Preprocessing
Found invariant 0 ≤ X₀ for location l1
Found invariant 1 ≤ X₀ for location l2
Probabilistic Analysis
Probabilistic Program after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
g₀:l0(X₀,X₁) → t₁:l1(1,X₁) :|:
g₂:l1(X₀,X₁) → t₃:l2(X₀,X₁) :|: 1 ≤ X₀ ∧ 0 ≤ X₀
g₄:l2(X₀,X₁) → [1/2]:t₅:l1(X₀-1,X₁-10) :+: [1/2]:t₆:l1(X₀,X₁) :|: 101 ≤ X₁ ∧ 1 ≤ X₀
g₇:l2(X₀,X₁) → [1/2]:t₈:l1(1+X₀,11+X₁) :+: [1/2]:t₉:l1(X₀,X₁) :|: X₁ ≤ 100 ∧ 1 ≤ X₀
Show Graph
G
l0
l0
l1
l1
l0->l1
p = 1
t₁ ∈ g₀
η (X₀) = 1
l2
l2
l1->l2
p = 1
t₃ ∈ g₂
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l2->l1
p = 1/2
t₅ ∈ g₄
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2->l1
p = 1/2
t₆ ∈ g₄
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2->l1
p = 1/2
t₈ ∈ g₇
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2->l1
p = 1/2
t₉ ∈ g₇
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
Run classical analysis on SCC: [l0]
Classical Approximation after Lifting Classical Results
All Bounds
Timebounds
Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₇: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₇: inf {Infinity}
Sizebounds
(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
Run probabilistic analysis on SCC: [l0]
Run classical analysis on SCC: [l1; l2]
MPRF for transition t₈: l2(X₀,X₁) → l1(1+X₀,11+X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 100 of depth 1:
new bound:
X₁+101 {O(n)}
MPRF:
• l1: [91+10⋅X₀-X₁]
• l2: [91+10⋅X₀-X₁]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2
l2
l1->l2
t₃
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l2->l1
t₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2->l1
t₆
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2->l1
t₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2->l1
t₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
MPRF for transition t₅: l2(X₀,X₁) → l1(X₀-1,X₁-10) :|: 1 ≤ X₀ ∧ 101 ≤ X₁ of depth 1:
new bound:
X₁⋅X₁+203⋅X₁+10303 {O(n^2)}
MPRF:
• l1: [X₀]
• l2: [X₀]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2
l2
l1->l2
t₃
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l2->l1
t₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2->l1
t₆
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2->l1
t₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2->l1
t₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
Classical Approximation after Lifting Classical Results
All Bounds
Timebounds
Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₇: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₇: inf {Infinity}
Sizebounds
(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₂,l2), X₀: X₁+102 {O(n)}
(g₂,l2), X₁: 12⋅X₁+1111 {O(n)}
(g₄,l1), X₀: 2⋅X₁+204 {O(n)}
(g₄,l1), X₁: 24⋅X₁+2222 {O(n)}
(g₇,l1), X₀: 2⋅X₁+204 {O(n)}
(g₇,l1), X₁: 24⋅X₁+2222 {O(n)}
Run probabilistic analysis on SCC: [l1; l2]
Analysing control-flow refined program
Run classical analysis on SCC: [l1]
Classical Approximation after Lifting Classical Results
All Bounds
Timebounds
Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₄: 1 {O(1)}
g₁₇: 1 {O(1)}
g₁₉: inf {Infinity}
g₂₂: 1 {O(1)}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₈: inf {Infinity}
g₄₀: inf {Infinity}
g₄₃: inf {Infinity}
g₄₅: inf {Infinity}
g₄₇: inf {Infinity}
g₅₀: inf {Infinity}
g₅₂: inf {Infinity}
g₅₅: inf {Infinity}
g₅₇: inf {Infinity}
g₆₀: inf {Infinity}
g₆₂: inf {Infinity}
g₆₅: inf {Infinity}
g₆₈: 1 {O(1)}
g₇₀: inf {Infinity}
g₇₃: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₁₁: inf {Infinity}
g₁₄: inf {Infinity}
g₁₇: inf {Infinity}
g₁₉: inf {Infinity}
g₂₂: inf {Infinity}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₈: inf {Infinity}
g₄₀: inf {Infinity}
g₄₃: inf {Infinity}
g₄₅: inf {Infinity}
g₄₇: inf {Infinity}
g₅₀: inf {Infinity}
g₅₂: inf {Infinity}
g₅₅: inf {Infinity}
g₅₇: inf {Infinity}
g₆₀: inf {Infinity}
g₆₂: inf {Infinity}
g₆₅: inf {Infinity}
g₆₈: inf {Infinity}
g₇₀: inf {Infinity}
g₇₃: inf {Infinity}
Sizebounds
(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₁₁,l2_v1), X₀: 1 {O(1)}
(g₁₁,l2_v1), X₁: X₁ {O(n)}
Run probabilistic analysis on SCC: [l1]
Run classical analysis on SCC: [l2_v1]
Classical Approximation after Lifting Classical Results
All Bounds
Timebounds
Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₄: 2 {O(1)}
g₁₇: 2 {O(1)}
g₁₉: inf {Infinity}
g₂₂: 1 {O(1)}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₈: inf {Infinity}
g₄₀: inf {Infinity}
g₄₃: inf {Infinity}
g₄₅: inf {Infinity}
g₄₇: inf {Infinity}
g₅₀: inf {Infinity}
g₅₂: inf {Infinity}
g₅₅: inf {Infinity}
g₅₇: inf {Infinity}
g₆₀: inf {Infinity}
g₆₂: inf {Infinity}
g₆₅: inf {Infinity}
g₆₈: 1 {O(1)}
g₇₀: inf {Infinity}
g₇₃: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₁₁: inf {Infinity}
g₁₄: inf {Infinity}
g₁₇: inf {Infinity}
g₁₉: inf {Infinity}
g₂₂: inf {Infinity}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₈: inf {Infinity}
g₄₀: inf {Infinity}
g₄₃: inf {Infinity}
g₄₅: inf {Infinity}
g₄₇: inf {Infinity}
g₅₀: inf {Infinity}
g₅₂: inf {Infinity}
g₅₅: inf {Infinity}
g₅₇: inf {Infinity}
g₆₀: inf {Infinity}
g₆₂: inf {Infinity}
g₆₅: inf {Infinity}
g₆₈: inf {Infinity}
g₇₀: inf {Infinity}
g₇₃: inf {Infinity}
Sizebounds
(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₁₁,l2_v1), X₀: 1 {O(1)}
(g₁₁,l2_v1), X₁: X₁ {O(n)}
(g₁₄,l1_v1), X₀: 2 {O(1)}
(g₁₄,l1_v1), X₁: 2⋅X₁ {O(n)}
(g₁₄,l1_v2), X₀: 2 {O(1)}
(g₁₄,l1_v2), X₁: 2⋅X₁ {O(n)}
(g₁₇,l1_v3), X₀: 3 {O(1)}
(g₁₇,l1_v3), X₁: 2⋅X₁+11 {O(n)}
(g₁₇,l1_v4), X₀: 3 {O(1)}
(g₁₇,l1_v4), X₁: 2⋅X₁+11 {O(n)}
Run probabilistic analysis on SCC: [l2_v1]
Run classical analysis on SCC: [l1_v1; l1_v2; l2_v10; l2_v9]
MPRF for transition t₆₁: l1_v1(X₀,X₁) → l2_v9(X₀,X₁) :|: 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:
new bound:
3 {O(1)}
MPRF:
• l1_v1: [1+X₀]
• l1_v2: [X₀]
• l2_v10: [X₀]
• l2_v9: [X₀]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
MPRF for transition t₆₃: l2_v9(X₀,X₁) → l1_v1(X₀-1,X₁-10) :|: 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ of depth 1:
new bound:
2 {O(1)}
MPRF:
• l1_v1: [X₀]
• l1_v2: [X₀]
• l2_v10: [X₀]
• l2_v9: [X₀]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
MPRF for transition t₆₄: l2_v9(X₀,X₁) → l1_v2(X₀,X₁) :|: 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ of depth 1:
new bound:
3 {O(1)}
MPRF:
• l1_v1: [X₀]
• l1_v2: [X₀-1]
• l2_v10: [X₀-1]
• l2_v9: [X₀]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
MPRF for transition t₇₁: l2_v10(X₀,X₁) → l1_v1(X₀-1,X₁-10) :|: 1 ≤ X₀ ∧ 101 ≤ X₁ of depth 1:
new bound:
2 {O(1)}
MPRF:
• l1_v1: [X₀]
• l1_v2: [X₀]
• l2_v10: [X₀]
• l2_v9: [X₀]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
Classical Approximation after Lifting Classical Results
All Bounds
Timebounds
Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₄: 2 {O(1)}
g₁₇: 2 {O(1)}
g₁₉: inf {Infinity}
g₂₂: 1 {O(1)}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₈: inf {Infinity}
g₄₀: inf {Infinity}
g₄₃: inf {Infinity}
g₄₅: inf {Infinity}
g₄₇: inf {Infinity}
g₅₀: inf {Infinity}
g₅₂: inf {Infinity}
g₅₅: inf {Infinity}
g₅₇: inf {Infinity}
g₆₀: inf {Infinity}
g₆₂: 3 {O(1)}
g₆₅: 5 {O(1)}
g₆₈: 2 {O(1)}
g₇₀: inf {Infinity}
g₇₃: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₁₁: inf {Infinity}
g₁₄: inf {Infinity}
g₁₇: inf {Infinity}
g₁₉: inf {Infinity}
g₂₂: inf {Infinity}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₈: inf {Infinity}
g₄₀: inf {Infinity}
g₄₃: inf {Infinity}
g₄₅: inf {Infinity}
g₄₇: inf {Infinity}
g₅₀: inf {Infinity}
g₅₂: inf {Infinity}
g₅₅: inf {Infinity}
g₅₇: inf {Infinity}
g₆₀: inf {Infinity}
g₆₂: inf {Infinity}
g₆₅: inf {Infinity}
g₆₈: inf {Infinity}
g₇₀: inf {Infinity}
g₇₃: inf {Infinity}
Sizebounds
(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₁₁,l2_v1), X₀: 1 {O(1)}
(g₁₁,l2_v1), X₁: X₁ {O(n)}
(g₁₄,l1_v1), X₀: 2 {O(1)}
(g₁₄,l1_v1), X₁: X₁ {O(n)}
(g₁₄,l1_v2), X₀: 2 {O(1)}
(g₁₄,l1_v2), X₁: X₁ {O(n)}
(g₁₇,l1_v3), X₀: 3 {O(1)}
(g₁₇,l1_v3), X₁: 2⋅X₁+11 {O(n)}
(g₁₇,l1_v4), X₀: 3 {O(1)}
(g₁₇,l1_v4), X₁: X₁ {O(n)}
(g₆₂,l2_v9), X₀: 2 {O(1)}
(g₆₂,l2_v9), X₁: 2⋅X₁ {O(n)}
(g₆₅,l1_v1), X₀: 4 {O(1)}
(g₆₅,l1_v1), X₁: 4⋅X₁ {O(n)}
(g₆₅,l1_v2), X₀: 4 {O(1)}
(g₆₅,l1_v2), X₁: 4⋅X₁ {O(n)}
(g₆₈,l1_v10), X₀: 5 {O(1)}
(g₆₈,l1_v10), X₁: 211 {O(1)}
(g₆₈,l1_v6), X₀: 5 {O(1)}
(g₆₈,l1_v6), X₁: 211 {O(1)}
(g₇₀,l2_v10), X₀: 2 {O(1)}
(g₇₀,l2_v10), X₁: 2⋅X₁ {O(n)}
(g₇₃,l1_v1), X₀: 4 {O(1)}
(g₇₃,l1_v1), X₁: 4⋅X₁ {O(n)}
(g₇₃,l1_v2), X₀: 4 {O(1)}
(g₇₃,l1_v2), X₁: 4⋅X₁ {O(n)}
Run probabilistic analysis on SCC: [l1_v1; l1_v2; l2_v10; l2_v9]
Plrf for transition g₇₀:l1_v2(X₀,X₁) → t₆₉:l2_v10(X₀,X₁) :|: 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀:
new bound:
1/5⋅X₁+86/5 {O(n)}
PLRF:
• l1_v1: 1/10⋅X₁-91/10
• l1_v2: 1/10⋅X₁-81/10
• l2_v10: 1/10⋅X₁-91/10
• l2_v9: 1/10⋅X₁-91/10
Show Graph
G
l0
l0
l1
l1
l0->l1
p = 1
t₁ ∈ g₀
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
p = 1
t₁₀ ∈ g₁₁
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
p = 1
t₆₁ ∈ g₆₂
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
p = 1
t₃₉ ∈ g₄₀
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
p = 1
t₆₉ ∈ g₇₀
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
p = 1
t₁₈ ∈ g₁₉
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
p = 1
t₅₆ ∈ g₅₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
p = 1
t₃₁ ∈ g₃₂
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
p = 1
t₅₁ ∈ g₅₂
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
p = 1
t₂₆ ∈ g₂₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
p = 1
t₄₄ ∈ g₄₅
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
p = 1
t₄₆ ∈ g₄₇
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
p = 1/2
t₁₂ ∈ g₁₄
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
p = 1/2
t₁₃ ∈ g₁₄
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
p = 1/2
t₁₅ ∈ g₁₇
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
p = 1/2
t₁₆ ∈ g₁₇
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
p = 1/2
t₇₁ ∈ g₇₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
p = 1/2
t₇₂ ∈ g₇₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
p = 1/2
t₂₃ ∈ g₂₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
p = 1/2
t₂₀ ∈ g₂₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
p = 1/2
t₂₁ ∈ g₂₂
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
p = 1/2
t₂₄ ∈ g₂₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
p = 1/2
t₂₈ ∈ g₃₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
p = 1/2
t₂₉ ∈ g₃₀
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
p = 1/2
t₃₇ ∈ g₃₈
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
p = 1/2
t₃₆ ∈ g₃₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
p = 1/2
t₃₃ ∈ g₃₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
p = 1/2
t₃₄ ∈ g₃₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
p = 1/2
t₄₂ ∈ g₄₃
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
p = 1/2
t₄₁ ∈ g₄₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
p = 1/2
t₄₈ ∈ g₅₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
p = 1/2
t₄₉ ∈ g₅₀
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
p = 1/2
t₅₃ ∈ g₅₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
p = 1/2
t₅₄ ∈ g₅₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
p = 1/2
t₅₈ ∈ g₆₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
p = 1/2
t₅₉ ∈ g₆₀
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
p = 1/2
t₆₃ ∈ g₆₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
p = 1/2
t₆₇ ∈ g₆₈
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
p = 1/2
t₆₄ ∈ g₆₅
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
p = 1/2
t₆₆ ∈ g₆₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
Use expected size bounds for entry point (g₁₄:l2_v1→[t₁₂:1/2:l1_v1; t₁₃:1/2:l1_v2],l1_v1)
Use classical time bound for entry point (g₁₄:l2_v1→[t₁₂:1/2:l1_v1; t₁₃:1/2:l1_v2],l1_v1)
Use expected size bounds for entry point (g₁₄:l2_v1→[t₁₂:1/2:l1_v1; t₁₃:1/2:l1_v2],l1_v2)
Use classical time bound for entry point (g₁₄:l2_v1→[t₁₂:1/2:l1_v1; t₁₃:1/2:l1_v2],l1_v2)
Plrf for transition g₇₃:l2_v10(X₀,X₁) → [1/2]:t₇₁:l1_v1(X₀-1,X₁-10) :+: [1/2]:t₇₂:l1_v2(X₀,X₁) :|: 101 ≤ X₁ ∧ 1 ≤ X₀:
new bound:
8 {O(1)}
PLRF:
• l1_v1: 2⋅X₀
• l1_v2: 2⋅X₀
• l2_v10: 2⋅X₀
• l2_v9: 2⋅X₀
Show Graph
G
l0
l0
l1
l1
l0->l1
p = 1
t₁ ∈ g₀
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
p = 1
t₁₀ ∈ g₁₁
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
p = 1
t₆₁ ∈ g₆₂
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
p = 1
t₃₉ ∈ g₄₀
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
p = 1
t₆₉ ∈ g₇₀
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
p = 1
t₁₈ ∈ g₁₉
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
p = 1
t₅₆ ∈ g₅₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
p = 1
t₃₁ ∈ g₃₂
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
p = 1
t₅₁ ∈ g₅₂
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
p = 1
t₂₆ ∈ g₂₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
p = 1
t₄₄ ∈ g₄₅
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
p = 1
t₄₆ ∈ g₄₇
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
p = 1/2
t₁₂ ∈ g₁₄
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
p = 1/2
t₁₃ ∈ g₁₄
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
p = 1/2
t₁₅ ∈ g₁₇
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
p = 1/2
t₁₆ ∈ g₁₇
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
p = 1/2
t₇₁ ∈ g₇₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
p = 1/2
t₇₂ ∈ g₇₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
p = 1/2
t₂₃ ∈ g₂₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
p = 1/2
t₂₀ ∈ g₂₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
p = 1/2
t₂₁ ∈ g₂₂
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
p = 1/2
t₂₄ ∈ g₂₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
p = 1/2
t₂₈ ∈ g₃₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
p = 1/2
t₂₉ ∈ g₃₀
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
p = 1/2
t₃₇ ∈ g₃₈
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
p = 1/2
t₃₆ ∈ g₃₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
p = 1/2
t₃₃ ∈ g₃₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
p = 1/2
t₃₄ ∈ g₃₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
p = 1/2
t₄₂ ∈ g₄₃
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
p = 1/2
t₄₁ ∈ g₄₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
p = 1/2
t₄₈ ∈ g₅₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
p = 1/2
t₄₉ ∈ g₅₀
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
p = 1/2
t₅₃ ∈ g₅₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
p = 1/2
t₅₄ ∈ g₅₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
p = 1/2
t₅₈ ∈ g₆₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
p = 1/2
t₅₉ ∈ g₆₀
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
p = 1/2
t₆₃ ∈ g₆₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
p = 1/2
t₆₇ ∈ g₆₈
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
p = 1/2
t₆₄ ∈ g₆₅
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
p = 1/2
t₆₆ ∈ g₆₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
Use expected size bounds for entry point (g₁₄:l2_v1→[t₁₂:1/2:l1_v1; t₁₃:1/2:l1_v2],l1_v1)
Use classical time bound for entry point (g₁₄:l2_v1→[t₁₂:1/2:l1_v1; t₁₃:1/2:l1_v2],l1_v1)
Use expected size bounds for entry point (g₁₄:l2_v1→[t₁₂:1/2:l1_v1; t₁₃:1/2:l1_v2],l1_v2)
Use classical time bound for entry point (g₁₄:l2_v1→[t₁₂:1/2:l1_v1; t₁₃:1/2:l1_v2],l1_v2)
Run classical analysis on SCC: [l1_v4; l2_v8]
Classical Approximation after Lifting Classical Results
All Bounds
Timebounds
Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₄: 2 {O(1)}
g₁₇: 2 {O(1)}
g₁₉: inf {Infinity}
g₂₂: 1 {O(1)}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₈: inf {Infinity}
g₄₀: inf {Infinity}
g₄₃: inf {Infinity}
g₄₅: inf {Infinity}
g₄₇: inf {Infinity}
g₅₀: inf {Infinity}
g₅₂: inf {Infinity}
g₅₅: inf {Infinity}
g₅₇: inf {Infinity}
g₆₀: inf {Infinity}
g₆₂: 3 {O(1)}
g₆₅: 5 {O(1)}
g₆₈: 2 {O(1)}
g₇₀: 1/5⋅X₁+86/5 {O(n)}
g₇₃: 8 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₁₁: inf {Infinity}
g₁₄: inf {Infinity}
g₁₇: inf {Infinity}
g₁₉: inf {Infinity}
g₂₂: inf {Infinity}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₈: inf {Infinity}
g₄₀: inf {Infinity}
g₄₃: inf {Infinity}
g₄₅: inf {Infinity}
g₄₇: inf {Infinity}
g₅₀: inf {Infinity}
g₅₂: inf {Infinity}
g₅₅: inf {Infinity}
g₅₇: inf {Infinity}
g₆₀: inf {Infinity}
g₆₂: inf {Infinity}
g₆₅: inf {Infinity}
g₆₈: inf {Infinity}
g₇₀: inf {Infinity}
g₇₃: inf {Infinity}
Sizebounds
(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₁₁,l2_v1), X₀: 1 {O(1)}
(g₁₁,l2_v1), X₁: X₁ {O(n)}
(g₁₄,l1_v1), X₀: 2 {O(1)}
(g₁₄,l1_v1), X₁: X₁ {O(n)}
(g₁₄,l1_v2), X₀: 2 {O(1)}
(g₁₄,l1_v2), X₁: X₁ {O(n)}
(g₁₇,l1_v3), X₀: 3 {O(1)}
(g₁₇,l1_v3), X₁: 2⋅X₁+11 {O(n)}
(g₁₇,l1_v4), X₀: 3 {O(1)}
(g₁₇,l1_v4), X₁: X₁ {O(n)}
(g₅₇,l2_v8), X₀: 1 {O(1)}
(g₅₇,l2_v8), X₁: X₁ {O(n)}
(g₆₀,l1_v3), X₀: 3 {O(1)}
(g₆₀,l1_v3), X₁: 2⋅X₁+11 {O(n)}
(g₆₀,l1_v4), X₀: 3 {O(1)}
(g₆₀,l1_v4), X₁: 2⋅X₁+11 {O(n)}
(g₆₂,l2_v9), X₀: 2 {O(1)}
(g₆₂,l2_v9), X₁: 2⋅X₁ {O(n)}
(g₆₅,l1_v1), X₀: 4 {O(1)}
(g₆₅,l1_v1), X₁: 4⋅X₁ {O(n)}
(g₆₅,l1_v2), X₀: 4 {O(1)}
(g₆₅,l1_v2), X₁: 4⋅X₁ {O(n)}
(g₆₈,l1_v10), X₀: 5 {O(1)}
(g₆₈,l1_v10), X₁: 211 {O(1)}
(g₆₈,l1_v6), X₀: 5 {O(1)}
(g₆₈,l1_v6), X₁: 211 {O(1)}
(g₇₀,l2_v10), X₀: 2 {O(1)}
(g₇₀,l2_v10), X₁: 2⋅X₁ {O(n)}
(g₇₃,l1_v1), X₀: 4 {O(1)}
(g₇₃,l1_v1), X₁: 4⋅X₁ {O(n)}
(g₇₃,l1_v2), X₀: 4 {O(1)}
(g₇₃,l1_v2), X₁: 4⋅X₁ {O(n)}
Run probabilistic analysis on SCC: [l1_v4; l2_v8]
Plrf for transition g₅₇:l1_v4(X₀,X₁) → t₅₆:l2_v8(X₀,X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀:
new bound:
4 {O(1)}
PLRF:
• l1_v3: 0
• l1_v4: 1+X₀
• l2_v8: X₀
Show Graph
G
l0
l0
l1
l1
l0->l1
p = 1
t₁ ∈ g₀
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
p = 1
t₁₀ ∈ g₁₁
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
p = 1
t₆₁ ∈ g₆₂
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
p = 1
t₃₉ ∈ g₄₀
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
p = 1
t₆₉ ∈ g₇₀
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
p = 1
t₁₈ ∈ g₁₉
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
p = 1
t₅₆ ∈ g₅₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
p = 1
t₃₁ ∈ g₃₂
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
p = 1
t₅₁ ∈ g₅₂
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
p = 1
t₂₆ ∈ g₂₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
p = 1
t₄₄ ∈ g₄₅
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
p = 1
t₄₆ ∈ g₄₇
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
p = 1/2
t₁₂ ∈ g₁₄
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
p = 1/2
t₁₃ ∈ g₁₄
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
p = 1/2
t₁₅ ∈ g₁₇
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
p = 1/2
t₁₆ ∈ g₁₇
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
p = 1/2
t₇₁ ∈ g₇₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
p = 1/2
t₇₂ ∈ g₇₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
p = 1/2
t₂₃ ∈ g₂₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
p = 1/2
t₂₀ ∈ g₂₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
p = 1/2
t₂₁ ∈ g₂₂
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
p = 1/2
t₂₄ ∈ g₂₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
p = 1/2
t₂₈ ∈ g₃₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
p = 1/2
t₂₉ ∈ g₃₀
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
p = 1/2
t₃₇ ∈ g₃₈
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
p = 1/2
t₃₆ ∈ g₃₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
p = 1/2
t₃₃ ∈ g₃₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
p = 1/2
t₃₄ ∈ g₃₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
p = 1/2
t₄₂ ∈ g₄₃
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
p = 1/2
t₄₁ ∈ g₄₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
p = 1/2
t₄₈ ∈ g₅₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
p = 1/2
t₄₉ ∈ g₅₀
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
p = 1/2
t₅₃ ∈ g₅₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
p = 1/2
t₅₄ ∈ g₅₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
p = 1/2
t₅₈ ∈ g₆₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
p = 1/2
t₅₉ ∈ g₆₀
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
p = 1/2
t₆₃ ∈ g₆₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
p = 1/2
t₆₇ ∈ g₆₈
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
p = 1/2
t₆₄ ∈ g₆₅
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
p = 1/2
t₆₆ ∈ g₆₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
Use expected size bounds for entry point (g₁₇:l2_v1→[t₁₅:1/2:l1_v3; t₁₆:1/2:l1_v4],l1_v4)
Use classical time bound for entry point (g₁₇:l2_v1→[t₁₅:1/2:l1_v3; t₁₆:1/2:l1_v4],l1_v4)
Plrf for transition g₆₀:l2_v8(X₀,X₁) → [1/2]:t₅₈:l1_v3(1+X₀,11+X₁) :+: [1/2]:t₅₉:l1_v4(X₀,X₁) :|: X₁ ≤ 100 ∧ 1 ≤ X₀:
new bound:
6 {O(1)}
PLRF:
• l1_v3: 0
• l1_v4: 2⋅X₀
• l2_v8: 1+X₀
Show Graph
G
l0
l0
l1
l1
l0->l1
p = 1
t₁ ∈ g₀
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
p = 1
t₁₀ ∈ g₁₁
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
p = 1
t₆₁ ∈ g₆₂
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
p = 1
t₃₉ ∈ g₄₀
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
p = 1
t₆₉ ∈ g₇₀
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
p = 1
t₁₈ ∈ g₁₉
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
p = 1
t₅₆ ∈ g₅₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
p = 1
t₃₁ ∈ g₃₂
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
p = 1
t₅₁ ∈ g₅₂
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
p = 1
t₂₆ ∈ g₂₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
p = 1
t₄₄ ∈ g₄₅
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
p = 1
t₄₆ ∈ g₄₇
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
p = 1/2
t₁₂ ∈ g₁₄
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
p = 1/2
t₁₃ ∈ g₁₄
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
p = 1/2
t₁₅ ∈ g₁₇
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
p = 1/2
t₁₆ ∈ g₁₇
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
p = 1/2
t₇₁ ∈ g₇₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
p = 1/2
t₇₂ ∈ g₇₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
p = 1/2
t₂₃ ∈ g₂₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
p = 1/2
t₂₀ ∈ g₂₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
p = 1/2
t₂₁ ∈ g₂₂
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
p = 1/2
t₂₄ ∈ g₂₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
p = 1/2
t₂₈ ∈ g₃₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
p = 1/2
t₂₉ ∈ g₃₀
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
p = 1/2
t₃₇ ∈ g₃₈
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
p = 1/2
t₃₆ ∈ g₃₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
p = 1/2
t₃₃ ∈ g₃₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
p = 1/2
t₃₄ ∈ g₃₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
p = 1/2
t₄₂ ∈ g₄₃
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
p = 1/2
t₄₁ ∈ g₄₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
p = 1/2
t₄₈ ∈ g₅₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
p = 1/2
t₄₉ ∈ g₅₀
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
p = 1/2
t₅₃ ∈ g₅₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
p = 1/2
t₅₄ ∈ g₅₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
p = 1/2
t₅₈ ∈ g₆₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
p = 1/2
t₅₉ ∈ g₆₀
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
p = 1/2
t₆₃ ∈ g₆₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
p = 1/2
t₆₇ ∈ g₆₈
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
p = 1/2
t₆₄ ∈ g₆₅
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
p = 1/2
t₆₆ ∈ g₆₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
Use expected size bounds for entry point (g₁₇:l2_v1→[t₁₅:1/2:l1_v3; t₁₆:1/2:l1_v4],l1_v4)
Use classical time bound for entry point (g₁₇:l2_v1→[t₁₅:1/2:l1_v3; t₁₆:1/2:l1_v4],l1_v4)
Run classical analysis on SCC: [l1_v3; l1_v7; l2_v2; l2_v3]
MPRF for transition t₁₈: l1_v3(X₀,X₁) → l2_v2(X₀,X₁) :|: X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₁+246 {O(n)}
MPRF:
• l1_v3: [112-X₁]
• l1_v7: [101-X₁]
• l2_v2: [101-X₁]
• l2_v3: [101-X₁]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
MPRF for transition t₂₃: l2_v2(X₀,X₁) → l1_v3(1+X₀,11+X₁) :|: X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100 of depth 1:
new bound:
2⋅X₁+246 {O(n)}
MPRF:
• l1_v3: [112-X₁]
• l1_v7: [101-X₁]
• l2_v2: [112-X₁]
• l2_v3: [101-X₁]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
MPRF for transition t₂₄: l2_v2(X₀,X₁) → l1_v7(X₀,X₁) :|: X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100 of depth 1:
new bound:
2⋅X₁+246 {O(n)}
MPRF:
• l1_v3: [112-X₁]
• l1_v7: [101-X₁]
• l2_v2: [112-X₁]
• l2_v3: [101-X₁]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
MPRF for transition t₂₈: l2_v3(X₀,X₁) → l1_v3(1+X₀,11+X₁) :|: 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100 of depth 1:
new bound:
2⋅X₁+224 {O(n)}
MPRF:
• l1_v3: [101-X₁]
• l1_v7: [101-X₁]
• l2_v2: [101-X₁]
• l2_v3: [101-X₁]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
Classical Approximation after Lifting Classical Results
All Bounds
Timebounds
Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₄: 2 {O(1)}
g₁₇: 2 {O(1)}
g₁₉: 2⋅X₁+246 {O(n)}
g₂₂: 2 {O(1)}
g₂₅: 4⋅X₁+492 {O(n)}
g₂₇: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₈: inf {Infinity}
g₄₀: inf {Infinity}
g₄₃: inf {Infinity}
g₄₅: inf {Infinity}
g₄₇: inf {Infinity}
g₅₀: inf {Infinity}
g₅₂: inf {Infinity}
g₅₅: inf {Infinity}
g₅₇: 4 {O(1)}
g₆₀: 6 {O(1)}
g₆₂: 3 {O(1)}
g₆₅: 5 {O(1)}
g₆₈: 2 {O(1)}
g₇₀: 1/5⋅X₁+86/5 {O(n)}
g₇₃: 8 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₁₁: inf {Infinity}
g₁₄: inf {Infinity}
g₁₇: inf {Infinity}
g₁₉: inf {Infinity}
g₂₂: inf {Infinity}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₈: inf {Infinity}
g₄₀: inf {Infinity}
g₄₃: inf {Infinity}
g₄₅: inf {Infinity}
g₄₇: inf {Infinity}
g₅₀: inf {Infinity}
g₅₂: inf {Infinity}
g₅₅: inf {Infinity}
g₅₇: inf {Infinity}
g₆₀: inf {Infinity}
g₆₂: inf {Infinity}
g₆₅: inf {Infinity}
g₆₈: inf {Infinity}
g₇₀: inf {Infinity}
g₇₃: inf {Infinity}
Sizebounds
(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₁₁,l2_v1), X₀: 1 {O(1)}
(g₁₁,l2_v1), X₁: X₁ {O(n)}
(g₁₄,l1_v1), X₀: 2 {O(1)}
(g₁₄,l1_v1), X₁: X₁ {O(n)}
(g₁₄,l1_v2), X₀: 2 {O(1)}
(g₁₄,l1_v2), X₁: X₁ {O(n)}
(g₁₇,l1_v3), X₀: 3 {O(1)}
(g₁₇,l1_v3), X₁: 2⋅X₁+11 {O(n)}
(g₁₇,l1_v4), X₀: 3 {O(1)}
(g₁₇,l1_v4), X₁: X₁ {O(n)}
(g₁₉,l2_v2), X₀: 4⋅X₁+474 {O(n)}
(g₁₉,l2_v2), X₁: 46⋅X₁+5192 {O(n)}
(g₂₂,l1_v5), X₀: 8⋅X₁+948 {O(n)}
(g₂₂,l1_v5), X₁: 212 {O(1)}
(g₂₂,l1_v6), X₀: 8⋅X₁+948 {O(n)}
(g₂₂,l1_v6), X₁: 212 {O(1)}
(g₂₅,l1_v3), X₀: 8⋅X₁+948 {O(n)}
(g₂₅,l1_v3), X₁: 92⋅X₁+10384 {O(n)}
(g₂₅,l1_v7), X₀: 8⋅X₁+948 {O(n)}
(g₂₅,l1_v7), X₁: 92⋅X₁+10384 {O(n)}
(g₂₇,l2_v3), X₀: 4⋅X₁+474 {O(n)}
(g₂₇,l2_v3), X₁: 46⋅X₁+5192 {O(n)}
(g₃₀,l1_v3), X₀: 8⋅X₁+948 {O(n)}
(g₃₀,l1_v3), X₁: 92⋅X₁+10384 {O(n)}
(g₃₀,l1_v7), X₀: 8⋅X₁+948 {O(n)}
(g₃₀,l1_v7), X₁: 92⋅X₁+10384 {O(n)}
(g₅₇,l2_v8), X₀: 1 {O(1)}
(g₅₇,l2_v8), X₁: X₁ {O(n)}
(g₆₀,l1_v3), X₀: 3 {O(1)}
(g₆₀,l1_v3), X₁: X₁+33 {O(n)}
(g₆₀,l1_v4), X₀: 3 {O(1)}
(g₆₀,l1_v4), X₁: X₁+33 {O(n)}
(g₆₂,l2_v9), X₀: 2 {O(1)}
(g₆₂,l2_v9), X₁: 2⋅X₁ {O(n)}
(g₆₅,l1_v1), X₀: 4 {O(1)}
(g₆₅,l1_v1), X₁: 4⋅X₁ {O(n)}
(g₆₅,l1_v2), X₀: 4 {O(1)}
(g₆₅,l1_v2), X₁: 4⋅X₁ {O(n)}
(g₆₈,l1_v10), X₀: 5 {O(1)}
(g₆₈,l1_v10), X₁: 211 {O(1)}
(g₆₈,l1_v6), X₀: 5 {O(1)}
(g₆₈,l1_v6), X₁: 211 {O(1)}
(g₇₀,l2_v10), X₀: 2 {O(1)}
(g₇₀,l2_v10), X₁: 2⋅X₁ {O(n)}
(g₇₃,l1_v1), X₀: 4 {O(1)}
(g₇₃,l1_v1), X₁: 4⋅X₁ {O(n)}
(g₇₃,l1_v2), X₀: 4 {O(1)}
(g₇₃,l1_v2), X₁: 4⋅X₁ {O(n)}
Run probabilistic analysis on SCC: [l1_v3; l1_v7; l2_v2; l2_v3]
Plrf for transition g₂₇:l1_v7(X₀,X₁) → t₂₆:l2_v3(X₀,X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀:
new bound:
3/11⋅X₁+266/11 {O(n)}
PLRF:
• l1_v3: 111/11-1/11⋅X₁
• l1_v7: 122/11-1/11⋅X₁
• l2_v2: 111/11-1/11⋅X₁
• l2_v3: 111/11-1/11⋅X₁
Show Graph
G
l0
l0
l1
l1
l0->l1
p = 1
t₁ ∈ g₀
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
p = 1
t₁₀ ∈ g₁₁
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
p = 1
t₆₁ ∈ g₆₂
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
p = 1
t₃₉ ∈ g₄₀
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
p = 1
t₆₉ ∈ g₇₀
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
p = 1
t₁₈ ∈ g₁₉
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
p = 1
t₅₆ ∈ g₅₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
p = 1
t₃₁ ∈ g₃₂
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
p = 1
t₅₁ ∈ g₅₂
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
p = 1
t₂₆ ∈ g₂₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
p = 1
t₄₄ ∈ g₄₅
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
p = 1
t₄₆ ∈ g₄₇
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
p = 1/2
t₁₂ ∈ g₁₄
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
p = 1/2
t₁₃ ∈ g₁₄
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
p = 1/2
t₁₅ ∈ g₁₇
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
p = 1/2
t₁₆ ∈ g₁₇
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
p = 1/2
t₇₁ ∈ g₇₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
p = 1/2
t₇₂ ∈ g₇₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
p = 1/2
t₂₃ ∈ g₂₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
p = 1/2
t₂₀ ∈ g₂₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
p = 1/2
t₂₁ ∈ g₂₂
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
p = 1/2
t₂₄ ∈ g₂₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
p = 1/2
t₂₈ ∈ g₃₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
p = 1/2
t₂₉ ∈ g₃₀
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
p = 1/2
t₃₇ ∈ g₃₈
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
p = 1/2
t₃₆ ∈ g₃₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
p = 1/2
t₃₃ ∈ g₃₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
p = 1/2
t₃₄ ∈ g₃₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
p = 1/2
t₄₂ ∈ g₄₃
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
p = 1/2
t₄₁ ∈ g₄₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
p = 1/2
t₄₈ ∈ g₅₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
p = 1/2
t₄₉ ∈ g₅₀
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
p = 1/2
t₅₃ ∈ g₅₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
p = 1/2
t₅₄ ∈ g₅₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
p = 1/2
t₅₈ ∈ g₆₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
p = 1/2
t₅₉ ∈ g₆₀
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
p = 1/2
t₆₃ ∈ g₆₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
p = 1/2
t₆₇ ∈ g₆₈
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
p = 1/2
t₆₄ ∈ g₆₅
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
p = 1/2
t₆₆ ∈ g₆₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
Use expected size bounds for entry point (g₁₇:l2_v1→[t₁₅:1/2:l1_v3; t₁₆:1/2:l1_v4],l1_v3)
Use classical time bound for entry point (g₁₇:l2_v1→[t₁₅:1/2:l1_v3; t₁₆:1/2:l1_v4],l1_v3)
Use expected size bounds for entry point (g₆₀:l2_v8→[t₅₈:1/2:l1_v3; t₅₉:1/2:l1_v4],l1_v3)
Use classical time bound for entry point (g₆₀:l2_v8→[t₅₈:1/2:l1_v3; t₅₉:1/2:l1_v4],l1_v3)
Plrf for transition g₃₀:l2_v3(X₀,X₁) → [1/2]:t₂₈:l1_v3(1+X₀,11+X₁) :+: [1/2]:t₂₉:l1_v7(X₀,X₁) :|: X₁ ≤ 100 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀:
new bound:
3/11⋅X₁+266/11 {O(n)}
PLRF:
• l1_v3: 111/11-1/11⋅X₁
• l1_v7: 122/11-1/11⋅X₁
• l2_v2: 111/11-1/11⋅X₁
• l2_v3: 122/11-1/11⋅X₁
Show Graph
G
l0
l0
l1
l1
l0->l1
p = 1
t₁ ∈ g₀
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
p = 1
t₁₀ ∈ g₁₁
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
p = 1
t₆₁ ∈ g₆₂
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
p = 1
t₃₉ ∈ g₄₀
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
p = 1
t₆₉ ∈ g₇₀
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
p = 1
t₁₈ ∈ g₁₉
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
p = 1
t₅₆ ∈ g₅₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
p = 1
t₃₁ ∈ g₃₂
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
p = 1
t₅₁ ∈ g₅₂
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
p = 1
t₂₆ ∈ g₂₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
p = 1
t₄₄ ∈ g₄₅
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
p = 1
t₄₆ ∈ g₄₇
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
p = 1/2
t₁₂ ∈ g₁₄
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
p = 1/2
t₁₃ ∈ g₁₄
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
p = 1/2
t₁₅ ∈ g₁₇
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
p = 1/2
t₁₆ ∈ g₁₇
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
p = 1/2
t₇₁ ∈ g₇₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
p = 1/2
t₇₂ ∈ g₇₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
p = 1/2
t₂₃ ∈ g₂₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
p = 1/2
t₂₀ ∈ g₂₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
p = 1/2
t₂₁ ∈ g₂₂
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
p = 1/2
t₂₄ ∈ g₂₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
p = 1/2
t₂₈ ∈ g₃₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
p = 1/2
t₂₉ ∈ g₃₀
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
p = 1/2
t₃₇ ∈ g₃₈
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
p = 1/2
t₃₆ ∈ g₃₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
p = 1/2
t₃₃ ∈ g₃₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
p = 1/2
t₃₄ ∈ g₃₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
p = 1/2
t₄₂ ∈ g₄₃
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
p = 1/2
t₄₁ ∈ g₄₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
p = 1/2
t₄₈ ∈ g₅₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
p = 1/2
t₄₉ ∈ g₅₀
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
p = 1/2
t₅₃ ∈ g₅₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
p = 1/2
t₅₄ ∈ g₅₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
p = 1/2
t₅₈ ∈ g₆₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
p = 1/2
t₅₉ ∈ g₆₀
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
p = 1/2
t₆₃ ∈ g₆₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
p = 1/2
t₆₇ ∈ g₆₈
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
p = 1/2
t₆₄ ∈ g₆₅
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
p = 1/2
t₆₆ ∈ g₆₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
Use expected size bounds for entry point (g₁₇:l2_v1→[t₁₅:1/2:l1_v3; t₁₆:1/2:l1_v4],l1_v3)
Use classical time bound for entry point (g₁₇:l2_v1→[t₁₅:1/2:l1_v3; t₁₆:1/2:l1_v4],l1_v3)
Use expected size bounds for entry point (g₆₀:l2_v8→[t₅₈:1/2:l1_v3; t₅₉:1/2:l1_v4],l1_v3)
Use classical time bound for entry point (g₆₀:l2_v8→[t₅₈:1/2:l1_v3; t₅₉:1/2:l1_v4],l1_v3)
Run classical analysis on SCC: [l1_v10; l1_v5; l1_v6; l1_v8; l1_v9; l2_v4; l2_v5; l2_v6; l2_v7]
MPRF for transition t₃₁: l1_v5(X₀,X₁) → l2_v4(X₀,X₁) :|: X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:
new bound:
80⋅X₁+10360 {O(n)}
MPRF:
• l1_v10: [101+10⋅X₀-X₁]
• l1_v5: [102+10⋅X₀-X₁]
• l1_v6: [102+10⋅X₀-X₁]
• l1_v8: [101+10⋅X₀-X₁]
• l1_v9: [101+10⋅X₀-X₁]
• l2_v4: [101+10⋅X₀-X₁]
• l2_v5: [101+10⋅X₀-X₁]
• l2_v6: [101+10⋅X₀-X₁]
• l2_v7: [102+10⋅X₀-X₁]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
MPRF for transition t₃₃: l2_v4(X₀,X₁) → l1_v8(X₀-1,X₁-10) :|: X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ of depth 1:
new bound:
8⋅X₁+955 {O(n)}
MPRF:
• l1_v10: [X₀]
• l1_v5: [X₀]
• l1_v6: [X₀-1]
• l1_v8: [X₀]
• l1_v9: [X₀]
• l2_v4: [X₀]
• l2_v5: [X₀]
• l2_v6: [X₀]
• l2_v7: [X₀-1]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
MPRF for transition t₃₄: l2_v4(X₀,X₁) → l1_v9(X₀,X₁) :|: X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ of depth 1:
new bound:
8⋅X₁+955 {O(n)}
MPRF:
• l1_v10: [X₀]
• l1_v5: [X₀]
• l1_v6: [X₀-1]
• l1_v8: [X₀]
• l1_v9: [X₀-1]
• l2_v4: [X₀]
• l2_v5: [X₀]
• l2_v6: [X₀-1]
• l2_v7: [X₀-1]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
MPRF for transition t₃₆: l2_v4(X₀,X₁) → l1_v6(1+X₀,11+X₁) :|: X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100 of depth 1:
new bound:
1440⋅X₁+178247 {O(n)}
MPRF:
• l1_v10: [720+180⋅X₀-8⋅X₁]
• l1_v5: [820+180⋅X₀-9⋅X₁]
• l1_v6: [730+180⋅X₀-9⋅X₁]
• l1_v8: [1+180⋅X₀]
• l1_v9: [180⋅X₀-179]
• l2_v4: [820+180⋅X₀-9⋅X₁]
• l2_v5: [720+180⋅X₀-8⋅X₁]
• l2_v6: [180⋅X₀-179]
• l2_v7: [730+180⋅X₀-9⋅X₁]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
MPRF for transition t₃₇: l2_v4(X₀,X₁) → l1_v10(X₀,X₁) :|: X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100 of depth 1:
new bound:
80⋅X₁+10360 {O(n)}
MPRF:
• l1_v10: [101+10⋅X₀-X₁]
• l1_v5: [102+10⋅X₀-X₁]
• l1_v6: [102+10⋅X₀-X₁]
• l1_v8: [102+10⋅X₀-X₁]
• l1_v9: [102+10⋅X₀-X₁]
• l2_v4: [102+10⋅X₀-X₁]
• l2_v5: [101+10⋅X₀-X₁]
• l2_v6: [102+10⋅X₀-X₁]
• l2_v7: [102+10⋅X₀-X₁]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
MPRF for transition t₄₁: l2_v5(X₀,X₁) → l1_v6(1+X₀,11+X₁) :|: 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100 of depth 1:
new bound:
80⋅X₁+10317 {O(n)}
MPRF:
• l1_v10: [91+10⋅X₀-X₁]
• l1_v5: [91+10⋅X₀-X₁]
• l1_v6: [91+10⋅X₀-X₁]
• l1_v8: [91+10⋅X₀-X₁]
• l1_v9: [91+10⋅X₀-X₁]
• l2_v4: [91+10⋅X₀-X₁]
• l2_v5: [91+10⋅X₀-X₁]
• l2_v6: [91+10⋅X₀-X₁]
• l2_v7: [91+10⋅X₀-X₁]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
MPRF for transition t₄₄: l1_v8(X₀,X₁) → l2_v4(X₀,X₁) :|: X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:
new bound:
8⋅X₁+955 {O(n)}
MPRF:
• l1_v10: [X₀]
• l1_v5: [X₀]
• l1_v6: [X₀-1]
• l1_v8: [1+X₀]
• l1_v9: [X₀]
• l2_v4: [X₀]
• l2_v5: [X₀]
• l2_v6: [X₀]
• l2_v7: [X₀-1]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
MPRF for transition t₄₈: l2_v6(X₀,X₁) → l1_v8(X₀-1,X₁-10) :|: X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁ of depth 1:
new bound:
8⋅X₁+955 {O(n)}
MPRF:
• l1_v10: [X₀]
• l1_v5: [X₀]
• l1_v6: [X₀-1]
• l1_v8: [X₀]
• l1_v9: [X₀]
• l2_v4: [X₀]
• l2_v5: [X₀]
• l2_v6: [X₀]
• l2_v7: [X₀-1]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
MPRF for transition t₅₃: l2_v7(X₀,X₁) → l1_v5(X₀-1,X₁-10) :|: X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁ of depth 1:
new bound:
160⋅X₁+19909 {O(n)}
MPRF:
• l1_v10: [111+20⋅X₀-X₁]
• l1_v5: [111+20⋅X₀-X₁]
• l1_v6: [102+20⋅X₀-X₁]
• l1_v8: [20+20⋅X₀]
• l1_v9: [20⋅X₀]
• l2_v4: [111+20⋅X₀-X₁]
• l2_v5: [111+20⋅X₀-X₁]
• l2_v6: [20⋅X₀]
• l2_v7: [102+20⋅X₀-X₁]
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
Classical Approximation after Lifting Classical Results
All Bounds
Timebounds
Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₄: 2 {O(1)}
g₁₇: 2 {O(1)}
g₁₉: 2⋅X₁+246 {O(n)}
g₂₂: 2 {O(1)}
g₂₅: 4⋅X₁+492 {O(n)}
g₂₇: 3/11⋅X₁+266/11 {O(n)}
g₃₀: 3/11⋅X₁+266/11 {O(n)}
g₃₂: 80⋅X₁+10360 {O(n)}
g₃₅: 16⋅X₁+1910 {O(n)}
g₃₈: 1520⋅X₁+188607 {O(n)}
g₄₀: inf {Infinity}
g₄₃: inf {Infinity}
g₄₅: 8⋅X₁+955 {O(n)}
g₄₇: inf {Infinity}
g₅₀: inf {Infinity}
g₅₂: inf {Infinity}
g₅₅: inf {Infinity}
g₅₇: 4 {O(1)}
g₆₀: 6 {O(1)}
g₆₂: 3 {O(1)}
g₆₅: 5 {O(1)}
g₆₈: 2 {O(1)}
g₇₀: 1/5⋅X₁+86/5 {O(n)}
g₇₃: 8 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₁₁: inf {Infinity}
g₁₄: inf {Infinity}
g₁₇: inf {Infinity}
g₁₉: inf {Infinity}
g₂₂: inf {Infinity}
g₂₅: inf {Infinity}
g₂₇: inf {Infinity}
g₃₀: inf {Infinity}
g₃₂: inf {Infinity}
g₃₅: inf {Infinity}
g₃₈: inf {Infinity}
g₄₀: inf {Infinity}
g₄₃: inf {Infinity}
g₄₅: inf {Infinity}
g₄₇: inf {Infinity}
g₅₀: inf {Infinity}
g₅₂: inf {Infinity}
g₅₅: inf {Infinity}
g₅₇: inf {Infinity}
g₆₀: inf {Infinity}
g₆₂: inf {Infinity}
g₆₅: inf {Infinity}
g₆₈: inf {Infinity}
g₇₀: inf {Infinity}
g₇₃: inf {Infinity}
Sizebounds
(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₁₁,l2_v1), X₀: 1 {O(1)}
(g₁₁,l2_v1), X₁: X₁ {O(n)}
(g₁₄,l1_v1), X₀: 2 {O(1)}
(g₁₄,l1_v1), X₁: X₁ {O(n)}
(g₁₄,l1_v2), X₀: 2 {O(1)}
(g₁₄,l1_v2), X₁: X₁ {O(n)}
(g₁₇,l1_v3), X₀: 3 {O(1)}
(g₁₇,l1_v3), X₁: 2⋅X₁+11 {O(n)}
(g₁₇,l1_v4), X₀: 3 {O(1)}
(g₁₇,l1_v4), X₁: X₁ {O(n)}
(g₁₉,l2_v2), X₀: 4⋅X₁+474 {O(n)}
(g₁₉,l2_v2), X₁: 46⋅X₁+5192 {O(n)}
(g₂₂,l1_v5), X₀: 8⋅X₁+948 {O(n)}
(g₂₂,l1_v5), X₁: 212 {O(1)}
(g₂₂,l1_v6), X₀: 8⋅X₁+948 {O(n)}
(g₂₂,l1_v6), X₁: 212 {O(1)}
(g₂₅,l1_v3), X₀: 8⋅X₁+948 {O(n)}
(g₂₅,l1_v3), X₁: 92⋅X₁+10384 {O(n)}
(g₂₅,l1_v7), X₀: 8⋅X₁+948 {O(n)}
(g₂₅,l1_v7), X₁: 92⋅X₁+10384 {O(n)}
(g₂₇,l2_v3), X₀: 4⋅X₁+474 {O(n)}
(g₂₇,l2_v3), X₁: 46⋅X₁+5192 {O(n)}
(g₃₀,l1_v3), X₀: 8⋅X₁+948 {O(n)}
(g₃₀,l1_v3), X₁: 92⋅X₁+10384 {O(n)}
(g₃₀,l1_v7), X₀: 8⋅X₁+948 {O(n)}
(g₃₀,l1_v7), X₁: 92⋅X₁+10384 {O(n)}
(g₃₂,l2_v4), X₀: 1528⋅X₁+189517 {O(n)}
(g₃₂,l2_v4), X₁: 111 {O(1)}
(g₃₅,l1_v8), X₀: 3056⋅X₁+379034 {O(n)}
(g₃₅,l1_v8), X₁: 212 {O(1)}
(g₃₅,l1_v9), X₀: 3056⋅X₁+379034 {O(n)}
(g₃₅,l1_v9), X₁: 212 {O(1)}
(g₃₈,l1_v10), X₀: 3056⋅X₁+379034 {O(n)}
(g₃₈,l1_v10), X₁: 211 {O(1)}
(g₃₈,l1_v6), X₀: 3056⋅X₁+379034 {O(n)}
(g₃₈,l1_v6), X₁: 211 {O(1)}
(g₄₀,l2_v5), X₀: 1528⋅X₁+189517 {O(n)}
(g₄₀,l2_v5), X₁: 100 {O(1)}
(g₄₃,l1_v10), X₀: 3056⋅X₁+379034 {O(n)}
(g₄₃,l1_v10), X₁: 211 {O(1)}
(g₄₃,l1_v6), X₀: 3056⋅X₁+379034 {O(n)}
(g₄₃,l1_v6), X₁: 211 {O(1)}
(g₄₅,l2_v4), X₀: 1528⋅X₁+189517 {O(n)}
(g₄₅,l2_v4), X₁: 111 {O(1)}
(g₄₇,l2_v6), X₀: 1528⋅X₁+189517 {O(n)}
(g₄₇,l2_v6), X₁: 111 {O(1)}
(g₅₀,l1_v8), X₀: 3056⋅X₁+379034 {O(n)}
(g₅₀,l1_v8), X₁: 212 {O(1)}
(g₅₀,l1_v9), X₀: 3056⋅X₁+379034 {O(n)}
(g₅₀,l1_v9), X₁: 212 {O(1)}
(g₅₂,l2_v7), X₀: 1528⋅X₁+189517 {O(n)}
(g₅₂,l2_v7), X₁: 111 {O(1)}
(g₅₅,l1_v5), X₀: 3056⋅X₁+379034 {O(n)}
(g₅₅,l1_v5), X₁: 212 {O(1)}
(g₅₅,l1_v6), X₀: 3056⋅X₁+379034 {O(n)}
(g₅₅,l1_v6), X₁: 212 {O(1)}
(g₅₇,l2_v8), X₀: 1 {O(1)}
(g₅₇,l2_v8), X₁: X₁ {O(n)}
(g₆₀,l1_v3), X₀: 3 {O(1)}
(g₆₀,l1_v3), X₁: X₁+33 {O(n)}
(g₆₀,l1_v4), X₀: 3 {O(1)}
(g₆₀,l1_v4), X₁: X₁ {O(n)}
(g₆₂,l2_v9), X₀: 2 {O(1)}
(g₆₂,l2_v9), X₁: 2⋅X₁ {O(n)}
(g₆₅,l1_v1), X₀: 4 {O(1)}
(g₆₅,l1_v1), X₁: 4⋅X₁ {O(n)}
(g₆₅,l1_v2), X₀: 4 {O(1)}
(g₆₅,l1_v2), X₁: 4⋅X₁ {O(n)}
(g₆₈,l1_v10), X₀: 5 {O(1)}
(g₆₈,l1_v10), X₁: 211 {O(1)}
(g₆₈,l1_v6), X₀: 5 {O(1)}
(g₆₈,l1_v6), X₁: 211 {O(1)}
(g₇₀,l2_v10), X₀: 2 {O(1)}
(g₇₀,l2_v10), X₁: 2⋅X₁ {O(n)}
(g₇₃,l1_v1), X₀: 4 {O(1)}
(g₇₃,l1_v1), X₁: 4⋅X₁ {O(n)}
(g₇₃,l1_v2), X₀: 4 {O(1)}
(g₇₃,l1_v2), X₁: 4⋅X₁ {O(n)}
Run probabilistic analysis on SCC: [l1_v10; l1_v5; l1_v6; l1_v8; l1_v9; l2_v4; l2_v5; l2_v6; l2_v7]
Plrf for transition g₄₀:l1_v10(X₀,X₁) → t₃₉:l2_v5(X₀,X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀:
new bound:
160⋅X₁+20311 {O(n)}
PLRF:
• l1_v10: 102+10⋅X₀-X₁
• l1_v5: 101+10⋅X₀-X₁
• l1_v6: 101+10⋅X₀-X₁
• l1_v8: 101+10⋅X₀-X₁
• l1_v9: 101+10⋅X₀-X₁
• l2_v4: 101+10⋅X₀-X₁
• l2_v5: 101+10⋅X₀-X₁
• l2_v6: 101+10⋅X₀-X₁
• l2_v7: 101+10⋅X₀-X₁
Show Graph
G
l0
l0
l1
l1
l0->l1
p = 1
t₁ ∈ g₀
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
p = 1
t₁₀ ∈ g₁₁
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
p = 1
t₆₁ ∈ g₆₂
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
p = 1
t₃₉ ∈ g₄₀
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
p = 1
t₆₉ ∈ g₇₀
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
p = 1
t₁₈ ∈ g₁₉
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
p = 1
t₅₆ ∈ g₅₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
p = 1
t₃₁ ∈ g₃₂
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
p = 1
t₅₁ ∈ g₅₂
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
p = 1
t₂₆ ∈ g₂₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
p = 1
t₄₄ ∈ g₄₅
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
p = 1
t₄₆ ∈ g₄₇
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
p = 1/2
t₁₂ ∈ g₁₄
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
p = 1/2
t₁₃ ∈ g₁₄
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
p = 1/2
t₁₅ ∈ g₁₇
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
p = 1/2
t₁₆ ∈ g₁₇
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
p = 1/2
t₇₁ ∈ g₇₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
p = 1/2
t₇₂ ∈ g₇₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
p = 1/2
t₂₃ ∈ g₂₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
p = 1/2
t₂₀ ∈ g₂₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
p = 1/2
t₂₁ ∈ g₂₂
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
p = 1/2
t₂₄ ∈ g₂₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
p = 1/2
t₂₈ ∈ g₃₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
p = 1/2
t₂₉ ∈ g₃₀
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
p = 1/2
t₃₇ ∈ g₃₈
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
p = 1/2
t₃₆ ∈ g₃₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
p = 1/2
t₃₃ ∈ g₃₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
p = 1/2
t₃₄ ∈ g₃₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
p = 1/2
t₄₂ ∈ g₄₃
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
p = 1/2
t₄₁ ∈ g₄₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
p = 1/2
t₄₈ ∈ g₅₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
p = 1/2
t₄₉ ∈ g₅₀
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
p = 1/2
t₅₃ ∈ g₅₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
p = 1/2
t₅₄ ∈ g₅₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
p = 1/2
t₅₈ ∈ g₆₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
p = 1/2
t₅₉ ∈ g₆₀
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
p = 1/2
t₆₃ ∈ g₆₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
p = 1/2
t₆₇ ∈ g₆₈
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
p = 1/2
t₆₄ ∈ g₆₅
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
p = 1/2
t₆₆ ∈ g₆₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v5)
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v5)
Use classical time bound for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v5)
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v6)
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v6)
Use classical time bound for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v6)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v10)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v10)
Use classical time bound for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v10)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v6)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v6)
Use classical time bound for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v6)
Plrf for transition g₄₃:l2_v5(X₀,X₁) → [1/2]:t₄₁:l1_v6(1+X₀,11+X₁) :+: [1/2]:t₄₂:l1_v10(X₀,X₁) :|: X₁ ≤ 100 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁:
new bound:
160⋅X₁+20311 {O(n)}
PLRF:
• l1_v10: 102+10⋅X₀-X₁
• l1_v5: 101+10⋅X₀-X₁
• l1_v6: 101+10⋅X₀-X₁
• l1_v8: 101+10⋅X₀-X₁
• l1_v9: 101+10⋅X₀-X₁
• l2_v4: 101+10⋅X₀-X₁
• l2_v5: 102+10⋅X₀-X₁
• l2_v6: 101+10⋅X₀-X₁
• l2_v7: 101+10⋅X₀-X₁
Show Graph
G
l0
l0
l1
l1
l0->l1
p = 1
t₁ ∈ g₀
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
p = 1
t₁₀ ∈ g₁₁
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
p = 1
t₆₁ ∈ g₆₂
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
p = 1
t₃₉ ∈ g₄₀
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
p = 1
t₆₉ ∈ g₇₀
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
p = 1
t₁₈ ∈ g₁₉
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
p = 1
t₅₆ ∈ g₅₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
p = 1
t₃₁ ∈ g₃₂
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
p = 1
t₅₁ ∈ g₅₂
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
p = 1
t₂₆ ∈ g₂₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
p = 1
t₄₄ ∈ g₄₅
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
p = 1
t₄₆ ∈ g₄₇
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
p = 1/2
t₁₂ ∈ g₁₄
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
p = 1/2
t₁₃ ∈ g₁₄
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
p = 1/2
t₁₅ ∈ g₁₇
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
p = 1/2
t₁₆ ∈ g₁₇
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
p = 1/2
t₇₁ ∈ g₇₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
p = 1/2
t₇₂ ∈ g₇₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
p = 1/2
t₂₃ ∈ g₂₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
p = 1/2
t₂₀ ∈ g₂₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
p = 1/2
t₂₁ ∈ g₂₂
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
p = 1/2
t₂₄ ∈ g₂₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
p = 1/2
t₂₈ ∈ g₃₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
p = 1/2
t₂₉ ∈ g₃₀
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
p = 1/2
t₃₇ ∈ g₃₈
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
p = 1/2
t₃₆ ∈ g₃₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
p = 1/2
t₃₃ ∈ g₃₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
p = 1/2
t₃₄ ∈ g₃₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
p = 1/2
t₄₂ ∈ g₄₃
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
p = 1/2
t₄₁ ∈ g₄₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
p = 1/2
t₄₈ ∈ g₅₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
p = 1/2
t₄₉ ∈ g₅₀
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
p = 1/2
t₅₃ ∈ g₅₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
p = 1/2
t₅₄ ∈ g₅₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
p = 1/2
t₅₈ ∈ g₆₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
p = 1/2
t₅₉ ∈ g₆₀
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
p = 1/2
t₆₃ ∈ g₆₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
p = 1/2
t₆₇ ∈ g₆₈
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
p = 1/2
t₆₄ ∈ g₆₅
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
p = 1/2
t₆₆ ∈ g₆₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v5)
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v5)
Use classical time bound for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v5)
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v6)
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v6)
Use classical time bound for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v6)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v10)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v10)
Use classical time bound for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v10)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v6)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v6)
Use classical time bound for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v6)
Plrf for transition g₄₇:l1_v9(X₀,X₁) → t₄₆:l2_v6(X₀,X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀:
new bound:
16⋅X₁+1908 {O(n)}
PLRF:
• l1_v10: X₀
• l1_v5: X₀
• l1_v6: X₀-1
• l1_v8: X₀
• l1_v9: 1+X₀
• l2_v4: X₀
• l2_v5: X₀
• l2_v6: X₀
• l2_v7: X₀-1
Show Graph
G
l0
l0
l1
l1
l0->l1
p = 1
t₁ ∈ g₀
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
p = 1
t₁₀ ∈ g₁₁
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
p = 1
t₆₁ ∈ g₆₂
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
p = 1
t₃₉ ∈ g₄₀
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
p = 1
t₆₉ ∈ g₇₀
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
p = 1
t₁₈ ∈ g₁₉
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
p = 1
t₅₆ ∈ g₅₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
p = 1
t₃₁ ∈ g₃₂
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
p = 1
t₅₁ ∈ g₅₂
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
p = 1
t₂₆ ∈ g₂₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
p = 1
t₄₄ ∈ g₄₅
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
p = 1
t₄₆ ∈ g₄₇
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
p = 1/2
t₁₂ ∈ g₁₄
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
p = 1/2
t₁₃ ∈ g₁₄
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
p = 1/2
t₁₅ ∈ g₁₇
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
p = 1/2
t₁₆ ∈ g₁₇
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
p = 1/2
t₇₁ ∈ g₇₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
p = 1/2
t₇₂ ∈ g₇₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
p = 1/2
t₂₃ ∈ g₂₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
p = 1/2
t₂₀ ∈ g₂₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
p = 1/2
t₂₁ ∈ g₂₂
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
p = 1/2
t₂₄ ∈ g₂₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
p = 1/2
t₂₈ ∈ g₃₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
p = 1/2
t₂₉ ∈ g₃₀
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
p = 1/2
t₃₇ ∈ g₃₈
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
p = 1/2
t₃₆ ∈ g₃₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
p = 1/2
t₃₃ ∈ g₃₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
p = 1/2
t₃₄ ∈ g₃₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
p = 1/2
t₄₂ ∈ g₄₃
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
p = 1/2
t₄₁ ∈ g₄₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
p = 1/2
t₄₈ ∈ g₅₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
p = 1/2
t₄₉ ∈ g₅₀
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
p = 1/2
t₅₃ ∈ g₅₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
p = 1/2
t₅₄ ∈ g₅₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
p = 1/2
t₅₈ ∈ g₆₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
p = 1/2
t₅₉ ∈ g₆₀
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
p = 1/2
t₆₃ ∈ g₆₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
p = 1/2
t₆₇ ∈ g₆₈
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
p = 1/2
t₆₄ ∈ g₆₅
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
p = 1/2
t₆₆ ∈ g₆₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v5)
Use classical time bound for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v5)
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v6)
Use classical time bound for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v6)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v10)
Use classical time bound for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v10)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v6)
Use classical time bound for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v6)
Plrf for transition g₅₀:l2_v6(X₀,X₁) → [1/2]:t₄₈:l1_v8(X₀-1,X₁-10) :+: [1/2]:t₄₉:l1_v9(X₀,X₁) :|: 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ 1 ≤ X₀:
new bound:
32⋅X₁+3816 {O(n)}
PLRF:
• l1_v10: 2⋅X₀
• l1_v5: 2⋅X₀
• l1_v6: 2⋅X₀-2
• l1_v8: 2⋅X₀
• l1_v9: 2⋅X₀
• l2_v4: 2⋅X₀
• l2_v5: 2⋅X₀
• l2_v6: 2⋅X₀
• l2_v7: 2⋅X₀-2
Show Graph
G
l0
l0
l1
l1
l0->l1
p = 1
t₁ ∈ g₀
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
p = 1
t₁₀ ∈ g₁₁
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
p = 1
t₆₁ ∈ g₆₂
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
p = 1
t₃₉ ∈ g₄₀
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
p = 1
t₆₉ ∈ g₇₀
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
p = 1
t₁₈ ∈ g₁₉
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
p = 1
t₅₆ ∈ g₅₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
p = 1
t₃₁ ∈ g₃₂
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
p = 1
t₅₁ ∈ g₅₂
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
p = 1
t₂₆ ∈ g₂₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
p = 1
t₄₄ ∈ g₄₅
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
p = 1
t₄₆ ∈ g₄₇
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
p = 1/2
t₁₂ ∈ g₁₄
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
p = 1/2
t₁₃ ∈ g₁₄
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
p = 1/2
t₁₅ ∈ g₁₇
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
p = 1/2
t₁₆ ∈ g₁₇
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
p = 1/2
t₇₁ ∈ g₇₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
p = 1/2
t₇₂ ∈ g₇₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
p = 1/2
t₂₃ ∈ g₂₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
p = 1/2
t₂₀ ∈ g₂₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
p = 1/2
t₂₁ ∈ g₂₂
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
p = 1/2
t₂₄ ∈ g₂₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
p = 1/2
t₂₈ ∈ g₃₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
p = 1/2
t₂₉ ∈ g₃₀
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
p = 1/2
t₃₇ ∈ g₃₈
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
p = 1/2
t₃₆ ∈ g₃₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
p = 1/2
t₃₃ ∈ g₃₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
p = 1/2
t₃₄ ∈ g₃₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
p = 1/2
t₄₂ ∈ g₄₃
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
p = 1/2
t₄₁ ∈ g₄₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
p = 1/2
t₄₈ ∈ g₅₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
p = 1/2
t₄₉ ∈ g₅₀
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
p = 1/2
t₅₃ ∈ g₅₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
p = 1/2
t₅₄ ∈ g₅₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
p = 1/2
t₅₈ ∈ g₆₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
p = 1/2
t₅₉ ∈ g₆₀
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
p = 1/2
t₆₃ ∈ g₆₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
p = 1/2
t₆₇ ∈ g₆₈
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
p = 1/2
t₆₄ ∈ g₆₅
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
p = 1/2
t₆₆ ∈ g₆₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v5)
Use classical time bound for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v5)
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v6)
Use classical time bound for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v6)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v10)
Use classical time bound for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v10)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v6)
Use classical time bound for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v6)
Plrf for transition g₅₂:l1_v6(X₀,X₁) → t₅₁:l2_v7(X₀,X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀:
new bound:
320⋅X₁+40624 {O(n)}
PLRF:
• l1_v10: 202+20⋅X₀-2⋅X₁
• l1_v5: 202+20⋅X₀-2⋅X₁
• l1_v6: 204+20⋅X₀-2⋅X₁
• l1_v8: 202+20⋅X₀-2⋅X₁
• l1_v9: 202+20⋅X₀-2⋅X₁
• l2_v4: 202+20⋅X₀-2⋅X₁
• l2_v5: 202+20⋅X₀-2⋅X₁
• l2_v6: 202+20⋅X₀-2⋅X₁
• l2_v7: 203+20⋅X₀-2⋅X₁
Show Graph
G
l0
l0
l1
l1
l0->l1
p = 1
t₁ ∈ g₀
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
p = 1
t₁₀ ∈ g₁₁
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
p = 1
t₆₁ ∈ g₆₂
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
p = 1
t₃₉ ∈ g₄₀
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
p = 1
t₆₉ ∈ g₇₀
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
p = 1
t₁₈ ∈ g₁₉
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
p = 1
t₅₆ ∈ g₅₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
p = 1
t₃₁ ∈ g₃₂
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
p = 1
t₅₁ ∈ g₅₂
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
p = 1
t₂₆ ∈ g₂₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
p = 1
t₄₄ ∈ g₄₅
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
p = 1
t₄₆ ∈ g₄₇
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
p = 1/2
t₁₂ ∈ g₁₄
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
p = 1/2
t₁₃ ∈ g₁₄
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
p = 1/2
t₁₅ ∈ g₁₇
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
p = 1/2
t₁₆ ∈ g₁₇
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
p = 1/2
t₇₁ ∈ g₇₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
p = 1/2
t₇₂ ∈ g₇₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
p = 1/2
t₂₃ ∈ g₂₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
p = 1/2
t₂₀ ∈ g₂₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
p = 1/2
t₂₁ ∈ g₂₂
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
p = 1/2
t₂₄ ∈ g₂₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
p = 1/2
t₂₈ ∈ g₃₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
p = 1/2
t₂₉ ∈ g₃₀
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
p = 1/2
t₃₇ ∈ g₃₈
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
p = 1/2
t₃₆ ∈ g₃₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
p = 1/2
t₃₃ ∈ g₃₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
p = 1/2
t₃₄ ∈ g₃₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
p = 1/2
t₄₂ ∈ g₄₃
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
p = 1/2
t₄₁ ∈ g₄₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
p = 1/2
t₄₈ ∈ g₅₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
p = 1/2
t₄₉ ∈ g₅₀
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
p = 1/2
t₅₃ ∈ g₅₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
p = 1/2
t₅₄ ∈ g₅₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
p = 1/2
t₅₈ ∈ g₆₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
p = 1/2
t₅₉ ∈ g₆₀
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
p = 1/2
t₆₃ ∈ g₆₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
p = 1/2
t₆₇ ∈ g₆₈
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
p = 1/2
t₆₄ ∈ g₆₅
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
p = 1/2
t₆₆ ∈ g₆₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v5)
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v5)
Use classical time bound for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v5)
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v6)
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v6)
Use classical time bound for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v6)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v10)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v10)
Use classical time bound for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v10)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v6)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v6)
Use classical time bound for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v6)
Plrf for transition g₅₅:l2_v7(X₀,X₁) → [1/2]:t₅₃:l1_v5(X₀-1,X₁-10) :+: [1/2]:t₅₄:l1_v6(X₀,X₁) :|: 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀:
new bound:
320⋅X₁+40624 {O(n)}
PLRF:
• l1_v10: 202+20⋅X₀-2⋅X₁
• l1_v5: 202+20⋅X₀-2⋅X₁
• l1_v6: 204+20⋅X₀-2⋅X₁
• l1_v8: 202+20⋅X₀-2⋅X₁
• l1_v9: 202+20⋅X₀-2⋅X₁
• l2_v4: 202+20⋅X₀-2⋅X₁
• l2_v5: 202+20⋅X₀-2⋅X₁
• l2_v6: 202+20⋅X₀-2⋅X₁
• l2_v7: 204+20⋅X₀-2⋅X₁
Show Graph
G
l0
l0
l1
l1
l0->l1
p = 1
t₁ ∈ g₀
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
p = 1
t₁₀ ∈ g₁₁
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
p = 1
t₆₁ ∈ g₆₂
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
p = 1
t₃₉ ∈ g₄₀
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
p = 1
t₆₉ ∈ g₇₀
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
p = 1
t₁₈ ∈ g₁₉
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
p = 1
t₅₆ ∈ g₅₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
p = 1
t₃₁ ∈ g₃₂
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
p = 1
t₅₁ ∈ g₅₂
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
p = 1
t₂₆ ∈ g₂₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
p = 1
t₄₄ ∈ g₄₅
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
p = 1
t₄₆ ∈ g₄₇
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
p = 1/2
t₁₂ ∈ g₁₄
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
p = 1/2
t₁₃ ∈ g₁₄
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
p = 1/2
t₁₅ ∈ g₁₇
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
p = 1/2
t₁₆ ∈ g₁₇
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
p = 1/2
t₇₁ ∈ g₇₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
p = 1/2
t₇₂ ∈ g₇₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
p = 1/2
t₂₃ ∈ g₂₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
p = 1/2
t₂₀ ∈ g₂₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
p = 1/2
t₂₁ ∈ g₂₂
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
p = 1/2
t₂₄ ∈ g₂₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
p = 1/2
t₂₈ ∈ g₃₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
p = 1/2
t₂₉ ∈ g₃₀
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
p = 1/2
t₃₇ ∈ g₃₈
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
p = 1/2
t₃₆ ∈ g₃₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
p = 1/2
t₃₃ ∈ g₃₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
p = 1/2
t₃₄ ∈ g₃₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
p = 1/2
t₄₂ ∈ g₄₃
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
p = 1/2
t₄₁ ∈ g₄₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
p = 1/2
t₄₈ ∈ g₅₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
p = 1/2
t₄₉ ∈ g₅₀
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
p = 1/2
t₅₃ ∈ g₅₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
p = 1/2
t₅₄ ∈ g₅₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
p = 1/2
t₅₈ ∈ g₆₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
p = 1/2
t₅₉ ∈ g₆₀
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
p = 1/2
t₆₃ ∈ g₆₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
p = 1/2
t₆₇ ∈ g₆₈
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
p = 1/2
t₆₄ ∈ g₆₅
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
p = 1/2
t₆₆ ∈ g₆₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v5)
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v5)
Use classical time bound for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v5)
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v6)
Use expected size bounds for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v6)
Use classical time bound for entry point (g₂₂:l2_v2→[t₂₀:1/2:l1_v5; t₂₁:1/2:l1_v6],l1_v6)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v10)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v10)
Use classical time bound for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v10)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v6)
Use expected size bounds for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v6)
Use classical time bound for entry point (g₆₈:l2_v9→[t₆₆:1/2:l1_v6; t₆₇:1/2:l1_v10],l1_v6)
CFR: Improvement to new bound with the following program:
method: PartialEvaluationProbabilistic new bound:
O(n)
cfr-program:
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l1_v1, l1_v10, l1_v2, l1_v3, l1_v4, l1_v5, l1_v6, l1_v7, l1_v8, l1_v9, l2_v1, l2_v10, l2_v2, l2_v3, l2_v4, l2_v5, l2_v6, l2_v7, l2_v8, l2_v9
Transitions:
g₀:l0(X₀,X₁) → t₁:l1(1,X₁) :|:
g₁₁:l1(X₀,X₁) → t₁₀:l2_v1(X₀,X₁) :|: 1 ≤ X₀ ∧ 0 ≤ X₀
g₁₄:l2_v1(X₀,X₁) → [1/2]:t₁₂:l1_v1(X₀-1,X₁-10) :+: [1/2]:t₁₃:l1_v2(X₀,X₁) :|: 101 ≤ X₁ ∧ 1 ≤ X₀
g₁₇:l2_v1(X₀,X₁) → [1/2]:t₁₅:l1_v3(1+X₀,11+X₁) :+: [1/2]:t₁₆:l1_v4(X₀,X₁) :|: X₁ ≤ 100 ∧ 1 ≤ X₀
g₁₉:l1_v3(X₀,X₁) → t₁₈:l2_v2(X₀,X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀
g₂₂:l2_v2(X₀,X₁) → [1/2]:t₂₀:l1_v5(X₀-1,X₁-10) :+: [1/2]:t₂₁:l1_v6(X₀,X₁) :|: 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀
g₂₅:l2_v2(X₀,X₁) → [1/2]:t₂₃:l1_v3(1+X₀,11+X₁) :+: [1/2]:t₂₄:l1_v7(X₀,X₁) :|: X₁ ≤ 100 ∧ X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀
g₂₇:l1_v7(X₀,X₁) → t₂₆:l2_v3(X₀,X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀
g₃₀:l2_v3(X₀,X₁) → [1/2]:t₂₈:l1_v3(1+X₀,11+X₁) :+: [1/2]:t₂₉:l1_v7(X₀,X₁) :|: X₁ ≤ 100 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀
g₃₂:l1_v5(X₀,X₁) → t₃₁:l2_v4(X₀,X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀
g₃₅:l2_v4(X₀,X₁) → [1/2]:t₃₃:l1_v8(X₀-1,X₁-10) :+: [1/2]:t₃₄:l1_v9(X₀,X₁) :|: 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁
g₃₈:l2_v4(X₀,X₁) → [1/2]:t₃₆:l1_v6(1+X₀,11+X₁) :+: [1/2]:t₃₇:l1_v10(X₀,X₁) :|: X₁ ≤ 100 ∧ X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁
g₄₀:l1_v10(X₀,X₁) → t₃₉:l2_v5(X₀,X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀
g₄₃:l2_v5(X₀,X₁) → [1/2]:t₄₁:l1_v6(1+X₀,11+X₁) :+: [1/2]:t₄₂:l1_v10(X₀,X₁) :|: X₁ ≤ 100 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁
g₄₅:l1_v8(X₀,X₁) → t₄₄:l2_v4(X₀,X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀
g₄₇:l1_v9(X₀,X₁) → t₄₆:l2_v6(X₀,X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀
g₅₀:l2_v6(X₀,X₁) → [1/2]:t₄₈:l1_v8(X₀-1,X₁-10) :+: [1/2]:t₄₉:l1_v9(X₀,X₁) :|: 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ 1 ≤ X₀
g₅₂:l1_v6(X₀,X₁) → t₅₁:l2_v7(X₀,X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀
g₅₅:l2_v7(X₀,X₁) → [1/2]:t₅₃:l1_v5(X₀-1,X₁-10) :+: [1/2]:t₅₄:l1_v6(X₀,X₁) :|: 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀
g₅₇:l1_v4(X₀,X₁) → t₅₆:l2_v8(X₀,X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀
g₆₀:l2_v8(X₀,X₁) → [1/2]:t₅₈:l1_v3(1+X₀,11+X₁) :+: [1/2]:t₅₉:l1_v4(X₀,X₁) :|: X₁ ≤ 100 ∧ 1 ≤ X₀
g₆₂:l1_v1(X₀,X₁) → t₆₁:l2_v9(X₀,X₁) :|: 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 0 ≤ X₀
g₆₅:l2_v9(X₀,X₁) → [1/2]:t₆₃:l1_v1(X₀-1,X₁-10) :+: [1/2]:t₆₄:l1_v2(X₀,X₁) :|: 101 ≤ X₁ ∧ 1 ≤ X₀ ∧ 91 ≤ X₁
g₆₈:l2_v9(X₀,X₁) → [1/2]:t₆₆:l1_v6(1+X₀,11+X₁) :+: [1/2]:t₆₇:l1_v10(X₀,X₁) :|: X₁ ≤ 100 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁
g₇₀:l1_v2(X₀,X₁) → t₆₉:l2_v10(X₀,X₁) :|: 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀
g₇₃:l2_v10(X₀,X₁) → [1/2]:t₇₁:l1_v1(X₀-1,X₁-10) :+: [1/2]:t₇₂:l1_v2(X₀,X₁) :|: 101 ≤ X₁ ∧ 1 ≤ X₀
Show Graph
G
l0
l0
l1
l1
l0->l1
t₁ ∈ g₀
η (X₀) = 1
l2_v1
l2_v1
l1->l2_v1
t₁₀ ∈ g₁₁
τ = 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v1
l1_v1
l2_v9
l2_v9
l1_v1->l2_v9
t₆₁ ∈ g₆₂
τ = 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v10
l1_v10
l2_v5
l2_v5
l1_v10->l2_v5
t₃₉ ∈ g₄₀
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v2
l1_v2
l2_v10
l2_v10
l1_v2->l2_v10
t₆₉ ∈ g₇₀
τ = 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v3
l1_v3
l2_v2
l2_v2
l1_v3->l2_v2
t₁₈ ∈ g₁₉
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v4
l1_v4
l2_v8
l2_v8
l1_v4->l2_v8
t₅₆ ∈ g₅₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v5
l1_v5
l2_v4
l2_v4
l1_v5->l2_v4
t₃₁ ∈ g₃₂
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v6
l1_v6
l2_v7
l2_v7
l1_v6->l2_v7
t₅₁ ∈ g₅₂
τ = X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v7
l1_v7
l2_v3
l2_v3
l1_v7->l2_v3
t₂₆ ∈ g₂₇
τ = X₁ ≤ 111 ∧ X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v8
l1_v8
l1_v8->l2_v4
t₄₄ ∈ g₄₅
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l1_v9
l1_v9
l2_v6
l2_v6
l1_v9->l2_v6
t₄₆ ∈ g₄₇
τ = X₁ ≤ 111 ∧ 91 ≤ X₁ ∧ 101 ≤ X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₀
l2_v1->l1_v1
t₁₂ ∈ g₁₄
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v2
t₁₃ ∈ g₁₄
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v1->l1_v3
t₁₅ ∈ g₁₇
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v1->l1_v4
t₁₆ ∈ g₁₇
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v10->l1_v1
t₇₁ ∈ g₇₃
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v10->l1_v2
t₇₂ ∈ g₇₃
τ = 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v3
t₂₃ ∈ g₂₅
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v2->l1_v5
t₂₀ ∈ g₂₂
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v6
t₂₁ ∈ g₂₂
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v2->l1_v7
t₂₄ ∈ g₂₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v3
t₂₈ ∈ g₃₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v3->l1_v7
t₂₉ ∈ g₃₀
τ = 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 100
l2_v4->l1_v10
t₃₇ ∈ g₃₈
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v6
t₃₆ ∈ g₃₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v4->l1_v8
t₃₃ ∈ g₃₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v4->l1_v9
t₃₄ ∈ g₃₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v5->l1_v10
t₄₂ ∈ g₄₃
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v5->l1_v6
t₄₁ ∈ g₄₃
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v6->l1_v8
t₄₈ ∈ g₅₀
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v6->l1_v9
t₄₉ ∈ g₅₀
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v5
t₅₃ ∈ g₅₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v7->l1_v6
t₅₄ ∈ g₅₅
τ = X₁ ≤ 111 ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ 101 ≤ X₁
l2_v8->l1_v3
t₅₈ ∈ g₆₀
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v8->l1_v4
t₅₉ ∈ g₆₀
τ = 1 ≤ X₀ ∧ X₁ ≤ 100
l2_v9->l1_v1
t₆₃ ∈ g₆₅
η (X₀) = X₀-1
η (X₁) = X₁-10
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v10
t₆₇ ∈ g₆₈
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
l2_v9->l1_v2
t₆₄ ∈ g₆₅
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ 101 ≤ X₁
l2_v9->l1_v6
t₆₆ ∈ g₆₈
η (X₀) = 1+X₀
η (X₁) = 11+X₁
τ = 1 ≤ X₀ ∧ 91 ≤ X₁ ∧ X₁ ≤ 100
Results of Probabilistic Analysis
All Bounds
Timebounds
Overall timebound:145131/55⋅X₁+18164606/55 {O(n)}
g₀: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₄: 2 {O(1)}
g₁₇: 2 {O(1)}
g₁₉: 2⋅X₁+246 {O(n)}
g₂₂: 2 {O(1)}
g₂₅: 4⋅X₁+492 {O(n)}
g₂₇: 3/11⋅X₁+266/11 {O(n)}
g₃₀: 3/11⋅X₁+266/11 {O(n)}
g₃₂: 80⋅X₁+10360 {O(n)}
g₃₅: 16⋅X₁+1910 {O(n)}
g₃₈: 1520⋅X₁+188607 {O(n)}
g₄₀: 160⋅X₁+20311 {O(n)}
g₄₃: 160⋅X₁+20311 {O(n)}
g₄₅: 8⋅X₁+955 {O(n)}
g₄₇: 16⋅X₁+1908 {O(n)}
g₅₀: 32⋅X₁+3816 {O(n)}
g₅₂: 320⋅X₁+40624 {O(n)}
g₅₅: 320⋅X₁+40624 {O(n)}
g₅₇: 4 {O(1)}
g₆₀: 6 {O(1)}
g₆₂: 3 {O(1)}
g₆₅: 5 {O(1)}
g₆₈: 2 {O(1)}
g₇₀: 1/5⋅X₁+86/5 {O(n)}
g₇₃: 8 {O(1)}
Costbounds
Overall costbound: 258006/55⋅X₁+32234221/55 {O(n)}
g₀: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₄: 4 {O(1)}
g₁₇: 4 {O(1)}
g₁₉: 2⋅X₁+246 {O(n)}
g₂₂: 4 {O(1)}
g₂₅: 8⋅X₁+984 {O(n)}
g₂₇: 3/11⋅X₁+266/11 {O(n)}
g₃₀: 6/11⋅X₁+532/11 {O(n)}
g₃₂: 80⋅X₁+10360 {O(n)}
g₃₅: 32⋅X₁+3820 {O(n)}
g₃₈: 3040⋅X₁+377214 {O(n)}
g₄₀: 160⋅X₁+20311 {O(n)}
g₄₃: 320⋅X₁+40622 {O(n)}
g₄₅: 8⋅X₁+955 {O(n)}
g₄₇: 16⋅X₁+1908 {O(n)}
g₅₀: 64⋅X₁+7632 {O(n)}
g₅₂: 320⋅X₁+40624 {O(n)}
g₅₅: 640⋅X₁+81248 {O(n)}
g₅₇: 4 {O(1)}
g₆₀: 12 {O(1)}
g₆₂: 3 {O(1)}
g₆₅: 10 {O(1)}
g₆₈: 4 {O(1)}
g₇₀: 1/5⋅X₁+86/5 {O(n)}
g₇₃: 16 {O(1)}
Sizebounds
(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₁₁,l2_v1), X₀: 1 {O(1)}
(g₁₁,l2_v1), X₁: X₁ {O(n)}
(g₁₄,l1_v1), X₀: 2 {O(1)}
(g₁₄,l1_v1), X₁: X₁ {O(n)}
(g₁₄,l1_v2), X₀: 2 {O(1)}
(g₁₄,l1_v2), X₁: X₁ {O(n)}
(g₁₇,l1_v3), X₀: 3 {O(1)}
(g₁₇,l1_v3), X₁: 2⋅X₁+11 {O(n)}
(g₁₇,l1_v4), X₀: 3 {O(1)}
(g₁₇,l1_v4), X₁: X₁ {O(n)}
(g₁₉,l2_v2), X₀: 4⋅X₁+474 {O(n)}
(g₁₉,l2_v2), X₁: 46⋅X₁+5192 {O(n)}
(g₂₂,l1_v5), X₀: 8⋅X₁+948 {O(n)}
(g₂₂,l1_v5), X₁: 212 {O(1)}
(g₂₂,l1_v6), X₀: 8⋅X₁+948 {O(n)}
(g₂₂,l1_v6), X₁: 212 {O(1)}
(g₂₅,l1_v3), X₀: 8⋅X₁+948 {O(n)}
(g₂₅,l1_v3), X₁: 92⋅X₁+10384 {O(n)}
(g₂₅,l1_v7), X₀: 8⋅X₁+948 {O(n)}
(g₂₅,l1_v7), X₁: 92⋅X₁+10384 {O(n)}
(g₂₇,l2_v3), X₀: 4⋅X₁+474 {O(n)}
(g₂₇,l2_v3), X₁: 46⋅X₁+5192 {O(n)}
(g₃₀,l1_v3), X₀: 8⋅X₁+948 {O(n)}
(g₃₀,l1_v3), X₁: 92⋅X₁+10384 {O(n)}
(g₃₀,l1_v7), X₀: 8⋅X₁+948 {O(n)}
(g₃₀,l1_v7), X₁: 92⋅X₁+10384 {O(n)}
(g₃₂,l2_v4), X₀: 856⋅X₁+106365 {O(n)}
(g₃₂,l2_v4), X₁: 111 {O(1)}
(g₃₅,l1_v8), X₀: 856⋅X₁+106365 {O(n)}
(g₃₅,l1_v8), X₁: 212 {O(1)}
(g₃₅,l1_v9), X₀: 856⋅X₁+106365 {O(n)}
(g₃₅,l1_v9), X₁: 212 {O(1)}
(g₃₈,l1_v10), X₀: 856⋅X₁+106365 {O(n)}
(g₃₈,l1_v10), X₁: 211 {O(1)}
(g₃₈,l1_v6), X₀: 856⋅X₁+106365 {O(n)}
(g₃₈,l1_v6), X₁: 211 {O(1)}
(g₄₀,l2_v5), X₀: 856⋅X₁+106365 {O(n)}
(g₄₀,l2_v5), X₁: 100 {O(1)}
(g₄₃,l1_v10), X₀: 856⋅X₁+106365 {O(n)}
(g₄₃,l1_v10), X₁: 211 {O(1)}
(g₄₃,l1_v6), X₀: 856⋅X₁+106365 {O(n)}
(g₄₃,l1_v6), X₁: 211 {O(1)}
(g₄₅,l2_v4), X₀: 856⋅X₁+106365 {O(n)}
(g₄₅,l2_v4), X₁: 111 {O(1)}
(g₄₇,l2_v6), X₀: 856⋅X₁+106365 {O(n)}
(g₄₇,l2_v6), X₁: 111 {O(1)}
(g₅₀,l1_v8), X₀: 856⋅X₁+106365 {O(n)}
(g₅₀,l1_v8), X₁: 212 {O(1)}
(g₅₀,l1_v9), X₀: 856⋅X₁+106365 {O(n)}
(g₅₀,l1_v9), X₁: 212 {O(1)}
(g₅₂,l2_v7), X₀: 856⋅X₁+106365 {O(n)}
(g₅₂,l2_v7), X₁: 111 {O(1)}
(g₅₅,l1_v5), X₀: 856⋅X₁+106365 {O(n)}
(g₅₅,l1_v5), X₁: 212 {O(1)}
(g₅₅,l1_v6), X₀: 856⋅X₁+106365 {O(n)}
(g₅₅,l1_v6), X₁: 212 {O(1)}
(g₅₇,l2_v8), X₀: 1 {O(1)}
(g₅₇,l2_v8), X₁: X₁ {O(n)}
(g₆₀,l1_v3), X₀: 3 {O(1)}
(g₆₀,l1_v3), X₁: X₁+33 {O(n)}
(g₆₀,l1_v4), X₀: 3 {O(1)}
(g₆₀,l1_v4), X₁: X₁ {O(n)}
(g₆₂,l2_v9), X₀: 2 {O(1)}
(g₆₂,l2_v9), X₁: 2⋅X₁ {O(n)}
(g₆₅,l1_v1), X₀: 4 {O(1)}
(g₆₅,l1_v1), X₁: 4⋅X₁ {O(n)}
(g₆₅,l1_v2), X₀: 4 {O(1)}
(g₆₅,l1_v2), X₁: 4⋅X₁ {O(n)}
(g₆₈,l1_v10), X₀: 5 {O(1)}
(g₆₈,l1_v10), X₁: 211 {O(1)}
(g₆₈,l1_v6), X₀: 5 {O(1)}
(g₆₈,l1_v6), X₁: 211 {O(1)}
(g₇₀,l2_v10), X₀: 2 {O(1)}
(g₇₀,l2_v10), X₁: 2⋅X₁ {O(n)}
(g₇₃,l1_v1), X₀: 4 {O(1)}
(g₇₃,l1_v1), X₁: 4⋅X₁ {O(n)}
(g₇₃,l1_v2), X₀: 4 {O(1)}
(g₇₃,l1_v2), X₁: 4⋅X₁ {O(n)}