Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
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, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₁
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0 ∧ X₁ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₅, X₆, X₂, X₃, X₄, X₅, X₆)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₀
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0
t₁₁: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₀: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₂, X₃, X₂, X₃, X₄, X₅, X₆)
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀-1, X₁, X₄, X₅, X₆)
t₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀, X₁-1, X₄, X₅, X₆) :|: 0 < X₁
t₉: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₀, X₁, X₄, X₅, X₆) :|: X₁ ≤ 0
Eliminate variables {X₄} that do not contribute to the problem
Found invariant X₁ ≤ X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l6
Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₀ ≤ 0 for location l7
Found invariant X₃ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₂ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ 1+X₂ for location l5
Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location l8
Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l1
Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location l4
Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₂₄: l0(X₀, X₁, X₂, X₃, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₅, X₆)
t₂₅: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₅, X₆) :|: 0 < X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₆: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₅, X₆) :|: 0 < X₁ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₇: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₅, X₆) :|: X₀ ≤ 0 ∧ X₁ ≤ 0 ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₈: l2(X₀, X₁, X₂, X₃, X₅, X₆) → l1(X₅, X₆, X₂, X₃, X₅, X₆)
t₂₉: l3(X₀, X₁, X₂, X₃, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₅, X₆) :|: 0 < X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₃₀: l3(X₀, X₁, X₂, X₃, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₅, X₆) :|: X₀ ≤ 0 ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₃₁: l4(X₀, X₁, X₂, X₃, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₅, X₆) :|: X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ 0
t₃₂: l5(X₀, X₁, X₂, X₃, X₅, X₆) → l1(X₂, X₃, X₂, X₃, X₅, X₆) :|: X₃ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₂ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ 1+X₂
t₃₃: l6(X₀, X₁, X₂, X₃, X₅, X₆) → l5(X₀, X₁, X₀-1, X₁, X₅, X₆) :|: X₁ ≤ X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₃₄: l7(X₀, X₁, X₂, X₃, X₅, X₆) → l5(X₀, X₁, X₀, X₁-1, X₅, X₆) :|: 0 < X₁ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₀ ≤ 0
t₃₅: l7(X₀, X₁, X₂, X₃, X₅, X₆) → l5(X₀, X₁, X₀, X₁, X₅, X₆) :|: X₁ ≤ 0 ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅ ∧ X₀ ≤ 0
new bound:
X₅ {O(n)}
MPRF:
l3 [X₀ ]
l1 [X₀ ]
l6 [X₀-1 ]
l7 [X₀ ]
l5 [X₂ ]
new bound:
X₅ {O(n)}
MPRF:
l3 [X₀ ]
l1 [X₀ ]
l6 [X₀ ]
l7 [X₀ ]
l5 [X₂ ]
new bound:
X₆ {O(n)}
MPRF:
l3 [X₁ ]
l1 [X₁ ]
l6 [X₁ ]
l7 [X₁ ]
l5 [X₃ ]
new bound:
X₅+X₆+1 {O(n)}
MPRF:
l3 [1-X₁ ]
l1 [1 ]
l6 [1 ]
l7 [1-X₁ ]
l5 [1 ]
new bound:
2⋅X₅⋅X₆+2⋅X₆⋅X₆+X₆ {O(n^2)}
MPRF:
l3 [X₆+1-X₁ ]
l1 [X₆ ]
l6 [X₆ ]
l7 [X₆-X₁ ]
l5 [X₆ ]
new bound:
X₅+X₆ {O(n)}
MPRF:
l3 [1-X₁ ]
l1 [0 ]
l6 [1 ]
l7 [1-X₁ ]
l5 [1 ]
new bound:
0 {O(1)}
MPRF:
l3 [1-X₁ ]
l1 [0 ]
l6 [0 ]
l7 [1-X₁ ]
l5 [0 ]
knowledge_propagation leads to new time bound X₅+X₆+1 {O(n)} for transition t₂₅: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₅, X₆) :|: 0 < X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
knowledge_propagation leads to new time bound X₅+X₆+1 {O(n)} for transition t₃₀: l3(X₀, X₁, X₂, X₃, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₅, X₆) :|: X₀ ≤ 0 ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
Overall timebound:5⋅X₆+6⋅X₅+7 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₅+X₆+1 {O(n)}
t₂₆: X₅+X₆+1 {O(n)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: X₅ {O(n)}
t₃₀: X₅+X₆+1 {O(n)}
t₃₁: 1 {O(1)}
t₃₂: X₅+X₆ {O(n)}
t₃₃: X₅ {O(n)}
t₃₄: X₆ {O(n)}
t₃₅: 0 {O(1)}
Overall costbound: 5⋅X₆+6⋅X₅+7 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₅+X₆+1 {O(n)}
t₂₆: X₅+X₆+1 {O(n)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: X₅ {O(n)}
t₃₀: X₅+X₆+1 {O(n)}
t₃₁: 1 {O(1)}
t₃₂: X₅+X₆ {O(n)}
t₃₃: X₅ {O(n)}
t₃₄: X₆ {O(n)}
t₃₅: 0 {O(1)}
t₂₄, X₀: X₀ {O(n)}
t₂₄, X₁: X₁ {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₄, X₅: X₅ {O(n)}
t₂₄, X₆: X₆ {O(n)}
t₂₅, X₀: 3⋅X₅+X₆ {O(n)}
t₂₅, X₁: 3⋅X₆+X₅ {O(n)}
t₂₅, X₂: 3⋅X₆+9⋅X₅+X₂ {O(n)}
t₂₅, X₃: 3⋅X₅+9⋅X₆+X₃ {O(n)}
t₂₅, X₅: 2⋅X₅ {O(n)}
t₂₅, X₆: 2⋅X₆ {O(n)}
t₂₆, X₀: 3⋅X₅+X₆ {O(n)}
t₂₆, X₁: 3⋅X₆+X₅ {O(n)}
t₂₆, X₂: 3⋅X₆+9⋅X₅+X₂ {O(n)}
t₂₆, X₃: 3⋅X₅+9⋅X₆+X₃ {O(n)}
t₂₆, X₅: 2⋅X₅ {O(n)}
t₂₆, X₆: 2⋅X₆ {O(n)}
t₂₇, X₀: 4⋅X₅+X₆ {O(n)}
t₂₇, X₁: 4⋅X₆+X₅ {O(n)}
t₂₇, X₂: 3⋅X₆+9⋅X₅+X₂ {O(n)}
t₂₇, X₃: 3⋅X₅+9⋅X₆+X₃ {O(n)}
t₂₇, X₅: 3⋅X₅ {O(n)}
t₂₇, X₆: 3⋅X₆ {O(n)}
t₂₈, X₀: X₅ {O(n)}
t₂₈, X₁: X₆ {O(n)}
t₂₈, X₂: X₂ {O(n)}
t₂₈, X₃: X₃ {O(n)}
t₂₈, X₅: X₅ {O(n)}
t₂₈, X₆: X₆ {O(n)}
t₂₉, X₀: 3⋅X₅+X₆ {O(n)}
t₂₉, X₁: 3⋅X₆+X₅ {O(n)}
t₂₉, X₂: 18⋅X₅+2⋅X₂+6⋅X₆ {O(n)}
t₂₉, X₃: 18⋅X₆+2⋅X₃+6⋅X₅ {O(n)}
t₂₉, X₅: 2⋅X₅ {O(n)}
t₂₉, X₆: 2⋅X₆ {O(n)}
t₃₀, X₀: 3⋅X₅+X₆ {O(n)}
t₃₀, X₁: 3⋅X₆+X₅ {O(n)}
t₃₀, X₂: 3⋅X₆+9⋅X₅+X₂ {O(n)}
t₃₀, X₃: 3⋅X₅+9⋅X₆+X₃ {O(n)}
t₃₀, X₅: 2⋅X₅ {O(n)}
t₃₀, X₆: 2⋅X₆ {O(n)}
t₃₁, X₀: 4⋅X₅+X₆ {O(n)}
t₃₁, X₁: 4⋅X₆+X₅ {O(n)}
t₃₁, X₂: 3⋅X₆+9⋅X₅+X₂ {O(n)}
t₃₁, X₃: 3⋅X₅+9⋅X₆+X₃ {O(n)}
t₃₁, X₅: 3⋅X₅ {O(n)}
t₃₁, X₆: 3⋅X₆ {O(n)}
t₃₂, X₀: 3⋅X₅+X₆ {O(n)}
t₃₂, X₁: 3⋅X₆+X₅ {O(n)}
t₃₂, X₂: 3⋅X₆+9⋅X₅ {O(n)}
t₃₂, X₃: 3⋅X₅+9⋅X₆ {O(n)}
t₃₂, X₅: 2⋅X₅ {O(n)}
t₃₂, X₆: 2⋅X₆ {O(n)}
t₃₃, X₀: 3⋅X₅+X₆ {O(n)}
t₃₃, X₁: 3⋅X₆+X₅ {O(n)}
t₃₃, X₂: 3⋅X₅+X₆ {O(n)}
t₃₃, X₃: 3⋅X₆+X₅ {O(n)}
t₃₃, X₅: 2⋅X₅ {O(n)}
t₃₃, X₆: 2⋅X₆ {O(n)}
t₃₄, X₀: 3⋅X₅+X₆ {O(n)}
t₃₄, X₁: 3⋅X₆+X₅ {O(n)}
t₃₄, X₂: 3⋅X₅+X₆ {O(n)}
t₃₄, X₃: 3⋅X₆+X₅ {O(n)}
t₃₄, X₅: 2⋅X₅ {O(n)}
t₃₄, X₆: 2⋅X₆ {O(n)}
t₃₅, X₀: 3⋅X₅+X₆ {O(n)}
t₃₅, X₁: 3⋅X₆+X₅ {O(n)}
t₃₅, X₂: 3⋅X₅+X₆ {O(n)}
t₃₅, X₃: 3⋅X₆+X₅ {O(n)}
t₃₅, X₅: 2⋅X₅ {O(n)}
t₃₅, X₆: 2⋅X₆ {O(n)}