Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₂: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₂, X₂, X₄, X₄, X₆, X₆, X₀)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃-X₅, X₄, X₅, X₆, X₇) :|: X₅ ≤ X₃ ∧ X₅+1 ≤ X₀ ∧ X₅+X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₅ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₇, X₄, X₅-1, X₆, X₇) :|: X₃+1 ≤ X₅ ∧ X₃+1 ≤ 0 ∧ X₅+1 ≤ X₀ ∧ X₅+X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₅ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₇, X₄, X₅-1, X₆, X₇) :|: X₃+1 ≤ X₅ ∧ 1 ≤ X₃ ∧ X₅+1 ≤ X₀ ∧ X₅+X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₅ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇
t₆: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁-X₅, X₂, X₇, X₄, X₅-1, X₆, X₇) :|: 1 ≤ X₅ ∧ X₅+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇
t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃-X₅, X₄, X₅, X₆, X₇) :|: 1 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅+2 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁+1 ≤ X₀+X₅ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₉: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₇, X₄, X₅-1, X₆, X₇) :|: X₀+1 ≤ X₅ ∧ 1 ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅+2 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁+1 ≤ X₀+X₅ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁₀: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₇, X₄, X₅-1, X₆, X₇) :|: 1 ≤ X₅ ∧ X₀+1 ≤ 0 ∧ 0 ≤ X₅ ∧ X₅+2 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁+1 ≤ X₀+X₅ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁-X₅, X₂, X₇, X₄, X₅-1, X₆, X₇) :|: 1 ≤ X₅ ∧ 0 ≤ X₅ ∧ X₅+2 ≤ 0 ∧ X₁ ≤ 0 ∧ X₁+1 ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₇ ≤ 0 ∧ 0 ≤ X₇ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 2 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁+1 ≤ X₀ ∧ X₅ ≤ 0 ∧ 0 ≤ X₅ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₇, X₂, 1, X₄, X₇-1, X₆, X₇) :|: 2 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₆ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇
t₀: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₆ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇
t₂: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 2 ≤ X₀ ∧ X₁+1 ≤ X₀ ∧ X₅ ≤ 0 ∧ 0 ≤ X₅ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
Preprocessing
Cut unsatisfiable transition t₄: l1→l2
Cut unsatisfiable transition t₉: l2→l2
Cut unsatisfiable transition t₁₀: l2→l2
Cut unsatisfiable transition t₁₁: l2→l2
Found invariant X₇ ≤ X₃ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 2 ≤ X₅+X₇ ∧ 2+X₅ ≤ X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 2+X₅ ≤ X₃ ∧ 2+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l2
Found invariant X₇ ≤ X₃ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 2 ≤ X₅+X₇ ∧ 2+X₅ ≤ X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 1+X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₅ ≤ 0 ∧ 2+X₅ ≤ X₃ ∧ 2+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l5
Found invariant X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l1
Found invariant X₇ ≤ X₀ ∧ X₀ ≤ X₇ for location l4
Found invariant X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₂: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₂, X₂, X₄, X₄, X₆, X₆, X₀)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃-X₅, X₄, X₅, X₆, X₇) :|: X₅ ≤ X₃ ∧ X₅+1 ≤ X₀ ∧ X₅+X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₅ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₇, X₄, X₅-1, X₆, X₇) :|: X₃+1 ≤ X₅ ∧ 1 ≤ X₃ ∧ X₅+1 ≤ X₀ ∧ X₅+X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₅ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀
t₆: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁-X₅, X₂, X₇, X₄, X₅-1, X₆, X₇) :|: 1 ≤ X₅ ∧ X₅+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀
t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃-X₅, X₄, X₅, X₆, X₇) :|: 1 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅+2 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁+1 ≤ X₀+X₅ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₇ ≤ X₃ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 2 ≤ X₅+X₇ ∧ 2+X₅ ≤ X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 2+X₅ ≤ X₃ ∧ 2+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 2 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁+1 ≤ X₀ ∧ X₅ ≤ 0 ∧ 0 ≤ X₅ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₇ ≤ X₃ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 2 ≤ X₅+X₇ ∧ 2+X₅ ≤ X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 2+X₅ ≤ X₃ ∧ 2+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₇, X₂, 1, X₄, X₇-1, X₆, X₇) :|: 2 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₆ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₀: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₆ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₂: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 2 ≤ X₀ ∧ X₁+1 ≤ X₀ ∧ X₅ ≤ 0 ∧ 0 ≤ X₅ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₇ ≤ X₃ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 2 ≤ X₅+X₇ ∧ 2+X₅ ≤ X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 1+X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₅ ≤ 0 ∧ 2+X₅ ≤ X₃ ∧ 2+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
MPRF for transition t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₇, X₄, X₅-1, X₆, X₇) :|: X₃+1 ≤ X₅ ∧ 1 ≤ X₃ ∧ X₅+1 ≤ X₀ ∧ X₅+X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₅ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l2 [X₅ ]
l1 [X₅ ]
MPRF for transition t₆: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁-X₅, X₂, X₇, X₄, X₅-1, X₆, X₇) :|: 1 ≤ X₅ ∧ X₅+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l2 [X₅ ]
l1 [X₅ ]
MPRF for transition t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃-X₅, X₄, X₅, X₆, X₇) :|: 1 ≤ X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅+2 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁+1 ≤ X₀+X₅ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₇ ≤ X₃ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 2 ≤ X₅+X₇ ∧ 2+X₅ ≤ X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 2+X₅ ≤ X₃ ∧ 2+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l2 [X₅+1 ]
l1 [X₅ ]
MPRF for transition t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃-X₅, X₄, X₅, X₆, X₇) :|: X₅ ≤ X₃ ∧ X₅+1 ≤ X₀ ∧ X₅+X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₅ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:
new bound:
7⋅X₀⋅X₀+X₀+2 {O(n^2)}
MPRF:
l1 [X₃+1 ]
l2 [0 ]
Analysing control-flow refined program
Cut unsatisfiable transition t₆: l1→l2
Found invariant X₇ ≤ X₃ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 2 ≤ X₅+X₇ ∧ 2+X₅ ≤ X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 2+X₅ ≤ X₃ ∧ 2+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l2
Found invariant X₇ ≤ X₃ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 2 ≤ X₅+X₇ ∧ 2+X₅ ≤ X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 1+X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₅ ≤ 0 ∧ 2+X₅ ≤ X₃ ∧ 2+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l5
Found invariant X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 3 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₀ ∧ 3 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l1
Found invariant X₇ ≤ X₀ ∧ X₀ ≤ X₇ for location l4
Found invariant X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l3
Found invariant X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₃+X₇ ∧ 2+X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₅ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ for location n_l1___1
knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₁₀₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l1___1(X₀, X₁, X₂, X₃-X₅, X₄, X₅, X₆, X₀) :|: X₁ ≤ X₀ ∧ X₃+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₃+X₅ ∧ X₃+X₅ ≤ X₀ ∧ 2 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ X₃+X₅ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 3 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₀ ∧ 3 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₀₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l1___1(X₀, X₁, X₂, X₃-X₅, X₄, X₅, X₆, X₀) :|: X₁ ≤ X₀ ∧ X₃+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ 1+X₅ ∧ 1+X₅ ≤ X₀ ∧ 2 ≤ X₀ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ X₃+X₅ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 3 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₀ ∧ 3 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀
MPRF for transition t₉₉: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l1___1(X₀, X₁, X₂, X₃-X₅, X₄, X₅, X₆, X₀) :|: X₁ ≤ X₀ ∧ X₃+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ 1 ≤ X₅ ∧ 0 ≤ X₃ ∧ X₃+2⋅X₅ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ X₃+X₅ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₃+X₇ ∧ 2+X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₅ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀⋅X₀+4⋅X₀+1 {O(n^2)}
MPRF:
l1 [X₀+1 ]
n_l1___1 [X₃+1 ]
l2 [X₀+1-X₇ ]
MPRF for transition t₁₀₅: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₇, X₄, X₅-1, X₆, X₇) :|: X₃+1 ≤ X₅ ∧ 1 ≤ X₃ ∧ X₅+1 ≤ X₀ ∧ X₅+X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₅ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₃+X₇ ∧ 2+X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₅ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
l1 [X₅+1 ]
n_l1___1 [X₅+1 ]
l2 [X₅+1 ]
MPRF for transition t₁₀₆: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁-X₅, X₂, X₇, X₄, X₅-1, X₆, X₇) :|: 1 ≤ X₅ ∧ X₅+1 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ X₇ ≤ X₀ ∧ 2 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₃+X₇ ∧ 2+X₃ ≤ X₇ ∧ X₁ ≤ X₇ ∧ 4 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₅ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₀+1 {O(n)}
MPRF:
l1 [X₀+X₅+1 ]
n_l1___1 [X₀+X₅+1 ]
l2 [X₃+X₅+1 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:7⋅X₀⋅X₀+4⋅X₀+7 {O(n^2)}
t₁₂: 1 {O(1)}
t₃: 7⋅X₀⋅X₀+X₀+2 {O(n^2)}
t₅: X₀ {O(n)}
t₆: X₀ {O(n)}
t₇: 1 {O(1)}
t₈: X₀ {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
Costbounds
Overall costbound: 7⋅X₀⋅X₀+4⋅X₀+7 {O(n^2)}
t₁₂: 1 {O(1)}
t₃: 7⋅X₀⋅X₀+X₀+2 {O(n^2)}
t₅: X₀ {O(n)}
t₆: X₀ {O(n)}
t₇: 1 {O(1)}
t₈: X₀ {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
Sizebounds
t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₂ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₄ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₂, X₅: X₆ {O(n)}
t₁₂, X₆: X₆ {O(n)}
t₁₂, X₇: X₀ {O(n)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: 2⋅X₀⋅X₀+4⋅X₀ {O(n^2)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 7⋅X₀+1 {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₀ {O(n)}
t₃, X₆: 2⋅X₆ {O(n)}
t₃, X₇: 2⋅X₀ {O(n)}
t₅, X₀: 2⋅X₀ {O(n)}
t₅, X₁: 2⋅X₀⋅X₀+4⋅X₀ {O(n^2)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 5⋅X₀ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₅, X₅: 2⋅X₀ {O(n)}
t₅, X₆: 2⋅X₆ {O(n)}
t₅, X₇: 2⋅X₀ {O(n)}
t₆, X₀: 2⋅X₀ {O(n)}
t₆, X₁: 2⋅X₀⋅X₀+4⋅X₀ {O(n^2)}
t₆, X₂: 2⋅X₂ {O(n)}
t₆, X₃: 2⋅X₀ {O(n)}
t₆, X₄: 2⋅X₄ {O(n)}
t₆, X₅: 2⋅X₀ {O(n)}
t₆, X₆: 2⋅X₆ {O(n)}
t₆, X₇: 2⋅X₀ {O(n)}
t₇, X₀: 2⋅X₀ {O(n)}
t₇, X₁: 2⋅X₀⋅X₀+4⋅X₀ {O(n^2)}
t₇, X₂: 2⋅X₂ {O(n)}
t₇, X₃: 2⋅X₀ {O(n)}
t₇, X₄: 2⋅X₄ {O(n)}
t₇, X₅: 0 {O(1)}
t₇, X₆: 2⋅X₆ {O(n)}
t₇, X₇: 2⋅X₀ {O(n)}
t₈, X₀: 2⋅X₀ {O(n)}
t₈, X₁: 2⋅X₀⋅X₀+4⋅X₀ {O(n^2)}
t₈, X₂: 2⋅X₂ {O(n)}
t₈, X₃: 7⋅X₀ {O(n)}
t₈, X₄: 2⋅X₄ {O(n)}
t₈, X₅: 2⋅X₀ {O(n)}
t₈, X₆: 2⋅X₆ {O(n)}
t₈, X₇: 2⋅X₀ {O(n)}
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: X₆ {O(n)}
t₀, X₆: X₆ {O(n)}
t₀, X₇: X₀ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: 1 {O(1)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₀ {O(n)}
t₁, X₆: X₆ {O(n)}
t₁, X₇: X₀ {O(n)}
t₂, X₀: 2⋅X₀ {O(n)}
t₂, X₁: 2⋅X₀⋅X₀+4⋅X₀ {O(n^2)}
t₂, X₂: 2⋅X₂ {O(n)}
t₂, X₃: 2⋅X₀ {O(n)}
t₂, X₄: 2⋅X₄ {O(n)}
t₂, X₅: 0 {O(1)}
t₂, X₆: 2⋅X₆ {O(n)}
t₂, X₇: 2⋅X₀ {O(n)}