Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < 0
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(1, X₄, X₂, X₃, X₄, X₅)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(0, X₁+1, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₁
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁+1, X₂, X₃, X₄, X₅) :|: X₁ < X₅
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅)
Eliminate variables {X₂,X₃} that do not contribute to the problem
Found invariant X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l5
Found invariant X₂ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ for location l1
Found invariant X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Found invariant X₂ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location l3
Cut unsatisfiable transition t₁₆: l1→l3
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₅: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₁₇: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ X₂ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀
t₁₈: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀
t₁₉: l2(X₀, X₁, X₂, X₃) → l1(1, X₂, X₂, X₃)
t₂₀: l3(X₀, X₁, X₂, X₃) → l1(0, X₁+1, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂₁: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₁ < X₃ ∧ X₂ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂₂: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
new bound:
1 {O(1)}
new bound:
X₂+X₃ {O(n)}
cycle: [t₁₇: l1→l3; t₂₁: l3→l1]
Termination: true
Formula:
Overall timebound:3⋅X₂+3⋅X₃+10 {O(n)}
t₁₅: 1 {O(1)}
t₁₇: 2⋅X₂+2⋅X₃+5 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₂+X₃ {O(n)}
t₂₂: 1 {O(1)}
Overall costbound: 3⋅X₂+3⋅X₃+10 {O(n)}
t₁₅: 1 {O(1)}
t₁₇: 2⋅X₂+2⋅X₃+5 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₂+X₃ {O(n)}
t₂₂: 1 {O(1)}
t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₇, X₀: 1 {O(1)}
t₁₇, X₁: 2⋅X₂+X₃ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₈, X₀: 0 {O(1)}
t₁₈, X₁: 2⋅X₂+X₃+1 {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₉, X₀: 1 {O(1)}
t₁₉, X₁: X₂ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₂₀, X₀: 0 {O(1)}
t₂₀, X₁: 2⋅X₂+X₃+1 {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₁, X₀: 1 {O(1)}
t₂₁, X₁: 2⋅X₂+X₃ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₂, X₀: 0 {O(1)}
t₂₂, X₁: 2⋅X₂+X₃+1 {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}