Preprocessing
Found invariant 0 ≤ X₀ for location l1
Found invariant 1 ≤ X₀ for location l2
Probabilistic Analysis
Probabilistic Program after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
g₀:l0(X₀,X₁) → t₁:l1(1,X₁) :|:
g₂:l1(X₀,X₁) → t₃:l2(X₀,X₁) :|: 1 ≤ X₀ ∧ 0 ≤ X₀
g₄:l2(X₀,X₁) → [1/2]:t₅:l1(X₀-1,X₁-10) :+: [1/2]:t₆:l1(X₀,X₁) :|: 101 ≤ X₁ ∧ 1 ≤ X₀
g₇:l2(X₀,X₁) → [1/2]:t₈:l1(1+X₀,11+X₁) :+: [1/2]:t₉:l1(X₀,X₁) :|: X₁ ≤ 100 ∧ 1 ≤ X₀
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}
g₇: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₇: 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; l2]
MPRF for transition t₈: l2(X₀,X₁) → l1(1+X₀,11+X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 100 of depth 1:
new bound:
X₁+101 {O(n)}
MPRF:
• l1: [91+10⋅X₀-X₁]
• l2: [91+10⋅X₀-X₁]
MPRF for transition t₅: l2(X₀,X₁) → l1(X₀-1,X₁-10) :|: 1 ≤ X₀ ∧ 101 ≤ X₁ of depth 1:
new bound:
X₁⋅X₁+203⋅X₁+10303 {O(n^2)}
MPRF:
• l1: [X₀]
• l2: [X₀]
Classical Approximation after Lifting Classical Results
All Bounds
Timebounds
Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₇: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₇: inf {Infinity}
Sizebounds
(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₂,l2), X₀: X₁+102 {O(n)}
(g₂,l2), X₁: 12⋅X₁+1111 {O(n)}
(g₄,l1), X₀: 2⋅X₁+204 {O(n)}
(g₄,l1), X₁: 24⋅X₁+2222 {O(n)}
(g₇,l1), X₀: 2⋅X₁+204 {O(n)}
(g₇,l1), X₁: 24⋅X₁+2222 {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}
g₇: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
g₄: inf {Infinity}
g₇: inf {Infinity}
Sizebounds
(g₀,l1), X₀: 1 {O(1)}
(g₀,l1), X₁: X₁ {O(n)}
(g₂,l2), X₀: X₁+102 {O(n)}
(g₂,l2), X₁: 12⋅X₁+1111 {O(n)}
(g₄,l1), X₀: 2⋅X₁+204 {O(n)}
(g₄,l1), X₁: 24⋅X₁+2222 {O(n)}
(g₇,l1), X₀: 2⋅X₁+204 {O(n)}
(g₇,l1), X₁: 24⋅X₁+2222 {O(n)}