diff --git a/pkg/memory/dag/budget.go b/pkg/memory/dag/budget.go
new file mode 100644
index 000000000..3379acb04
--- /dev/null
+++ b/pkg/memory/dag/budget.go
@@ -0,0 +1,109 @@
+package dag
+
+// BudgetConfig defines the percentage allocation for each context section.
+// All percentages should sum to 100.
+type BudgetConfig struct {
+	SystemPromptPct  int // % for system prompt (identity, rules, skills)
+	ObservationsPct  int // % for observation block
+	KnowledgePct     int // % for knowledge block (Focus completions)
+	DAGSummariesPct  int // % for DAG compressed history
+	RawTailPct       int // % for raw recent messages (uncompressed tail)
+	ToolResultsPct   int // % for tool call results
+}
+
+// DefaultBudgetConfig returns a balanced allocation.
+func DefaultBudgetConfig() BudgetConfig {
+	return BudgetConfig{
+		SystemPromptPct: 20,
+		ObservationsPct: 10,
+		KnowledgePct:    5,
+		DAGSummariesPct: 25,
+		RawTailPct:      30,
+		ToolResultsPct:  10,
+	}
+}
+
+// Budget represents concrete token allocations computed from config and context window.
+type Budget struct {
+	Total        int
+	SystemPrompt int
+	Observations int
+	Knowledge    int
+	DAGSummaries int
+	RawTail      int
+	ToolResults  int
+}
+
+// ComputeBudget calculates token allocations from a context window size and config.
+func ComputeBudget(contextWindow int, cfg BudgetConfig) Budget {
+	return Budget{
+		Total:        contextWindow,
+		SystemPrompt: contextWindow * cfg.SystemPromptPct / 100,
+		Observations: contextWindow * cfg.ObservationsPct / 100,
+		Knowledge:    contextWindow * cfg.KnowledgePct / 100,
+		DAGSummaries: contextWindow * cfg.DAGSummariesPct / 100,
+		RawTail:      contextWindow * cfg.RawTailPct / 100,
+		ToolResults:  contextWindow * cfg.ToolResultsPct / 100,
+	}
+}
+
+// Remaining returns tokens available after accounting for used amounts.
+func (b Budget) Remaining(usedSystem, usedObs, usedKnowledge, usedDAG, usedTail, usedTools int) int {
+	used := usedSystem + usedObs + usedKnowledge + usedDAG + usedTail + usedTools
+	remaining := b.Total - used
+	if remaining < 0 {
+		return 0
+	}
+	return remaining
+}
+
+// SelectDAGLevel determines which DAG compression level to use given
+// the available token budget for DAG summaries.
+func SelectDAGLevel(d *DAG, budgetTokens int) Level {
+	if d == nil || len(d.Nodes) == 0 {
+		return LevelRaw
+	}
+
+	sessionTokens := d.TotalTokens(LevelSession)
+	if sessionTokens > 0 && sessionTokens <= budgetTokens {
+		sectionTokens := d.TotalTokens(LevelSection)
+		if sectionTokens > 0 && sectionTokens <= budgetTokens {
+			chunkTokens := d.TotalTokens(LevelChunk)
+			if chunkTokens <= budgetTokens {
+				return LevelChunk
+			}
+			return LevelSection
+		}
+		return LevelSession
+	}
+
+	return LevelSession
+}
+
+// RenderDAGForBudget renders DAG nodes at the most detailed level
+// that fits within the given token budget.
+func RenderDAGForBudget(d *DAG, budgetTokens int) string {
+	if d == nil || len(d.Nodes) == 0 {
+		return ""
+	}
+
+	level := SelectDAGLevel(d, budgetTokens)
+	return d.FormatLevel(level)
+}
+
+// TailMessageCount estimates how many raw messages fit in the tail budget.
+// Uses a rough average of ~50 tokens per message.
+func TailMessageCount(tailBudget int) int {
+	const (
+		avgTokensPerMessage = 50
+		minTail             = 4
+	)
+	if tailBudget <= 0 {
+		return minTail
+	}
+	count := tailBudget / avgTokensPerMessage
+	if count < minTail {
+		return minTail
+	}
+	return count
+}
diff --git a/pkg/memory/dag/compress.go b/pkg/memory/dag/compress.go
new file mode 100644
index 000000000..5bb75be1b
--- /dev/null
+++ b/pkg/memory/dag/compress.go
@@ -0,0 +1,232 @@
+package dag
+
+import (
+	"fmt"
+	"strings"
+	"unicode/utf8"
+)
+
+// Message is a minimal message representation for DAG compression.
+type Message struct {
+	Role    string
+	Content string
+}
+
+// CompressorConfig controls the deterministic compression behavior.
+type CompressorConfig struct {
+	ChunkSize       int // Messages per chunk node (default 8)
+	SectionSize     int // Chunks per section node (default 4)
+	MaxSentences    int // Max sentences to extract per message (default 2)
+	TargetRatio     float64 // Target compression ratio (default 0.25 = 4:1)
+}
+
+// DefaultCompressorConfig returns sensible defaults.
+func DefaultCompressorConfig() CompressorConfig {
+	return CompressorConfig{
+		ChunkSize:    8,
+		SectionSize:  4,
+		MaxSentences: 2,
+		TargetRatio:  0.25,
+	}
+}
+
+// Compressor builds a DAG from raw messages using deterministic
+// extractive summarization. No LLM calls — fully reproducible.
+type Compressor struct {
+	cfg     CompressorConfig
+	counter int
+}
+
+// NewCompressor creates a new deterministic compressor.
+func NewCompressor(cfg CompressorConfig) *Compressor {
+	return &Compressor{cfg: cfg}
+}
+
+// Compress builds a hierarchical DAG from the given messages.
+// Messages are grouped into chunks, chunks into sections, and
+// sections into a session summary.
+func (c *Compressor) Compress(msgs []Message) *DAG {
+	d := NewDAG()
+	if len(msgs) == 0 {
+		return d
+	}
+
+	// Level 1: Chunk summaries
+	chunkNodes := c.buildChunks(msgs, d)
+	if len(chunkNodes) == 0 {
+		return d
+	}
+
+	// Level 2: Section summaries (groups of chunks)
+	sectionNodes := c.buildSections(chunkNodes, d)
+
+	// Level 3: Session summary (if multiple sections)
+	if len(sectionNodes) > 1 {
+		sessionNode := c.buildSessionSummary(sectionNodes, d)
+		d.SetRoots([]string{sessionNode.ID})
+	} else if len(sectionNodes) == 1 {
+		d.SetRoots([]string{sectionNodes[0].ID})
+	} else {
+		ids := make([]string, len(chunkNodes))
+		for i, n := range chunkNodes {
+			ids[i] = n.ID
+		}
+		d.SetRoots(ids)
+	}
+
+	return d
+}
+
+func (c *Compressor) nextID(prefix string) string {
+	c.counter++
+	return fmt.Sprintf("%s-%d", prefix, c.counter)
+}
+
+func (c *Compressor) buildChunks(msgs []Message, d *DAG) []*Node {
+	var chunks []*Node
+	for i := 0; i < len(msgs); i += c.cfg.ChunkSize {
+		end := i + c.cfg.ChunkSize
+		if end > len(msgs) {
+			end = len(msgs)
+		}
+
+		chunk := msgs[i:end]
+		summary := c.extractChunkSummary(chunk)
+		node := &Node{
+			ID:       c.nextID("chunk"),
+			Level:    LevelChunk,
+			Summary:  summary,
+			Tokens:   estimateTokens(summary),
+			StartIdx: i,
+			EndIdx:   end,
+		}
+		d.Add(node)
+		chunks = append(chunks, node)
+	}
+	return chunks
+}
+
+func (c *Compressor) buildSections(chunks []*Node, d *DAG) []*Node {
+	if len(chunks) <= c.cfg.SectionSize {
+		return chunks
+	}
+
+	var sections []*Node
+	for i := 0; i < len(chunks); i += c.cfg.SectionSize {
+		end := i + c.cfg.SectionSize
+		if end > len(chunks) {
+			end = len(chunks)
+		}
+
+		group := chunks[i:end]
+		childIDs := make([]string, len(group))
+		var summaryParts []string
+		for j, ch := range group {
+			childIDs[j] = ch.ID
+			summaryParts = append(summaryParts, ch.Summary)
+		}
+
+		combined := strings.Join(summaryParts, " ")
+		summary := extractSentences(combined, c.cfg.MaxSentences)
+		node := &Node{
+			ID:       c.nextID("section"),
+			Level:    LevelSection,
+			Summary:  summary,
+			Tokens:   estimateTokens(summary),
+			StartIdx: group[0].StartIdx,
+			EndIdx:   group[len(group)-1].EndIdx,
+			Children: childIDs,
+		}
+		d.Add(node)
+		sections = append(sections, node)
+	}
+	return sections
+}
+
+func (c *Compressor) buildSessionSummary(sections []*Node, d *DAG) *Node {
+	childIDs := make([]string, len(sections))
+	var summaryParts []string
+	for i, s := range sections {
+		childIDs[i] = s.ID
+		summaryParts = append(summaryParts, s.Summary)
+	}
+
+	combined := strings.Join(summaryParts, " ")
+	summary := extractSentences(combined, c.cfg.MaxSentences)
+	node := &Node{
+		ID:       c.nextID("session"),
+		Level:    LevelSession,
+		Summary:  summary,
+		Tokens:   estimateTokens(summary),
+		StartIdx: sections[0].StartIdx,
+		EndIdx:   sections[len(sections)-1].EndIdx,
+		Children: childIDs,
+	}
+	d.Add(node)
+	return node
+}
+
+// extractChunkSummary produces a deterministic summary of a message chunk.
+// Strategy: for each message, take the first sentence (or first N chars if short).
+// Prefix with role to preserve conversational structure.
+func (c *Compressor) extractChunkSummary(msgs []Message) string {
+	var parts []string
+	for _, m := range msgs {
+		sentence := extractSentences(m.Content, 1)
+		if sentence == "" {
+			continue
+		}
+		parts = append(parts, fmt.Sprintf("%s: %s", m.Role, sentence))
+	}
+	return strings.Join(parts, " | ")
+}
+
+// extractSentences pulls the first N sentences from text.
+// A sentence ends at '.', '!', '?', or '\n\n'.
+func extractSentences(text string, n int) string {
+	if n <= 0 || text == "" {
+		return ""
+	}
+
+	text = strings.TrimSpace(text)
+	var result []string
+	remaining := text
+
+	for i := 0; i < n && remaining != ""; i++ {
+		idx := findSentenceEnd(remaining)
+		if idx < 0 {
+			result = append(result, strings.TrimSpace(remaining))
+			break
+		}
+		sentence := strings.TrimSpace(remaining[:idx+1])
+		if sentence != "" {
+			result = append(result, sentence)
+		}
+		remaining = strings.TrimSpace(remaining[idx+1:])
+	}
+
+	joined := strings.Join(result, " ")
+	const maxLen = 200
+	if utf8.RuneCountInString(joined) > maxLen {
+		runes := []rune(joined)
+		return string(runes[:maxLen]) + "..."
+	}
+	return joined
+}
+
+func findSentenceEnd(s string) int {
+	for i, r := range s {
+		if r == '.' || r == '!' || r == '?' {
+			return i
+		}
+		if r == '\n' && i+1 < len(s) && s[i+1] == '\n' {
+			return i
+		}
+	}
+	return -1
+}
+
+// estimateTokens provides a rough token count (chars * 2/5 heuristic).
+func estimateTokens(s string) int {
+	return utf8.RuneCountInString(s) * 2 / 5
+}
diff --git a/pkg/memory/dag/dag_test.go b/pkg/memory/dag/dag_test.go
new file mode 100644
index 000000000..0e9afd59f
--- /dev/null
+++ b/pkg/memory/dag/dag_test.go
@@ -0,0 +1,245 @@
+package dag
+
+import (
+	"strings"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func makeMessages(n int) []Message {
+	msgs := make([]Message, n)
+	for i := range msgs {
+		role := "user"
+		if i%2 == 1 {
+			role = "assistant"
+		}
+		msgs[i] = Message{
+			Role:    role,
+			Content: strings.Repeat("word ", 20) + ".",
+		}
+	}
+	return msgs
+}
+
+func TestCompressor_EmptyInput(t *testing.T) {
+	c := NewCompressor(DefaultCompressorConfig())
+	d := c.Compress(nil)
+	assert.Empty(t, d.Nodes)
+	assert.Empty(t, d.Roots)
+}
+
+func TestCompressor_SmallInput(t *testing.T) {
+	c := NewCompressor(DefaultCompressorConfig())
+	msgs := []Message{
+		{Role: "user", Content: "Hello, how are you?"},
+		{Role: "assistant", Content: "I'm doing well. Thanks for asking!"},
+	}
+	d := c.Compress(msgs)
+
+	require.Len(t, d.Nodes, 1)
+	chunk := d.NodesAtLevel(LevelChunk)
+	require.Len(t, chunk, 1)
+	assert.Equal(t, 0, chunk[0].StartIdx)
+	assert.Equal(t, 2, chunk[0].EndIdx)
+	assert.Contains(t, chunk[0].Summary, "user:")
+	assert.Contains(t, chunk[0].Summary, "assistant:")
+}
+
+func TestCompressor_ChunkSplitting(t *testing.T) {
+	cfg := DefaultCompressorConfig()
+	cfg.ChunkSize = 4
+	c := NewCompressor(cfg)
+
+	msgs := makeMessages(12)
+	d := c.Compress(msgs)
+
+	chunks := d.NodesAtLevel(LevelChunk)
+	require.Len(t, chunks, 3)
+
+	assert.Equal(t, 0, chunks[0].StartIdx)
+	assert.Equal(t, 4, chunks[0].EndIdx)
+	assert.Equal(t, 4, chunks[1].StartIdx)
+	assert.Equal(t, 8, chunks[1].EndIdx)
+	assert.Equal(t, 8, chunks[2].StartIdx)
+	assert.Equal(t, 12, chunks[2].EndIdx)
+}
+
+func TestCompressor_SectionBuilding(t *testing.T) {
+	cfg := DefaultCompressorConfig()
+	cfg.ChunkSize = 4
+	cfg.SectionSize = 2
+	c := NewCompressor(cfg)
+
+	// 20 messages = 5 chunks, section_size=2 => 3 sections
+	msgs := makeMessages(20)
+	d := c.Compress(msgs)
+
+	chunks := d.NodesAtLevel(LevelChunk)
+	assert.Len(t, chunks, 5)
+
+	sections := d.NodesAtLevel(LevelSection)
+	assert.Len(t, sections, 3)
+
+	// First section covers chunks 0-1 (msgs 0-7)
+	assert.Equal(t, 0, sections[0].StartIdx)
+	assert.Equal(t, 8, sections[0].EndIdx)
+	assert.Len(t, sections[0].Children, 2)
+}
+
+func TestCompressor_SessionSummary(t *testing.T) {
+	cfg := DefaultCompressorConfig()
+	cfg.ChunkSize = 4
+	cfg.SectionSize = 2
+	c := NewCompressor(cfg)
+
+	// 24 messages => 6 chunks => 3 sections => 1 session
+	msgs := makeMessages(24)
+	d := c.Compress(msgs)
+
+	sessions := d.NodesAtLevel(LevelSession)
+	require.Len(t, sessions, 1)
+	assert.Equal(t, 0, sessions[0].StartIdx)
+	assert.Equal(t, 24, sessions[0].EndIdx)
+	assert.Len(t, sessions[0].Children, 3)
+
+	require.Len(t, d.Roots, 1)
+	assert.Equal(t, sessions[0].ID, d.Roots[0])
+}
+
+func TestExtractSentences(t *testing.T) {
+	tests := []struct {
+		name string
+		text string
+		n    int
+		want string
+	}{
+		{"single sentence", "Hello world.", 1, "Hello world."},
+		{"two sentences", "First sentence. Second sentence.", 2, "First sentence. Second sentence."},
+		{"extract one from many", "A. B. C. D.", 1, "A."},
+		{"empty", "", 1, ""},
+		{"no period", "Hello world", 1, "Hello world"},
+		{"question mark", "What? Who knows.", 1, "What?"},
+		{"exclamation", "Wow! Amazing.", 2, "Wow! Amazing."},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := extractSentences(tt.text, tt.n)
+			assert.Equal(t, tt.want, got)
+		})
+	}
+}
+
+func TestExtractSentences_Truncation(t *testing.T) {
+	long := strings.Repeat("This is a very long sentence with many words. ", 20)
+	result := extractSentences(long, 5)
+	assert.LessOrEqual(t, len([]rune(result)), 210)
+	assert.True(t, strings.HasSuffix(result, "..."))
+}
+
+func TestNode_FormatForPrompt(t *testing.T) {
+	n := &Node{
+		ID:       "chunk-1",
+		Level:    LevelChunk,
+		Summary:  "User asked about auth. Assistant explained JWT flow.",
+		StartIdx: 0,
+		EndIdx:   8,
+	}
+	formatted := n.FormatForPrompt()
+	assert.Contains(t, formatted, "[chunk msgs 0-7]")
+	assert.Contains(t, formatted, "User asked about auth")
+}
+
+func TestDAG_FormatLevel(t *testing.T) {
+	cfg := DefaultCompressorConfig()
+	cfg.ChunkSize = 4
+	c := NewCompressor(cfg)
+
+	msgs := makeMessages(8)
+	d := c.Compress(msgs)
+
+	output := d.FormatLevel(LevelChunk)
+	assert.NotEmpty(t, output)
+	lines := strings.Split(strings.TrimSpace(output), "\n")
+	assert.Len(t, lines, 2)
+}
+
+func TestDAG_TotalTokens(t *testing.T) {
+	cfg := DefaultCompressorConfig()
+	cfg.ChunkSize = 4
+	c := NewCompressor(cfg)
+
+	msgs := makeMessages(12)
+	d := c.Compress(msgs)
+
+	chunkTokens := d.TotalTokens(LevelChunk)
+	assert.Greater(t, chunkTokens, 0)
+}
+
+func TestComputeBudget(t *testing.T) {
+	cfg := DefaultBudgetConfig()
+	b := ComputeBudget(100000, cfg)
+
+	assert.Equal(t, 100000, b.Total)
+	assert.Equal(t, 20000, b.SystemPrompt)
+	assert.Equal(t, 10000, b.Observations)
+	assert.Equal(t, 5000, b.Knowledge)
+	assert.Equal(t, 25000, b.DAGSummaries)
+	assert.Equal(t, 30000, b.RawTail)
+	assert.Equal(t, 10000, b.ToolResults)
+}
+
+func TestBudget_Remaining(t *testing.T) {
+	b := Budget{Total: 10000}
+	assert.Equal(t, 7000, b.Remaining(1000, 500, 500, 500, 500, 0))
+	assert.Equal(t, 0, b.Remaining(5000, 3000, 1000, 1000, 1000, 0))
+}
+
+func TestSelectDAGLevel(t *testing.T) {
+	cfg := DefaultCompressorConfig()
+	cfg.ChunkSize = 4
+	cfg.SectionSize = 2
+	c := NewCompressor(cfg)
+
+	msgs := makeMessages(24)
+	d := c.Compress(msgs)
+
+	chunkTokens := d.TotalTokens(LevelChunk)
+
+	// Large budget -> most detailed (chunk)
+	assert.Equal(t, LevelChunk, SelectDAGLevel(d, chunkTokens+1000))
+
+	// Very small budget -> session level
+	assert.Equal(t, LevelSession, SelectDAGLevel(d, 10))
+
+	// Nil DAG
+	assert.Equal(t, LevelRaw, SelectDAGLevel(nil, 1000))
+}
+
+func TestTailMessageCount(t *testing.T) {
+	assert.Equal(t, 4, TailMessageCount(100))   // Minimum
+	assert.Equal(t, 20, TailMessageCount(1000))  // 1000/50
+	assert.Equal(t, 4, TailMessageCount(0))      // Zero budget
+	assert.Equal(t, 4, TailMessageCount(-1))     // Negative
+}
+
+func TestRenderDAGForBudget(t *testing.T) {
+	assert.Empty(t, RenderDAGForBudget(nil, 1000))
+
+	cfg := DefaultCompressorConfig()
+	cfg.ChunkSize = 4
+	cfg.SectionSize = 2
+	c := NewCompressor(cfg)
+
+	// 16 messages => 4 chunks => 2 sections => 1 session
+	msgs := makeMessages(16)
+	d := c.Compress(msgs)
+
+	// Large budget should get chunk-level detail
+	chunkTokens := d.TotalTokens(LevelChunk)
+	output := RenderDAGForBudget(d, chunkTokens+1000)
+	assert.NotEmpty(t, output)
+	assert.Contains(t, output, "[chunk")
+}
diff --git a/pkg/memory/dag/node.go b/pkg/memory/dag/node.go
new file mode 100644
index 000000000..df5399c66
--- /dev/null
+++ b/pkg/memory/dag/node.go
@@ -0,0 +1,134 @@
+package dag
+
+import (
+	"fmt"
+	"strings"
+)
+
+// Level represents the compression tier of a DAG node.
+type Level int
+
+const (
+	LevelRaw     Level = 0 // Original messages (not stored as nodes)
+	LevelChunk   Level = 1 // Chunk summary (~8-16 messages)
+	LevelSection Level = 2 // Section summary (group of chunks)
+	LevelSession Level = 3 // Session summary (top-level)
+)
+
+func (l Level) String() string {
+	switch l {
+	case LevelRaw:
+		return "raw"
+	case LevelChunk:
+		return "chunk"
+	case LevelSection:
+		return "section"
+	case LevelSession:
+		return "session"
+	default:
+		return fmt.Sprintf("level-%d", l)
+	}
+}
+
+// Node is a single node in the compression DAG. Each node stores an
+// extractive summary and retains lossless pointers back to the
+// original message range it covers.
+type Node struct {
+	ID       string `json:"id"`
+	Level    Level  `json:"level"`
+	Summary  string `json:"summary"`
+	Tokens   int    `json:"tokens"`
+	StartIdx int    `json:"start_idx"` // Inclusive index into original message slice
+	EndIdx   int    `json:"end_idx"`   // Exclusive index into original message slice
+	Children []string `json:"children,omitempty"` // Child node IDs (lower level)
+}
+
+// MessageRange returns the [start, end) range of original messages this node covers.
+func (n *Node) MessageRange() (int, int) {
+	return n.StartIdx, n.EndIdx
+}
+
+// Span returns how many original messages this node covers.
+func (n *Node) Span() int {
+	return n.EndIdx - n.StartIdx
+}
+
+// FormatForPrompt renders the node as a compact block for context injection.
+func (n *Node) FormatForPrompt() string {
+	return fmt.Sprintf("[%s msgs %d-%d] %s", n.Level, n.StartIdx, n.EndIdx-1, n.Summary)
+}
+
+// DAG is the hierarchical compression tree. Nodes at higher levels
+// summarize groups of lower-level nodes. The root level covers the
+// entire session.
+type DAG struct {
+	Nodes map[string]*Node `json:"nodes"`
+	Roots []string         `json:"roots"` // Top-level node IDs (highest compression)
+}
+
+// NewDAG creates an empty DAG.
+func NewDAG() *DAG {
+	return &DAG{
+		Nodes: make(map[string]*Node),
+	}
+}
+
+// Add inserts a node into the DAG.
+func (d *DAG) Add(node *Node) {
+	d.Nodes[node.ID] = node
+}
+
+// SetRoots sets the top-level node IDs.
+func (d *DAG) SetRoots(ids []string) {
+	d.Roots = ids
+}
+
+// Get returns a node by ID, or nil if not found.
+func (d *DAG) Get(id string) *Node {
+	return d.Nodes[id]
+}
+
+// NodesAtLevel returns all nodes at the given compression level, ordered by StartIdx.
+func (d *DAG) NodesAtLevel(level Level) []*Node {
+	var result []*Node
+	for _, n := range d.Nodes {
+		if n.Level == level {
+			result = append(result, n)
+		}
+	}
+	sortByStart(result)
+	return result
+}
+
+// TotalTokens returns the sum of tokens across all nodes at the given level.
+func (d *DAG) TotalTokens(level Level) int {
+	total := 0
+	for _, n := range d.Nodes {
+		if n.Level == level {
+			total += n.Tokens
+		}
+	}
+	return total
+}
+
+// FormatLevel renders all nodes at a given level as a prompt-ready string.
+func (d *DAG) FormatLevel(level Level) string {
+	nodes := d.NodesAtLevel(level)
+	if len(nodes) == 0 {
+		return ""
+	}
+	var sb strings.Builder
+	for _, n := range nodes {
+		sb.WriteString(n.FormatForPrompt())
+		sb.WriteByte('\n')
+	}
+	return sb.String()
+}
+
+func sortByStart(nodes []*Node) {
+	for i := 1; i < len(nodes); i++ {
+		for j := i; j > 0 && nodes[j].StartIdx < nodes[j-1].StartIdx; j-- {
+			nodes[j], nodes[j-1] = nodes[j-1], nodes[j]
+		}
+	}
+}