Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₀ < X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₁ < X₃
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l1(X₇, X₈, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l1(X₀+1, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
Eliminate variables {X₄,X₅,X₆} that do not contribute to the problem
Found invariant X₈ ≤ X₁ ∧ X₇ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l5
Found invariant X₈ ≤ X₁ ∧ X₇ ≤ X₀ for location l1
Found invariant X₈ ≤ X₁ ∧ X₇ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l4
Found invariant X₈ ≤ X₁ ∧ X₇ ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₇, X₈
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₄: l0(X₀, X₁, X₂, X₃, X₇, X₈) → l2(X₀, X₁, X₂, X₃, X₇, X₈)
t₁₅: l1(X₀, X₁, X₂, X₃, X₇, X₈) → l3(X₀, X₁, X₂, X₃, X₇, X₈) :|: X₀ < X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₀
t₁₆: l1(X₀, X₁, X₂, X₃, X₇, X₈) → l3(X₀, X₁, X₂, X₃, X₇, X₈) :|: X₁ < X₃ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₀
t₁₇: l1(X₀, X₁, X₂, X₃, X₇, X₈) → l4(X₀, X₁, X₂, X₃, X₇, X₈) :|: X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₀
t₁₈: l2(X₀, X₁, X₂, X₃, X₇, X₈) → l1(X₇, X₈, X₂, X₃, X₇, X₈)
t₁₉: l3(X₀, X₁, X₂, X₃, X₇, X₈) → l1(X₀+1, X₁+1, X₂, X₃, X₇, X₈) :|: X₈ ≤ X₁ ∧ X₇ ≤ X₀
t₂₀: l4(X₀, X₁, X₂, X₃, X₇, X₈) → l5(X₀, X₁, X₂, X₃, X₇, X₈) :|: X₈ ≤ X₁ ∧ X₇ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀
Found invariant X₈ ≤ X₁ ∧ X₇ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l5
Found invariant X₈ ≤ X₁ ∧ X₇ ≤ X₀ for location l1
Found invariant X₈ ≤ X₁ ∧ X₇ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l4
Found invariant X₈ ≤ X₁ ∧ X₇ ≤ X₀ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₁₈:
X₀: X₇ {O(n)}
X₁: X₈ {O(n)}
X₂: X₂ {O(n)}
X₃: X₃ {O(n)}
Runtime-bound of t₁₈: 1 {O(1)}
Results in: 2⋅X₂+2⋅X₃+2⋅X₇+2⋅X₈+6 {O(n)}
knowledge_propagation leads to new time bound 2⋅X₂+2⋅X₃+2⋅X₇+2⋅X₈+7 {O(n)} for transition t₁₅: l1(X₀, X₁, X₂, X₃, X₇, X₈) → l3(X₀, X₁, X₂, X₃, X₇, X₈) :|: X₀ < X₂ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₀
knowledge_propagation leads to new time bound 2⋅X₂+2⋅X₃+2⋅X₇+2⋅X₈+7 {O(n)} for transition t₁₆: l1(X₀, X₁, X₂, X₃, X₇, X₈) → l3(X₀, X₁, X₂, X₃, X₇, X₈) :|: X₁ < X₃ ∧ X₈ ≤ X₁ ∧ X₇ ≤ X₀
Overall timebound:6⋅X₂+6⋅X₃+6⋅X₇+6⋅X₈+24 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: 2⋅X₂+2⋅X₃+2⋅X₇+2⋅X₈+7 {O(n)}
t₁₆: 2⋅X₂+2⋅X₃+2⋅X₇+2⋅X₈+7 {O(n)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 2⋅X₂+2⋅X₃+2⋅X₇+2⋅X₈+6 {O(n)}
t₂₀: 1 {O(1)}
Overall costbound: 6⋅X₂+6⋅X₃+6⋅X₇+6⋅X₈+24 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: 2⋅X₂+2⋅X₃+2⋅X₇+2⋅X₈+7 {O(n)}
t₁₆: 2⋅X₂+2⋅X₃+2⋅X₇+2⋅X₈+7 {O(n)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 2⋅X₂+2⋅X₃+2⋅X₇+2⋅X₈+6 {O(n)}
t₂₀: 1 {O(1)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₇: X₇ {O(n)}
t₁₄, X₈: X₈ {O(n)}
t₁₅, X₀: 2⋅X₂+2⋅X₃+2⋅X₈+4⋅X₇+6 {O(n)}
t₁₅, X₁: 2⋅X₂+2⋅X₃+2⋅X₇+4⋅X₈+6 {O(n)}
t₁₅, X₂: 2⋅X₂ {O(n)}
t₁₅, X₃: 2⋅X₃ {O(n)}
t₁₅, X₇: 2⋅X₇ {O(n)}
t₁₅, X₈: 2⋅X₈ {O(n)}
t₁₆, X₀: 2⋅X₂+2⋅X₃+2⋅X₈+4⋅X₇+6 {O(n)}
t₁₆, X₁: 2⋅X₂+2⋅X₃+2⋅X₇+4⋅X₈+6 {O(n)}
t₁₆, X₂: 2⋅X₂ {O(n)}
t₁₆, X₃: 2⋅X₃ {O(n)}
t₁₆, X₇: 2⋅X₇ {O(n)}
t₁₆, X₈: 2⋅X₈ {O(n)}
t₁₇, X₀: 2⋅X₂+2⋅X₃+2⋅X₈+5⋅X₇+6 {O(n)}
t₁₇, X₁: 2⋅X₂+2⋅X₃+2⋅X₇+5⋅X₈+6 {O(n)}
t₁₇, X₂: 3⋅X₂ {O(n)}
t₁₇, X₃: 3⋅X₃ {O(n)}
t₁₇, X₇: 3⋅X₇ {O(n)}
t₁₇, X₈: 3⋅X₈ {O(n)}
t₁₈, X₀: X₇ {O(n)}
t₁₈, X₁: X₈ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₈, X₇: X₇ {O(n)}
t₁₈, X₈: X₈ {O(n)}
t₁₉, X₀: 2⋅X₂+2⋅X₃+2⋅X₈+4⋅X₇+6 {O(n)}
t₁₉, X₁: 2⋅X₂+2⋅X₃+2⋅X₇+4⋅X₈+6 {O(n)}
t₁₉, X₂: 2⋅X₂ {O(n)}
t₁₉, X₃: 2⋅X₃ {O(n)}
t₁₉, X₇: 2⋅X₇ {O(n)}
t₁₉, X₈: 2⋅X₈ {O(n)}
t₂₀, X₀: 2⋅X₂+2⋅X₃+2⋅X₈+5⋅X₇+6 {O(n)}
t₂₀, X₁: 2⋅X₂+2⋅X₃+2⋅X₇+5⋅X₈+6 {O(n)}
t₂₀, X₂: 3⋅X₂ {O(n)}
t₂₀, X₃: 3⋅X₃ {O(n)}
t₂₀, X₇: 3⋅X₇ {O(n)}
t₂₀, X₈: 3⋅X₈ {O(n)}