Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: nondef_0
Locations: l0, l1, l10, l11, l12, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁₃: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ X₅
t₁₂: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ < X₁
t₁₉: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l10(X₀, X₁, X₂, X₃, X₄, X₅-X₁, X₆, X₇)
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(nondef_0, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l10(X₀, X₄-1, X₂, X₃, X₄, X₃, X₆, X₇) :|: X₄ < 1
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l10(X₀, X₄-1, X₂, X₃, X₄, X₃, X₆, X₇) :|: 1 < X₄
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₆) :|: X₄ ≤ 1 ∧ 1 ≤ X₄
t₁₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁₆: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₆, X₇) :|: X₅ < 0
t₁₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₆, X₇) :|: 0 < X₅
t₁₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₂, X₇) :|: X₅ ≤ 0 ∧ 0 ≤ X₅
t₅: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₃, X₅, X₃, X₇) :|: 1 < X₃
t₄: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₀) :|: X₃ ≤ 1
t₉: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₇ < 0
t₁₀: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₇
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₇ ≤ 0 ∧ 0 ≤ X₇
t₁₄: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₆-X₁, X₃, X₄, X₅, X₆, X₇)

Preprocessing

Found invariant X₆ ≤ X₃ ∧ 1+X₂ ≤ X₆ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l6

Found invariant X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 3 ≤ X₃+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l12

Found invariant X₆ ≤ X₃ ∧ 1+X₂ ≤ X₆ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l5

Found invariant X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l10

Found invariant X₆ ≤ X₃ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 2 ≤ X₃ for location l4

Found invariant X₆ ≤ X₃ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l9

Cut unsatisfiable transition t₇: l4→l10

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: nondef_0
Locations: l0, l1, l10, l11, l12, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁₃: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ X₅ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁
t₁₂: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ < X₁ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁
t₁₉: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l10(X₀, X₁, X₂, X₃, X₄, X₅-X₁, X₆, X₇) :|: X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 3 ≤ X₃+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(nondef_0, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l10(X₀, X₄-1, X₂, X₃, X₄, X₃, X₆, X₇) :|: 1 < X₄ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 2 ≤ X₃
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₆) :|: X₄ ≤ 1 ∧ 1 ≤ X₄ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 2 ≤ X₃
t₁₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₆ ≤ X₃ ∧ 1+X₂ ≤ X₆ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁
t₁₆: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₆, X₇) :|: X₅ < 0 ∧ X₆ ≤ X₃ ∧ 1+X₂ ≤ X₆ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁
t₁₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₆, X₇) :|: 0 < X₅ ∧ X₆ ≤ X₃ ∧ 1+X₂ ≤ X₆ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁
t₁₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₂, X₇) :|: X₅ ≤ 0 ∧ 0 ≤ X₅ ∧ X₆ ≤ X₃ ∧ 1+X₂ ≤ X₆ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁
t₅: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₃, X₅, X₃, X₇) :|: 1 < X₃
t₄: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₀) :|: X₃ ≤ 1
t₉: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₇ < 0
t₁₀: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₇
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₇ ≤ 0 ∧ 0 ≤ X₇
t₁₄: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₆-X₁, X₃, X₄, X₅, X₆, X₇) :|: X₆ ≤ X₃ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁

MPRF for transition t₁₂: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ < X₁ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

2⋅X₃ {O(n)}

MPRF:

l12 [X₃+X₄ ]
l10 [X₁+X₃+1 ]
l6 [X₁+X₃ ]
l4 [X₃+X₄ ]
l9 [X₁+X₃ ]
l5 [X₁+X₃ ]

MPRF for transition t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l10(X₀, X₄-1, X₂, X₃, X₄, X₃, X₆, X₇) :|: 1 < X₄ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 2 ≤ X₃ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l12 [X₁ ]
l10 [X₁ ]
l6 [X₁ ]
l4 [X₄ ]
l9 [X₁ ]
l5 [X₁ ]

MPRF for transition t₁₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₆ ≤ X₃ ∧ 1+X₂ ≤ X₆ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

2⋅X₃+3 {O(n)}

MPRF:

l12 [X₁+X₃-2 ]
l10 [X₃+X₄-3 ]
l6 [X₃+X₄-4 ]
l4 [X₃+X₄-3 ]
l9 [X₃+X₄-3 ]
l5 [X₃+X₄-3 ]

MPRF for transition t₁₆: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₆, X₇) :|: X₅ < 0 ∧ X₆ ≤ X₃ ∧ 1+X₂ ≤ X₆ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₃+2 {O(n)}

MPRF:

l12 [X₁-1 ]
l10 [X₁-1 ]
l6 [X₄-2 ]
l4 [X₄-2 ]
l9 [X₄-2 ]
l5 [X₄-2 ]

MPRF for transition t₁₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₆, X₇) :|: 0 < X₅ ∧ X₆ ≤ X₃ ∧ 1+X₂ ≤ X₆ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

l12 [X₁ ]
l10 [X₁ ]
l6 [X₁ ]
l4 [X₄-1 ]
l9 [X₁ ]
l5 [X₁ ]

MPRF for transition t₁₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₂, X₇) :|: X₅ ≤ 0 ∧ 0 ≤ X₅ ∧ X₆ ≤ X₃ ∧ 1+X₂ ≤ X₆ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

l12 [X₄-1 ]
l10 [X₄-1 ]
l6 [X₁ ]
l4 [X₄-1 ]
l9 [X₁ ]
l5 [X₁ ]

MPRF for transition t₁₄: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₆-X₁, X₃, X₄, X₅, X₆, X₇) :|: X₆ ≤ X₃ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

l12 [X₄-1 ]
l10 [X₁ ]
l6 [X₁-1 ]
l4 [X₄-1 ]
l9 [X₁ ]
l5 [X₁-1 ]

Found invariant X₆ ≤ X₃ ∧ 1+X₂ ≤ X₆ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l6

Found invariant X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 3 ≤ X₃+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l12

Found invariant X₆ ≤ X₃ ∧ 1+X₂ ≤ X₆ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l5

Found invariant X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l10

Found invariant X₆ ≤ X₃ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 2 ≤ X₃ for location l4

Found invariant X₆ ≤ X₃ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l9

Found invariant X₆ ≤ X₃ ∧ 1+X₂ ≤ X₆ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l6

Found invariant X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 3 ≤ X₃+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l12

Found invariant X₆ ≤ X₃ ∧ 1+X₂ ≤ X₆ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l5

Found invariant X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l10

Found invariant X₆ ≤ X₃ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 2 ≤ X₃ for location l4

Found invariant X₆ ≤ X₃ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l9

MPRF for transition t₁₃: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ X₅ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

7⋅X₃⋅X₃+10⋅X₃+3 {O(n^2)}

MPRF:

l9 [X₅-X₁ ]
l12 [X₅+1-2⋅X₁ ]
l10 [X₅+1-X₁ ]
l5 [X₃+X₄+1-2⋅X₁ ]
l6 [X₃+2-X₁ ]
l4 [X₃+2-X₄ ]

MPRF for transition t₁₉: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l10(X₀, X₁, X₂, X₃, X₄, X₅-X₁, X₆, X₇) :|: X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 3 ≤ X₃+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

2⋅X₃⋅X₃+4⋅X₃ {O(n^2)}

MPRF:

l9 [X₁+X₅-1 ]
l12 [X₄+X₅-2 ]
l10 [X₁+X₅-1 ]
l5 [X₁+X₃ ]
l6 [X₁+X₃ ]
l4 [X₃+X₄ ]

Analysing control-flow refined program

Cut unsatisfiable transition t₁₂: l10→l9

Found invariant X₆ ≤ X₃ ∧ 1+X₂ ≤ X₆ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l6

Found invariant X₆ ≤ X₃ ∧ 1+X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location n_l10___2

Found invariant X₆ ≤ X₅ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location n_l12___3

Found invariant X₆ ≤ X₃ ∧ 1+X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 3 ≤ X₃+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location n_l12___1

Found invariant X₆ ≤ X₃ ∧ 1+X₂ ≤ X₆ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l5

Found invariant X₆ ≤ X₅ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l10

Found invariant X₆ ≤ X₃ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 2 ≤ X₃ for location l4

Found invariant X₆ ≤ X₃ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location l9

knowledge_propagation leads to new time bound X₃ {O(n)} for transition t₁₈₇: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l12___3(X₀, X₁, X₂, X₃, X₁+1, X₅, X₆, X₇) :|: X₅ ≤ X₃ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ X₃ ∧ X₆ ≤ X₃ ∧ X₁+1 ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ X₅ ≤ X₃ ∧ X₆ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₅ ∧ X₁+1 ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁

knowledge_propagation leads to new time bound X₃ {O(n)} for transition t₁₈₉: n_l12___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l10___2(X₀, X₁, X₂, X₃, X₁+1, X₅-X₁, X₆, X₇) :|: X₅ ≤ X₃ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ X₃ ∧ X₆ ≤ X₃ ∧ 2 ≤ X₄ ∧ X₁+1 ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₅ ∧ X₁+1 ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁

MPRF for transition t₁₈₆: n_l10___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l12___1(X₀, X₁, X₂, X₃, X₁+1, X₅, X₆, X₇) :|: X₅ ≤ X₃ ∧ X₄ ≤ X₃ ∧ X₆ ≤ X₃ ∧ 2 ≤ X₄ ∧ X₁+1 ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₅ ∧ X₄+X₅ ≤ 1+X₃ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₃ ∧ X₆ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₅ ∧ X₁+1 ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ X₆ ≤ X₃ ∧ 1+X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

6⋅X₃⋅X₃+X₃ {O(n^2)}

MPRF:

n_l12___3 [X₅ ]
l10 [X₃ ]
l6 [X₃ ]
l4 [X₃ ]
l5 [X₃+X₄+X₅-1 ]
l9 [X₃+X₄+X₅-1 ]
n_l12___1 [X₁+X₃+X₅+1-X₄ ]
n_l10___2 [X₁+X₃+X₅ ]

MPRF for transition t₁₉₃: n_l10___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ < X₁ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ ∧ X₆ ≤ X₃ ∧ 1+X₅ ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l10 [X₁+1 ]
l6 [X₄-1 ]
l4 [X₄ ]
l5 [X₄-1 ]
l9 [X₁ ]
n_l12___1 [X₁+1 ]
n_l12___3 [X₁+1 ]
n_l10___2 [X₁+1 ]

MPRF for transition t₁₈₈: n_l12___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l10___2(X₀, X₁, X₂, X₃, X₁+1, X₅-X₁, X₆, X₇) :|: X₆ ≤ X₃ ∧ X₄+X₅ ≤ 1+X₃ ∧ X₄ ≤ 1+X₅ ∧ 2 ≤ X₄ ∧ X₁+1 ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₅ ∧ X₁+1 ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ X₆ ≤ X₃ ∧ 1+X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 3 ≤ X₃+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

5⋅X₃⋅X₃+X₃ {O(n^2)}

MPRF:

n_l12___3 [0 ]
l10 [0 ]
l6 [0 ]
l4 [0 ]
l5 [0 ]
l9 [0 ]
n_l12___1 [X₅ ]
n_l10___2 [X₁+X₅-1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:9⋅X₃⋅X₃+23⋅X₃+21 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₂: 2⋅X₃ {O(n)}
t₁₃: 7⋅X₃⋅X₃+10⋅X₃+3 {O(n^2)}
t₁₉: 2⋅X₃⋅X₃+4⋅X₃ {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₆: 1 {O(1)}
t₈: X₃ {O(n)}
t₁₅: 2⋅X₃+3 {O(n)}
t₁₆: X₃+2 {O(n)}
t₁₇: X₃+1 {O(n)}
t₁₈: X₃+1 {O(n)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁₄: X₃+1 {O(n)}

Costbounds

Overall costbound: 9⋅X₃⋅X₃+23⋅X₃+21 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₂: 2⋅X₃ {O(n)}
t₁₃: 7⋅X₃⋅X₃+10⋅X₃+3 {O(n^2)}
t₁₉: 2⋅X₃⋅X₃+4⋅X₃ {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₆: 1 {O(1)}
t₈: X₃ {O(n)}
t₁₅: 2⋅X₃+3 {O(n)}
t₁₆: X₃+2 {O(n)}
t₁₇: X₃+1 {O(n)}
t₁₈: X₃+1 {O(n)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁₄: X₃+1 {O(n)}

Sizebounds

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)}
t₀, X₆: X₆ {O(n)}
t₀, X₇: X₇ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₃, X₅: X₅ {O(n)}
t₃, X₆: X₆ {O(n)}
t₃, X₇: X₇ {O(n)}
t₁₂, X₁: X₃ {O(n)}
t₁₂, X₂: 3⋅X₃⋅X₃+9⋅X₃+X₂ {O(n^2)}
t₁₂, X₃: X₃ {O(n)}
t₁₂, X₄: 4⋅X₃ {O(n)}
t₁₂, X₅: 4⋅X₃ {O(n)}
t₁₂, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₂, X₇: X₇ {O(n)}
t₁₃, X₁: X₃ {O(n)}
t₁₃, X₂: 3⋅X₃⋅X₃+9⋅X₃+X₂ {O(n^2)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: 4⋅X₃ {O(n)}
t₁₃, X₅: 4⋅X₃ {O(n)}
t₁₃, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₃, X₇: X₇ {O(n)}
t₁₉, X₁: X₃ {O(n)}
t₁₉, X₂: 3⋅X₃⋅X₃+9⋅X₃+X₂ {O(n^2)}
t₁₉, X₃: X₃ {O(n)}
t₁₉, X₄: 4⋅X₃ {O(n)}
t₁₉, X₅: 4⋅X₃ {O(n)}
t₁₉, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₉, X₇: X₇ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₁, X₇: X₇ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₂, X₇: X₇ {O(n)}
t₆, X₁: X₃ {O(n)}
t₆, X₂: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: 1 {O(1)}
t₆, X₅: 0 {O(1)}
t₆, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₆, X₇: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₈, X₁: X₃ {O(n)}
t₈, X₂: 3⋅X₃⋅X₃+9⋅X₃+X₂ {O(n^2)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: 4⋅X₃ {O(n)}
t₈, X₅: 4⋅X₃ {O(n)}
t₈, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₈, X₇: X₇ {O(n)}
t₁₅, X₁: X₃ {O(n)}
t₁₅, X₂: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: 4⋅X₃ {O(n)}
t₁₅, X₅: 4⋅X₃ {O(n)}
t₁₅, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₅, X₇: X₇ {O(n)}
t₁₆, X₁: X₃ {O(n)}
t₁₆, X₂: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₆, X₃: X₃ {O(n)}
t₁₆, X₄: X₃ {O(n)}
t₁₆, X₅: 4⋅X₃ {O(n)}
t₁₆, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₆, X₇: X₇ {O(n)}
t₁₇, X₁: X₃ {O(n)}
t₁₇, X₂: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: X₃ {O(n)}
t₁₇, X₅: 4⋅X₃ {O(n)}
t₁₇, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₇, X₇: X₇ {O(n)}
t₁₈, X₁: X₃ {O(n)}
t₁₈, X₂: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₈, X₃: X₃ {O(n)}
t₁₈, X₄: X₃ {O(n)}
t₁₈, X₅: 0 {O(1)}
t₁₈, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₈, X₇: X₇ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₃ {O(n)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₃ {O(n)}
t₅, X₇: X₇ {O(n)}
t₉, X₁: X₁+X₃ {O(n)}
t₉, X₂: X₃⋅X₃+3⋅X₃+X₂ {O(n^2)}
t₉, X₃: 2⋅X₃ {O(n)}
t₉, X₄: X₄+1 {O(n)}
t₉, X₅: X₅ {O(n)}
t₉, X₆: X₃⋅X₃+3⋅X₃+X₆ {O(n^2)}
t₁₀, X₁: X₁+X₃ {O(n)}
t₁₀, X₂: X₃⋅X₃+3⋅X₃+X₂ {O(n^2)}
t₁₀, X₃: 2⋅X₃ {O(n)}
t₁₀, X₄: X₄+1 {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₀, X₆: X₃⋅X₃+3⋅X₃+X₆ {O(n^2)}
t₁₁, X₁: X₁+X₃ {O(n)}
t₁₁, X₂: X₃⋅X₃+3⋅X₃+X₂ {O(n^2)}
t₁₁, X₃: 2⋅X₃ {O(n)}
t₁₁, X₄: X₄+1 {O(n)}
t₁₁, X₅: X₅ {O(n)}
t₁₁, X₆: X₃⋅X₃+3⋅X₃+X₆ {O(n^2)}
t₁₁, X₇: 0 {O(1)}
t₁₄, X₁: X₃ {O(n)}
t₁₄, X₂: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: 4⋅X₃ {O(n)}
t₁₄, X₅: 4⋅X₃ {O(n)}
t₁₄, X₆: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₁₄, X₇: X₇ {O(n)}