Preprocessing
Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2
Probabilistic Analysis
Probabilistic Program after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars: T
Locations: l0, l1, l2
Transitions:
g₀:l0(X₀,X₁) → t₁:l1(X₀,X₁) :|:
g₂:l1(X₀,X₁) → t₃:l2(X₀,X₁) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁
g₄:l2(X₀,X₁) → [1/4]:t₅:l1(T,X₀-1) :+: [1/4]:t₆:l1(X₀-1,T) :+: [1/4]:t₇:l1(T,X₀) :+: [1/4]:t₈:l1(X₀,T) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁
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}
Costbounds
Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
g₄: inf {Infinity}
Sizebounds
(g₀,l1), X₀: X₀ {O(n)}
(g₀,l1), X₁: X₁ {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}
Costbounds
Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
g₄: inf {Infinity}
Sizebounds
(g₀,l1), X₀: X₀ {O(n)}
(g₀,l1), X₁: X₁ {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}
Costbounds
Overall costbound: inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
g₄: inf {Infinity}
Sizebounds
(g₀,l1), X₀: X₀ {O(n)}
(g₀,l1), X₁: X₁ {O(n)}