Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₀, X₁, X₄, X₅, X₆) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ < X₁
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ < X₀
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₅, X₆, X₂, X₃, X₄, X₅, X₆)
t₇: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₂, X₃, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 0
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₃
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂-1, X₃-1, X₄, X₅, X₆)
Eliminate variables {X₄} that do not contribute to the problem
Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l6
Found invariant 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 2 ≤ X₃+X₆ ∧ X₃ ≤ X₆ ∧ 2 ≤ X₂+X₆ ∧ X₂ ≤ X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l5
Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l1
Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l4
Found invariant 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 1 ≤ X₃+X₆ ∧ X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ X₂ ≤ X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₂₁: l0(X₀, X₁, X₂, X₃, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₅, X₆)
t₂₂: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l3(X₀, X₁, X₀, X₁, X₅, X₆) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₃: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₅, X₆) :|: X₀ < X₁ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₄: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₅, X₆) :|: X₁ < X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₅: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₅, X₆) :|: X₀ ≤ 0 ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₆: l2(X₀, X₁, X₂, X₃, X₅, X₆) → l1(X₅, X₆, X₂, X₃, X₅, X₆)
t₂₈: l3(X₀, X₁, X₂, X₃, X₅, X₆) → l1(X₂, X₃, X₂, X₃, X₅, X₆) :|: X₃ ≤ 0 ∧ 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 1 ≤ X₃+X₆ ∧ X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ X₂ ≤ X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₇: l3(X₀, X₁, X₂, X₃, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₅, X₆) :|: 0 < X₃ ∧ 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 1 ≤ X₃+X₆ ∧ X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ X₂ ≤ X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₉: l4(X₀, X₁, X₂, X₃, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₅, X₆) :|: X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₃₀: l5(X₀, X₁, X₂, X₃, X₅, X₆) → l3(X₀, X₁, X₂-1, X₃-1, X₅, X₆) :|: 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 2 ≤ X₃+X₆ ∧ X₃ ≤ X₆ ∧ 2 ≤ X₂+X₆ ∧ X₂ ≤ X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₂₂: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l3(X₀, X₁, X₀, X₁, X₅, X₆) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l6
Found invariant 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 2 ≤ X₃+X₆ ∧ X₃ ≤ X₆ ∧ 2 ≤ X₂+X₆ ∧ X₂ ≤ X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l5
Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l1
Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l4
Found invariant 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 1 ≤ X₃+X₆ ∧ X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ X₂ ≤ X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₂₂:
X₃: X₆ {O(n)}
Runtime-bound of t₂₂: 1 {O(1)}
Results in: 2⋅X₆+4 {O(n)}
relevant size-bounds w.r.t. t₂₂:
X₃: X₆ {O(n)}
Runtime-bound of t₂₂: 1 {O(1)}
Results in: 2⋅X₆+4 {O(n)}
knowledge_propagation leads to new time bound 2⋅X₆+4 {O(n)} for transition t₂₈: l3(X₀, X₁, X₂, X₃, X₅, X₆) → l1(X₂, X₃, X₂, X₃, X₅, X₆) :|: X₃ ≤ 0 ∧ 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 1 ≤ X₃+X₆ ∧ X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ X₂ ≤ X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
Overall timebound:6⋅X₆+19 {O(n)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 2⋅X₆+4 {O(n)}
t₂₈: 2⋅X₆+4 {O(n)}
t₂₉: 1 {O(1)}
t₃₀: 2⋅X₆+4 {O(n)}
Overall costbound: 6⋅X₆+19 {O(n)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 2⋅X₆+4 {O(n)}
t₂₈: 2⋅X₆+4 {O(n)}
t₂₉: 1 {O(1)}
t₃₀: 2⋅X₆+4 {O(n)}
t₂₁, X₀: X₀ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₁, X₅: X₅ {O(n)}
t₂₁, X₆: X₆ {O(n)}
t₂₂, X₀: X₅ {O(n)}
t₂₂, X₁: X₆ {O(n)}
t₂₂, X₂: X₅ {O(n)}
t₂₂, X₃: X₆ {O(n)}
t₂₂, X₅: X₅ {O(n)}
t₂₂, X₆: X₆ {O(n)}
t₂₃, X₀: X₅ {O(n)}
t₂₃, X₁: X₆ {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₃, X₅: X₅ {O(n)}
t₂₃, X₆: X₆ {O(n)}
t₂₄, X₀: X₅ {O(n)}
t₂₄, X₁: X₆ {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₄, X₅: X₅ {O(n)}
t₂₄, X₆: X₆ {O(n)}
t₂₅, X₀: X₅ {O(n)}
t₂₅, X₁: X₆ {O(n)}
t₂₅, X₂: X₂ {O(n)}
t₂₅, X₃: X₃ {O(n)}
t₂₅, X₅: 2⋅X₅ {O(n)}
t₂₅, X₆: 2⋅X₆ {O(n)}
t₂₆, X₀: X₅ {O(n)}
t₂₆, X₁: X₆ {O(n)}
t₂₆, X₂: X₂ {O(n)}
t₂₆, X₃: X₃ {O(n)}
t₂₆, X₅: X₅ {O(n)}
t₂₆, X₆: X₆ {O(n)}
t₂₇, X₀: X₅ {O(n)}
t₂₇, X₁: X₆ {O(n)}
t₂₇, X₂: X₅ {O(n)}
t₂₇, X₃: X₆ {O(n)}
t₂₇, X₅: X₅ {O(n)}
t₂₇, X₆: X₆ {O(n)}
t₂₈, X₀: 0 {O(1)}
t₂₈, X₁: 0 {O(1)}
t₂₈, X₂: 0 {O(1)}
t₂₈, X₃: 0 {O(1)}
t₂₈, X₅: X₅ {O(n)}
t₂₈, X₆: X₆ {O(n)}
t₂₉, X₀: 3⋅X₅ {O(n)}
t₂₉, X₁: 3⋅X₆ {O(n)}
t₂₉, X₂: 3⋅X₂ {O(n)}
t₂₉, X₃: 3⋅X₃ {O(n)}
t₂₉, X₅: 4⋅X₅ {O(n)}
t₂₉, X₆: 4⋅X₆ {O(n)}
t₃₀, X₀: X₅ {O(n)}
t₃₀, X₁: X₆ {O(n)}
t₃₀, X₂: X₅ {O(n)}
t₃₀, X₃: X₆ {O(n)}
t₃₀, X₅: X₅ {O(n)}
t₃₀, X₆: X₆ {O(n)}