Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(0, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁-1, D) :|: 1 ≤ X₁ ∧ 1 ≤ D
t₂: l1(X₀, X₁, X₂) → l1(X₀, X₁-2, D) :|: 1 ≤ X₁ ∧ D ≤ 0
t₃: l1(X₀, X₁, X₂) → l2(X₀, X₁, D) :|: X₁ ≤ 0
t₄: l2(X₀, X₁, X₂) → l2(1, X₁, D) :|: 1 ≤ X₂
t₅: l2(X₀, X₁, X₂) → l2(2, X₁, D) :|: X₂ ≤ 0
Eliminate variables {X₀} that do not contribute to the problem
Found invariant X₀ ≤ 0 for location l2
Start: l0
Program_Vars: X₀, X₁
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₁₃: l0(X₀, X₁) → l1(X₀, X₁)
t₁₄: l1(X₀, X₁) → l1(X₀-1, D) :|: 1 ≤ X₀ ∧ 1 ≤ D
t₁₅: l1(X₀, X₁) → l1(X₀-2, D) :|: 1 ≤ X₀ ∧ D ≤ 0
t₁₆: l1(X₀, X₁) → l2(X₀, D) :|: X₀ ≤ 0
t₁₇: l2(X₀, X₁) → l2(X₀, D) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
t₁₈: l2(X₀, X₁) → l2(X₀, D) :|: X₁ ≤ 0 ∧ X₀ ≤ 0
new bound:
X₀ {O(n)}
new bound:
X₀ {O(n)}
Found invariant X₀ ≤ 0 for location l2
Overall timebound:inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: X₀ {O(n)}
t₁₅: X₀ {O(n)}
t₁₆: 1 {O(1)}
t₁₇: inf {Infinity}
t₁₈: inf {Infinity}
Overall costbound: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: X₀ {O(n)}
t₁₅: X₀ {O(n)}
t₁₆: 1 {O(1)}
t₁₇: inf {Infinity}
t₁₈: inf {Infinity}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₅, X₀: X₀ {O(n)}
t₁₆, X₀: 3⋅X₀ {O(n)}
t₁₇, X₀: 3⋅X₀ {O(n)}
t₁₈, X₀: 3⋅X₀ {O(n)}