Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location h
Found invariant X₂ ≤ 0 ∧ 0 ≤ X₂ for location g
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location i
Overall timebound:inf {Infinity}
g₁: 1 {O(1)}
g₃: inf {Infinity}
g₅: inf {Infinity}
g₇: inf {Infinity}
Overall costbound: inf {Infinity}
g₁: inf {Infinity}
g₃: inf {Infinity}
g₅: inf {Infinity}
g₇: inf {Infinity}
(g₁,g), X₀: X₀ {O(n)}
(g₁,g), X₁: X₁ {O(n)}
(g₁,g), X₂: 0 {O(1)}
Overall timebound:inf {Infinity}
g₁: 1 {O(1)}
g₃: inf {Infinity}
g₅: inf {Infinity}
g₇: inf {Infinity}
Overall costbound: inf {Infinity}
g₁: inf {Infinity}
g₃: inf {Infinity}
g₅: inf {Infinity}
g₇: inf {Infinity}
(g₁,g), X₀: X₀ {O(n)}
(g₁,g), X₁: X₁ {O(n)}
(g₁,g), X₂: 0 {O(1)}
(g₃,h), X₁: X₁ {O(n)}
(g₅,i), X₁: X₁ {O(n)}
(g₇,g), X₁: X₁ {O(n)}
(g₇,g), X₂: 0 {O(1)}
Overall timebound:inf {Infinity}
g₁: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₃: 1 {O(1)}
g₁₅: inf {Infinity}
g₁₇: inf {Infinity}
g₁₉: inf {Infinity}
Overall costbound: inf {Infinity}
g₁: inf {Infinity}
g₁₁: inf {Infinity}
g₁₃: inf {Infinity}
g₁₅: inf {Infinity}
g₁₇: inf {Infinity}
g₁₉: inf {Infinity}
(g₁,g), X₀: X₀ {O(n)}
(g₁,g), X₁: X₁ {O(n)}
(g₁,g), X₂: 0 {O(1)}
(g₁₁,h_v1), X₀: X₀ {O(n)}
(g₁₁,h_v1), X₁: X₁ {O(n)}
(g₁₁,h_v1), X₂: X₀ {O(n)}
Overall timebound:inf {Infinity}
g₁: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₃: 1 {O(1)}
g₁₅: inf {Infinity}
g₁₇: inf {Infinity}
g₁₉: inf {Infinity}
Overall costbound: inf {Infinity}
g₁: inf {Infinity}
g₁₁: inf {Infinity}
g₁₃: inf {Infinity}
g₁₅: inf {Infinity}
g₁₇: inf {Infinity}
g₁₉: inf {Infinity}
(g₁,g), X₀: X₀ {O(n)}
(g₁,g), X₁: X₁ {O(n)}
(g₁,g), X₂: 0 {O(1)}
(g₁₁,h_v1), X₀: X₀ {O(n)}
(g₁₁,h_v1), X₁: X₁ {O(n)}
(g₁₁,h_v1), X₂: X₀ {O(n)}
(g₁₃,i_v1), X₀: X₀ {O(n)}
(g₁₃,i_v1), X₁: X₁ {O(n)}
(g₁₃,i_v1), X₂: X₀+1 {O(n)}
Overall timebound:inf {Infinity}
g₁: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₃: 1 {O(1)}
g₁₅: inf {Infinity}
g₁₇: inf {Infinity}
g₁₉: inf {Infinity}
Overall costbound: inf {Infinity}
g₁: inf {Infinity}
g₁₁: inf {Infinity}
g₁₃: inf {Infinity}
g₁₅: inf {Infinity}
g₁₇: inf {Infinity}
g₁₉: inf {Infinity}
(g₁,g), X₀: X₀ {O(n)}
(g₁,g), X₁: X₁ {O(n)}
(g₁,g), X₂: 0 {O(1)}
(g₁₁,h_v1), X₀: X₀ {O(n)}
(g₁₁,h_v1), X₁: X₁ {O(n)}
(g₁₁,h_v1), X₂: X₀ {O(n)}
(g₁₃,i_v1), X₀: X₀ {O(n)}
(g₁₃,i_v1), X₁: X₁ {O(n)}
(g₁₃,i_v1), X₂: X₀+1 {O(n)}
(g₁₅,g_v1), X₁: X₁ {O(n)}
(g₁₅,g_v1), X₂: 0 {O(1)}
(g₁₇,h_v2), X₁: X₁ {O(n)}
(g₁₉,i_v1), X₁: X₁ {O(n)}
new bound:
2⋅X₀+2⋅X₁+3 {O(n)}
PLRF:
• g_v1: 2⋅X₁-2⋅X₀
• h_v2: 2⋅X₁-2⋅X₀
• i_v1: 1+2⋅X₁-2⋅X₂
new bound:
2⋅X₀+2⋅X₁+3 {O(n)}
PLRF:
• g_v1: 1+2⋅X₁-2⋅X₀
• h_v2: 2⋅X₁-2⋅X₂
• i_v1: 1+2⋅X₁-2⋅X₂
new bound:
2⋅X₀+2⋅X₁+2 {O(n)}
PLRF:
• g_v1: 2⋅X₁-2⋅X₀
• h_v2: 2⋅X₁-2⋅X₂
• i_v1: 2⋅X₁-2⋅X₂
method: PartialEvaluationProbabilistic new bound:
O(n)
cfr-program:
Start: f
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: f, g, g_v1, h_v1, h_v2, i_v1
Transitions:
g₁:f(X₀,X₁,X₂) -{0}> t₂:g(X₀,X₁,0) :|:
g₁₁:g(X₀,X₁,X₂) -{0}> t₁₀:h_v1(X₀,X₁,X₀) :|: 0 ≤ X₂ ∧ X₂ ≤ 0
g₁₃:h_v1(X₀,X₁,X₂) -{0}> t₁₂:i_v1(X₀,X₁,X₂+UNIFORM(0, 1)) :|: 1+X₂ ≤ X₁ ∧ 0 ≤ 1 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
g₁₅:i_v1(X₀,X₁,X₂) → t₁₄:g_v1(X₂,X₁,0) :|: X₂ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁
g₁₇:g_v1(X₀,X₁,X₂) -{0}> t₁₆:h_v2(X₀,X₁,X₀) :|: X₀ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
g₁₉:h_v2(X₀,X₁,X₂) -{0}> t₁₈:i_v1(X₀,X₁,X₂+UNIFORM(0, 1)) :|: 1+X₂ ≤ X₁ ∧ 0 ≤ 1 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂
Overall timebound:6⋅X₀+6⋅X₁+11 {O(n)}
g₁: 1 {O(1)}
g₁₁: 1 {O(1)}
g₁₃: 1 {O(1)}
g₁₅: 2⋅X₀+2⋅X₁+3 {O(n)}
g₁₇: 2⋅X₀+2⋅X₁+3 {O(n)}
g₁₉: 2⋅X₀+2⋅X₁+2 {O(n)}
Overall costbound: 2⋅X₀+2⋅X₁+3 {O(n)}
g₁: 0 {O(1)}
g₁₁: 0 {O(1)}
g₁₃: 0 {O(1)}
g₁₅: 2⋅X₀+2⋅X₁+3 {O(n)}
g₁₇: 0 {O(1)}
g₁₉: 0 {O(1)}
(g₁,g), X₀: X₀ {O(n)}
(g₁,g), X₁: X₁ {O(n)}
(g₁,g), X₂: 0 {O(1)}
(g₁₁,h_v1), X₀: X₀ {O(n)}
(g₁₁,h_v1), X₁: X₁ {O(n)}
(g₁₁,h_v1), X₂: X₀ {O(n)}
(g₁₃,i_v1), X₀: X₀ {O(n)}
(g₁₃,i_v1), X₁: X₁ {O(n)}
(g₁₃,i_v1), X₂: X₀+1 {O(n)}
(g₁₅,g_v1), X₁: X₁ {O(n)}
(g₁₅,g_v1), X₂: 0 {O(1)}
(g₁₇,h_v2), X₁: X₁ {O(n)}
(g₁₉,i_v1), X₁: X₁ {O(n)}