Preprocessing
Found invariant X₀ ≤ 7 for location h
Probabilistic Analysis
Probabilistic Program after Preprocessing
Start: f
Program_Vars: X₀
Temp_Vars:
Locations: f, g, h
Transitions:
g₁:f(X₀) -{0}> t₂:g(X₀) :|:
g₃:g(X₀) -{10}> t₄:g(X₀+UNIFORM(-8, -6)) :|: 8 ≤ X₀ ∧ 0 ≤ 1
g₅:g(X₀) → t₆:h(X₀) :|: X₀ ≤ 7
g₇:h(X₀) → t₈:h(X₀-1) :|: 1 ≤ X₀ ∧ X₀ ≤ 7
Run classical analysis on SCC: [f]
Classical Approximation after Lifting Classical Results
All Bounds
Timebounds
Overall timebound:inf {Infinity}
g₁: 1 {O(1)}
g₃: inf {Infinity}
g₅: 1 {O(1)}
g₇: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
g₁: inf {Infinity}
g₃: inf {Infinity}
g₅: inf {Infinity}
g₇: inf {Infinity}
Sizebounds
(g₁,g), X₀: X₀ {O(n)}
Run probabilistic analysis on SCC: [f]
Run classical analysis on SCC: [g]
MPRF for transition t₄: g(X₀) -{10}> g(Temp_Int₂₇) :|: 0 ≤ 1 ∧ X₀ ≤ 8+Temp_Int₁ ∧ X₀ ≤ 8+Temp_Int₂₇ ∧ 6+Temp_Int₂₇ ≤ X₀ ∧ 6+Temp_Int₁ ≤ X₀ ∧ 8 ≤ X₀ ∧ Temp_Int₂+X₀ ≤ Temp_Int₁ ∧ Temp_Int₁ ≤ Temp_Int₂+X₀ ∧ Temp_Int₁ ≤ Temp_Int₂+X₀ ∧ Temp_Int₂+X₀ ≤ Temp_Int₁ ∧ 0 ≤ 8+Temp_Int₂ ∧ 6+Temp_Int₂ ≤ 0 ∧ 8 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
• g: [X₀]
Classical Approximation after Lifting Classical Results
All Bounds
Timebounds
Overall timebound:inf {Infinity}
g₁: 1 {O(1)}
g₃: X₀ {O(n)}
g₅: 1 {O(1)}
g₇: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
g₁: inf {Infinity}
g₃: inf {Infinity}
g₅: inf {Infinity}
g₇: inf {Infinity}
Sizebounds
(g₁,g), X₀: X₀ {O(n)}
(g₃,g), X₀: X₀ {O(n)}
(g₅,h), X₀: 2⋅X₀ {O(n)}
Run probabilistic analysis on SCC: [g]
Run classical analysis on SCC: [h]
MPRF for transition t₈: h(X₀) → h(X₀-1) :|: X₀ ≤ 7 ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₀ {O(n)}
MPRF:
• h: [X₀]
Classical Approximation after Lifting Classical Results
All Bounds
Timebounds
Overall timebound:3⋅X₀+2 {O(n)}
g₁: 1 {O(1)}
g₃: X₀ {O(n)}
g₅: 1 {O(1)}
g₇: 2⋅X₀ {O(n)}
Costbounds
Overall costbound: inf {Infinity}
g₁: inf {Infinity}
g₃: inf {Infinity}
g₅: inf {Infinity}
g₇: inf {Infinity}
Sizebounds
(g₁,g), X₀: X₀ {O(n)}
(g₃,g), X₀: X₀ {O(n)}
(g₅,h), X₀: 2⋅X₀ {O(n)}
(g₇,h), X₀: 6 {O(1)}
Run probabilistic analysis on SCC: [h]
Results of Probabilistic Analysis
All Bounds
Timebounds
Overall timebound:3⋅X₀+2 {O(n)}
g₁: 1 {O(1)}
g₃: X₀ {O(n)}
g₅: 1 {O(1)}
g₇: 2⋅X₀ {O(n)}
Costbounds
Overall costbound: 12⋅X₀+1 {O(n)}
g₁: 0 {O(1)}
g₃: 10⋅X₀ {O(n)}
g₅: 1 {O(1)}
g₇: 2⋅X₀ {O(n)}
Sizebounds
(g₁,g), X₀: X₀ {O(n)}
(g₃,g), X₀: X₀ {O(n)}
(g₅,h), X₀: 2⋅X₀ {O(n)}
(g₇,h), X₀: 6 {O(1)}