Preprocessing

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ for location l2

Probabilistic Analysis

Probabilistic Program after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
g₀:l0(X₀,X₁,X₂) → t₁:l1(X₀,X₁,X₂) :|:
g₂:l1(X₀,X₁,X₂) → t₃:l2(X₀,X₁,X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ X₂
g₄:l2(X₀,X₁,X₂) → [1/2]:t₅:l1(1+X₀,X₁,X₂) :+: [1/2]:t₆:l1(X₀,X₁,X₂) :|: X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₂
g₇:l2(X₀,X₁,X₂) → [1/2]:t₈:l1(X₀-1,X₁,X₂) :+: [1/2]:t₉:l1(X₀,X₁,X₂) :|: 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₂

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: 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}
g₇: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₇: 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)}
(g₂,l2), X₂: X₂ {O(n)}
(g₄,l1), X₁: 2⋅X₁ {O(n)}
(g₄,l1), X₂: 2⋅X₂ {O(n)}
(g₇,l1), X₁: 2⋅X₁ {O(n)}
(g₇,l1), X₂: 2⋅X₂ {O(n)}

Run probabilistic analysis on SCC: [l1; l2]

Results of Probabilistic Analysis

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: 1 {O(1)}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₇: 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)}
(g₂,l2), X₂: X₂ {O(n)}
(g₄,l1), X₁: X₁ {O(n)}
(g₄,l1), X₂: X₂ {O(n)}
(g₇,l1), X₁: X₁ {O(n)}
(g₇,l1), X₂: X₂ {O(n)}