Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars: K
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₈: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l5(X₀, X₂, X₂, X₄, X₄, X₀, X₇, X₇, X₉, X₉)
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₈-2, X₇, X₈, X₉) :|: 1 ≤ X₈ ∧ X₈+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₈, X₄, X₅, X₈-1, X₇, 1+X₈, X₉) :|: 1 ≤ X₈ ∧ X₈+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1, X₇, X₈, X₉) :|: 0 ≤ X₆ ∧ X₆+2 ≤ X₈ ∧ 0 ≤ 1+X₆ ∧ X₈+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₈, X₄, X₅, X₆, X₇, 1+X₈, X₉) :|: X₆+2 ≤ X₈ ∧ 0 ≤ 1+X₆ ∧ X₈+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀, K, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₃+2 ≤ X₀ ∧ 1 ≤ X₆+X₃ ∧ 0 ≤ 1+X₆ ∧ X₃+1 ≤ X₀ ∧ X₆+1 ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₈ ≤ X₃+1 ∧ X₃+1 ≤ X₈
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 2 ≤ X₆+X₀ ∧ 0 ≤ 1+X₆ ∧ 2+X₆ ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₈ ≤ X₀ ∧ X₀ ≤ X₈ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1
t₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀, K, X₂, X₃, X₄, X₅, X₆, X₇, 1, X₉) :|: 2 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₈ ≤ X₉ ∧ X₉ ≤ X₈
t₀: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, 1, X₉) :|: X₀ ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₈ ≤ X₉ ∧ X₉ ≤ X₈
Preprocessing
Found invariant 1 ≤ X₈ ∧ X₅ ≤ X₈ ∧ X₀ ≤ X₈ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ for location l2
Found invariant X₉ ≤ X₈ ∧ X₈ ≤ X₉ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l5
Found invariant 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀ for location l1
Found invariant X₈ ≤ X₅ ∧ X₈ ≤ 1+X₃ ∧ X₈ ≤ X₀ ∧ 2 ≤ X₈ ∧ 1 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 4 ≤ X₅+X₈ ∧ 3 ≤ X₃+X₈ ∧ 1+X₃ ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ 2+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₃ ∧ 2+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₀ for location l4
Found invariant 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 0 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ 3+X₆ ≤ X₅ ∧ 3+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars: K
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₈: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l5(X₀, X₂, X₂, X₄, X₄, X₀, X₇, X₇, X₉, X₉)
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₈-2, X₇, X₈, X₉) :|: 1 ≤ X₈ ∧ X₈+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₈, X₄, X₅, X₈-1, X₇, 1+X₈, X₉) :|: 1 ≤ X₈ ∧ X₈+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1, X₇, X₈, X₉) :|: 0 ≤ X₆ ∧ X₆+2 ≤ X₈ ∧ 0 ≤ 1+X₆ ∧ X₈+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 0 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ 3+X₆ ≤ X₅ ∧ 3+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₈, X₄, X₅, X₆, X₇, 1+X₈, X₉) :|: X₆+2 ≤ X₈ ∧ 0 ≤ 1+X₆ ∧ X₈+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 0 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ 3+X₆ ≤ X₅ ∧ 3+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀, K, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₃+2 ≤ X₀ ∧ 1 ≤ X₆+X₃ ∧ 0 ≤ 1+X₆ ∧ X₃+1 ≤ X₀ ∧ X₆+1 ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₈ ≤ X₃+1 ∧ X₃+1 ≤ X₈ ∧ X₈ ≤ X₅ ∧ X₈ ≤ 1+X₃ ∧ X₈ ≤ X₀ ∧ 2 ≤ X₈ ∧ 1 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 4 ≤ X₅+X₈ ∧ 3 ≤ X₃+X₈ ∧ 1+X₃ ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ 2+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₃ ∧ 2+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 2 ≤ X₆+X₀ ∧ 0 ≤ 1+X₆ ∧ 2+X₆ ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₈ ≤ X₀ ∧ X₀ ≤ X₈ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ X₈ ≤ X₅ ∧ X₈ ≤ 1+X₃ ∧ X₈ ≤ X₀ ∧ 2 ≤ X₈ ∧ 1 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 4 ≤ X₅+X₈ ∧ 3 ≤ X₃+X₈ ∧ 1+X₃ ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ 2+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₃ ∧ 2+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₀
t₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀, K, X₂, X₃, X₄, X₅, X₆, X₇, 1, X₉) :|: 2 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₈ ≤ X₉ ∧ X₉ ≤ X₈ ∧ X₉ ≤ X₈ ∧ X₈ ≤ X₉ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₀: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, 1, X₉) :|: X₀ ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₈ ≤ X₉ ∧ X₉ ≤ X₈ ∧ X₉ ≤ X₈ ∧ X₈ ≤ X₉ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
MPRF for transition t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₈, X₄, X₅, X₆, X₇, 1+X₈, X₉) :|: X₆+2 ≤ X₈ ∧ 0 ≤ 1+X₆ ∧ X₈+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 0 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ 3+X₆ ≤ X₅ ∧ 3+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₈-2, X₇, X₈, X₉) :|: 1 ≤ X₈ ∧ X₈+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₈, X₄, X₅, X₈-1, X₇, 1+X₈, X₉) :|: 1 ≤ X₈ ∧ X₈+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀, K, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₃+2 ≤ X₀ ∧ 1 ≤ X₆+X₃ ∧ 0 ≤ 1+X₆ ∧ X₃+1 ≤ X₀ ∧ X₆+1 ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₈ ≤ X₃+1 ∧ X₃+1 ≤ X₈ ∧ X₈ ≤ X₅ ∧ X₈ ≤ 1+X₃ ∧ X₈ ≤ X₀ ∧ 2 ≤ X₈ ∧ 1 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 4 ≤ X₅+X₈ ∧ 3 ≤ X₃+X₈ ∧ 1+X₃ ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ 2+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₃ ∧ 2+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1, X₇, X₈, X₉) :|: 0 ≤ X₆ ∧ X₆+2 ≤ X₈ ∧ 0 ≤ 1+X₆ ∧ X₈+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 0 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ 3+X₆ ≤ X₅ ∧ 3+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₀⋅X₀+5⋅X₀+4 {O(n^2)}
Chain transitions t₁: l5→l1 and t₅: l1→l4 to t₅₅: l5→l4
Chain transitions t₇: l4→l1 and t₅: l1→l4 to t₅₆: l4→l4
Chain transitions t₇: l4→l1 and t₄: l1→l3 to t₅₇: l4→l3
Chain transitions t₁: l5→l1 and t₄: l1→l3 to t₅₈: l5→l3
Analysing control-flow refined program
Found invariant 1 ≤ X₈ ∧ X₅ ≤ X₈ ∧ X₀ ≤ X₈ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ for location l2
Found invariant X₉ ≤ X₈ ∧ X₈ ≤ X₉ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l5
Found invariant 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀ for location l1
Found invariant X₈ ≤ X₅ ∧ X₈ ≤ 1+X₃ ∧ X₈ ≤ X₀ ∧ 2 ≤ X₈ ∧ 1 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 4 ≤ X₅+X₈ ∧ 3 ≤ X₃+X₈ ∧ 1+X₃ ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ 2+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₃ ∧ 2+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₀ for location l4
Found invariant 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 0 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ 3+X₆ ≤ X₅ ∧ 3+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀ for location l3
MPRF for transition t₅₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) -{2}> l4(X₀, K, X₂, X₈, X₄, X₅, X₈-1, X₇, 1+X₈, X₉) :|: X₃+2 ≤ X₀ ∧ 1 ≤ X₆+X₃ ∧ 0 ≤ 1+X₆ ∧ X₃+1 ≤ X₀ ∧ X₆+1 ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₈ ≤ X₃+1 ∧ X₃+1 ≤ X₈ ∧ 1 ≤ X₈ ∧ X₈+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₈ ≤ X₅ ∧ X₈ ≤ 1+X₃ ∧ X₈ ≤ X₀ ∧ 2 ≤ X₈ ∧ 1 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 4 ≤ X₅+X₈ ∧ 3 ≤ X₃+X₈ ∧ 1+X₃ ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ 2+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₃ ∧ 2+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₀ ∧ 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀ ∧ X₈ ≤ X₅ ∧ X₈ ≤ 1+X₃ ∧ X₈ ≤ X₀ ∧ 2 ≤ X₈ ∧ 1 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 4 ≤ X₅+X₈ ∧ 3 ≤ X₃+X₈ ∧ 1+X₃ ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ 2+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₃ ∧ 2+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₀ of depth 1:
new bound:
4⋅X₀+6 {O(n)}
MPRF for transition t₅₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) -{2}> l3(X₀, K, X₂, X₃, X₄, X₅, X₈-2, X₇, X₈, X₉) :|: X₃+2 ≤ X₀ ∧ 1 ≤ X₆+X₃ ∧ 0 ≤ 1+X₆ ∧ X₃+1 ≤ X₀ ∧ X₆+1 ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₈ ≤ X₃+1 ∧ X₃+1 ≤ X₈ ∧ 1 ≤ X₈ ∧ X₈+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₈ ≤ X₅ ∧ X₈ ≤ 1+X₃ ∧ X₈ ≤ X₀ ∧ 2 ≤ X₈ ∧ 1 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 4 ≤ X₅+X₈ ∧ 3 ≤ X₃+X₈ ∧ 1+X₃ ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ 2+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₃ ∧ 2+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₀ ∧ 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀ ∧ X₈ ≤ X₅ ∧ X₈ ≤ 1+X₃ ∧ X₈ ≤ X₀ ∧ 2 ≤ X₈ ∧ 1 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 4 ≤ X₅+X₈ ∧ 3 ≤ X₃+X₈ ∧ 1+X₃ ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ 2+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₃ ∧ 2+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₀ of depth 1:
new bound:
4⋅X₀+6 {O(n)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Found invariant 1 ≤ X₈ ∧ X₅ ≤ X₈ ∧ X₀ ≤ X₈ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ for location l2
Found invariant X₉ ≤ X₈ ∧ X₈ ≤ X₉ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l5
Found invariant 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀ for location l1
Found invariant X₈ ≤ X₅ ∧ X₈ ≤ 1+X₃ ∧ X₈ ≤ X₀ ∧ 2 ≤ X₈ ∧ 1 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 4 ≤ X₅+X₈ ∧ 3 ≤ X₃+X₈ ∧ 1+X₃ ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ 2+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₃ ∧ 2+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₀ for location l4
Found invariant 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 2 ≤ X₈ ∧ 1 ≤ X₆+X₈ ∧ 3+X₆ ≤ X₈ ∧ 5 ≤ X₅+X₈ ∧ 5 ≤ X₀+X₈ ∧ 4+X₆ ≤ X₅ ∧ 4+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 2 ≤ X₅+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 3 ≤ X₅ ∧ 6 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 3 ≤ X₀ for location n_l3___1
Found invariant X₈ ≤ 2+X₆ ∧ 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 0 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ 3+X₆ ≤ X₅ ∧ 3+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀ for location l3
knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₁₀₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → n_l3___1(X₀, X₁, X₂, X₃, X₄, X₀, X₆-1, X₇, X₈, X₉) :|: X₈ ≤ 2+X₆ ∧ 0 ≤ X₆ ∧ 1+X₈ ≤ X₀ ∧ 2+X₆ ≤ X₈ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 2+X₆ ≤ X₈ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 3+X₆ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 2+X₆ ≤ X₈ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₈ ≤ 2+X₆ ∧ 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 0 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ 3+X₆ ≤ X₅ ∧ 3+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀
MPRF for transition t₁₀₅: n_l3___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → n_l3___1(X₀, X₁, X₂, X₃, X₄, X₀, X₆-1, X₇, X₈, X₉) :|: 3+X₆ ≤ X₈ ∧ 0 ≤ X₆ ∧ 1+X₈ ≤ X₀ ∧ 2+X₆ ≤ X₈ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1+X₈ ≤ X₀ ∧ 1+X₈ ≤ X₀ ∧ 2+X₆ ≤ X₈ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 2 ≤ X₈ ∧ 1 ≤ X₆+X₈ ∧ 3+X₆ ≤ X₈ ∧ 5 ≤ X₅+X₈ ∧ 5 ≤ X₀+X₈ ∧ 4+X₆ ≤ X₅ ∧ 4+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 2 ≤ X₅+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 3 ≤ X₅ ∧ 6 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 3 ≤ X₀ of depth 1:
new bound:
4⋅X₀⋅X₀+11⋅X₀+7 {O(n^2)}
MPRF for transition t₁₀₉: n_l3___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₈, X₄, X₅, X₆, X₇, 1+X₈, X₉) :|: X₆+2 ≤ X₈ ∧ 0 ≤ 1+X₆ ∧ X₈+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 1 ≤ X₈ ∧ 0 ≤ X₆+X₈ ∧ 2+X₆ ≤ X₈ ∧ 3 ≤ X₅+X₈ ∧ 3 ≤ X₀+X₈ ∧ 3+X₆ ≤ X₅ ∧ 3+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2 ≤ X₀ ∧ 1+X₈ ≤ X₅ ∧ 1+X₈ ≤ X₀ ∧ 2 ≤ X₈ ∧ 1 ≤ X₆+X₈ ∧ 3+X₆ ≤ X₈ ∧ 5 ≤ X₅+X₈ ∧ 5 ≤ X₀+X₈ ∧ 4+X₆ ≤ X₅ ∧ 4+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 2 ≤ X₅+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₅ ≤ X₀ ∧ 3 ≤ X₅ ∧ 6 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 3 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:2⋅X₀⋅X₀+9⋅X₀+12 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 2⋅X₀⋅X₀+5⋅X₀+4 {O(n^2)}
t₃: X₀+1 {O(n)}
t₄: X₀+1 {O(n)}
t₅: X₀+1 {O(n)}
t₆: 1 {O(1)}
t₇: X₀+1 {O(n)}
t₈: 1 {O(1)}
Costbounds
Overall costbound: 2⋅X₀⋅X₀+9⋅X₀+12 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 2⋅X₀⋅X₀+5⋅X₀+4 {O(n^2)}
t₃: X₀+1 {O(n)}
t₄: X₀+1 {O(n)}
t₅: X₀+1 {O(n)}
t₆: 1 {O(1)}
t₇: X₀+1 {O(n)}
t₈: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₂ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₄ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₀ {O(n)}
t₀, X₆: X₇ {O(n)}
t₀, X₇: X₇ {O(n)}
t₀, X₈: 1 {O(1)}
t₀, X₉: X₉ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₄ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₀ {O(n)}
t₁, X₆: X₇ {O(n)}
t₁, X₇: X₇ {O(n)}
t₁, X₈: 1 {O(1)}
t₁, X₉: X₉ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: 6⋅X₀+X₄+10 {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₀ {O(n)}
t₂, X₆: 2⋅X₀+5 {O(n)}
t₂, X₇: X₇ {O(n)}
t₂, X₈: 2⋅X₀+3 {O(n)}
t₂, X₉: X₉ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: 4⋅X₀+6 {O(n)}
t₃, X₄: X₄ {O(n)}
t₃, X₅: X₀ {O(n)}
t₃, X₆: 4⋅X₀+9 {O(n)}
t₃, X₇: X₇ {O(n)}
t₃, X₈: 2⋅X₀+3 {O(n)}
t₃, X₉: X₉ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: 6⋅X₀+X₄+10 {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₀ {O(n)}
t₄, X₆: 2⋅X₀+4 {O(n)}
t₄, X₇: X₇ {O(n)}
t₄, X₈: 2⋅X₀+3 {O(n)}
t₄, X₉: X₉ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: 2⋅X₀+4 {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₀ {O(n)}
t₅, X₆: 2⋅X₀+4 {O(n)}
t₅, X₇: X₇ {O(n)}
t₅, X₈: 2⋅X₀+3 {O(n)}
t₅, X₉: X₉ {O(n)}
t₆, X₀: 2⋅X₀ {O(n)}
t₆, X₂: 2⋅X₂ {O(n)}
t₆, X₃: 6⋅X₀+10 {O(n)}
t₆, X₄: 2⋅X₄ {O(n)}
t₆, X₅: 2⋅X₀ {O(n)}
t₆, X₆: 6⋅X₀+13 {O(n)}
t₆, X₇: 2⋅X₇ {O(n)}
t₆, X₈: 4⋅X₀+6 {O(n)}
t₆, X₉: 2⋅X₉ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: 6⋅X₀+10 {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₀ {O(n)}
t₇, X₆: 6⋅X₀+13 {O(n)}
t₇, X₇: X₇ {O(n)}
t₇, X₈: 2⋅X₀+3 {O(n)}
t₇, X₉: X₉ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₂ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₄ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₀ {O(n)}
t₈, X₆: X₇ {O(n)}
t₈, X₇: X₇ {O(n)}
t₈, X₈: X₉ {O(n)}
t₈, X₉: X₉ {O(n)}