Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(0, 0, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₁+1 ≤ X₂
t₂: l1(X₀, X₁, X₂, X₃) → l1(X₀+2, X₁+1, X₂, X₃) :|: X₁+1 ≤ X₂
t₈: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₀, 1) :|: X₂ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀
t₆: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₀+1 ≤ X₂
t₇: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ X₁
t₃: l3(X₀, X₁, X₂, X₃) → l2(X₂+1, X₁, X₂, 1) :|: X₀ ≤ X₂+1 ∧ X₂+1 ≤ X₀
t₄: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, 0) :|: X₀ ≤ X₂
t₅: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, 0) :|: 2+X₂ ≤ X₀
Eliminate variables {X₃} that do not contribute to the problem
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l1
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₁₉: l0(X₀, X₁, X₂) → l1(0, 0, X₂)
t₂₀: l1(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂) :|: X₁+1 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₁: l1(X₀, X₁, X₂) → l1(X₀+2, X₁+1, X₂) :|: X₁+1 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₀) :|: X₂ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₃: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₀+1 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₄: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₅: l3(X₀, X₁, X₂) → l2(X₂+1, X₁, X₂) :|: X₀ ≤ X₂+1 ∧ X₂+1 ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₆: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₇: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 2+X₂ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
new bound:
X₂ {O(n)}
new bound:
X₂ {O(n)}
Overall timebound:2⋅X₂+7 {O(n)}
t₁₉: 1 {O(1)}
t₂₀: X₂ {O(n)}
t₂₁: X₂ {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
Overall costbound: 2⋅X₂+7 {O(n)}
t₁₉: 1 {O(1)}
t₂₀: X₂ {O(n)}
t₂₁: X₂ {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₁₉, X₀: 0 {O(1)}
t₁₉, X₁: 0 {O(1)}
t₁₉, X₂: X₂ {O(n)}
t₂₀, X₀: 2⋅X₂ {O(n)}
t₂₀, X₁: 2⋅X₂ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₁, X₀: 2⋅X₂ {O(n)}
t₂₁, X₁: 2⋅X₂ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₂, X₀: 4⋅X₂ {O(n)}
t₂₂, X₁: 4⋅X₂ {O(n)}
t₂₂, X₂: 4⋅X₂ {O(n)}
t₂₃, X₀: 4⋅X₂ {O(n)}
t₂₃, X₁: 4⋅X₂ {O(n)}
t₂₃, X₂: 2⋅X₂ {O(n)}
t₂₄, X₀: 4⋅X₂ {O(n)}
t₂₄, X₁: 4⋅X₂ {O(n)}
t₂₄, X₂: 3⋅X₂ {O(n)}
t₂₅, X₀: 4⋅X₂ {O(n)}
t₂₅, X₁: 4⋅X₂ {O(n)}
t₂₅, X₂: 3⋅X₂ {O(n)}
t₂₆, X₀: 4⋅X₂ {O(n)}
t₂₆, X₁: 4⋅X₂ {O(n)}
t₂₆, X₂: 2⋅X₂ {O(n)}
t₂₇, X₀: 4⋅X₂ {O(n)}
t₂₇, X₁: 4⋅X₂ {O(n)}
t₂₇, X₂: 3⋅X₂ {O(n)}