Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0
t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 < X₀
t₉: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃) :|: 0 < X₂ ∧ 0 < X₃
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₃: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0
t₇: l4(X₀, X₁, X₂, X₃) → l1(X₃, X₁, X₂, X₃) :|: X₃ < X₀
t₈: l4(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: X₀ ≤ X₃
Eliminate variables {X₁} that do not contribute to the problem
Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1
Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4
Cut unsatisfiable transition t₂₁: l1→l4
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₉: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₂₀: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂₂: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 0 < X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂₃: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₂₄: l3(X₀, X₁, X₂) → l1(X₁, X₁, X₂) :|: 0 < X₁ ∧ 0 < X₂
t₂₅: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁ ≤ 0
t₂₆: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ 0
t₂₇: l4(X₀, X₁, X₂) → l1(X₂, X₁, X₂) :|: X₂ < X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₈: l4(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
new bound:
X₁+1 {O(n)}
new bound:
X₁ {O(n)}
new bound:
X₁ {O(n)}
Overall timebound:3⋅X₁+7 {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₂: X₁+1 {O(n)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: X₁ {O(n)}
t₂₈: X₁ {O(n)}
Overall costbound: 3⋅X₁+7 {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₂: X₁+1 {O(n)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: X₁ {O(n)}
t₂₈: X₁ {O(n)}
t₁₉, X₀: X₀ {O(n)}
t₁₉, X₁: X₁ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₂₀, X₀: 0 {O(1)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₂, X₀: X₁ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₃, X₀: 2⋅X₀ {O(n)}
t₂₃, X₁: 3⋅X₁ {O(n)}
t₂₃, X₂: 3⋅X₂ {O(n)}
t₂₄, X₀: X₁ {O(n)}
t₂₄, X₁: X₁ {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₅, X₀: X₀ {O(n)}
t₂₅, X₁: X₁ {O(n)}
t₂₅, X₂: X₂ {O(n)}
t₂₆, X₀: X₀ {O(n)}
t₂₆, X₁: X₁ {O(n)}
t₂₆, X₂: X₂ {O(n)}
t₂₇, X₀: X₁ {O(n)}
t₂₇, X₁: X₁ {O(n)}
t₂₇, X₂: X₂ {O(n)}
t₂₈, X₀: X₁ {O(n)}
t₂₈, X₁: X₁ {O(n)}
t₂₈, X₂: X₂ {O(n)}