Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₇ < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₇ < X₁
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ X₇ ∧ X₁ ≤ X₇
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₅, X₆, X₂, X₃, X₄, X₅, X₆, X₇)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₇ < X₀
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ X₇
t₁₁: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁₀: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₂, X₃, X₂, X₃, X₄, X₅, X₆, X₇)
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₀-1, X₁, X₄, X₅, X₆, X₇)
t₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₀, X₁-1, X₄, X₅, X₆, X₇) :|: X₇ < X₁
t₉: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₀, X₁, X₄, X₅, X₆, X₇) :|: X₁ ≤ X₇
Eliminate variables {X₄} that do not contribute to the problem
Found invariant 1+X₇ ≤ X₅ ∧ 1+X₇ ≤ X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l6
Found invariant X₀ ≤ X₇ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅ 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 ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l8
Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l1
Found invariant X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l4
Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₅, X₆, X₇
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₂₄: l0(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₅, X₆, X₇)
t₂₅: l1(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₅, X₆, X₇) :|: X₇ < X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₆: l1(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₅, X₆, X₇) :|: X₇ < X₁ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₇: l1(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₅, X₆, X₇) :|: X₀ ≤ X₇ ∧ X₁ ≤ X₇ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₈: l2(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l1(X₅, X₆, X₂, X₃, X₅, X₆, X₇)
t₂₉: l3(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₅, X₆, X₇) :|: X₇ < X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₃₀: l3(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₅, X₆, X₇) :|: X₀ ≤ X₇ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₃₁: l4(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l8(X₀, X₁, X₂, X₃, X₅, X₆, X₇) :|: X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₃₂: l5(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l1(X₂, X₃, X₂, X₃, X₅, X₆, X₇) :|: 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, X₇) → l5(X₀, X₁, X₀-1, X₁, X₅, X₆, X₇) :|: 1+X₇ ≤ X₅ ∧ 1+X₇ ≤ X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₃₄: l7(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l5(X₀, X₁, X₀, X₁-1, X₅, X₆, X₇) :|: X₇ < X₁ ∧ X₀ ≤ X₇ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₃₅: l7(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l5(X₀, X₁, X₀, X₁, X₅, X₆, X₇) :|: X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
new bound:
X₅+X₇ {O(n)}
MPRF:
l3 [X₀-X₇ ]
l1 [X₀-X₇ ]
l6 [X₀-X₇-1 ]
l7 [X₀-X₇ ]
l5 [X₂-X₇ ]
new bound:
X₅+X₇ {O(n)}
MPRF:
l3 [X₀-X₇ ]
l1 [X₀-X₇ ]
l6 [X₀-X₇ ]
l7 [X₀-X₇ ]
l5 [X₂-X₇ ]
new bound:
X₆+X₇ {O(n)}
MPRF:
l3 [X₁-X₇ ]
l1 [X₁-X₇ ]
l6 [X₁-X₇ ]
l7 [X₁-X₇ ]
l5 [X₃-X₇ ]
new bound:
2⋅X₇+X₅+X₆+1 {O(n)}
MPRF:
l3 [X₇+1-X₁ ]
l1 [1 ]
l6 [1 ]
l7 [X₇+1-X₁ ]
l5 [1 ]
new bound:
2⋅X₅⋅X₆+2⋅X₅⋅X₇+2⋅X₆⋅X₆+4⋅X₇⋅X₇+6⋅X₆⋅X₇+X₆+X₇ {O(n^2)}
MPRF:
l3 [X₆+1-X₁ ]
l1 [X₆-X₇ ]
l6 [X₆-X₇ ]
l7 [X₆-X₁ ]
l5 [X₆-X₇ ]
new bound:
2⋅X₇+X₅+X₆ {O(n)}
MPRF:
l3 [X₇+1-X₁ ]
l1 [0 ]
l6 [1 ]
l7 [X₇+1-X₁ ]
l5 [1 ]
new bound:
2⋅X₅⋅X₆+2⋅X₅⋅X₇+2⋅X₆⋅X₆+4⋅X₇⋅X₇+6⋅X₆⋅X₇+X₆+X₇ {O(n^2)}
MPRF:
l3 [X₆+1-X₁ ]
l1 [X₆-X₇ ]
l6 [X₆-X₇ ]
l7 [X₆+1-X₁ ]
l5 [X₆-X₇ ]
knowledge_propagation leads to new time bound 2⋅X₇+X₅+X₆+1 {O(n)} for transition t₂₅: l1(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₅, X₆, X₇) :|: X₇ < X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
knowledge_propagation leads to new time bound 2⋅X₇+X₅+X₆+1 {O(n)} for transition t₃₀: l3(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₅, X₆, X₇) :|: X₀ ≤ X₇ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
knowledge_propagation leads to new time bound 2⋅X₇+X₅+X₆+1 {O(n)} for transition t₃₅: l7(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l5(X₀, X₁, X₀, X₁, X₅, X₆, X₇) :|: X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
Overall timebound:13⋅X₇+6⋅X₆+7⋅X₅+8 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 2⋅X₇+X₅+X₆+1 {O(n)}
t₂₆: 2⋅X₇+X₅+X₆+1 {O(n)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: X₅+X₇ {O(n)}
t₃₀: 2⋅X₇+X₅+X₆+1 {O(n)}
t₃₁: 1 {O(1)}
t₃₂: 2⋅X₇+X₅+X₆ {O(n)}
t₃₃: X₅+X₇ {O(n)}
t₃₄: X₆+X₇ {O(n)}
t₃₅: 2⋅X₇+X₅+X₆+1 {O(n)}
Overall costbound: 13⋅X₇+6⋅X₆+7⋅X₅+8 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 2⋅X₇+X₅+X₆+1 {O(n)}
t₂₆: 2⋅X₇+X₅+X₆+1 {O(n)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: X₅+X₇ {O(n)}
t₃₀: 2⋅X₇+X₅+X₆+1 {O(n)}
t₃₁: 1 {O(1)}
t₃₂: 2⋅X₇+X₅+X₆ {O(n)}
t₃₃: X₅+X₇ {O(n)}
t₃₄: X₆+X₇ {O(n)}
t₃₅: 2⋅X₇+X₅+X₆+1 {O(n)}
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)}
t₂₄, X₇: X₇ {O(n)}
t₂₅, X₀: 2⋅X₇+3⋅X₅+X₆ {O(n)}
t₂₅, X₁: 2⋅X₇+3⋅X₆+X₅ {O(n)}
t₂₅, X₂: 3⋅X₆+6⋅X₇+9⋅X₅+X₂+1 {O(n)}
t₂₅, X₃: 3⋅X₅+6⋅X₇+9⋅X₆+X₃+1 {O(n)}
t₂₅, X₅: 2⋅X₅ {O(n)}
t₂₅, X₆: 2⋅X₆ {O(n)}
t₂₅, X₇: 2⋅X₇ {O(n)}
t₂₆, X₀: 2⋅X₇+3⋅X₅+X₆ {O(n)}
t₂₆, X₁: 2⋅X₇+3⋅X₆+X₅ {O(n)}
t₂₆, X₂: 3⋅X₆+6⋅X₇+9⋅X₅+X₂+1 {O(n)}
t₂₆, X₃: 3⋅X₅+6⋅X₇+9⋅X₆+X₃+1 {O(n)}
t₂₆, X₅: 2⋅X₅ {O(n)}
t₂₆, X₆: 2⋅X₆ {O(n)}
t₂₆, X₇: 2⋅X₇ {O(n)}
t₂₇, X₀: 2⋅X₇+4⋅X₅+X₆ {O(n)}
t₂₇, X₁: 2⋅X₇+4⋅X₆+X₅ {O(n)}
t₂₇, X₂: 3⋅X₆+6⋅X₇+9⋅X₅+X₂+1 {O(n)}
t₂₇, X₃: 3⋅X₅+6⋅X₇+9⋅X₆+X₃+1 {O(n)}
t₂₇, X₅: 3⋅X₅ {O(n)}
t₂₇, X₆: 3⋅X₆ {O(n)}
t₂₇, X₇: 3⋅X₇ {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)}
t₂₈, X₇: X₇ {O(n)}
t₂₉, X₀: 2⋅X₇+3⋅X₅+X₆ {O(n)}
t₂₉, X₁: 2⋅X₇+3⋅X₆+X₅ {O(n)}
t₂₉, X₂: 12⋅X₇+18⋅X₅+2⋅X₂+6⋅X₆+2 {O(n)}
t₂₉, X₃: 12⋅X₇+18⋅X₆+2⋅X₃+6⋅X₅+2 {O(n)}
t₂₉, X₅: 2⋅X₅ {O(n)}
t₂₉, X₆: 2⋅X₆ {O(n)}
t₂₉, X₇: 2⋅X₇ {O(n)}
t₃₀, X₀: 2⋅X₇+3⋅X₅+X₆ {O(n)}
t₃₀, X₁: 2⋅X₇+3⋅X₆+X₅ {O(n)}
t₃₀, X₂: 3⋅X₆+6⋅X₇+9⋅X₅+X₂+1 {O(n)}
t₃₀, X₃: 3⋅X₅+6⋅X₇+9⋅X₆+X₃+1 {O(n)}
t₃₀, X₅: 2⋅X₅ {O(n)}
t₃₀, X₆: 2⋅X₆ {O(n)}
t₃₀, X₇: 2⋅X₇ {O(n)}
t₃₁, X₀: 2⋅X₇+4⋅X₅+X₆ {O(n)}
t₃₁, X₁: 2⋅X₇+4⋅X₆+X₅ {O(n)}
t₃₁, X₂: 3⋅X₆+6⋅X₇+9⋅X₅+X₂+1 {O(n)}
t₃₁, X₃: 3⋅X₅+6⋅X₇+9⋅X₆+X₃+1 {O(n)}
t₃₁, X₅: 3⋅X₅ {O(n)}
t₃₁, X₆: 3⋅X₆ {O(n)}
t₃₁, X₇: 3⋅X₇ {O(n)}
t₃₂, X₀: 2⋅X₇+3⋅X₅+X₆ {O(n)}
t₃₂, X₁: 2⋅X₇+3⋅X₆+X₅ {O(n)}
t₃₂, X₂: 3⋅X₆+6⋅X₇+9⋅X₅+1 {O(n)}
t₃₂, X₃: 3⋅X₅+6⋅X₇+9⋅X₆+1 {O(n)}
t₃₂, X₅: 2⋅X₅ {O(n)}
t₃₂, X₆: 2⋅X₆ {O(n)}
t₃₂, X₇: 2⋅X₇ {O(n)}
t₃₃, X₀: 2⋅X₇+3⋅X₅+X₆ {O(n)}
t₃₃, X₁: 2⋅X₇+3⋅X₆+X₅ {O(n)}
t₃₃, X₂: 2⋅X₇+3⋅X₅+X₆+1 {O(n)}
t₃₃, X₃: 2⋅X₇+3⋅X₆+X₅ {O(n)}
t₃₃, X₅: 2⋅X₅ {O(n)}
t₃₃, X₆: 2⋅X₆ {O(n)}
t₃₃, X₇: 2⋅X₇ {O(n)}
t₃₄, X₀: 2⋅X₇+3⋅X₅+X₆ {O(n)}
t₃₄, X₁: 2⋅X₇+3⋅X₆+X₅ {O(n)}
t₃₄, X₂: 2⋅X₇+3⋅X₅+X₆ {O(n)}
t₃₄, X₃: 2⋅X₇+3⋅X₆+X₅+1 {O(n)}
t₃₄, X₅: 2⋅X₅ {O(n)}
t₃₄, X₆: 2⋅X₆ {O(n)}
t₃₄, X₇: 2⋅X₇ {O(n)}
t₃₅, X₀: 2⋅X₇+3⋅X₅+X₆ {O(n)}
t₃₅, X₁: 2⋅X₇+3⋅X₆+X₅ {O(n)}
t₃₅, X₂: 2⋅X₇+3⋅X₅+X₆ {O(n)}
t₃₅, X₃: 2⋅X₇+3⋅X₆+X₅ {O(n)}
t₃₅, X₅: 2⋅X₅ {O(n)}
t₃₅, X₆: 2⋅X₆ {O(n)}
t₃₅, X₇: 2⋅X₇ {O(n)}