Preprocessing

Found invariant X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l1

Probabilistic Analysis

Probabilistic Program after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
g₀:l0(X₀,X₁) → t₁:l1(1,X₁) :|:
g₂:l1(X₀,X₁) → [1/2]:t₃:l1(-X₀,-X₁) :+: [1/2]:t₄:l1(-X₀,-X₀-X₁) :|: X₁ ≤ 10 ∧ 0 ≤ 1+X₀ ∧ X₀ ≤ 1

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}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: 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]

Classical Approximation after Lifting Classical Results

All Bounds
Timebounds

Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}

Sizebounds

(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₂,l1), X₀: 2 {O(1)}

Run probabilistic analysis on SCC: [l1]

Results of Probabilistic Analysis

All Bounds

Timebounds

Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}

Sizebounds

(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₂,l1), X₀: 2 {O(1)}