taillabel=0 color=red];
+	If17 -> Start2:p2[taillabel=1];
+	Store22 -> If17:p0[taillabel=0 color=red];
+	Store22 -> Store14[taillabel=1 color=blue];
+	Store22 -> new9[taillabel=2];
+	Store22 -> Con_21[taillabel=3];
+	Store22 -> Load16[taillabel=4];
+	Region23 -> If17:p0[taillabel=1 color=red];
+	Region23 -> If17:p1[taillabel=2 color=red];
+	Phi_224 -> Region23 [style=dotted taillabel=0];
+	Phi_224 -> Store22[taillabel=1 color=blue];
+	Phi_224 -> Store14[taillabel=2 color=blue constraint=false];
+	Return25 -> Region23[taillabel=0 color=red];
+	Return25 -> Load16[taillabel=2];
+	Return25 -> MemMerge[taillabel=1 color=blue];
+	MemMerge -> Start2:p1[taillabel=1 color=blue];
+	MemMerge -> Phi_224[taillabel=2 color=blue];
+	MemMerge -> Region23[taillabel=0 color=green];
+}
diff --git a/docs/chapter13/graph3.json b/docs/chapter13/graph3.json
new file mode 100644
index 00000000..e44eb1b1
--- /dev/null
+++ b/docs/chapter13/graph3.json
@@ -0,0 +1,26 @@
+{
+  "ver": 1,
+  "comp": "chapter13/docs/graph3.svg",
+  "step": 1,
+  "roots": [25],
+  "scope": 0,
+  "nodes": [
+    {"id": 1, "label": "MemMerge", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 6, "role": "MEM", "label": null}, {"idx": 2, "def": 224, "role": "MEM", "label": null}], "proj": null},
+    {"id": 2, "label": "Start", "type": null, "kind": "CTRL", "edges": [], "proj": null},
+    {"id": 4, "label": "#0", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 6, "label": "$mem", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 2, "role": "MEM", "label": null}], "proj": {"par": 2, "idx": 1}},
+    {"id": 8, "label": "True", "type": null, "kind": "CTRL", "edges": [], "proj": {"par": 0, "idx": 0}},
+    {"id": 9, "label": "new S", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}], "proj": null},
+    {"id": 11, "label": "#2", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 12, "label": ".f =", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 6, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}, {"idx": 3, "def": 11, "role": "DATA", "label": null}], "proj": null},
+    {"id": 13, "label": "new S", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}], "proj": null},
+    {"id": 14, "label": ".f =", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 12, "role": "MEM", "label": null}, {"idx": 2, "def": 13, "role": "DATA", "label": null}, {"idx": 3, "def": 4, "role": "DATA", "label": null}], "proj": null},
+    {"id": 16, "label": ".f", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 14, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}], "proj": null},
+    {"id": 21, "label": "#1", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 22, "label": ".f =", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 8, "role": "CTRL", "label": null}, {"idx": 1, "def": 14, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}, {"idx": 3, "def": 21, "role": "DATA", "label": null}, {"idx": 4, "def": 16, "role": "DATA", "label": null}], "proj": null},
+    {"id": 25, "label": "Return", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 1, "role": "MEM", "label": null}, {"idx": 2, "def": 16, "role": "DATA", "label": null}], "proj": null},
+    {"id": 224, "label": "MemPhi_2", "type": null, "kind": "PHI", "edges": [{"idx": 0, "def": 0, "role": "ASSOC", "label": null}, {"idx": 1, "def": 22, "role": "MEM", "label": null}, {"idx": 2, "def": 14, "role": "MEM", "label": null}], "proj": null}
+  ],
+  "groups": [
+  ]
+}
diff --git a/docs/chapter13/graph3.svg b/docs/chapter13/graph3.svg
new file mode 100644
index 00000000..0247b5c6
--- /dev/null
+++ b/docs/chapter13/graph3.svg
@@ -0,0 +1,128 @@
+<svg aria-label="Compiler graph" width="661" height="872" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 661 872" style="font-family: sans-serif;"><style>
+    html, body { height:100%; margin:0; font-family:sans-serif; }
+    .viewer { height:100%; display:grid; grid-template-rows:auto minmax(0,1fr) auto; }
+    .source { padding:8px; border-bottom:1px solid #ccc; }
+    #program { width:min(600px,80vw); vertical-align:middle; }
+    #status { margin-top:4px; }
+    #graph { min-height:0; overflow:hidden; position:relative; background:#fafbfc; }
+    #elk { width:100%; height:100%; }
+    #graph svg { display:block; }
+    .tools { display:flex; flex-wrap:wrap; align-items:center; gap:14px; margin-top:8px; font-size:12px; }
+    .hint { color:#616c78; }
+    .ctrl { color:#b63838; } .mem { color:#2867b2; } .data { color:#536477; }
+    .edge { fill:none; stroke-width:1.5; }
+    .edge.CTRL { stroke-width:2; }
+    .edge.ASSOC { stroke-dasharray:4 4; }
+    .edge.PARSER { stroke-dasharray:5 4; }
+    .parser rect { fill:#f6f0ff; stroke:#7956a5; stroke-width:1.5; stroke-dasharray:5 4; }
+    .edge.selected { stroke-width:3.5; }
+    .edge.bundle { stroke-width:4; }
+    .edge.bundle.selected { stroke-width:6; }
+    .edge-hit { fill:none; stroke:transparent; stroke-width:12; vector-effect:non-scaling-stroke; pointer-events:stroke; cursor:pointer; }
+    .edge-jump { fill:transparent; pointer-events:all; cursor:pointer; }
+    .node { cursor:pointer; }
+    .box { stroke:#758191; stroke-width:1; }
+    .node.held .box { stroke-dasharray:5 3; }
+    .node.near .box { stroke:#c18221; stroke-width:2; }
+    .node.focus .box { stroke:#9c4900; stroke-width:3; }
+    .node.selected .box { stroke:#1569b9; stroke-width:3; }
+    .node.folded .box { stroke-width:4; }
+    .node.folding .box { fill:#f4ccd7; }
+    .fold-tag { font-size:9px; font-weight:700; fill:#963751; }
+    .peep-area { fill:#fff3d9; fill-opacity:.8; stroke:#c18221; stroke-width:2; pointer-events:none; }
+    .node.peep-edit .box { stroke:#9c4900; stroke-width:3; }
+    .node.error .box { stroke:#b42318; stroke-width:4; }
+    #event.error { color:#b42318; font-weight:600; white-space:pre-wrap; overflow-wrap:anywhere; }
+    .peep-ghosts { pointer-events:none; }
+    .region-box { stroke:#9da9b8; stroke-width:1.5; }
+    .fold-btn { cursor:pointer; }
+    .fold-btn rect { fill:white; stroke:#596674; }
+    .fold-btn text { font-size:14px; fill:#152330; }
+    .fold-btn:focus rect { stroke:#1569b9; stroke-width:2; }
+    .shortcut { cursor:pointer; }
+    .shortcut path { fill:none; stroke-width:1.5; }
+    .shortcut rect { fill:#fff8ec; stroke:#b63838; stroke-dasharray:3 2; }
+    .shortcut text { font-size:11px; fill:#783030; }
+    .shortcut.selected rect, .shortcut:focus rect { stroke-width:2.5; }
+    .label { font-size:12px; fill:#152330; font-weight:600; }
+    .node-id { font-size:10px; fill:#596674; font-weight:400; }
+    .type { font-size:11px; fill:#455768; }
+    .port { stroke:#536477; stroke-width:1; }
+    .row { stroke:#b6afcf; stroke-width:1; }
+    .bind { font-size:12px; fill:#152330; }
+    .slot { font-size:10px; fill:#364352; paint-order:stroke; stroke:#fafbfc; stroke-width:3; }
+    #detail { position:absolute; top:8px; right:8px; margin:0; padding:12px; max-width:320px;
+      max-height:45%; overflow:auto; white-space:pre-wrap; overflow-wrap:anywhere;
+      background:#fffffff2; border:1px solid #bac5d0; border-radius:4px; font-size:12px; }
+    .controls { display:flex; flex-wrap:wrap; justify-content:center; align-items:center; gap:6px; padding:6px; }
+    .button { color:white; background:black; font-size:20px; min-width:30px; }
+    .button:disabled { background:grey; }
+    .count { font-size:20px; min-width:35px; text-align:center; }
+    #N { width:6ch; }
+    #scrub { width:clamp(120px,35vw,600px); }
+  </style><defs><marker id="arrow-CTRL" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#b63838"/></marker><marker id="arrow-DATA" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#536477"/></marker><marker id="arrow-MEM" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#2867b2"/></marker><marker id="arrow-ASSOC" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#9396a3"/></marker><marker id="arrow-PARSER" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#7956a5"/></marker></defs><rect width="100%" height="100%" fill="rgb(250, 251, 252)"/><g><g class="regions" style="opacity: 1;"/><rect class="peep-area" rx="36" style="opacity: 0;"/><g class="edges"><path class="edge MEM" id="e1i1" d="M84,118 L84,642 Q84,650 92,650 L387,650 Q395,650 395,658 L395,688" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#1[1] → #6 · MEM</title></path><path class="edge MEM" id="e1i2" d="M425,640 L425,688" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#1[2] → #224 · MEM</title></path><path class="edge MEM" id="e12i1" d="M84,118 L84,140 Q84,148 92,148 L242,148 Q250,148 250,156 L250,166" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#12[1] → #6 · MEM</title></path><path class="edge DATA" id="e12i2" d="M274,118 L274,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#12[2] → #9 · DATA</title></path><path class="edge DATA" id="e12i3" d="M426,118 L426,123 Q426,128 421,128 L306,128 Q298,128 298,136 L298,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#12[3] → #11 · DATA</title></path><path class="edge MEM" id="e14i1" d="M262,222 L262,227 Q262,232 267,232 L382,232 Q390,232 390,240 L390,270" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#14[1] → #12 · MEM</title></path><path class="edge DATA" id="e14i2" d="M414,222 L414,270" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#14[2] → #13 · DATA</title></path><path class="edge DATA" id="e14i3" d="M566,222 L566,227 Q566,232 561,232 L446,232 Q438,232 438,240 L438,270" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#14[3] → #4 · DATA</title></path><path class="edge MEM" id="e16i1" d="M402,326 L402,340 Q402,346 408,346 L408,346 Q414,346 414,352 L414,374" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#16[1] → #14 · MEM</title></path><path class="edge DATA" id="e16i2" d="M274,118 L274,130 Q274,138 282,138 L628,138 Q636,138 636,146 L636,328 Q636,336 628,336 L452,336 Q444,336 444,344 L444,374" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#16[2] → #9 · DATA</title></path><path class="edge CTRL" id="e22i0" d="M133,430 L133,480" stroke="#b63838" marker-start="url(#arrow-CTRL)" style="opacity: 1;"><title>#22[0] → #8 · CTRL</title></path><path class="edge MEM" id="e22i1" d="M402,326 L402,338 Q402,346 394,346 L188,346 Q180,346 180,354 L180,432 Q180,440 172,440 L161,440 Q153,440 153,448 L153,480" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#22[1] → #14 · MEM</title></path><path class="edge DATA" id="e22i2" d="M274,118 L274,130 Q274,138 266,138 L199,138 Q191,138 191,146 L191,442 Q191,450 183,450 L181,450 Q173,450 173,458 L173,480" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#22[2] → #9 · DATA</title></path><path class="edge DATA" id="e22i3" d="M262,430 L262,452 Q262,460 254,460 L201,460 Q193,460 193,468 L193,480" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#22[3] → #21 · DATA</title></path><path class="edge DATA" id="e22i4" d="M414,430 L414,462 Q414,470 406,470 L218,470 Q213,470 213,475 L213,480" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#22[4] → #16 · DATA</title></path><path class="edge MEM" id="e25i1" d="M395,744 L395,749 Q395,754 400,754 L457,754 Q465,754 465,762 L465,792" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#25[1] → #1 · MEM</title></path><path class="edge DATA" id="e25i2" d="M414,430 L414,462 Q414,470 422,470 L487,470 Q495,470 495,478 L495,792" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#25[2] → #16 · DATA</title></path><path class="edge MEM" id="e224i1" d="M173,536 L173,541 Q173,546 178,546 L397,546 Q405,546 405,554 L405,584" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#224[1] → #22 · MEM</title></path><path class="edge MEM" id="e224i2" d="M402,326 L402,338 Q402,346 410,346 L476,346 Q484,346 484,354 L484,432 Q484,440 476,440 L453,440 Q445,440 445,448 L445,584" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#224[2] → #14 · MEM</title></path></g><g class="edge-hits"/><g class="parser" style="opacity: 1;"/><g class="nodes"><g class="node" id="n1" data-id="1" transform="translate(335,694)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>MemMerge</tspan><tspan class="node-id">  #1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#1 MemMerge
+Type not computed
+
+[0] → —  CTRL
+[1] → #6  MEM
+[2] → #224  MEM</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n2" data-id="2" transform="translate(24,24)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Start</tspan><tspan class="node-id">  #2</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#2 Start
+Type not computed
+
+</title></g><g class="node" id="n4" data-id="4" transform="translate(506,172)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#0</tspan><tspan class="node-id">  #4</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#4 #0
+Type not computed
+
+</title></g><g class="node" id="n6" data-id="6" transform="translate(24,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>$mem</tspan><tspan class="node-id">  #6/1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#6 $mem
+Projection 1 of #2
+Type not computed
+
+[0] → #2  MEM</title></g><g class="node" id="n8" data-id="8" transform="translate(95,398)" style="opacity: 1;"><path class="box" d="M0,0H75V26H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="37.5" y="17"><tspan>True</tspan><tspan class="node-id">  #8/0</tspan></text><text class="type" text-anchor="middle" y="35" x="37.5"/><title>#8 True
+Projection 0 of #0
+Type not computed
+
+</title></g><g class="node" id="n9" data-id="9" transform="translate(214,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>new S</tspan><tspan class="node-id">  #9</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#9 new S
+Type not computed
+
+[0] → —  CTRL</title><circle class="port" cx="60" cy="-3" r="3" fill="white"/><text class="slot" x="60" y="-10" text-anchor="middle">0</text></g><g class="node" id="n11" data-id="11" transform="translate(366,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#2</tspan><tspan class="node-id">  #11</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#11 #2
+Type not computed
+
+</title></g><g class="node" id="n12" data-id="12" transform="translate(202,172)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f =</tspan><tspan class="node-id">  #12</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#12 .f =
+Type not computed
+
+[0] → —  CTRL
+[1] → #6  MEM
+[2] → #9  DATA
+[3] → #11  DATA</title><circle class="port" cx="24" cy="-3" r="3" fill="white"/><circle class="port" cx="48" cy="-3" r="3" fill="#536477"/><circle class="port" cx="72" cy="-3" r="3" fill="#536477"/><circle class="port" cx="96" cy="-3" r="3" fill="#536477"/><text class="slot" x="24" y="-10" text-anchor="middle">0</text><text class="slot" x="48" y="-10" text-anchor="middle">1</text><text class="slot" x="72" y="-10" text-anchor="middle">2</text><text class="slot" x="96" y="-10" text-anchor="middle">3</text></g><g class="node" id="n13" data-id="13" transform="translate(354,172)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>new S</tspan><tspan class="node-id">  #13</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#13 new S
+Type not computed
+
+[0] → —  CTRL</title><circle class="port" cx="60" cy="-3" r="3" fill="white"/><text class="slot" x="60" y="-10" text-anchor="middle">0</text></g><g class="node" id="n14" data-id="14" transform="translate(342,276)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f =</tspan><tspan class="node-id">  #14</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#14 .f =
+Type not computed
+
+[0] → —  CTRL
+[1] → #12  MEM
+[2] → #13  DATA
+[3] → #4  DATA</title><circle class="port" cx="24" cy="-3" r="3" fill="white"/><circle class="port" cx="48" cy="-3" r="3" fill="#536477"/><circle class="port" cx="72" cy="-3" r="3" fill="#536477"/><circle class="port" cx="96" cy="-3" r="3" fill="#536477"/><text class="slot" x="24" y="-10" text-anchor="middle">0</text><text class="slot" x="48" y="-10" text-anchor="middle">1</text><text class="slot" x="72" y="-10" text-anchor="middle">2</text><text class="slot" x="96" y="-10" text-anchor="middle">3</text></g><g class="node" id="n16" data-id="16" transform="translate(354,380)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f</tspan><tspan class="node-id">  #16</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#16 .f
+Type not computed
+
+[0] → —  CTRL
+[1] → #14  MEM
+[2] → #9  DATA</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n21" data-id="21" transform="translate(202,380)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#1</tspan><tspan class="node-id">  #21</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#21 #1
+Type not computed
+
+</title></g><g class="node" id="n22" data-id="22" transform="translate(113,486)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f =</tspan><tspan class="node-id">  #22</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#22 .f =
+Type not computed
+
+[0] → #8  CTRL
+[1] → #14  MEM
+[2] → #9  DATA
+[3] → #21  DATA
+[4] → #16  DATA</title><circle class="port" cx="20" cy="-3" r="3" fill="#536477"/><circle class="port" cx="40" cy="-3" r="3" fill="#536477"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="80" cy="-3" r="3" fill="#536477"/><circle class="port" cx="100" cy="-3" r="3" fill="#536477"/><text class="slot" x="20" y="-10" text-anchor="middle">0</text><text class="slot" x="40" y="-10" text-anchor="middle">1</text><text class="slot" x="60" y="-10" text-anchor="middle">2</text><text class="slot" x="80" y="-10" text-anchor="middle">3</text><text class="slot" x="100" y="-10" text-anchor="middle">4</text></g><g class="node" id="n25" data-id="25" transform="translate(405,798)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Return</tspan><tspan class="node-id">  #25</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#25 Return
+Type not computed
+
+[0] → —  CTRL
+[1] → #1  MEM
+[2] → #16  DATA</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n224" data-id="224" transform="translate(365,590)" style="opacity: 1;"><path class="box" d="M12,0H108L120,22L108,44H12L0,22Z" fill="#f5e4fa"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>MemPhi_2</tspan><tspan class="node-id">  #224</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#224 MemPhi_2
+Type not computed
+
+[0] → —  ASSOC
+[1] → #22  MEM
+[2] → #14  MEM</title><circle class="port" cx="0" cy="-3" r="3" fill="white"/><circle class="port" cx="40" cy="-3" r="3" fill="#536477"/><circle class="port" cx="80" cy="-3" r="3" fill="#536477"/><text class="slot" x="0" y="-10" text-anchor="middle">0</text><text class="slot" x="40" y="-10" text-anchor="middle">1</text><text class="slot" x="80" y="-10" text-anchor="middle">2</text></g></g><g class="region-heads" style="opacity: 1;"/><g class="shortcuts" style="opacity: 1;"/><g class="peep-ghosts" pointer-events="none"/></g></svg>
diff --git a/docs/chapter13/graph4.gv b/docs/chapter13/graph4.gv
new file mode 100644
index 00000000..d7082072
--- /dev/null
+++ b/docs/chapter13/graph4.gv
@@ -0,0 +1,110 @@
+digraph chapter13 {
+/*
+struct S { int f; }
+S v = new S;
+int i = arg;
+while (arg > 0) {
+    int j = i/3;
+    if (arg == 5)
+        v.f = j;
+    arg = arg - 1;
+}
+return v;
+
+*/
+	rankdir=BT;
+	concentrate="true";
+	compound="true";
+	subgraph cluster_Nodes {
+		Start2 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">Start</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">$ctrl</TD><TD PORT="p1">$mem</TD><TD PORT="p2">arg</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		MemMerge [ shape=box label="MemMerge" ];
+		Stop3 [ shape=box style=filled fillcolor=yellow label="Stop" ];
+		Con_4 [ label="#0" ];
+		new9 [ label="new S" ];
+		Store10 [ label=".f =" ];
+		Loop11 [ shape=box style=filled fillcolor=yellow label="Loop" ];
+		Phi_arg13 [ style=filled fillcolor=lightyellow label="&phi;_arg" ];
+		LT14 [ label="<" ];
+		If16 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">If</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">True</TD><TD PORT="p1" BGCOLOR="yellow">False</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Div21 [ label="//" ];
+		Con_22 [ label="#3" ];
+		EQ23 [ label="==" ];
+		Con_24 [ label="#5" ];
+		If25 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">If</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">True</TD><TD PORT="p1" BGCOLOR="yellow">False</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Phi_230 [ style=filled fillcolor=lightyellow label="MemPhi_2" ];
+		Store31 [ label=".f =" ];
+		Region32 [ shape=box style=filled fillcolor=yellow label="Region" ];
+		Phi_233 [ style=filled fillcolor=lightyellow label="MemPhi_2" ];
+		Sub35 [ label="-" ];
+		Con_36 [ label="#1" ];
+		Return37 [ shape=box style=filled fillcolor=yellow label="Return" ];
+		{ rank=same; Loop11;Phi_230;Phi_arg13;}
+		{ rank=same; Region32;Phi_233;}
+	}
+	edge [ fontname=Helvetica, fontsize=8 ];
+	Stop3 -> Return37[taillabel=0 color=red];
+	new9 -> Start2:p0[taillabel=0 color=green];
+	Store10 -> Start2:p1[taillabel=1 color=blue];
+	Store10 -> new9[taillabel=2];
+	Store10 -> Con_4[taillabel=3];
+	Loop11 -> Start2:p0[taillabel=1 color=red];
+	Loop11 -> Region32[taillabel=2 color=red constraint=false];
+	Phi_arg13 -> Loop11 [style=dotted taillabel=0];
+	Phi_arg13 -> Start2:p2[taillabel=1];
+	Phi_arg13 -> Sub35[taillabel=2 constraint=false];
+	LT14 -> Con_4[taillabel=1];
+	LT14 -> Phi_arg13[taillabel=2];
+	If16 -> Loop11[taillabel=0 color=red];
+	If16 -> LT14[taillabel=1];
+	Div21 -> Start2:p2[taillabel=1];
+	Div21 -> Con_22[taillabel=2];
+	EQ23 -> Phi_arg13[taillabel=1];
+	EQ23 -> Con_24[taillabel=2];
+	If25 -> If16:p0[taillabel=0 color=red];
+	If25 -> EQ23[taillabel=1];
+	Phi_230 -> Loop11 [style=dotted taillabel=0];
+	Phi_230 -> Store10[taillabel=1 color=blue];
+	Phi_230 -> Phi_233[taillabel=2 color=blue constraint=false];
+	Store31 -> Phi_230[taillabel=1 color=blue];
+	Store31 -> new9[taillabel=2];
+	Store31 -> Div21[taillabel=3];
+	Region32 -> If25:p0[taillabel=1 color=red];
+	Region32 -> If25:p1[taillabel=2 color=red];
+	Phi_233 -> Region32 [style=dotted taillabel=0];
+	Phi_233 -> Store31[taillabel=1 color=blue];
+	Phi_233 -> Phi_230[taillabel=2 color=blue constraint=false];
+	Sub35 -> Phi_arg13[taillabel=1];
+	Sub35 -> Con_36[taillabel=2];
+	Return37 -> If16:p1[taillabel=0 color=red];
+	Return37 -> new9[taillabel=2];
+	Return37 -> MemMerge[taillabel=1 color=blue];
+	MemMerge -> Start2:p1[taillabel=1 color=blue];
+	MemMerge -> Phi_230[taillabel=2 color=blue];
+}
diff --git a/docs/chapter13/graph4.json b/docs/chapter13/graph4.json
new file mode 100644
index 00000000..add08b6b
--- /dev/null
+++ b/docs/chapter13/graph4.json
@@ -0,0 +1,24 @@
+{
+  "ver": 1,
+  "comp": "chapter13/docs/graph4.svg",
+  "step": 1,
+  "roots": [37],
+  "scope": 0,
+  "nodes": [
+    {"id": 1, "label": "MemMerge", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "DATA", "label": null}, {"idx": 1, "def": 6, "role": "MEM", "label": null}, {"idx": 2, "def": 230, "role": "MEM", "label": null}], "proj": null},
+    {"id": 2, "label": "Start", "type": null, "kind": "CTRL", "edges": [], "proj": null},
+    {"id": 4, "label": "#0", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 6, "label": "$mem", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 2, "role": "MEM", "label": null}], "proj": {"par": 2, "idx": 1}},
+    {"id": 7, "label": "arg", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 2, "role": "DATA", "label": null}], "proj": {"par": 2, "idx": 2}},
+    {"id": 9, "label": "new S", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}], "proj": null},
+    {"id": 10, "label": ".f =", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "DATA", "label": null}, {"idx": 1, "def": 6, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}, {"idx": 3, "def": 4, "role": "DATA", "label": null}], "proj": null},
+    {"id": 21, "label": "//", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "DATA", "label": null}, {"idx": 1, "def": 7, "role": "DATA", "label": null}, {"idx": 2, "def": 22, "role": "DATA", "label": null}], "proj": null},
+    {"id": 22, "label": "#3", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 31, "label": ".f =", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "DATA", "label": null}, {"idx": 1, "def": 230, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}, {"idx": 3, "def": 21, "role": "DATA", "label": null}], "proj": null},
+    {"id": 37, "label": "Return", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 1, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}], "proj": null},
+    {"id": 230, "label": "MemPhi_2", "type": null, "kind": "PHI", "edges": [{"idx": 0, "def": 0, "role": "ASSOC", "label": null}, {"idx": 1, "def": 10, "role": "MEM", "label": null}, {"idx": 2, "def": 233, "role": "MEM", "label": null}], "proj": null},
+    {"id": 233, "label": "MemPhi_2", "type": null, "kind": "PHI", "edges": [{"idx": 0, "def": 0, "role": "ASSOC", "label": null}, {"idx": 1, "def": 31, "role": "MEM", "label": null}, {"idx": 2, "def": 230, "role": "MEM", "label": null}], "proj": null}
+  ],
+  "groups": [
+  ]
+}
diff --git a/docs/chapter13/graph4.svg b/docs/chapter13/graph4.svg
new file mode 100644
index 00000000..9ca92879
--- /dev/null
+++ b/docs/chapter13/graph4.svg
@@ -0,0 +1,120 @@
+<svg aria-label="Compiler graph" width="780" height="568" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 780 568" style="font-family: sans-serif;"><style>
+    html, body { height:100%; margin:0; font-family:sans-serif; }
+    .viewer { height:100%; display:grid; grid-template-rows:auto minmax(0,1fr) auto; }
+    .source { padding:8px; border-bottom:1px solid #ccc; }
+    #program { width:min(600px,80vw); vertical-align:middle; }
+    #status { margin-top:4px; }
+    #graph { min-height:0; overflow:hidden; position:relative; background:#fafbfc; }
+    #elk { width:100%; height:100%; }
+    #graph svg { display:block; }
+    .tools { display:flex; flex-wrap:wrap; align-items:center; gap:14px; margin-top:8px; font-size:12px; }
+    .hint { color:#616c78; }
+    .ctrl { color:#b63838; } .mem { color:#2867b2; } .data { color:#536477; }
+    .edge { fill:none; stroke-width:1.5; }
+    .edge.CTRL { stroke-width:2; }
+    .edge.ASSOC { stroke-dasharray:4 4; }
+    .edge.PARSER { stroke-dasharray:5 4; }
+    .parser rect { fill:#f6f0ff; stroke:#7956a5; stroke-width:1.5; stroke-dasharray:5 4; }
+    .edge.selected { stroke-width:3.5; }
+    .edge.bundle { stroke-width:4; }
+    .edge.bundle.selected { stroke-width:6; }
+    .edge-hit { fill:none; stroke:transparent; stroke-width:12; vector-effect:non-scaling-stroke; pointer-events:stroke; cursor:pointer; }
+    .edge-jump { fill:transparent; pointer-events:all; cursor:pointer; }
+    .node { cursor:pointer; }
+    .box { stroke:#758191; stroke-width:1; }
+    .node.held .box { stroke-dasharray:5 3; }
+    .node.near .box { stroke:#c18221; stroke-width:2; }
+    .node.focus .box { stroke:#9c4900; stroke-width:3; }
+    .node.selected .box { stroke:#1569b9; stroke-width:3; }
+    .node.folded .box { stroke-width:4; }
+    .node.folding .box { fill:#f4ccd7; }
+    .fold-tag { font-size:9px; font-weight:700; fill:#963751; }
+    .peep-area { fill:#fff3d9; fill-opacity:.8; stroke:#c18221; stroke-width:2; pointer-events:none; }
+    .node.peep-edit .box { stroke:#9c4900; stroke-width:3; }
+    .node.error .box { stroke:#b42318; stroke-width:4; }
+    #event.error { color:#b42318; font-weight:600; white-space:pre-wrap; overflow-wrap:anywhere; }
+    .peep-ghosts { pointer-events:none; }
+    .region-box { stroke:#9da9b8; stroke-width:1.5; }
+    .fold-btn { cursor:pointer; }
+    .fold-btn rect { fill:white; stroke:#596674; }
+    .fold-btn text { font-size:14px; fill:#152330; }
+    .fold-btn:focus rect { stroke:#1569b9; stroke-width:2; }
+    .shortcut { cursor:pointer; }
+    .shortcut path { fill:none; stroke-width:1.5; }
+    .shortcut rect { fill:#fff8ec; stroke:#b63838; stroke-dasharray:3 2; }
+    .shortcut text { font-size:11px; fill:#783030; }
+    .shortcut.selected rect, .shortcut:focus rect { stroke-width:2.5; }
+    .label { font-size:12px; fill:#152330; font-weight:600; }
+    .node-id { font-size:10px; fill:#596674; font-weight:400; }
+    .type { font-size:11px; fill:#455768; }
+    .port { stroke:#536477; stroke-width:1; }
+    .row { stroke:#b6afcf; stroke-width:1; }
+    .bind { font-size:12px; fill:#152330; }
+    .slot { font-size:10px; fill:#364352; paint-order:stroke; stroke:#fafbfc; stroke-width:3; }
+    #detail { position:absolute; top:8px; right:8px; margin:0; padding:12px; max-width:320px;
+      max-height:45%; overflow:auto; white-space:pre-wrap; overflow-wrap:anywhere;
+      background:#fffffff2; border:1px solid #bac5d0; border-radius:4px; font-size:12px; }
+    .controls { display:flex; flex-wrap:wrap; justify-content:center; align-items:center; gap:6px; padding:6px; }
+    .button { color:white; background:black; font-size:20px; min-width:30px; }
+    .button:disabled { background:grey; }
+    .count { font-size:20px; min-width:35px; text-align:center; }
+    #N { width:6ch; }
+    #scrub { width:clamp(120px,35vw,600px); }
+  </style><defs><marker id="arrow-CTRL" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#b63838"/></marker><marker id="arrow-DATA" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#536477"/></marker><marker id="arrow-MEM" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#2867b2"/></marker><marker id="arrow-ASSOC" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#9396a3"/></marker><marker id="arrow-PARSER" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#7956a5"/></marker></defs><rect width="100%" height="100%" fill="rgb(250, 251, 252)"/><g><g class="regions" style="opacity: 1;"/><rect class="peep-area" rx="36" style="opacity: 0;"/><g class="edges"><path class="edge MEM" id="e1i1" d="M266,118 L266,123 Q266,128 261,128 L193,128 Q185,128 185,136 L185,374" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#1[1] → #6 · MEM</title></path><path class="edge MEM" id="e1i2" d="M259,326 L259,338 Q259,346 251,346 L223,346 Q215,346 215,354 L215,374" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#1[2] → #230 · MEM</title></path><path class="edge MEM" id="e10i1" d="M266,118 L266,123 Q266,128 261,128 L252,128 Q244,128 244,136 L244,166" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#10[1] → #6 · MEM</title></path><path class="edge DATA" id="e10i2" d="M114,118 L114,130 Q114,138 122,138 L260,138 Q268,138 268,146 L268,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#10[2] → #9 · DATA</title></path><path class="edge DATA" id="e10i3" d="M544,118 L544,123 Q544,128 539,128 L300,128 Q292,128 292,136 L292,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#10[3] → #4 · DATA</title></path><path class="edge DATA" id="e21i1" d="M386,118 L386,130 Q386,138 394,138 L400,138 Q408,138 408,146 L408,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#21[1] → #7 · DATA</title></path><path class="edge DATA" id="e21i2" d="M696,118 L696,130 Q696,138 688,138 L446,138 Q438,138 438,146 L438,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#21[2] → #22 · DATA</title></path><path class="edge MEM" id="e31i1" d="M259,326 L259,338 Q259,346 267,346 L306,346 Q314,346 314,354 L314,374" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#31[1] → #230 · MEM</title></path><path class="edge DATA" id="e31i2" d="M114,118 L114,328 Q114,336 122,336 L330,336 Q338,336 338,344 L338,374" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#31[2] → #9 · DATA</title></path><path class="edge DATA" id="e31i3" d="M408,222 L408,328 Q408,336 400,336 L370,336 Q362,336 362,344 L362,374" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#31[3] → #21 · DATA</title></path><path class="edge MEM" id="e37i1" d="M185,430 L185,435 Q185,440 180,440 L92,440 Q84,440 84,448 L84,478" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#37[1] → #1 · MEM</title></path><path class="edge DATA" id="e37i2" d="M114,118 L114,478" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#37[2] → #9 · DATA</title></path><path class="edge MEM" id="e230i1" d="M256,222 L256,227 Q256,232 251,232 L247,232 Q239,232 239,240 L239,270" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#230[1] → #10 · MEM</title></path><path class="edge MEM" id="e230i2" d="M326,534 L326,539 Q326,544 331,544 L388,544 Q396,544 396,536 L396,240 Q396,232 388,232 L287,232 Q279,232 279,240 L279,270" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#230[2] → #233 · MEM</title></path><path class="edge MEM" id="e233i1" d="M326,430 L326,435 Q326,440 321,440 L314,440 Q306,440 306,448 L306,478" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#233[1] → #31 · MEM</title></path><path class="edge MEM" id="e233i2" d="M259,326 L259,344 Q259,346 257,346 L257,346 Q255,346 255,348 L255,442 Q255,450 263,450 L338,450 Q346,450 346,458 L346,478" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#233[2] → #230 · MEM</title></path></g><g class="edge-hits"/><g class="parser" style="opacity: 1;"/><g class="nodes"><g class="node" id="n1" data-id="1" transform="translate(125,380)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>MemMerge</tspan><tspan class="node-id">  #1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#1 MemMerge
+Type not computed
+
+[0] → —  DATA
+[1] → #6  MEM
+[2] → #230  MEM</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n2" data-id="2" transform="translate(206,24)" style="opacity: 1;"><path class="box" d="M0,0H240V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="120" y="18"><tspan>Start</tspan><tspan class="node-id">  #2</tspan></text><text class="type" text-anchor="middle" y="35" x="120"/><title>#2 Start
+Type not computed
+
+</title></g><g class="node" id="n4" data-id="4" transform="translate(484,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#0</tspan><tspan class="node-id">  #4</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#4 #0
+Type not computed
+
+</title></g><g class="node" id="n6" data-id="6" transform="translate(206,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>$mem</tspan><tspan class="node-id">  #6/1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#6 $mem
+Projection 1 of #2
+Type not computed
+
+[0] → #2  MEM</title></g><g class="node" id="n7" data-id="7" transform="translate(326,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>arg</tspan><tspan class="node-id">  #7/2</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#7 arg
+Projection 2 of #2
+Type not computed
+
+[0] → #2  DATA</title></g><g class="node" id="n9" data-id="9" transform="translate(54,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>new S</tspan><tspan class="node-id">  #9</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#9 new S
+Type not computed
+
+[0] → —  CTRL</title><circle class="port" cx="60" cy="-3" r="3" fill="white"/><text class="slot" x="60" y="-10" text-anchor="middle">0</text></g><g class="node" id="n10" data-id="10" transform="translate(196,172)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f =</tspan><tspan class="node-id">  #10</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#10 .f =
+Type not computed
+
+[0] → —  DATA
+[1] → #6  MEM
+[2] → #9  DATA
+[3] → #4  DATA</title><circle class="port" cx="24" cy="-3" r="3" fill="white"/><circle class="port" cx="48" cy="-3" r="3" fill="#536477"/><circle class="port" cx="72" cy="-3" r="3" fill="#536477"/><circle class="port" cx="96" cy="-3" r="3" fill="#536477"/><text class="slot" x="24" y="-10" text-anchor="middle">0</text><text class="slot" x="48" y="-10" text-anchor="middle">1</text><text class="slot" x="72" y="-10" text-anchor="middle">2</text><text class="slot" x="96" y="-10" text-anchor="middle">3</text></g><g class="node" id="n21" data-id="21" transform="translate(348,172)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>//</tspan><tspan class="node-id">  #21</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#21 //
+Type not computed
+
+[0] → —  DATA
+[1] → #7  DATA
+[2] → #22  DATA</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n22" data-id="22" transform="translate(636,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#3</tspan><tspan class="node-id">  #22</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#22 #3
+Type not computed
+
+</title></g><g class="node" id="n31" data-id="31" transform="translate(266,380)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f =</tspan><tspan class="node-id">  #31</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#31 .f =
+Type not computed
+
+[0] → —  DATA
+[1] → #230  MEM
+[2] → #9  DATA
+[3] → #21  DATA</title><circle class="port" cx="24" cy="-3" r="3" fill="white"/><circle class="port" cx="48" cy="-3" r="3" fill="#536477"/><circle class="port" cx="72" cy="-3" r="3" fill="#536477"/><circle class="port" cx="96" cy="-3" r="3" fill="#536477"/><text class="slot" x="24" y="-10" text-anchor="middle">0</text><text class="slot" x="48" y="-10" text-anchor="middle">1</text><text class="slot" x="72" y="-10" text-anchor="middle">2</text><text class="slot" x="96" y="-10" text-anchor="middle">3</text></g><g class="node" id="n37" data-id="37" transform="translate(24,484)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Return</tspan><tspan class="node-id">  #37</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#37 Return
+Type not computed
+
+[0] → —  CTRL
+[1] → #1  MEM
+[2] → #9  DATA</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n230" data-id="230" transform="translate(199,276)" style="opacity: 1;"><path class="box" d="M12,0H108L120,22L108,44H12L0,22Z" fill="#f5e4fa"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>MemPhi_2</tspan><tspan class="node-id">  #230</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#230 MemPhi_2
+Type not computed
+
+[0] → —  ASSOC
+[1] → #10  MEM
+[2] → #233  MEM</title><circle class="port" cx="0" cy="-3" r="3" fill="white"/><circle class="port" cx="40" cy="-3" r="3" fill="#536477"/><circle class="port" cx="80" cy="-3" r="3" fill="#536477"/><text class="slot" x="0" y="-10" text-anchor="middle">0</text><text class="slot" x="40" y="-10" text-anchor="middle">1</text><text class="slot" x="80" y="-10" text-anchor="middle">2</text></g><g class="node" id="n233" data-id="233" transform="translate(266,484)" style="opacity: 1;"><path class="box" d="M12,0H108L120,22L108,44H12L0,22Z" fill="#f5e4fa"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>MemPhi_2</tspan><tspan class="node-id">  #233</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#233 MemPhi_2
+Type not computed
+
+[0] → —  ASSOC
+[1] → #31  MEM
+[2] → #230  MEM</title><circle class="port" cx="0" cy="-3" r="3" fill="white"/><circle class="port" cx="40" cy="-3" r="3" fill="#536477"/><circle class="port" cx="80" cy="-3" r="3" fill="#536477"/><text class="slot" x="0" y="-10" text-anchor="middle">0</text><text class="slot" x="40" y="-10" text-anchor="middle">1</text><text class="slot" x="80" y="-10" text-anchor="middle">2</text></g></g><g class="region-heads" style="opacity: 1;"/><g class="shortcuts" style="opacity: 1;"/><g class="peep-ghosts" pointer-events="none"/></g></svg>
diff --git a/docs/chapter13/graph5.gv b/docs/chapter13/graph5.gv
new file mode 100644
index 00000000..8189f6dd
--- /dev/null
+++ b/docs/chapter13/graph5.gv
@@ -0,0 +1,117 @@
+digraph chapter13 {
+/*
+struct S { int f; }
+S v = new S;
+int i = arg;
+while (arg > 0) {
+    int j = i/3;
+    if (arg == 5)
+        v.f = j;
+    arg = arg - 1;
+}
+return v;
+
+*/
+	rankdir=BT;
+	concentrate="true";
+	compound="true";
+	subgraph cluster_Nodes {
+		Start2 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">Start</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">$ctrl</TD><TD PORT="p1">$mem</TD><TD PORT="p2">arg</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		MemMerge [ shape=box label="MemMerge" ];
+		Stop3 [ shape=box style=filled fillcolor=yellow label="Stop" ];
+		Con_4 [ label="#0" ];
+		new9 [ label="new S" ];
+		Store10 [ label=".f =" ];
+		Loop11 [ shape=box style=filled fillcolor=yellow label="Loop" ];
+		Phi_arg13 [ style=filled fillcolor=lightyellow label="&phi;_arg" ];
+		LT14 [ label="<" ];
+		If16 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">If</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">True</TD><TD PORT="p1" BGCOLOR="yellow">False</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Div21 [ label="//" ];
+		Con_22 [ label="#3" ];
+		EQ23 [ label="==" ];
+		Con_24 [ label="#5" ];
+		If25 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">If</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">True</TD><TD PORT="p1" BGCOLOR="yellow">False</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Phi_230 [ style=filled fillcolor=lightyellow label="MemPhi_2" ];
+		Store31 [ label=".f =" ];
+		Region32 [ shape=box style=filled fillcolor=yellow label="Region" ];
+		Phi_233 [ style=filled fillcolor=lightyellow label="MemPhi_2" ];
+		Sub35 [ label="-" ];
+		Con_36 [ label="#1" ];
+		Return37 [ shape=box style=filled fillcolor=yellow label="Return" ];
+		{ rank=same; Loop11;Phi_230;Phi_arg13;}
+		{ rank=same; Region32;Phi_233;}
+	}
+	edge [ fontname=Helvetica, fontsize=8 ];
+	Stop3 -> Return37[taillabel=0 color=red];
+	new9 -> Start2:p0[taillabel=0 color=green];
+	Store10 -> Start2:p0[taillabel=0 color=red];
+	Store10 -> Start2:p1[taillabel=1 color=blue];
+	Store10 -> new9[taillabel=2];
+	Store10 -> Con_4[taillabel=3];
+	Loop11 -> Start2:p0[taillabel=1 color=red];
+	Loop11 -> Region32[taillabel=2 color=red constraint=false];
+	Phi_arg13 -> Loop11 [style=dotted taillabel=0];
+	Phi_arg13 -> Start2:p2[taillabel=1];
+	Phi_arg13 -> Sub35[taillabel=2 constraint=false];
+	LT14 -> Loop11[taillabel=0 color=red];
+	LT14 -> Con_4[taillabel=1];
+	LT14 -> Phi_arg13[taillabel=2];
+	If16 -> Loop11[taillabel=0 color=red];
+	If16 -> LT14[taillabel=1];
+	Div21 -> Start2[taillabel=0 color=red];
+	Div21 -> Start2:p2[taillabel=1];
+	Div21 -> Con_22[taillabel=2];
+	EQ23 -> Loop11[taillabel=0 color=red];
+	EQ23 -> Phi_arg13[taillabel=1];
+	EQ23 -> Con_24[taillabel=2];
+	If25 -> If16:p0[taillabel=0 color=red];
+	If25 -> EQ23[taillabel=1];
+	Phi_230 -> Loop11 [style=dotted taillabel=0];
+	Phi_230 -> Store10[taillabel=1 color=blue];
+	Phi_230 -> Phi_233[taillabel=2 color=blue constraint=false];
+	Store31 -> Loop11[taillabel=0 color=red];
+	Store31 -> Phi_230[taillabel=1 color=blue];
+	Store31 -> new9[taillabel=2];
+	Store31 -> Div21[taillabel=3];
+	Region32 -> If25:p0[taillabel=1 color=red];
+	Region32 -> If25:p1[taillabel=2 color=red];
+	Phi_233 -> Region32 [style=dotted taillabel=0];
+	Phi_233 -> Store31[taillabel=1 color=blue];
+	Phi_233 -> Phi_230[taillabel=2 color=blue constraint=false];
+	Sub35 -> Loop11[taillabel=0 color=red];
+	Sub35 -> Phi_arg13[taillabel=1];
+	Sub35 -> Con_36[taillabel=2];
+	Return37 -> If16:p1[taillabel=0 color=red];
+	Return37 -> new9[taillabel=2];
+	Return37 -> MemMerge[taillabel=1 color=blue];
+	MemMerge -> Start2:p1[taillabel=1 color=blue];
+	MemMerge -> Phi_230[taillabel=2 color=blue];
+	MemMerge -> Loop11[taillabel=0 color=green];
+}
diff --git a/docs/chapter13/graph5.json b/docs/chapter13/graph5.json
new file mode 100644
index 00000000..6b1722f6
--- /dev/null
+++ b/docs/chapter13/graph5.json
@@ -0,0 +1,24 @@
+{
+  "ver": 1,
+  "comp": "chapter13/docs/graph5.svg",
+  "step": 1,
+  "roots": [37],
+  "scope": 0,
+  "nodes": [
+    {"id": 1, "label": "MemMerge", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 6, "role": "MEM", "label": null}, {"idx": 2, "def": 230, "role": "MEM", "label": null}], "proj": null},
+    {"id": 2, "label": "Start", "type": null, "kind": "CTRL", "edges": [], "proj": null},
+    {"id": 4, "label": "#0", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 6, "label": "$mem", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 2, "role": "MEM", "label": null}], "proj": {"par": 2, "idx": 1}},
+    {"id": 7, "label": "arg", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 2, "role": "DATA", "label": null}], "proj": {"par": 2, "idx": 2}},
+    {"id": 9, "label": "new S", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}], "proj": null},
+    {"id": 10, "label": ".f =", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 6, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}, {"idx": 3, "def": 4, "role": "DATA", "label": null}], "proj": null},
+    {"id": 21, "label": "//", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 7, "role": "DATA", "label": null}, {"idx": 2, "def": 22, "role": "DATA", "label": null}], "proj": null},
+    {"id": 22, "label": "#3", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 31, "label": ".f =", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 230, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}, {"idx": 3, "def": 21, "role": "DATA", "label": null}], "proj": null},
+    {"id": 37, "label": "Return", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 1, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}], "proj": null},
+    {"id": 230, "label": "MemPhi_2", "type": null, "kind": "PHI", "edges": [{"idx": 0, "def": 0, "role": "ASSOC", "label": null}, {"idx": 1, "def": 10, "role": "MEM", "label": null}, {"idx": 2, "def": 233, "role": "MEM", "label": null}], "proj": null},
+    {"id": 233, "label": "MemPhi_2", "type": null, "kind": "PHI", "edges": [{"idx": 0, "def": 0, "role": "ASSOC", "label": null}, {"idx": 1, "def": 31, "role": "MEM", "label": null}, {"idx": 2, "def": 230, "role": "MEM", "label": null}], "proj": null}
+  ],
+  "groups": [
+  ]
+}
diff --git a/docs/chapter13/graph5.svg b/docs/chapter13/graph5.svg
new file mode 100644
index 00000000..c120550f
--- /dev/null
+++ b/docs/chapter13/graph5.svg
@@ -0,0 +1,120 @@
+<svg aria-label="Compiler graph" width="780" height="568" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 780 568" style="font-family: sans-serif;"><style>
+    html, body { height:100%; margin:0; font-family:sans-serif; }
+    .viewer { height:100%; display:grid; grid-template-rows:auto minmax(0,1fr) auto; }
+    .source { padding:8px; border-bottom:1px solid #ccc; }
+    #program { width:min(600px,80vw); vertical-align:middle; }
+    #status { margin-top:4px; }
+    #graph { min-height:0; overflow:hidden; position:relative; background:#fafbfc; }
+    #elk { width:100%; height:100%; }
+    #graph svg { display:block; }
+    .tools { display:flex; flex-wrap:wrap; align-items:center; gap:14px; margin-top:8px; font-size:12px; }
+    .hint { color:#616c78; }
+    .ctrl { color:#b63838; } .mem { color:#2867b2; } .data { color:#536477; }
+    .edge { fill:none; stroke-width:1.5; }
+    .edge.CTRL { stroke-width:2; }
+    .edge.ASSOC { stroke-dasharray:4 4; }
+    .edge.PARSER { stroke-dasharray:5 4; }
+    .parser rect { fill:#f6f0ff; stroke:#7956a5; stroke-width:1.5; stroke-dasharray:5 4; }
+    .edge.selected { stroke-width:3.5; }
+    .edge.bundle { stroke-width:4; }
+    .edge.bundle.selected { stroke-width:6; }
+    .edge-hit { fill:none; stroke:transparent; stroke-width:12; vector-effect:non-scaling-stroke; pointer-events:stroke; cursor:pointer; }
+    .edge-jump { fill:transparent; pointer-events:all; cursor:pointer; }
+    .node { cursor:pointer; }
+    .box { stroke:#758191; stroke-width:1; }
+    .node.held .box { stroke-dasharray:5 3; }
+    .node.near .box { stroke:#c18221; stroke-width:2; }
+    .node.focus .box { stroke:#9c4900; stroke-width:3; }
+    .node.selected .box { stroke:#1569b9; stroke-width:3; }
+    .node.folded .box { stroke-width:4; }
+    .node.folding .box { fill:#f4ccd7; }
+    .fold-tag { font-size:9px; font-weight:700; fill:#963751; }
+    .peep-area { fill:#fff3d9; fill-opacity:.8; stroke:#c18221; stroke-width:2; pointer-events:none; }
+    .node.peep-edit .box { stroke:#9c4900; stroke-width:3; }
+    .node.error .box { stroke:#b42318; stroke-width:4; }
+    #event.error { color:#b42318; font-weight:600; white-space:pre-wrap; overflow-wrap:anywhere; }
+    .peep-ghosts { pointer-events:none; }
+    .region-box { stroke:#9da9b8; stroke-width:1.5; }
+    .fold-btn { cursor:pointer; }
+    .fold-btn rect { fill:white; stroke:#596674; }
+    .fold-btn text { font-size:14px; fill:#152330; }
+    .fold-btn:focus rect { stroke:#1569b9; stroke-width:2; }
+    .shortcut { cursor:pointer; }
+    .shortcut path { fill:none; stroke-width:1.5; }
+    .shortcut rect { fill:#fff8ec; stroke:#b63838; stroke-dasharray:3 2; }
+    .shortcut text { font-size:11px; fill:#783030; }
+    .shortcut.selected rect, .shortcut:focus rect { stroke-width:2.5; }
+    .label { font-size:12px; fill:#152330; font-weight:600; }
+    .node-id { font-size:10px; fill:#596674; font-weight:400; }
+    .type { font-size:11px; fill:#455768; }
+    .port { stroke:#536477; stroke-width:1; }
+    .row { stroke:#b6afcf; stroke-width:1; }
+    .bind { font-size:12px; fill:#152330; }
+    .slot { font-size:10px; fill:#364352; paint-order:stroke; stroke:#fafbfc; stroke-width:3; }
+    #detail { position:absolute; top:8px; right:8px; margin:0; padding:12px; max-width:320px;
+      max-height:45%; overflow:auto; white-space:pre-wrap; overflow-wrap:anywhere;
+      background:#fffffff2; border:1px solid #bac5d0; border-radius:4px; font-size:12px; }
+    .controls { display:flex; flex-wrap:wrap; justify-content:center; align-items:center; gap:6px; padding:6px; }
+    .button { color:white; background:black; font-size:20px; min-width:30px; }
+    .button:disabled { background:grey; }
+    .count { font-size:20px; min-width:35px; text-align:center; }
+    #N { width:6ch; }
+    #scrub { width:clamp(120px,35vw,600px); }
+  </style><defs><marker id="arrow-CTRL" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#b63838"/></marker><marker id="arrow-DATA" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#536477"/></marker><marker id="arrow-MEM" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#2867b2"/></marker><marker id="arrow-ASSOC" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#9396a3"/></marker><marker id="arrow-PARSER" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#7956a5"/></marker></defs><rect width="100%" height="100%" fill="rgb(250, 251, 252)"/><g><g class="regions" style="opacity: 1;"/><rect class="peep-area" rx="36" style="opacity: 0;"/><g class="edges"><path class="edge MEM" id="e1i1" d="M266,118 L266,123 Q266,128 261,128 L193,128 Q185,128 185,136 L185,374" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#1[1] → #6 · MEM</title></path><path class="edge MEM" id="e1i2" d="M259,326 L259,338 Q259,346 251,346 L223,346 Q215,346 215,354 L215,374" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#1[2] → #230 · MEM</title></path><path class="edge MEM" id="e10i1" d="M266,118 L266,123 Q266,128 261,128 L252,128 Q244,128 244,136 L244,166" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#10[1] → #6 · MEM</title></path><path class="edge DATA" id="e10i2" d="M114,118 L114,130 Q114,138 122,138 L260,138 Q268,138 268,146 L268,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#10[2] → #9 · DATA</title></path><path class="edge DATA" id="e10i3" d="M544,118 L544,123 Q544,128 539,128 L300,128 Q292,128 292,136 L292,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#10[3] → #4 · DATA</title></path><path class="edge DATA" id="e21i1" d="M386,118 L386,130 Q386,138 394,138 L400,138 Q408,138 408,146 L408,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#21[1] → #7 · DATA</title></path><path class="edge DATA" id="e21i2" d="M696,118 L696,130 Q696,138 688,138 L446,138 Q438,138 438,146 L438,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#21[2] → #22 · DATA</title></path><path class="edge MEM" id="e31i1" d="M259,326 L259,338 Q259,346 267,346 L306,346 Q314,346 314,354 L314,374" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#31[1] → #230 · MEM</title></path><path class="edge DATA" id="e31i2" d="M114,118 L114,328 Q114,336 122,336 L330,336 Q338,336 338,344 L338,374" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#31[2] → #9 · DATA</title></path><path class="edge DATA" id="e31i3" d="M408,222 L408,328 Q408,336 400,336 L370,336 Q362,336 362,344 L362,374" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#31[3] → #21 · DATA</title></path><path class="edge MEM" id="e37i1" d="M185,430 L185,435 Q185,440 180,440 L92,440 Q84,440 84,448 L84,478" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#37[1] → #1 · MEM</title></path><path class="edge DATA" id="e37i2" d="M114,118 L114,478" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#37[2] → #9 · DATA</title></path><path class="edge MEM" id="e230i1" d="M256,222 L256,227 Q256,232 251,232 L247,232 Q239,232 239,240 L239,270" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#230[1] → #10 · MEM</title></path><path class="edge MEM" id="e230i2" d="M326,534 L326,539 Q326,544 331,544 L388,544 Q396,544 396,536 L396,240 Q396,232 388,232 L287,232 Q279,232 279,240 L279,270" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#230[2] → #233 · MEM</title></path><path class="edge MEM" id="e233i1" d="M326,430 L326,435 Q326,440 321,440 L314,440 Q306,440 306,448 L306,478" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#233[1] → #31 · MEM</title></path><path class="edge MEM" id="e233i2" d="M259,326 L259,344 Q259,346 257,346 L257,346 Q255,346 255,348 L255,442 Q255,450 263,450 L338,450 Q346,450 346,458 L346,478" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#233[2] → #230 · MEM</title></path></g><g class="edge-hits"/><g class="parser" style="opacity: 1;"/><g class="nodes"><g class="node" id="n1" data-id="1" transform="translate(125,380)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>MemMerge</tspan><tspan class="node-id">  #1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#1 MemMerge
+Type not computed
+
+[0] → —  CTRL
+[1] → #6  MEM
+[2] → #230  MEM</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n2" data-id="2" transform="translate(206,24)" style="opacity: 1;"><path class="box" d="M0,0H240V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="120" y="18"><tspan>Start</tspan><tspan class="node-id">  #2</tspan></text><text class="type" text-anchor="middle" y="35" x="120"/><title>#2 Start
+Type not computed
+
+</title></g><g class="node" id="n4" data-id="4" transform="translate(484,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#0</tspan><tspan class="node-id">  #4</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#4 #0
+Type not computed
+
+</title></g><g class="node" id="n6" data-id="6" transform="translate(206,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>$mem</tspan><tspan class="node-id">  #6/1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#6 $mem
+Projection 1 of #2
+Type not computed
+
+[0] → #2  MEM</title></g><g class="node" id="n7" data-id="7" transform="translate(326,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>arg</tspan><tspan class="node-id">  #7/2</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#7 arg
+Projection 2 of #2
+Type not computed
+
+[0] → #2  DATA</title></g><g class="node" id="n9" data-id="9" transform="translate(54,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>new S</tspan><tspan class="node-id">  #9</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#9 new S
+Type not computed
+
+[0] → —  CTRL</title><circle class="port" cx="60" cy="-3" r="3" fill="white"/><text class="slot" x="60" y="-10" text-anchor="middle">0</text></g><g class="node" id="n10" data-id="10" transform="translate(196,172)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f =</tspan><tspan class="node-id">  #10</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#10 .f =
+Type not computed
+
+[0] → —  CTRL
+[1] → #6  MEM
+[2] → #9  DATA
+[3] → #4  DATA</title><circle class="port" cx="24" cy="-3" r="3" fill="white"/><circle class="port" cx="48" cy="-3" r="3" fill="#536477"/><circle class="port" cx="72" cy="-3" r="3" fill="#536477"/><circle class="port" cx="96" cy="-3" r="3" fill="#536477"/><text class="slot" x="24" y="-10" text-anchor="middle">0</text><text class="slot" x="48" y="-10" text-anchor="middle">1</text><text class="slot" x="72" y="-10" text-anchor="middle">2</text><text class="slot" x="96" y="-10" text-anchor="middle">3</text></g><g class="node" id="n21" data-id="21" transform="translate(348,172)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>//</tspan><tspan class="node-id">  #21</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#21 //
+Type not computed
+
+[0] → —  CTRL
+[1] → #7  DATA
+[2] → #22  DATA</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n22" data-id="22" transform="translate(636,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#3</tspan><tspan class="node-id">  #22</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#22 #3
+Type not computed
+
+</title></g><g class="node" id="n31" data-id="31" transform="translate(266,380)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f =</tspan><tspan class="node-id">  #31</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#31 .f =
+Type not computed
+
+[0] → —  CTRL
+[1] → #230  MEM
+[2] → #9  DATA
+[3] → #21  DATA</title><circle class="port" cx="24" cy="-3" r="3" fill="white"/><circle class="port" cx="48" cy="-3" r="3" fill="#536477"/><circle class="port" cx="72" cy="-3" r="3" fill="#536477"/><circle class="port" cx="96" cy="-3" r="3" fill="#536477"/><text class="slot" x="24" y="-10" text-anchor="middle">0</text><text class="slot" x="48" y="-10" text-anchor="middle">1</text><text class="slot" x="72" y="-10" text-anchor="middle">2</text><text class="slot" x="96" y="-10" text-anchor="middle">3</text></g><g class="node" id="n37" data-id="37" transform="translate(24,484)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Return</tspan><tspan class="node-id">  #37</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#37 Return
+Type not computed
+
+[0] → —  CTRL
+[1] → #1  MEM
+[2] → #9  DATA</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n230" data-id="230" transform="translate(199,276)" style="opacity: 1;"><path class="box" d="M12,0H108L120,22L108,44H12L0,22Z" fill="#f5e4fa"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>MemPhi_2</tspan><tspan class="node-id">  #230</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#230 MemPhi_2
+Type not computed
+
+[0] → —  ASSOC
+[1] → #10  MEM
+[2] → #233  MEM</title><circle class="port" cx="0" cy="-3" r="3" fill="white"/><circle class="port" cx="40" cy="-3" r="3" fill="#536477"/><circle class="port" cx="80" cy="-3" r="3" fill="#536477"/><text class="slot" x="0" y="-10" text-anchor="middle">0</text><text class="slot" x="40" y="-10" text-anchor="middle">1</text><text class="slot" x="80" y="-10" text-anchor="middle">2</text></g><g class="node" id="n233" data-id="233" transform="translate(266,484)" style="opacity: 1;"><path class="box" d="M12,0H108L120,22L108,44H12L0,22Z" fill="#f5e4fa"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>MemPhi_2</tspan><tspan class="node-id">  #233</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#233 MemPhi_2
+Type not computed
+
+[0] → —  ASSOC
+[1] → #31  MEM
+[2] → #230  MEM</title><circle class="port" cx="0" cy="-3" r="3" fill="white"/><circle class="port" cx="40" cy="-3" r="3" fill="#536477"/><circle class="port" cx="80" cy="-3" r="3" fill="#536477"/><text class="slot" x="0" y="-10" text-anchor="middle">0</text><text class="slot" x="40" y="-10" text-anchor="middle">1</text><text class="slot" x="80" y="-10" text-anchor="middle">2</text></g></g><g class="region-heads" style="opacity: 1;"/><g class="shortcuts" style="opacity: 1;"/><g class="peep-ghosts" pointer-events="none"/></g></svg>
diff --git a/docs/chapter13/graph6.gv b/docs/chapter13/graph6.gv
new file mode 100644
index 00000000..47165fdb
--- /dev/null
+++ b/docs/chapter13/graph6.gv
@@ -0,0 +1,117 @@
+digraph chapter13 {
+/*
+struct S { int f; }
+S v = new S;
+int i = arg;
+while (arg > 0) {
+    int j = i/3;
+    if (arg == 5)
+        v.f = j;
+    arg = arg - 1;
+}
+return v;
+
+*/
+	rankdir=BT;
+	concentrate="true";
+	compound="true";
+	subgraph cluster_Nodes {
+		Start2 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">Start</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">$ctrl</TD><TD PORT="p1">$mem</TD><TD PORT="p2">arg</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		MemMerge [ shape=box label="MemMerge" ];
+		Stop3 [ shape=box style=filled fillcolor=yellow label="Stop" ];
+		Con_4 [ label="#0" ];
+		new9 [ label="new S" ];
+		Store10 [ label=".f =" ];
+		Loop11 [ shape=box style=filled fillcolor=yellow label="Loop" ];
+		Phi_arg13 [ style=filled fillcolor=lightyellow label="&phi;_arg" ];
+		LT14 [ label="<" ];
+		If16 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">If</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">True</TD><TD PORT="p1" BGCOLOR="yellow">False</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Div21 [ label="//" ];
+		Con_22 [ label="#3" ];
+		EQ23 [ label="==" ];
+		Con_24 [ label="#5" ];
+		If25 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">If</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">True</TD><TD PORT="p1" BGCOLOR="yellow">False</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Phi_230 [ style=filled fillcolor=lightyellow label="MemPhi_2" ];
+		Store31 [ label=".f =" ];
+		Region32 [ shape=box style=filled fillcolor=yellow label="Region" ];
+		Phi_233 [ style=filled fillcolor=lightyellow label="MemPhi_2" ];
+		Sub35 [ label="-" ];
+		Con_36 [ label="#1" ];
+		Return37 [ shape=box style=filled fillcolor=yellow label="Return" ];
+		{ rank=same; Loop11;Phi_230;Phi_arg13;}
+		{ rank=same; Region32;Phi_233;}
+	}
+	edge [ fontname=Helvetica, fontsize=8 ];
+	Stop3 -> Return37[taillabel=0 color=red];
+	new9 -> Start2:p0[taillabel=0 color=green];
+	Store10 -> Start2:p0[taillabel=0 color=red];
+	Store10 -> Start2:p1[taillabel=1 color=blue];
+	Store10 -> new9[taillabel=2];
+	Store10 -> Con_4[taillabel=3];
+	Loop11 -> Start2:p0[taillabel=1 color=red];
+	Loop11 -> Region32[taillabel=2 color=red constraint=false];
+	Phi_arg13 -> Loop11 [style=dotted taillabel=0];
+	Phi_arg13 -> Start2:p2[taillabel=1];
+	Phi_arg13 -> Sub35[taillabel=2 constraint=false];
+	LT14 -> Loop11[taillabel=0 color=red];
+	LT14 -> Con_4[taillabel=1];
+	LT14 -> Phi_arg13[taillabel=2];
+	If16 -> Loop11[taillabel=0 color=red];
+	If16 -> LT14[taillabel=1];
+	Div21 -> Start2:p0[taillabel=0 color=red];
+	Div21 -> Start2:p2[taillabel=1];
+	Div21 -> Con_22[taillabel=2];
+	EQ23 -> If16:p0[taillabel=0 color=red];
+	EQ23 -> Phi_arg13[taillabel=1];
+	EQ23 -> Con_24[taillabel=2];
+	If25 -> If16:p0[taillabel=0 color=red];
+	If25 -> EQ23[taillabel=1];
+	Phi_230 -> Loop11 [style=dotted taillabel=0];
+	Phi_230 -> Store10[taillabel=1 color=blue];
+	Phi_230 -> Phi_233[taillabel=2 color=blue constraint=false];
+	Store31 -> If25:p0[taillabel=0 color=red];
+	Store31 -> Phi_230[taillabel=1 color=blue];
+	Store31 -> new9[taillabel=2];
+	Store31 -> Div21[taillabel=3];
+	Region32 -> If25:p0[taillabel=1 color=red];
+	Region32 -> If25:p1[taillabel=2 color=red];
+	Phi_233 -> Region32 [style=dotted taillabel=0];
+	Phi_233 -> Store31[taillabel=1 color=blue];
+	Phi_233 -> Phi_230[taillabel=2 color=blue constraint=false];
+	Sub35 -> Region32[taillabel=0 color=red];
+	Sub35 -> Phi_arg13[taillabel=1];
+	Sub35 -> Con_36[taillabel=2];
+	Return37 -> If16:p1[taillabel=0 color=red];
+	Return37 -> new9[taillabel=2];
+	Return37 -> MemMerge[taillabel=1 color=blue];
+	MemMerge -> Start2:p1[taillabel=1 color=blue];
+	MemMerge -> Phi_230[taillabel=2 color=blue];
+	MemMerge -> If16:p1[taillabel=0 color=green];
+}
diff --git a/docs/chapter13/graph6.json b/docs/chapter13/graph6.json
new file mode 100644
index 00000000..c63c717f
--- /dev/null
+++ b/docs/chapter13/graph6.json
@@ -0,0 +1,25 @@
+{
+  "ver": 1,
+  "comp": "chapter13/docs/graph6.svg",
+  "step": 1,
+  "roots": [37],
+  "scope": 0,
+  "nodes": [
+    {"id": 1, "label": "MemMerge", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 6, "role": "MEM", "label": null}, {"idx": 2, "def": 230, "role": "MEM", "label": null}], "proj": null},
+    {"id": 2, "label": "Start", "type": null, "kind": "CTRL", "edges": [], "proj": null},
+    {"id": 4, "label": "#0", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 6, "label": "$mem", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 2, "role": "MEM", "label": null}], "proj": {"par": 2, "idx": 1}},
+    {"id": 7, "label": "arg", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 2, "role": "DATA", "label": null}], "proj": {"par": 2, "idx": 2}},
+    {"id": 9, "label": "new S", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}], "proj": null},
+    {"id": 10, "label": ".f =", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 6, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}, {"idx": 3, "def": 4, "role": "DATA", "label": null}], "proj": null},
+    {"id": 15, "label": "True", "type": null, "kind": "CTRL", "edges": [], "proj": {"par": 0, "idx": 0}},
+    {"id": 21, "label": "//", "type": null, "kind": "DATA", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 7, "role": "DATA", "label": null}, {"idx": 2, "def": 22, "role": "DATA", "label": null}], "proj": null},
+    {"id": 22, "label": "#3", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 31, "label": ".f =", "type": null, "kind": "MEM", "edges": [{"idx": 0, "def": 15, "role": "CTRL", "label": null}, {"idx": 1, "def": 230, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}, {"idx": 3, "def": 21, "role": "DATA", "label": null}], "proj": null},
+    {"id": 37, "label": "Return", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 0, "role": "CTRL", "label": null}, {"idx": 1, "def": 1, "role": "MEM", "label": null}, {"idx": 2, "def": 9, "role": "DATA", "label": null}], "proj": null},
+    {"id": 230, "label": "MemPhi_2", "type": null, "kind": "PHI", "edges": [{"idx": 0, "def": 0, "role": "ASSOC", "label": null}, {"idx": 1, "def": 10, "role": "MEM", "label": null}, {"idx": 2, "def": 233, "role": "MEM", "label": null}], "proj": null},
+    {"id": 233, "label": "MemPhi_2", "type": null, "kind": "PHI", "edges": [{"idx": 0, "def": 0, "role": "ASSOC", "label": null}, {"idx": 1, "def": 31, "role": "MEM", "label": null}, {"idx": 2, "def": 230, "role": "MEM", "label": null}], "proj": null}
+  ],
+  "groups": [
+  ]
+}
diff --git a/docs/chapter13/graph6.svg b/docs/chapter13/graph6.svg
new file mode 100644
index 00000000..d6dec88f
--- /dev/null
+++ b/docs/chapter13/graph6.svg
@@ -0,0 +1,124 @@
+<svg aria-label="Compiler graph" width="820" height="568" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 820 568" style="font-family: sans-serif;"><style>
+    html, body { height:100%; margin:0; font-family:sans-serif; }
+    .viewer { height:100%; display:grid; grid-template-rows:auto minmax(0,1fr) auto; }
+    .source { padding:8px; border-bottom:1px solid #ccc; }
+    #program { width:min(600px,80vw); vertical-align:middle; }
+    #status { margin-top:4px; }
+    #graph { min-height:0; overflow:hidden; position:relative; background:#fafbfc; }
+    #elk { width:100%; height:100%; }
+    #graph svg { display:block; }
+    .tools { display:flex; flex-wrap:wrap; align-items:center; gap:14px; margin-top:8px; font-size:12px; }
+    .hint { color:#616c78; }
+    .ctrl { color:#b63838; } .mem { color:#2867b2; } .data { color:#536477; }
+    .edge { fill:none; stroke-width:1.5; }
+    .edge.CTRL { stroke-width:2; }
+    .edge.ASSOC { stroke-dasharray:4 4; }
+    .edge.PARSER { stroke-dasharray:5 4; }
+    .parser rect { fill:#f6f0ff; stroke:#7956a5; stroke-width:1.5; stroke-dasharray:5 4; }
+    .edge.selected { stroke-width:3.5; }
+    .edge.bundle { stroke-width:4; }
+    .edge.bundle.selected { stroke-width:6; }
+    .edge-hit { fill:none; stroke:transparent; stroke-width:12; vector-effect:non-scaling-stroke; pointer-events:stroke; cursor:pointer; }
+    .edge-jump { fill:transparent; pointer-events:all; cursor:pointer; }
+    .node { cursor:pointer; }
+    .box { stroke:#758191; stroke-width:1; }
+    .node.held .box { stroke-dasharray:5 3; }
+    .node.near .box { stroke:#c18221; stroke-width:2; }
+    .node.focus .box { stroke:#9c4900; stroke-width:3; }
+    .node.selected .box { stroke:#1569b9; stroke-width:3; }
+    .node.folded .box { stroke-width:4; }
+    .node.folding .box { fill:#f4ccd7; }
+    .fold-tag { font-size:9px; font-weight:700; fill:#963751; }
+    .peep-area { fill:#fff3d9; fill-opacity:.8; stroke:#c18221; stroke-width:2; pointer-events:none; }
+    .node.peep-edit .box { stroke:#9c4900; stroke-width:3; }
+    .node.error .box { stroke:#b42318; stroke-width:4; }
+    #event.error { color:#b42318; font-weight:600; white-space:pre-wrap; overflow-wrap:anywhere; }
+    .peep-ghosts { pointer-events:none; }
+    .region-box { stroke:#9da9b8; stroke-width:1.5; }
+    .fold-btn { cursor:pointer; }
+    .fold-btn rect { fill:white; stroke:#596674; }
+    .fold-btn text { font-size:14px; fill:#152330; }
+    .fold-btn:focus rect { stroke:#1569b9; stroke-width:2; }
+    .shortcut { cursor:pointer; }
+    .shortcut path { fill:none; stroke-width:1.5; }
+    .shortcut rect { fill:#fff8ec; stroke:#b63838; stroke-dasharray:3 2; }
+    .shortcut text { font-size:11px; fill:#783030; }
+    .shortcut.selected rect, .shortcut:focus rect { stroke-width:2.5; }
+    .label { font-size:12px; fill:#152330; font-weight:600; }
+    .node-id { font-size:10px; fill:#596674; font-weight:400; }
+    .type { font-size:11px; fill:#455768; }
+    .port { stroke:#536477; stroke-width:1; }
+    .row { stroke:#b6afcf; stroke-width:1; }
+    .bind { font-size:12px; fill:#152330; }
+    .slot { font-size:10px; fill:#364352; paint-order:stroke; stroke:#fafbfc; stroke-width:3; }
+    #detail { position:absolute; top:8px; right:8px; margin:0; padding:12px; max-width:320px;
+      max-height:45%; overflow:auto; white-space:pre-wrap; overflow-wrap:anywhere;
+      background:#fffffff2; border:1px solid #bac5d0; border-radius:4px; font-size:12px; }
+    .controls { display:flex; flex-wrap:wrap; justify-content:center; align-items:center; gap:6px; padding:6px; }
+    .button { color:white; background:black; font-size:20px; min-width:30px; }
+    .button:disabled { background:grey; }
+    .count { font-size:20px; min-width:35px; text-align:center; }
+    #N { width:6ch; }
+    #scrub { width:clamp(120px,35vw,600px); }
+  </style><defs><marker id="arrow-CTRL" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#b63838"/></marker><marker id="arrow-DATA" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#536477"/></marker><marker id="arrow-MEM" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#2867b2"/></marker><marker id="arrow-ASSOC" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#9396a3"/></marker><marker id="arrow-PARSER" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#7956a5"/></marker></defs><rect width="100%" height="100%" fill="rgb(250, 251, 252)"/><g><g class="regions" style="opacity: 1;"/><rect class="peep-area" rx="36" style="opacity: 0;"/><g class="edges"><path class="edge MEM" id="e1i1" d="M306,118 L306,123 Q306,128 301,128 L151,128 Q143,128 143,136 L143,328 Q143,336 135,336 L92,336 Q84,336 84,344 L84,374" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#1[1] → #6 · MEM</title></path><path class="edge MEM" id="e1i2" d="M331,326 L331,338 Q331,346 323,346 L122,346 Q114,346 114,354 L114,374" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#1[2] → #230 · MEM</title></path><path class="edge MEM" id="e10i1" d="M306,118 L306,123 Q306,128 301,128 L270,128 Q262,128 262,136 L262,166" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#10[1] → #6 · MEM</title></path><path class="edge DATA" id="e10i2" d="M154,118 L154,130 Q154,138 162,138 L278,138 Q286,138 286,146 L286,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#10[2] → #9 · DATA</title></path><path class="edge DATA" id="e10i3" d="M584,118 L584,130 Q584,138 576,138 L318,138 Q310,138 310,146 L310,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#10[3] → #4 · DATA</title></path><path class="edge DATA" id="e21i1" d="M426,118 L426,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#21[1] → #7 · DATA</title></path><path class="edge DATA" id="e21i2" d="M736,118 L736,140 Q736,148 728,148 L464,148 Q456,148 456,156 L456,166" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#21[2] → #22 · DATA</title></path><path class="edge CTRL" id="e31i0" d="M206,326 L206,374" stroke="#b63838" marker-start="url(#arrow-CTRL)" style="opacity: 1;"><title>#31[0] → #15 · CTRL</title></path><path class="edge MEM" id="e31i1" d="M331,326 L331,338 Q331,346 323,346 L238,346 Q230,346 230,354 L230,374" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#31[1] → #230 · MEM</title></path><path class="edge DATA" id="e31i2" d="M154,118 L154,224 Q154,232 162,232 L249,232 Q257,232 257,240 L257,354.5 Q257,356 255.5,356 L255.5,356 Q254,356 254,357.5 L254,374" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#31[2] → #9 · DATA</title></path><path class="edge DATA" id="e31i3" d="M426,222 L426,234 Q426,242 418,242 L409,242 Q401,242 401,250 L401,348 Q401,356 393,356 L286,356 Q278,356 278,364 L278,374" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#31[3] → #21 · DATA</title></path><path class="edge MEM" id="e37i1" d="M84,430 L84,435 Q84,440 89,440 L116,440 Q124,440 124,448 L124,478" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#37[1] → #1 · MEM</title></path><path class="edge DATA" id="e37i2" d="M154,118 L154,478" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#37[2] → #9 · DATA</title></path><path class="edge MEM" id="e230i1" d="M274,222 L274,227 Q274,232 279,232 L303,232 Q311,232 311,240 L311,270" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#230[1] → #10 · MEM</title></path><path class="edge MEM" id="e230i2" d="M311,534 L311,539 Q311,544 316,544 L404,544 Q412,544 412,536 L412,240 Q412,232 404,232 L359,232 Q351,232 351,240 L351,270" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#230[2] → #233 · MEM</title></path><path class="edge MEM" id="e233i1" d="M242,430 L242,435 Q242,440 247,440 L283,440 Q291,440 291,448 L291,478" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#233[1] → #31 · MEM</title></path><path class="edge MEM" id="e233i2" d="M331,326 L331,478" stroke="#2867b2" marker-start="url(#arrow-MEM)" style="opacity: 1;"><title>#233[2] → #230 · MEM</title></path></g><g class="edge-hits"/><g class="parser" style="opacity: 1;"/><g class="nodes"><g class="node" id="n1" data-id="1" transform="translate(24,380)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>MemMerge</tspan><tspan class="node-id">  #1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#1 MemMerge
+Type not computed
+
+[0] → —  CTRL
+[1] → #6  MEM
+[2] → #230  MEM</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n2" data-id="2" transform="translate(246,24)" style="opacity: 1;"><path class="box" d="M0,0H240V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="120" y="18"><tspan>Start</tspan><tspan class="node-id">  #2</tspan></text><text class="type" text-anchor="middle" y="35" x="120"/><title>#2 Start
+Type not computed
+
+</title></g><g class="node" id="n4" data-id="4" transform="translate(524,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#0</tspan><tspan class="node-id">  #4</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#4 #0
+Type not computed
+
+</title></g><g class="node" id="n6" data-id="6" transform="translate(246,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>$mem</tspan><tspan class="node-id">  #6/1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#6 $mem
+Projection 1 of #2
+Type not computed
+
+[0] → #2  MEM</title></g><g class="node" id="n7" data-id="7" transform="translate(366,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>arg</tspan><tspan class="node-id">  #7/2</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#7 arg
+Projection 2 of #2
+Type not computed
+
+[0] → #2  DATA</title></g><g class="node" id="n9" data-id="9" transform="translate(94,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>new S</tspan><tspan class="node-id">  #9</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#9 new S
+Type not computed
+
+[0] → —  CTRL</title><circle class="port" cx="60" cy="-3" r="3" fill="white"/><text class="slot" x="60" y="-10" text-anchor="middle">0</text></g><g class="node" id="n10" data-id="10" transform="translate(214,172)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f =</tspan><tspan class="node-id">  #10</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#10 .f =
+Type not computed
+
+[0] → —  CTRL
+[1] → #6  MEM
+[2] → #9  DATA
+[3] → #4  DATA</title><circle class="port" cx="24" cy="-3" r="3" fill="white"/><circle class="port" cx="48" cy="-3" r="3" fill="#536477"/><circle class="port" cx="72" cy="-3" r="3" fill="#536477"/><circle class="port" cx="96" cy="-3" r="3" fill="#536477"/><text class="slot" x="24" y="-10" text-anchor="middle">0</text><text class="slot" x="48" y="-10" text-anchor="middle">1</text><text class="slot" x="72" y="-10" text-anchor="middle">2</text><text class="slot" x="96" y="-10" text-anchor="middle">3</text></g><g class="node" id="n15" data-id="15" transform="translate(165,294)" style="opacity: 1;"><path class="box" d="M0,0H82V26H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="41" y="17"><tspan>True</tspan><tspan class="node-id">  #15/0</tspan></text><text class="type" text-anchor="middle" y="35" x="41"/><title>#15 True
+Projection 0 of #0
+Type not computed
+
+</title></g><g class="node" id="n21" data-id="21" transform="translate(366,172)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>//</tspan><tspan class="node-id">  #21</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#21 //
+Type not computed
+
+[0] → —  CTRL
+[1] → #7  DATA
+[2] → #22  DATA</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n22" data-id="22" transform="translate(676,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#3</tspan><tspan class="node-id">  #22</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#22 #3
+Type not computed
+
+</title></g><g class="node" id="n31" data-id="31" transform="translate(182,380)" style="opacity: 1;"><path class="box" d="M10,0H110L120,10V34L110,44H10L0,34V10Z" fill="#dcecff"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>.f =</tspan><tspan class="node-id">  #31</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#31 .f =
+Type not computed
+
+[0] → #15  CTRL
+[1] → #230  MEM
+[2] → #9  DATA
+[3] → #21  DATA</title><circle class="port" cx="24" cy="-3" r="3" fill="#536477"/><circle class="port" cx="48" cy="-3" r="3" fill="#536477"/><circle class="port" cx="72" cy="-3" r="3" fill="#536477"/><circle class="port" cx="96" cy="-3" r="3" fill="#536477"/><text class="slot" x="24" y="-10" text-anchor="middle">0</text><text class="slot" x="48" y="-10" text-anchor="middle">1</text><text class="slot" x="72" y="-10" text-anchor="middle">2</text><text class="slot" x="96" y="-10" text-anchor="middle">3</text></g><g class="node" id="n37" data-id="37" transform="translate(64,484)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Return</tspan><tspan class="node-id">  #37</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#37 Return
+Type not computed
+
+[0] → —  CTRL
+[1] → #1  MEM
+[2] → #9  DATA</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n230" data-id="230" transform="translate(271,276)" style="opacity: 1;"><path class="box" d="M12,0H108L120,22L108,44H12L0,22Z" fill="#f5e4fa"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>MemPhi_2</tspan><tspan class="node-id">  #230</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#230 MemPhi_2
+Type not computed
+
+[0] → —  ASSOC
+[1] → #10  MEM
+[2] → #233  MEM</title><circle class="port" cx="0" cy="-3" r="3" fill="white"/><circle class="port" cx="40" cy="-3" r="3" fill="#536477"/><circle class="port" cx="80" cy="-3" r="3" fill="#536477"/><text class="slot" x="0" y="-10" text-anchor="middle">0</text><text class="slot" x="40" y="-10" text-anchor="middle">1</text><text class="slot" x="80" y="-10" text-anchor="middle">2</text></g><g class="node" id="n233" data-id="233" transform="translate(251,484)" style="opacity: 1;"><path class="box" d="M12,0H108L120,22L108,44H12L0,22Z" fill="#f5e4fa"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>MemPhi_2</tspan><tspan class="node-id">  #233</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#233 MemPhi_2
+Type not computed
+
+[0] → —  ASSOC
+[1] → #31  MEM
+[2] → #230  MEM</title><circle class="port" cx="0" cy="-3" r="3" fill="white"/><circle class="port" cx="40" cy="-3" r="3" fill="#536477"/><circle class="port" cx="80" cy="-3" r="3" fill="#536477"/><text class="slot" x="0" y="-10" text-anchor="middle">0</text><text class="slot" x="40" y="-10" text-anchor="middle">1</text><text class="slot" x="80" y="-10" text-anchor="middle">2</text></g></g><g class="region-heads" style="opacity: 1;"/><g class="shortcuts" style="opacity: 1;"/><g class="peep-ghosts" pointer-events="none"/></g></svg>
diff --git a/docs/chapter13/graph7.gv b/docs/chapter13/graph7.gv
new file mode 100644
index 00000000..b6507e53
--- /dev/null
+++ b/docs/chapter13/graph7.gv
@@ -0,0 +1,23 @@
+digraph chapter13 {
+	rankdir=BT;
+	concentrate="true";
+	compound="true";
+	subgraph cluster_Nodes {
+		Start2 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">Start</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">$ctrl</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Con_4 [ label="#0" ];
+		Loop8 [ shape=box style=filled fillcolor=yellow label="Loop" ];
+		{ rank=same; Loop8;}
+	}
+	edge [ fontname=Helvetica, fontsize=8 ];
+	Loop8 -> Start2:p0[taillabel=1 color=red];
+	Loop8 -> Loop8[taillabel=2 color=red constraint=false];
+}
diff --git a/docs/chapter13/graph7.json b/docs/chapter13/graph7.json
new file mode 100644
index 00000000..0e3efb9f
--- /dev/null
+++ b/docs/chapter13/graph7.json
@@ -0,0 +1,16 @@
+{
+  "ver": 1,
+  "comp": "chapter13/docs/graph7.svg",
+  "step": 1,
+  "roots": [],
+  "scope": 0,
+  "nodes": [
+    {"id": 1, "label": "$ctrl", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 2, "role": "CTRL", "label": null}], "proj": {"par": 2, "idx": 0}},
+    {"id": 2, "label": "Start", "type": null, "kind": "CTRL", "edges": [], "proj": null},
+    {"id": 4, "label": "#0", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 8, "label": "Loop", "type": null, "kind": "LOOP", "edges": [{"idx": 0, "def": 0, "role": "DATA", "label": null}, {"idx": 1, "def": 1, "role": "CTRL", "label": null}, {"idx": 2, "def": 8, "role": "CTRL", "label": null}], "proj": null}
+  ],
+  "groups": [
+    {"id": 8, "par": 0, "nodes": [8]}
+  ]
+}
diff --git a/docs/chapter13/graph7.svg b/docs/chapter13/graph7.svg
new file mode 100644
index 00000000..15d886dc
--- /dev/null
+++ b/docs/chapter13/graph7.svg
@@ -0,0 +1,78 @@
+<svg aria-label="Compiler graph" width="364" height="325" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 364 325" style="font-family: sans-serif;"><style>
+    html, body { height:100%; margin:0; font-family:sans-serif; }
+    .viewer { height:100%; display:grid; grid-template-rows:auto minmax(0,1fr) auto; }
+    .source { padding:8px; border-bottom:1px solid #ccc; }
+    #program { width:min(600px,80vw); vertical-align:middle; }
+    #status { margin-top:4px; }
+    #graph { min-height:0; overflow:hidden; position:relative; background:#fafbfc; }
+    #elk { width:100%; height:100%; }
+    #graph svg { display:block; }
+    .tools { display:flex; flex-wrap:wrap; align-items:center; gap:14px; margin-top:8px; font-size:12px; }
+    .hint { color:#616c78; }
+    .ctrl { color:#b63838; } .mem { color:#2867b2; } .data { color:#536477; }
+    .edge { fill:none; stroke-width:1.5; }
+    .edge.CTRL { stroke-width:2; }
+    .edge.ASSOC { stroke-dasharray:4 4; }
+    .edge.PARSER { stroke-dasharray:5 4; }
+    .parser rect { fill:#f6f0ff; stroke:#7956a5; stroke-width:1.5; stroke-dasharray:5 4; }
+    .edge.selected { stroke-width:3.5; }
+    .edge.bundle { stroke-width:4; }
+    .edge.bundle.selected { stroke-width:6; }
+    .edge-hit { fill:none; stroke:transparent; stroke-width:12; vector-effect:non-scaling-stroke; pointer-events:stroke; cursor:pointer; }
+    .edge-jump { fill:transparent; pointer-events:all; cursor:pointer; }
+    .node { cursor:pointer; }
+    .box { stroke:#758191; stroke-width:1; }
+    .node.held .box { stroke-dasharray:5 3; }
+    .node.near .box { stroke:#c18221; stroke-width:2; }
+    .node.focus .box { stroke:#9c4900; stroke-width:3; }
+    .node.selected .box { stroke:#1569b9; stroke-width:3; }
+    .node.folded .box { stroke-width:4; }
+    .node.folding .box { fill:#f4ccd7; }
+    .fold-tag { font-size:9px; font-weight:700; fill:#963751; }
+    .peep-area { fill:#fff3d9; fill-opacity:.8; stroke:#c18221; stroke-width:2; pointer-events:none; }
+    .node.peep-edit .box { stroke:#9c4900; stroke-width:3; }
+    .node.error .box { stroke:#b42318; stroke-width:4; }
+    #event.error { color:#b42318; font-weight:600; white-space:pre-wrap; overflow-wrap:anywhere; }
+    .peep-ghosts { pointer-events:none; }
+    .region-box { stroke:#9da9b8; stroke-width:1.5; }
+    .fold-btn { cursor:pointer; }
+    .fold-btn rect { fill:white; stroke:#596674; }
+    .fold-btn text { font-size:14px; fill:#152330; }
+    .fold-btn:focus rect { stroke:#1569b9; stroke-width:2; }
+    .shortcut { cursor:pointer; }
+    .shortcut path { fill:none; stroke-width:1.5; }
+    .shortcut rect { fill:#fff8ec; stroke:#b63838; stroke-dasharray:3 2; }
+    .shortcut text { font-size:11px; fill:#783030; }
+    .shortcut.selected rect, .shortcut:focus rect { stroke-width:2.5; }
+    .label { font-size:12px; fill:#152330; font-weight:600; }
+    .node-id { font-size:10px; fill:#596674; font-weight:400; }
+    .type { font-size:11px; fill:#455768; }
+    .port { stroke:#536477; stroke-width:1; }
+    .row { stroke:#b6afcf; stroke-width:1; }
+    .bind { font-size:12px; fill:#152330; }
+    .slot { font-size:10px; fill:#364352; paint-order:stroke; stroke:#fafbfc; stroke-width:3; }
+    #detail { position:absolute; top:8px; right:8px; margin:0; padding:12px; max-width:320px;
+      max-height:45%; overflow:auto; white-space:pre-wrap; overflow-wrap:anywhere;
+      background:#fffffff2; border:1px solid #bac5d0; border-radius:4px; font-size:12px; }
+    .controls { display:flex; flex-wrap:wrap; justify-content:center; align-items:center; gap:6px; padding:6px; }
+    .button { color:white; background:black; font-size:20px; min-width:30px; }
+    .button:disabled { background:grey; }
+    .count { font-size:20px; min-width:35px; text-align:center; }
+    #N { width:6ch; }
+    #scrub { width:clamp(120px,35vw,600px); }
+  </style><defs><marker id="arrow-CTRL" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#b63838"/></marker><marker id="arrow-DATA" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#536477"/></marker><marker id="arrow-MEM" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#2867b2"/></marker><marker id="arrow-ASSOC" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#9396a3"/></marker><marker id="arrow-PARSER" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#7956a5"/></marker></defs><rect width="100%" height="100%" fill="rgb(250, 251, 252)"/><g><g class="regions" style="opacity: 1;"><g class="region" transform="translate(164,171)"><rect class="region-box" rx="8" width="176" height="130" fill="#f1f6fc"/></g></g><rect class="peep-area" rx="36" style="opacity: 0;"/><g class="edges"><path class="edge CTRL" id="e8i1" d="M236,118 L236,223" stroke="#b63838" marker-start="url(#arrow-CTRL)" style="opacity: 1;"><title>#8[1] → #1 · CTRL</title></path><path class="edge CTRL" id="e8i2" d="M236,276 L236,281 Q236,286 241,286 L320,286 Q328,286 328,278 L328,222 Q328,214 320,214 L272,214 Q266,214 266,220 L266,226" stroke="#b63838" marker-start="url(#arrow-CTRL)" style="opacity: 1;"><title>#8[2] → #8 · CTRL</title></path></g><g class="edge-hits"/><g class="parser" style="opacity: 1;"/><g class="nodes"><g class="node" id="n1" data-id="1" transform="translate(176,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>$ctrl</tspan><tspan class="node-id">  #1/0</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#1 $ctrl
+Projection 0 of #2
+Type not computed
+
+[0] → #2  CTRL</title></g><g class="node" id="n2" data-id="2" transform="translate(176,24)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Start</tspan><tspan class="node-id">  #2</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#2 Start
+Type not computed
+
+</title></g><g class="node" id="n4" data-id="4" transform="translate(24,49)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#0</tspan><tspan class="node-id">  #4</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#4 #0
+Type not computed
+
+</title></g><g class="node" id="n8" data-id="8" transform="translate(176,229)" style="opacity: 1;"><path class="box" d="M20,0H100Q120,0 120,20V24Q120,44 100,44H20Q0,44 0,24V20Q0,0 20,0Z" fill="#ffe0ab"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Loop</tspan><tspan class="node-id">  #8</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#8 Loop
+Type not computed
+
+[0] → —  DATA
+[1] → #1  CTRL
+[2] → #8  CTRL</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g></g><g class="region-heads" style="opacity: 1;"><g class="region-head" transform="translate(164,171)"><text class="label" x="26" y="17"><tspan>Loop</tspan><tspan class="node-id">  #8</tspan></text><title>Loop · 1 nodes</title><g class="fold-btn" role="button" tabindex="0" transform="translate(4,4)" aria-label="Fold region #8"><rect width="16" height="16" rx="2"/><text x="8" y="12" text-anchor="middle">−</text><title>Fold region</title></g></g></g><g class="shortcuts" style="opacity: 1;"/><g class="peep-ghosts" pointer-events="none"/></g></svg>
diff --git a/docs/chapter13/graph8.gv b/docs/chapter13/graph8.gv
new file mode 100644
index 00000000..442b6843
--- /dev/null
+++ b/docs/chapter13/graph8.gv
@@ -0,0 +1,45 @@
+digraph chapter13 {
+/*
+while (1) {}
+return 0;
+
+*/
+	rankdir=BT;
+	concentrate="true";
+	compound="true";
+	subgraph cluster_Nodes {
+		Never18 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">Never</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">True</TD><TD PORT="p1" BGCOLOR="yellow">False</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Start2 [ shape=plaintext label=<
+			<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+			<TR><TD BGCOLOR="yellow">Start</TD></TR>
+			<TR><TD>
+				<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+				<TR><TD PORT="p0" BGCOLOR="yellow">$ctrl</TD></TR>
+				</TABLE>
+			</TD></TR>
+			</TABLE>>
+		];
+		Stop3 [ shape=box style=filled fillcolor=yellow label="Stop" ];
+		Con_4 [ label="#0" ];
+		Return21 [ shape=box style=filled fillcolor=yellow label="Return" ];
+		Loop8 [ shape=box style=filled fillcolor=yellow label="Loop" ];
+		{ rank=same; Loop8;}
+	}
+	edge [ fontname=Helvetica, fontsize=8 ];
+	Never18 -> Loop8[taillabel=0 color=red];
+	Never18 -> Con_4[taillabel=1];
+	Stop3 -> Return21[taillabel=0 color=red];
+	Return21 -> Never18:p0[taillabel=0 color=red];
+	Return21 -> Con_4[taillabel=2];
+	Loop8 -> Start2:p0[taillabel=1 color=red];
+	Loop8 -> Never18:p1[taillabel=2 color=red constraint=false];
+}
diff --git a/docs/chapter13/graph8.json b/docs/chapter13/graph8.json
new file mode 100644
index 00000000..b7d4f41c
--- /dev/null
+++ b/docs/chapter13/graph8.json
@@ -0,0 +1,21 @@
+{
+  "ver": 1,
+  "comp": "chapter13/docs/graph8.svg",
+  "step": 1,
+  "roots": [],
+  "scope": 0,
+  "nodes": [
+    {"id": 1, "label": "True", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 18, "role": "CTRL", "label": null}], "proj": {"par": 18, "idx": 0}},
+    {"id": 2, "label": "Start", "type": null, "kind": "CTRL", "edges": [], "proj": null},
+    {"id": 3, "label": "Stop", "type": null, "kind": "STOP", "edges": [{"idx": 0, "def": 21, "role": "CTRL", "label": null}], "proj": null},
+    {"id": 4, "label": "#0", "type": null, "kind": "DATA", "edges": [], "proj": null},
+    {"id": 5, "label": "False", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 18, "role": "CTRL", "label": null}], "proj": {"par": 18, "idx": 1}},
+    {"id": 6, "label": "$ctrl", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 2, "role": "CTRL", "label": null}], "proj": {"par": 2, "idx": 0}},
+    {"id": 8, "label": "Loop", "type": null, "kind": "LOOP", "edges": [{"idx": 0, "def": 0, "role": "DATA", "label": null}, {"idx": 1, "def": 6, "role": "CTRL", "label": null}, {"idx": 2, "def": 5, "role": "CTRL", "label": null}], "proj": null},
+    {"id": 18, "label": "Never", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 8, "role": "CTRL", "label": null}, {"idx": 1, "def": 4, "role": "DATA", "label": null}], "proj": null},
+    {"id": 21, "label": "Return", "type": null, "kind": "CTRL", "edges": [{"idx": 0, "def": 1, "role": "CTRL", "label": null}, {"idx": 1, "def": 0, "role": "DATA", "label": null}, {"idx": 2, "def": 4, "role": "DATA", "label": null}], "proj": null}
+  ],
+  "groups": [
+    {"id": 8, "par": 0, "nodes": [1, 5, 8, 18]}
+  ]
+}
diff --git a/docs/chapter13/graph8.svg b/docs/chapter13/graph8.svg
new file mode 100644
index 00000000..d96a9a7d
--- /dev/null
+++ b/docs/chapter13/graph8.svg
@@ -0,0 +1,98 @@
+<svg aria-label="Compiler graph" width="431" height="676" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 431 676" style="font-family: sans-serif;"><style>
+    html, body { height:100%; margin:0; font-family:sans-serif; }
+    .viewer { height:100%; display:grid; grid-template-rows:auto minmax(0,1fr) auto; }
+    .source { padding:8px; border-bottom:1px solid #ccc; }
+    #program { width:min(600px,80vw); vertical-align:middle; }
+    #status { margin-top:4px; }
+    #graph { min-height:0; overflow:hidden; position:relative; background:#fafbfc; }
+    #elk { width:100%; height:100%; }
+    #graph svg { display:block; }
+    .tools { display:flex; flex-wrap:wrap; align-items:center; gap:14px; margin-top:8px; font-size:12px; }
+    .hint { color:#616c78; }
+    .ctrl { color:#b63838; } .mem { color:#2867b2; } .data { color:#536477; }
+    .edge { fill:none; stroke-width:1.5; }
+    .edge.CTRL { stroke-width:2; }
+    .edge.ASSOC { stroke-dasharray:4 4; }
+    .edge.PARSER { stroke-dasharray:5 4; }
+    .parser rect { fill:#f6f0ff; stroke:#7956a5; stroke-width:1.5; stroke-dasharray:5 4; }
+    .edge.selected { stroke-width:3.5; }
+    .edge.bundle { stroke-width:4; }
+    .edge.bundle.selected { stroke-width:6; }
+    .edge-hit { fill:none; stroke:transparent; stroke-width:12; vector-effect:non-scaling-stroke; pointer-events:stroke; cursor:pointer; }
+    .edge-jump { fill:transparent; pointer-events:all; cursor:pointer; }
+    .node { cursor:pointer; }
+    .box { stroke:#758191; stroke-width:1; }
+    .node.held .box { stroke-dasharray:5 3; }
+    .node.near .box { stroke:#c18221; stroke-width:2; }
+    .node.focus .box { stroke:#9c4900; stroke-width:3; }
+    .node.selected .box { stroke:#1569b9; stroke-width:3; }
+    .node.folded .box { stroke-width:4; }
+    .node.folding .box { fill:#f4ccd7; }
+    .fold-tag { font-size:9px; font-weight:700; fill:#963751; }
+    .peep-area { fill:#fff3d9; fill-opacity:.8; stroke:#c18221; stroke-width:2; pointer-events:none; }
+    .node.peep-edit .box { stroke:#9c4900; stroke-width:3; }
+    .node.error .box { stroke:#b42318; stroke-width:4; }
+    #event.error { color:#b42318; font-weight:600; white-space:pre-wrap; overflow-wrap:anywhere; }
+    .peep-ghosts { pointer-events:none; }
+    .region-box { stroke:#9da9b8; stroke-width:1.5; }
+    .fold-btn { cursor:pointer; }
+    .fold-btn rect { fill:white; stroke:#596674; }
+    .fold-btn text { font-size:14px; fill:#152330; }
+    .fold-btn:focus rect { stroke:#1569b9; stroke-width:2; }
+    .shortcut { cursor:pointer; }
+    .shortcut path { fill:none; stroke-width:1.5; }
+    .shortcut rect { fill:#fff8ec; stroke:#b63838; stroke-dasharray:3 2; }
+    .shortcut text { font-size:11px; fill:#783030; }
+    .shortcut.selected rect, .shortcut:focus rect { stroke-width:2.5; }
+    .label { font-size:12px; fill:#152330; font-weight:600; }
+    .node-id { font-size:10px; fill:#596674; font-weight:400; }
+    .type { font-size:11px; fill:#455768; }
+    .port { stroke:#536477; stroke-width:1; }
+    .row { stroke:#b6afcf; stroke-width:1; }
+    .bind { font-size:12px; fill:#152330; }
+    .slot { font-size:10px; fill:#364352; paint-order:stroke; stroke:#fafbfc; stroke-width:3; }
+    #detail { position:absolute; top:8px; right:8px; margin:0; padding:12px; max-width:320px;
+      max-height:45%; overflow:auto; white-space:pre-wrap; overflow-wrap:anywhere;
+      background:#fffffff2; border:1px solid #bac5d0; border-radius:4px; font-size:12px; }
+    .controls { display:flex; flex-wrap:wrap; justify-content:center; align-items:center; gap:6px; padding:6px; }
+    .button { color:white; background:black; font-size:20px; min-width:30px; }
+    .button:disabled { background:grey; }
+    .count { font-size:20px; min-width:35px; text-align:center; }
+    #N { width:6ch; }
+    #scrub { width:clamp(120px,35vw,600px); }
+  </style><defs><marker id="arrow-CTRL" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#b63838"/></marker><marker id="arrow-DATA" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#536477"/></marker><marker id="arrow-MEM" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#2867b2"/></marker><marker id="arrow-ASSOC" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#9396a3"/></marker><marker id="arrow-PARSER" viewBox="0 -4 8 8" refX="8" refY="0" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path d="M0,-4L8,0L0,4Z" fill="#7956a5"/></marker></defs><rect width="100%" height="100%" fill="rgb(250, 251, 252)"/><g><g class="regions" style="opacity: 1;"><g class="region" transform="translate(24,171)"><rect class="region-box" rx="8" width="313" height="298" fill="#f1f6fc"/></g></g><rect class="peep-area" rx="36" style="opacity: 0;"/><g class="edges"><path class="edge CTRL" id="e3i0" d="M126,575 C126,599 215.5,602 215.5,626" stroke="#b63838" marker-start="url(#arrow-CTRL)" style="opacity: 1;"><title>#3[0] → #21 · CTRL</title></path><path class="edge CTRL" id="e8i1" d="M116,118 L116,233" stroke="#b63838" marker-start="url(#arrow-CTRL)" style="opacity: 1;"><title>#8[1] → #6 · CTRL</title></path><path class="edge CTRL" id="e8i2" d="M216,434 L216,439 Q216,444 221,444 L317,444 Q325,444 325,436 L325,232 Q325,224 317,224 L152,224 Q146,224 146,230 L146,236" stroke="#b63838" marker-start="url(#arrow-CTRL)" style="opacity: 1;"><title>#8[2] → #5 · CTRL</title></path><path class="edge CTRL" id="e18i0" d="M116,289 L116,337" stroke="#b63838" marker-start="url(#arrow-CTRL)" style="opacity: 1;"><title>#18[0] → #8 · CTRL</title></path><path class="edge DATA" id="e18i1" d="M347,118 L347,123 Q347,128 342,128 L310,128 Q302,128 302,136 L302,291 Q302,299 294,299 L204,299 Q196,299 196,307 L196,337" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#18[1] → #4 · DATA</title></path><path class="edge CTRL" id="e21i0" d="M96,437 L96,522" stroke="#b63838" marker-start="url(#arrow-CTRL)" style="opacity: 1;"><title>#21[0] → #1 · CTRL</title></path><path class="edge DATA" id="e21i2" d="M347,118 L347,476 Q347,484 339,484 L164,484 Q156,484 156,492 L156,522" stroke="#536477" marker-start="url(#arrow-DATA)" style="opacity: 1;"><title>#21[2] → #4 · DATA</title></path></g><g class="edge-hits"/><g class="parser" style="opacity: 1;"/><g class="nodes"><g class="node" id="n1" data-id="1" transform="translate(36,387)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>True</tspan><tspan class="node-id">  #1/0</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#1 True
+Projection 0 of #18
+Type not computed
+
+[0] → #18  CTRL</title></g><g class="node" id="n2" data-id="2" transform="translate(56,24)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Start</tspan><tspan class="node-id">  #2</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#2 Start
+Type not computed
+
+</title></g><g class="node" id="n3" data-id="3" transform="translate(179.5,626)" style="opacity: 1;"><path class="box" d="M0,0H72V26H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="36" y="17"><tspan>Stop</tspan><tspan class="node-id">  #3</tspan></text><text class="type" text-anchor="middle" y="35" x="36"/><title>#3 Stop
+Type not computed
+
+[0] → #21  CTRL</title><circle class="port" cx="36" cy="0" r="3" fill="#536477"/><text class="slot" x="36" y="-7" text-anchor="middle">0</text></g><g class="node" id="n4" data-id="4" transform="translate(287,68)" style="opacity: 1;"><path class="box" d="M14,0H106Q120,0 120,14V30Q120,44 106,44H14Q0,44 0,30V14Q0,0 14,0Z" fill="#edf3f7"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>#0</tspan><tspan class="node-id">  #4</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#4 #0
+Type not computed
+
+</title></g><g class="node" id="n5" data-id="5" transform="translate(156,387)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>False</tspan><tspan class="node-id">  #5/1</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#5 False
+Projection 1 of #18
+Type not computed
+
+[0] → #18  CTRL</title></g><g class="node" id="n6" data-id="6" transform="translate(56,68)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>$ctrl</tspan><tspan class="node-id">  #6/0</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#6 $ctrl
+Projection 0 of #2
+Type not computed
+
+[0] → #2  CTRL</title></g><g class="node" id="n8" data-id="8" transform="translate(56,239)" style="opacity: 1;"><path class="box" d="M20,0H100Q120,0 120,20V24Q120,44 100,44H20Q0,44 0,24V20Q0,0 20,0Z" fill="#ffe0ab"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Loop</tspan><tspan class="node-id">  #8</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#8 Loop
+Type not computed
+
+[0] → —  DATA
+[1] → #6  CTRL
+[2] → #5  CTRL</title><circle class="port" cx="30" cy="-3" r="3" fill="white"/><circle class="port" cx="60" cy="-3" r="3" fill="#536477"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g><g class="node" id="n18" data-id="18" transform="translate(36,343)" style="opacity: 1;"><path class="box" d="M0,0H240V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="120" y="18"><tspan>Never</tspan><tspan class="node-id">  #18</tspan></text><text class="type" text-anchor="middle" y="35" x="120"/><title>#18 Never
+Type not computed
+
+[0] → #8  CTRL
+[1] → #4  DATA</title><circle class="port" cx="80" cy="-3" r="3" fill="#536477"/><circle class="port" cx="160" cy="-3" r="3" fill="#536477"/><text class="slot" x="80" y="-10" text-anchor="middle">0</text><text class="slot" x="160" y="-10" text-anchor="middle">1</text></g><g class="node" id="n21" data-id="21" transform="translate(66,528)" style="opacity: 1;"><path class="box" d="M0,0H120V44H0Z" fill="#fff1c4"/><text class="label" text-anchor="middle" x="60" y="18"><tspan>Return</tspan><tspan class="node-id">  #21</tspan></text><text class="type" text-anchor="middle" y="35" x="60"/><title>#21 Return
+Type not computed
+
+[0] → #1  CTRL
+[1] → —  DATA
+[2] → #4  DATA</title><circle class="port" cx="30" cy="-3" r="3" fill="#536477"/><circle class="port" cx="60" cy="-3" r="3" fill="white"/><circle class="port" cx="90" cy="-3" r="3" fill="#536477"/><text class="slot" x="30" y="-10" text-anchor="middle">0</text><text class="slot" x="60" y="-10" text-anchor="middle">1</text><text class="slot" x="90" y="-10" text-anchor="middle">2</text></g></g><g class="region-heads" style="opacity: 1;"><g class="region-head" transform="translate(24,171)"><text class="label" x="26" y="17"><tspan>Loop</tspan><tspan class="node-id">  #8</tspan></text><title>Loop · 4 nodes</title><g class="fold-btn" role="button" tabindex="0" transform="translate(4,4)" aria-label="Fold region #8"><rect width="16" height="16" rx="2"/><text x="8" y="12" text-anchor="middle">−</text><title>Fold region</title></g></g></g><g class="shortcuts" style="opacity: 1;"/><g class="peep-ghosts" pointer-events="none"/></g></svg>