Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₂, X₃, X₂, X₃, X₄, X₅)
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₀-1, X₃, X₄, X₅)
t₉: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, nondef.0, X₄, X₅)
t₂: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ 0 ≤ X₁
t₃: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < 0
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < 0
t₁: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₄, X₅, X₂, X₃, X₄, X₅)
t₅: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < 1
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₁
t₁₁: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅)
Found invariant 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l6
Found invariant X₀ ≤ X₄ for location l7
Found invariant X₀ ≤ X₄ for location l8
Found invariant 0 ≤ X₄ ∧ 0 ≤ 1+X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l1
Found invariant X₀ ≤ X₄ for location l4
Found invariant 0 ≤ X₄ ∧ 0 ≤ 1+X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₂, X₃, X₂, X₃, X₄, X₅) :|: 0 ≤ X₄ ∧ 0 ≤ 1+X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₀-1, X₃, X₄, X₅) :|: 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₉: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, nondef.0, X₄, X₅) :|: 0 ≤ X₄ ∧ 0 ≤ 1+X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₄
t₃: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < 0 ∧ X₀ ≤ X₄
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < 0 ∧ X₀ ≤ X₄
t₁: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₄, X₅, X₂, X₃, X₄, X₅)
t₅: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < 1 ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₁: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₄
new bound:
X₄+1 {O(n)}
MPRF:
l3 [X₀+1 ]
l1 [X₂+2 ]
l2 [X₀+1 ]
l6 [X₀+1 ]
l4 [X₀+1 ]
new bound:
X₄+1 {O(n)}
MPRF:
l3 [X₂+1 ]
l1 [X₂+1 ]
l2 [X₀+1 ]
l6 [X₀+1 ]
l4 [X₀+1 ]
new bound:
X₄+1 {O(n)}
MPRF:
l3 [X₀+1 ]
l1 [X₀ ]
l2 [X₀+1 ]
l6 [X₀+1 ]
l4 [X₀+1 ]
new bound:
X₄+1 {O(n)}
MPRF:
l3 [X₂+1 ]
l1 [X₂+1 ]
l2 [X₀ ]
l6 [X₀+1 ]
l4 [X₀+1 ]
Found invariant 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l6___1
Found invariant 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l6___2
Found invariant X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l6___4
Found invariant 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l4___3
Found invariant X₀ ≤ X₄ for location l7
Found invariant X₀ ≤ X₄ for location l8
Found invariant 0 ≤ X₄ ∧ 0 ≤ 1+X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l1
Found invariant X₀ ≤ X₄ for location l4
Found invariant 0 ≤ X₄ ∧ 0 ≤ 1+X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3
knowledge_propagation leads to new time bound X₄+1 {O(n)} for transition t₈₀: l4(X₀, X₁, X₂, X₃, X₄, X₅) → n_l6___1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ 1+X₀ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₄
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₈₁: l4(X₀, X₁, X₂, X₃, X₄, X₅) → n_l6___4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₄ ∧ X₁ ≤ X₅ ∧ X₅ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₄
knowledge_propagation leads to new time bound X₄+1 {O(n)} for transition t₈₂: n_l6___1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___3(X₀, X₁-1, X₂, X₃, X₄, X₅) :|: 1+X₂ ≤ X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₄ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
knowledge_propagation leads to new time bound X₄+1 {O(n)} for transition t₉₀: n_l6___1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < 1 ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₈₄: n_l6___4(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___3(X₀, X₁-1, X₂, X₃, X₄, X₅) :|: 0 ≤ X₁ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₅ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₉₂: n_l6___4(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < 1 ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
new bound:
X₄+1 {O(n)}
MPRF:
l3 [X₂+1 ]
l1 [X₂+1 ]
l4 [X₀+1 ]
n_l6___1 [X₂+1 ]
n_l6___2 [X₀+1 ]
n_l4___3 [X₀+1 ]
n_l6___4 [X₀+1 ]
l2 [X₀ ]
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁₀: X₄+1 {O(n)}
t₇: X₄+1 {O(n)}
t₉: X₄+1 {O(n)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₅: X₄+1 {O(n)}
t₆: inf {Infinity}
t₁₁: 1 {O(1)}
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁₀: X₄+1 {O(n)}
t₇: X₄+1 {O(n)}
t₉: X₄+1 {O(n)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₅: X₄+1 {O(n)}
t₆: inf {Infinity}
t₁₁: 1 {O(1)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁₀, X₀: X₄+1 {O(n)}
t₁₀, X₂: X₄+2 {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₇, X₀: X₄+1 {O(n)}
t₇, X₁: 0 {O(1)}
t₇, X₂: X₄+2 {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₅ {O(n)}
t₉, X₀: X₄+1 {O(n)}
t₉, X₁: 0 {O(1)}
t₉, X₂: X₄+2 {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: X₅ {O(n)}
t₂, X₀: X₄+1 {O(n)}
t₂, X₂: X₂+X₄+2 {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: 2⋅X₄+1 {O(n)}
t₃, X₂: X₂+X₄+2 {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₄, X₀: 2⋅X₄+1 {O(n)}
t₄, X₂: X₂+X₄+2 {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅X₅ {O(n)}
t₁, X₀: X₄ {O(n)}
t₁, X₁: X₅ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₅, X₀: X₄+1 {O(n)}
t₅, X₁: 0 {O(1)}
t₅, X₂: X₂+X₄+2 {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₆, X₀: X₄+1 {O(n)}
t₆, X₂: X₂+X₄+2 {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₁₁, X₀: 4⋅X₄+2 {O(n)}
t₁₁, X₂: 2⋅X₂+2⋅X₄+4 {O(n)}
t₁₁, X₄: 4⋅X₄ {O(n)}
t₁₁, X₅: 4⋅X₅ {O(n)}