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)}