Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀
Temp_Vars: F1, G1, H1, I1, J1, K1, L1, M1, N1, O1, P1
Locations: l0, l1, l2, l3
Transitions:
t₆: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → l3(X₀, X₁, X₂, X₃, L1, X₅, 1, 4, 1, 4, X₁₀, X₁₁, X₁₂, F1, 2, 3, G1, H1, 4, J1, 0, K1, M1, M1, M1, M1, N1, O1, P1, 4, X₃₀) :|: X₅+1 ≤ I1
t₇: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → l3(X₀, X₁, X₂, X₃, L1, X₅, 1, 4, 1, 4, X₁₀, X₁₁, X₁₂, F1, 2, 3, G1, H1, 4, J1, 0, K1, M1, M1, M1, M1, N1, O1, P1, 4, X₃₀) :|: I1+1 ≤ X₅
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → l1(X₀, X₁, X₀, X₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: X₁+1 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → l1(X₀, X₁, X₀, X₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: X₀+1 ≤ X₁
t₀: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → l1(X₀, X₁, X₀, X₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: X₁+1 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → l1(X₀, X₁, X₀, X₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: X₀+1 ≤ X₁
t₈: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → l2(J1, X₁, J1, J1, X₄, X₄, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, F1, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, G1, X₂₆, X₂₇, X₂₈, X₂₉, H1) :|: X₁+1 ≤ J1 ∧ 0 ≤ X₆ ∧ 1 ≤ X₇ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄
t₉: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → l2(J1, X₁, J1, J1, X₄, X₄, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, F1, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, G1, X₂₆, X₂₇, X₂₈, X₂₉, H1) :|: J1+1 ≤ X₁ ∧ 0 ≤ X₆ ∧ 1 ≤ X₇ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → l3(X₀, X₁, X₂, X₃, H1, X₅, 1+X₆, X₇-1, 1+X₆, X₇-1, F1, G1, X₇-1, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: X₅+1 ≤ X₄ ∧ 0 ≤ X₆ ∧ 1 ≤ X₇
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → l3(X₀, X₁, X₂, X₃, H1, X₅, 1+X₆, X₇-1, 1+X₆, X₇-1, F1, G1, X₇-1, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: X₄+1 ≤ X₅ ∧ 0 ≤ X₆ ∧ 1 ≤ X₇
Show Graph
G
l0
l0
l3
l3
l0->l3
t₆
η (X₄) = L1
η (X₆) = 1
η (X₇) = 4
η (X₈) = 1
η (X₉) = 4
η (X₁₃) = F1
η (X₁₄) = 2
η (X₁₅) = 3
η (X₁₆) = G1
η (X₁₇) = H1
η (X₁₈) = 4
η (X₁₉) = J1
η (X₂₀) = 0
η (X₂₁) = K1
η (X₂₂) = M1
η (X₂₃) = M1
η (X₂₄) = M1
η (X₂₅) = M1
η (X₂₆) = N1
η (X₂₇) = O1
η (X₂₈) = P1
η (X₂₉) = 4
τ = X₅+1 ≤ I1
l0->l3
t₇
η (X₄) = L1
η (X₆) = 1
η (X₇) = 4
η (X₈) = 1
η (X₉) = 4
η (X₁₃) = F1
η (X₁₄) = 2
η (X₁₅) = 3
η (X₁₆) = G1
η (X₁₇) = H1
η (X₁₈) = 4
η (X₁₉) = J1
η (X₂₀) = 0
η (X₂₁) = K1
η (X₂₂) = M1
η (X₂₃) = M1
η (X₂₄) = M1
η (X₂₅) = M1
η (X₂₆) = N1
η (X₂₇) = O1
η (X₂₈) = P1
η (X₂₉) = 4
τ = I1+1 ≤ X₅
l1
l1
l1->l1
t₂
η (X₂) = X₀
η (X₃) = X₀
τ = X₁+1 ≤ X₀
l1->l1
t₃
η (X₂) = X₀
η (X₃) = X₀
τ = X₀+1 ≤ X₁
l2
l2
l2->l1
t₀
η (X₂) = X₀
η (X₃) = X₀
τ = X₁+1 ≤ X₀
l2->l1
t₁
η (X₂) = X₀
η (X₃) = X₀
τ = X₀+1 ≤ X₁
l3->l2
t₈
η (X₀) = J1
η (X₂) = J1
η (X₃) = J1
η (X₅) = X₄
η (X₁₃) = F1
η (X₂₅) = G1
η (X₃₀) = H1
τ = X₁+1 ≤ J1 ∧ 0 ≤ X₆ ∧ 1 ≤ X₇ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄
l3->l2
t₉
η (X₀) = J1
η (X₂) = J1
η (X₃) = J1
η (X₅) = X₄
η (X₁₃) = F1
η (X₂₅) = G1
η (X₃₀) = H1
τ = J1+1 ≤ X₁ ∧ 0 ≤ X₆ ∧ 1 ≤ X₇ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄
l3->l3
t₄
η (X₄) = H1
η (X₆) = 1+X₆
η (X₇) = X₇-1
η (X₈) = 1+X₆
η (X₉) = X₇-1
η (X₁₀) = F1
η (X₁₁) = G1
η (X₁₂) = X₇-1
τ = X₅+1 ≤ X₄ ∧ 0 ≤ X₆ ∧ 1 ≤ X₇
l3->l3
t₅
η (X₄) = H1
η (X₆) = 1+X₆
η (X₇) = X₇-1
η (X₈) = 1+X₆
η (X₉) = X₇-1
η (X₁₀) = F1
η (X₁₁) = G1
η (X₁₂) = X₇-1
τ = X₄+1 ≤ X₅ ∧ 0 ≤ X₆ ∧ 1 ≤ X₇
Preprocessing
Eliminate variables {F1,G1,K1,M1,N1,O1,P1,X₂,X₃,X₈,X₉,X₁₀,X₁₁,X₁₂,X₁₃,X₁₄,X₁₅,X₁₆,X₁₇,X₁₈,X₁₉,X₂₀,X₂₁,X₂₂,X₂₃,X₂₄,X₂₅,X₂₆,X₂₇,X₂₈,X₂₉,X₃₀} that do not contribute to the problem
Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location l2
Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location l1
Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: H1, I1, J1, L1
Locations: l0, l1, l2, l3
Transitions:
t₂₁: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, L1, X₃, 1, 4) :|: X₃+1 ≤ I1
t₂₂: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, L1, X₃, 1, 4) :|: I1+1 ≤ X₃
t₂₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁+1 ≤ X₀ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
t₂₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀+1 ≤ X₁ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
t₂₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁+1 ≤ X₀ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
t₂₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀+1 ≤ X₁ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
t₂₇: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(J1, X₁, X₂, X₂, X₄, X₅) :|: X₁+1 ≤ J1 ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
t₂₈: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(J1, X₁, X₂, X₂, X₄, X₅) :|: J1+1 ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
t₂₉: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, H1, X₃, 1+X₄, X₅-1) :|: X₃+1 ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
t₃₀: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, H1, X₃, 1+X₄, X₅-1) :|: X₂+1 ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
Show Graph
G
l0
l0
l3
l3
l0->l3
t₂₁
η (X₂) = L1
η (X₄) = 1
η (X₅) = 4
τ = X₃+1 ≤ I1
l0->l3
t₂₂
η (X₂) = L1
η (X₄) = 1
η (X₅) = 4
τ = I1+1 ≤ X₃
l1
l1
l1->l1
t₂₃
τ = X₁+1 ≤ X₀ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l1->l1
t₂₄
τ = X₀+1 ≤ X₁ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l2
l2
l2->l1
t₂₅
τ = X₁+1 ≤ X₀ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l2->l1
t₂₆
τ = X₀+1 ≤ X₁ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l3->l2
t₂₇
η (X₀) = J1
η (X₃) = X₂
τ = X₁+1 ≤ J1 ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
l3->l2
t₂₈
η (X₀) = J1
η (X₃) = X₂
τ = J1+1 ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
l3->l3
t₂₉
η (X₂) = H1
η (X₄) = 1+X₄
η (X₅) = X₅-1
τ = X₃+1 ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
l3->l3
t₃₀
η (X₂) = H1
η (X₄) = 1+X₄
η (X₅) = X₅-1
τ = X₂+1 ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
MPRF for transition t₂₉: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, H1, X₃, 1+X₄, X₅-1) :|: X₃+1 ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ of depth 1:
new bound:
14 {O(1)}
Show Graph
G
l0
l0
l3
l3
l0->l3
t₂₁
η (X₂) = L1
η (X₄) = 1
η (X₅) = 4
τ = X₃+1 ≤ I1
l0->l3
t₂₂
η (X₂) = L1
η (X₄) = 1
η (X₅) = 4
τ = I1+1 ≤ X₃
l1
l1
l1->l1
t₂₃
τ = X₁+1 ≤ X₀ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l1->l1
t₂₄
τ = X₀+1 ≤ X₁ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l2
l2
l2->l1
t₂₅
τ = X₁+1 ≤ X₀ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l2->l1
t₂₆
τ = X₀+1 ≤ X₁ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l3->l2
t₂₇
η (X₀) = J1
η (X₃) = X₂
τ = X₁+1 ≤ J1 ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
l3->l2
t₂₈
η (X₀) = J1
η (X₃) = X₂
τ = J1+1 ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
l3->l3
t₂₉
η (X₂) = H1
η (X₄) = 1+X₄
η (X₅) = X₅-1
τ = X₃+1 ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
l3->l3
t₃₀
η (X₂) = H1
η (X₄) = 1+X₄
η (X₅) = X₅-1
τ = X₂+1 ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
MPRF for transition t₃₀: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, H1, X₃, 1+X₄, X₅-1) :|: X₂+1 ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ of depth 1:
new bound:
14 {O(1)}
Show Graph
G
l0
l0
l3
l3
l0->l3
t₂₁
η (X₂) = L1
η (X₄) = 1
η (X₅) = 4
τ = X₃+1 ≤ I1
l0->l3
t₂₂
η (X₂) = L1
η (X₄) = 1
η (X₅) = 4
τ = I1+1 ≤ X₃
l1
l1
l1->l1
t₂₃
τ = X₁+1 ≤ X₀ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l1->l1
t₂₄
τ = X₀+1 ≤ X₁ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l2
l2
l2->l1
t₂₅
τ = X₁+1 ≤ X₀ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l2->l1
t₂₆
τ = X₀+1 ≤ X₁ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l3->l2
t₂₇
η (X₀) = J1
η (X₃) = X₂
τ = X₁+1 ≤ J1 ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
l3->l2
t₂₈
η (X₀) = J1
η (X₃) = X₂
τ = J1+1 ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
l3->l3
t₂₉
η (X₂) = H1
η (X₄) = 1+X₄
η (X₅) = X₅-1
τ = X₃+1 ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
l3->l3
t₃₀
η (X₂) = H1
η (X₄) = 1+X₄
η (X₅) = X₅-1
τ = X₂+1 ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
Analysing control-flow refined program
Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location l2
Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location l1
Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ for location l3
Solv. Size Bound: t₁₀₅: l1→l1 for X₀
Solv. Size Bound: t₁₀₅: l1→l1 for X₂
Solv. Size Bound: t₁₀₅: l1→l1 for X₃
Show Graph
G
l0
l0
l3
l3
l0->l3
t₂₁
η (X₂) = L1
η (X₄) = 1
η (X₅) = 4
τ = X₃+1 ≤ I1
l0->l3
t₂₂
η (X₂) = L1
η (X₄) = 1
η (X₅) = 4
τ = I1+1 ≤ X₃
l1
l1
l1->l1
t₁₀₅
η (X₃) = X₂
η (X₅) = 5-X₄
τ = X₄+X₅ ≤ 5 ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ 5 ≤ X₄+X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄+X₅ ≤ 5 ∧ 5 ≤ X₄+X₅ ∧ X₅ ≤ 4 ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄+X₅ ≤ 5 ∧ 5 ≤ X₄+X₅ ∧ X₅ ≤ 4 ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄+X₅ ≤ 5 ∧ 5 ≤ X₄+X₅ ∧ X₅ ≤ 4 ∧ 1 ≤ X₅ ∧ 1 ≤ X₄ ∧ X₄ ≤ 4 ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 5 ≤ X₄+X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l1->l1
t₁₀₆
η (X₃) = X₂
η (X₅) = 5-X₄
τ = 1+X₁ ≤ X₀ ∧ X₄+X₅ ≤ 5 ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ 5 ≤ X₄+X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄+X₅ ≤ 5 ∧ 5 ≤ X₄+X₅ ∧ X₅ ≤ 4 ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄+X₅ ≤ 5 ∧ 5 ≤ X₄+X₅ ∧ X₅ ≤ 4 ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄+X₅ ≤ 5 ∧ 5 ≤ X₄+X₅ ∧ X₅ ≤ 4 ∧ 1 ≤ X₅ ∧ 1 ≤ X₄ ∧ X₄ ≤ 4 ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 5 ≤ X₄+X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l2
l2
l2->l1
t₂₅
τ = X₁+1 ≤ X₀ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l2->l1
t₂₆
τ = X₀+1 ≤ X₁ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l3->l2
t₂₇
η (X₀) = J1
η (X₃) = X₂
τ = X₁+1 ≤ J1 ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
l3->l2
t₂₈
η (X₀) = J1
η (X₃) = X₂
τ = J1+1 ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
l3->l3
t₂₉
η (X₂) = H1
η (X₄) = 1+X₄
η (X₅) = X₅-1
τ = X₃+1 ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
l3->l3
t₃₀
η (X₂) = H1
η (X₄) = 1+X₄
η (X₅) = X₅-1
τ = X₂+1 ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
cycle: [t₁₀₅: l1→l1; t₁₀₆: l1→l1]
loop: (X₄+X₅ ≤ 5 ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₄+X₅ ≤ 5 ∨ 1+X₁ ≤ X₀ ∧ X₄+X₅ ≤ 5 ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₄+X₅ ≤ 5,(X₂,X₃) -> (X₂,X₂)
overappr. closed-form: 2⋅X₂ {O(n)}
runtime bound: inf {Infinity}
Solv. Size Bound - Lifting for t₁₀₅: l1→l1 and X₃: inf {Infinity}
Solv. Size Bound: t₁₀₆: l1→l1 for X₀
Solv. Size Bound: t₁₀₆: l1→l1 for X₂
Solv. Size Bound: t₁₀₆: l1→l1 for X₃
Show Graph
G
l0
l0
l3
l3
l0->l3
t₂₁
η (X₂) = L1
η (X₄) = 1
η (X₅) = 4
τ = X₃+1 ≤ I1
l0->l3
t₂₂
η (X₂) = L1
η (X₄) = 1
η (X₅) = 4
τ = I1+1 ≤ X₃
l1
l1
l1->l1
t₁₀₅
η (X₃) = X₂
η (X₅) = 5-X₄
τ = X₄+X₅ ≤ 5 ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ 5 ≤ X₄+X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄+X₅ ≤ 5 ∧ 5 ≤ X₄+X₅ ∧ X₅ ≤ 4 ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄+X₅ ≤ 5 ∧ 5 ≤ X₄+X₅ ∧ X₅ ≤ 4 ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄+X₅ ≤ 5 ∧ 5 ≤ X₄+X₅ ∧ X₅ ≤ 4 ∧ 1 ≤ X₅ ∧ 1 ≤ X₄ ∧ X₄ ≤ 4 ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 5 ≤ X₄+X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l1->l1
t₁₀₆
η (X₃) = X₂
η (X₅) = 5-X₄
τ = 1+X₁ ≤ X₀ ∧ X₄+X₅ ≤ 5 ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ 5 ≤ X₄+X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄+X₅ ≤ 5 ∧ 5 ≤ X₄+X₅ ∧ X₅ ≤ 4 ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄+X₅ ≤ 5 ∧ 5 ≤ X₄+X₅ ∧ X₅ ≤ 4 ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄+X₅ ≤ 5 ∧ 5 ≤ X₄+X₅ ∧ X₅ ≤ 4 ∧ 1 ≤ X₅ ∧ 1 ≤ X₄ ∧ X₄ ≤ 4 ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 5 ≤ X₄+X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l2
l2
l2->l1
t₂₅
τ = X₁+1 ≤ X₀ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l2->l1
t₂₆
τ = X₀+1 ≤ X₁ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
l3->l2
t₂₇
η (X₀) = J1
η (X₃) = X₂
τ = X₁+1 ≤ J1 ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
l3->l2
t₂₈
η (X₀) = J1
η (X₃) = X₂
τ = J1+1 ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
l3->l3
t₂₉
η (X₂) = H1
η (X₄) = 1+X₄
η (X₅) = X₅-1
τ = X₃+1 ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
l3->l3
t₃₀
η (X₂) = H1
η (X₄) = 1+X₄
η (X₅) = X₅-1
τ = X₂+1 ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₅ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄
cycle: [t₁₀₅: l1→l1; t₁₀₆: l1→l1]
loop: (X₄+X₅ ≤ 5 ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₄+X₅ ≤ 5 ∨ 1+X₁ ≤ X₀ ∧ X₄+X₅ ≤ 5 ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₄+X₅ ≤ 5,(X₂,X₃) -> (X₂,X₂)
overappr. closed-form: 2⋅X₂ {O(n)}
runtime bound: inf {Infinity}
Solv. Size Bound - Lifting for t₁₀₆: l1→l1 and X₃: inf {Infinity}
Solv. Size Bound: t₁₀₅: l1→l1 for X₀
Solv. Size Bound: t₁₀₅: l1→l1 for X₂
Solv. Size Bound - Lifting for t₁₀₅: l1→l1 and X₃: inf {Infinity}
Solv. Size Bound: t₁₀₆: l1→l1 for X₀
Solv. Size Bound: t₁₀₆: l1→l1 for X₂
Solv. Size Bound - Lifting for t₁₀₆: l1→l1 and X₃: inf {Infinity}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 14 {O(1)}
t₃₀: 14 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 14 {O(1)}
t₃₀: 14 {O(1)}
Sizebounds
t₂₁, X₀: X₀ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₁, X₄: 1 {O(1)}
t₂₁, X₅: 4 {O(1)}
t₂₂, X₀: X₀ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₂, X₄: 1 {O(1)}
t₂₂, X₅: 4 {O(1)}
t₂₃, X₁: 6⋅X₁ {O(n)}
t₂₃, X₄: 4 {O(1)}
t₂₃, X₅: 4 {O(1)}
t₂₄, X₁: 6⋅X₁ {O(n)}
t₂₄, X₄: 4 {O(1)}
t₂₄, X₅: 4 {O(1)}
t₂₅, X₁: 6⋅X₁ {O(n)}
t₂₅, X₄: 4 {O(1)}
t₂₅, X₅: 4 {O(1)}
t₂₆, X₁: 6⋅X₁ {O(n)}
t₂₆, X₄: 4 {O(1)}
t₂₆, X₅: 4 {O(1)}
t₂₇, X₁: 6⋅X₁ {O(n)}
t₂₇, X₄: 4 {O(1)}
t₂₇, X₅: 4 {O(1)}
t₂₈, X₁: 6⋅X₁ {O(n)}
t₂₈, X₄: 4 {O(1)}
t₂₈, X₅: 4 {O(1)}
t₂₉, X₀: 2⋅X₀ {O(n)}
t₂₉, X₁: 2⋅X₁ {O(n)}
t₂₉, X₃: 2⋅X₃ {O(n)}
t₂₉, X₄: 5 {O(1)}
t₂₉, X₅: 3 {O(1)}
t₃₀, X₀: 2⋅X₀ {O(n)}
t₃₀, X₁: 2⋅X₁ {O(n)}
t₃₀, X₃: 2⋅X₃ {O(n)}
t₃₀, X₄: 5 {O(1)}
t₃₀, X₅: 3 {O(1)}