Preprocessing

Found invariant 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l2

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l3

Probabilistic Analysis

Probabilistic Program after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
g₀:l0(X₀,X₁,X₂) → t₁:l1(X₀,X₁,X₂) :|:
g₂:l1(X₀,X₁,X₂) → t₃:l2(X₀,X₁,X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂
g₄:l2(X₀,X₁,X₂) → t₅:l1(3⋅X₀,X₁,2⋅X₂) :|: X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂
g₆:l2(X₀,X₁,X₂) → [1/2]:t₇:l1(X₀-1,X₁,1+X₂) :+: [1/2]:t₈:l1(X₀,X₁,X₂) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂
g₉:l1(X₀,X₁,X₂) → t₁₀:l3(X₀,X₁,X₂) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
g₁₁:l3(X₀,X₁,X₂) → t₁₂:l3(X₀,X₁,X₂-1) :|: 1 ≤ X₂ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0

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}
g₆: inf {Infinity}
g₉: 1 {O(1)}
g₁₁: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₆: inf {Infinity}
g₉: inf {Infinity}
g₁₁: inf {Infinity}

Sizebounds

(g₀,l1), X₀: X₀ {O(n)}
(g₀,l1), X₁: X₁ {O(n)}
(g₀,l1), X₂: X₂ {O(n)}

Run probabilistic analysis on SCC: [l0]

Run classical analysis on SCC: [l1; l2]

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₆: inf {Infinity}
g₉: 1 {O(1)}
g₁₁: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₆: inf {Infinity}
g₉: inf {Infinity}
g₁₁: inf {Infinity}

Sizebounds

(g₀,l1), X₀: X₀ {O(n)}
(g₀,l1), X₁: X₁ {O(n)}
(g₀,l1), X₂: X₂ {O(n)}
(g₂,l2), X₁: X₁ {O(n)}
(g₄,l1), X₁: X₁ {O(n)}
(g₆,l1), X₁: 2⋅X₁ {O(n)}
(g₉,l3), X₀: 0 {O(1)}
(g₉,l3), X₁: 2⋅X₁ {O(n)}

Run probabilistic analysis on SCC: [l1; l2]

Run classical analysis on SCC: [l3]

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₆: inf {Infinity}
g₉: 1 {O(1)}
g₁₁: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₆: inf {Infinity}
g₉: inf {Infinity}
g₁₁: inf {Infinity}

Sizebounds

(g₀,l1), X₀: X₀ {O(n)}
(g₀,l1), X₁: X₁ {O(n)}
(g₀,l1), X₂: X₂ {O(n)}
(g₂,l2), X₁: X₁ {O(n)}
(g₄,l1), X₁: X₁ {O(n)}
(g₆,l1), X₁: X₁ {O(n)}
(g₉,l3), X₀: 0 {O(1)}
(g₉,l3), X₁: 2⋅X₁ {O(n)}
(g₁₁,l3), X₀: 0 {O(1)}
(g₁₁,l3), X₁: 2⋅X₁ {O(n)}

Run probabilistic analysis on SCC: [l3]

Results of Probabilistic Analysis

All Bounds

Timebounds

Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₆: inf {Infinity}
g₉: 1 {O(1)}
g₁₁: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₆: inf {Infinity}
g₉: 1 {O(1)}
g₁₁: inf {Infinity}

Sizebounds

(g₀,l1), X₀: X₀ {O(n)}
(g₀,l1), X₁: X₁ {O(n)}
(g₀,l1), X₂: X₂ {O(n)}
(g₂,l2), X₁: X₁ {O(n)}
(g₄,l1), X₁: X₁ {O(n)}
(g₆,l1), X₁: X₁ {O(n)}
(g₉,l3), X₀: 0 {O(1)}
(g₉,l3), X₁: 2⋅X₁ {O(n)}
(g₁₁,l3), X₀: 0 {O(1)}
(g₁₁,l3), X₁: 2⋅X₁ {O(n)}