Preprocessing
Found invariant 1 ≤ X₀ for location h
Probabilistic Analysis
Probabilistic Program after Preprocessing
Start: f
Program_Vars: X₀
Temp_Vars: Y
Locations: f, g, h
Transitions:
g₀:f(X₀) → t₁:g(X₀) :|: 1 ≤ X₀
g₂:g(X₀) → [1/2]:t₃:g(X₀) :+: [1/4]:t₄:h(X₀) :+: [1/4]:t₅:h(1+X₀) :|: 1 ≤ X₀
g₆:h(X₀) → t₇:g(X₀-Y) :|: 1 ≤ Y ∧ 1 ≤ X₀
Run classical analysis on SCC: [f]
Classical Approximation after Lifting Classical Results
All Bounds
Timebounds
Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
g₆: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
g₆: inf {Infinity}
Sizebounds
(g₀,g), X₀: X₀ {O(n)}
Run probabilistic analysis on SCC: [f]
Run classical analysis on SCC: [g; h]
MPRF for transition t₄: g(X₀) → h(X₀) :|: 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
• g: [X₀]
• h: [X₀-1]
Classical Approximation after Lifting Classical Results
All Bounds
Timebounds
Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
g₆: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
g₆: inf {Infinity}
Sizebounds
(g₀,g), X₀: X₀ {O(n)}
Run probabilistic analysis on SCC: [g; h]
Results of Probabilistic Analysis
All Bounds
Timebounds
Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
g₆: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
g₆: inf {Infinity}
Sizebounds
(g₀,g), X₀: X₀ {O(n)}