Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l18, l19, l2, l20, l21, l22, l23, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂₂: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l11(X₀, X₆+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂₃: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₅: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₂: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l19(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃ < X₆
t₁₁: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₄, X₈) :|: X₆ ≤ X₃
t₆: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₇: l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₈: l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₉: l17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l18(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₀: l18(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₂, X₇, X₈)
t₂₅: l19(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l23(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₅: l20(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l21(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₆-X₇)
t₁₆: l21(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l22(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₈ ≤ X₆+X₇
t₁₇: l21(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₆+X₇ < X₈
t₁₈: l22(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l21(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈+1)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₀, X₈)
t₁₉: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l7(X₇+1, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂₀: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₄: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₅ < X₇
t₁₃: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l20(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₇ ≤ X₅
t₂₄: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₁, X₇, X₈)
Preprocessing
Found invariant 1+X₅ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ 1+X₆ ≤ X₁ ∧ X₂ ≤ X₆ ∧ X₁ ≤ 1+X₆ ∧ X₂ ≤ X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ for location l11
Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location l6
Found invariant 1+X₃ ≤ X₆ ∧ X₂ ≤ X₆ for location l19
Found invariant 1+X₃ ≤ X₆ ∧ X₂ ≤ X₆ for location l23
Found invariant X₇ ≤ X₅ ∧ 1+X₇ ≤ X₀ ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ for location l7
Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location l20
Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location l21
Found invariant X₇ ≤ X₅ ∧ 1+X₇ ≤ X₀ ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ for location l5
Found invariant X₂ ≤ X₆ for location l13
Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location l22
Found invariant X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₃ for location l8
Found invariant 1+X₅ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₃ for location l10
Found invariant 1+X₅ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ 1+X₆ ≤ X₁ ∧ X₂ ≤ X₆ ∧ X₁ ≤ 1+X₆ ∧ X₂ ≤ X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ for location l9
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l18, l19, l2, l20, l21, l22, l23, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂₂: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l11(X₀, X₆+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₅ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₃
t₂₃: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₅ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ 1+X₆ ≤ X₁ ∧ X₂ ≤ X₆ ∧ X₁ ≤ 1+X₆ ∧ X₂ ≤ X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁
t₅: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₂: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l19(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃ < X₆ ∧ X₂ ≤ X₆
t₁₁: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₄, X₈) :|: X₆ ≤ X₃ ∧ X₂ ≤ X₆
t₆: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₇: l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₈: l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₉: l17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l18(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₀: l18(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₂, X₇, X₈)
t₂₅: l19(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l23(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₃ ≤ X₆ ∧ X₂ ≤ X₆
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₅: l20(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l21(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₆-X₇) :|: X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃
t₁₆: l21(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l22(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₈ ≤ X₆+X₇ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃
t₁₇: l21(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₆+X₇ < X₈ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃
t₁₈: l22(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l21(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈+1) :|: X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₀, X₈) :|: X₇ ≤ X₅ ∧ 1+X₇ ≤ X₀ ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃
t₁₉: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l7(X₇+1, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃
t₂₀: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₇ ≤ X₅ ∧ 1+X₇ ≤ X₀ ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃
t₁₄: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₅ < X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₃
t₁₃: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l20(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₃
t₂₄: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₁, X₇, X₈) :|: 1+X₅ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ 1+X₆ ≤ X₁ ∧ X₂ ≤ X₆ ∧ X₁ ≤ 1+X₆ ∧ X₂ ≤ X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁
Solv. Size Bound: t₁₄: l8→l10 for X₀
Solv. Size Bound: t₁₄: l8→l10 for X₁
Solv. Size Bound: t₁₄: l8→l10 for X₆
Solv. Size Bound: t₁₄: l8→l10 for X₇
cycle: [t₁₄: l8→l10; t₂₂: l10→l11; t₂₃: l11→l9; t₂₄: l9→l13; t₁₁: l13→l8]
loop: (X₅ < X₇ ∧ 1+X₆ ≤ X₃,(X₄,X₇) -> (X₄,X₄)
overappr. closed-form: 2⋅X₄ {O(n)}
runtime bound: X₃+X₆+1 {O(n)}
Solv. Size Bound - Lifting for t₁₄: l8→l10 and X₇: 4⋅X₄ {O(n)}
Solv. Size Bound: t₂₂: l10→l11 for X₀
Solv. Size Bound: t₂₂: l10→l11 for X₁
Solv. Size Bound: t₂₂: l10→l11 for X₆
Solv. Size Bound: t₂₂: l10→l11 for X₇
cycle: [t₁₄: l8→l10; t₁₁: l13→l8; t₂₄: l9→l13; t₂₃: l11→l9; t₂₂: l10→l11]
loop: (X₅ < X₇ ∧ X₆ ≤ X₃,(X₄,X₇) -> (X₄,X₄)
overappr. closed-form: 2⋅X₄ {O(n)}
runtime bound: X₃+X₆+2 {O(n)}
Solv. Size Bound - Lifting for t₂₂: l10→l11 and X₇: 4⋅X₄ {O(n)}
Solv. Size Bound: t₂₃: l11→l9 for X₀
Solv. Size Bound: t₂₃: l11→l9 for X₁
Solv. Size Bound: t₂₃: l11→l9 for X₆
Solv. Size Bound: t₂₃: l11→l9 for X₇
cycle: [t₂₂: l10→l11; t₁₄: l8→l10; t₁₁: l13→l8; t₂₄: l9→l13; t₂₃: l11→l9]
loop: (X₅ < X₇ ∧ X₆ ≤ X₃,(X₄,X₇) -> (X₄,X₄)
overappr. closed-form: 2⋅X₄ {O(n)}
runtime bound: X₃+X₆+2 {O(n)}
Solv. Size Bound - Lifting for t₂₃: l11→l9 and X₇: 4⋅X₄ {O(n)}
Solv. Size Bound: t₂₄: l9→l13 for X₀
Solv. Size Bound: t₂₄: l9→l13 for X₁
Solv. Size Bound: t₂₄: l9→l13 for X₆
Solv. Size Bound: t₂₄: l9→l13 for X₇
cycle: [t₂₃: l11→l9; t₂₂: l10→l11; t₁₄: l8→l10; t₁₁: l13→l8; t₂₄: l9→l13]
loop: (X₅ < X₇ ∧ X₁ ≤ X₃,(X₄,X₇) -> (X₄,X₄)
overappr. closed-form: 2⋅X₄ {O(n)}
runtime bound: X₁+X₃+2 {O(n)}
Solv. Size Bound - Lifting for t₂₄: l9→l13 and X₇: 4⋅X₄ {O(n)}
MPRF for transition t₁₁: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₄, X₈) :|: X₆ ≤ X₃ ∧ X₂ ≤ X₆ of depth 1:
new bound:
X₂+X₃+1 {O(n)}
MPRF for transition t₁₄: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₅ < X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₃ of depth 1:
new bound:
X₂+X₃+1 {O(n)}
MPRF for transition t₂₂: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l11(X₀, X₆+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₅ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₃ of depth 1:
new bound:
X₂+X₃+1 {O(n)}
MPRF for transition t₂₃: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₅ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ 1+X₆ ≤ X₁ ∧ X₂ ≤ X₆ ∧ X₁ ≤ 1+X₆ ∧ X₂ ≤ X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ of depth 1:
new bound:
X₂+X₃+1 {O(n)}
MPRF for transition t₂₄: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₁, X₇, X₈) :|: 1+X₅ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ 1+X₆ ≤ X₁ ∧ X₂ ≤ X₆ ∧ X₁ ≤ 1+X₆ ∧ X₂ ≤ X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ of depth 1:
new bound:
X₂+X₃+1 {O(n)}
MPRF for transition t₁₃: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l20(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₃ of depth 1:
new bound:
X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
MPRF for transition t₁₅: l20(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l21(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₆-X₇) :|: X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ of depth 1:
new bound:
X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
MPRF for transition t₁₇: l21(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₆+X₇ < X₈ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ of depth 1:
new bound:
X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
MPRF for transition t₁₉: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l7(X₇+1, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ of depth 1:
new bound:
X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
MPRF for transition t₂₀: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₇ ≤ X₅ ∧ 1+X₇ ≤ X₀ ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ of depth 1:
new bound:
X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
MPRF for transition t₂₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₀, X₈) :|: X₇ ≤ X₅ ∧ 1+X₇ ≤ X₀ ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ of depth 1:
new bound:
X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
MPRF for transition t₁₆: l21(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l22(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₈ ≤ X₆+X₇ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ of depth 1:
new bound:
2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₅+3⋅X₃⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+X₂⋅X₄+X₃⋅X₄+2⋅X₄+8⋅X₅+X₂+X₃+3 {O(n^3)}
knowledge_propagation leads to new time bound 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₅+3⋅X₃⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+X₂⋅X₄+X₃⋅X₄+2⋅X₄+8⋅X₅+X₂+X₃+3 {O(n^3)} for transition t₁₈: l22(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l21(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈+1) :|: X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃
Chain transitions t₁₄: l8→l10 and t₂₂: l10→l11 to t₂₄₇: l8→l11
Chain transitions t₂₄₇: l8→l11 and t₂₃: l11→l9 to t₂₄₈: l8→l9
Chain transitions t₂₄: l9→l13 and t₁₁: l13→l8 to t₂₄₉: l9→l8
Chain transitions t₁₀: l18→l13 and t₁₁: l13→l8 to t₂₅₀: l18→l8
Chain transitions t₁₀: l18→l13 and t₁₂: l13→l19 to t₂₅₁: l18→l19
Chain transitions t₂₄: l9→l13 and t₁₂: l13→l19 to t₂₅₂: l9→l19
Chain transitions t₁₃: l8→l20 and t₁₅: l20→l21 to t₂₅₃: l8→l21
Chain transitions t₂₅₃: l8→l21 and t₁₇: l21→l6 to t₂₅₄: l8→l6
Chain transitions t₁₈: l22→l21 and t₁₇: l21→l6 to t₂₅₅: l22→l6
Chain transitions t₁₈: l22→l21 and t₁₆: l21→l22 to t₂₅₆: l22→l22
Chain transitions t₂₅₃: l8→l21 and t₁₆: l21→l22 to t₂₅₇: l8→l22
Chain transitions t₂₀: l7→l5 and t₂₁: l5→l8 to t₂₅₈: l7→l8
Chain transitions t₂₅₄: l8→l6 and t₁₉: l6→l7 to t₂₅₉: l8→l7
Chain transitions t₂₅₅: l22→l6 and t₁₉: l6→l7 to t₂₆₀: l22→l7
Chain transitions t₂₅₉: l8→l7 and t₂₅₈: l7→l8 to t₂₆₁: l8→l8
Chain transitions t₂₆₀: l22→l7 and t₂₅₈: l7→l8 to t₂₆₂: l22→l8
Chain transitions t₂₆₀: l22→l7 and t₂₀: l7→l5 to t₂₆₃: l22→l5
Chain transitions t₂₅₉: l8→l7 and t₂₀: l7→l5 to t₂₆₄: l8→l5
Chain transitions t₂₄₈: l8→l9 and t₂₄₉: l9→l8 to t₂₆₅: l8→l8
Chain transitions t₂₄₈: l8→l9 and t₂₅₂: l9→l19 to t₂₆₆: l8→l19
Chain transitions t₂₄₈: l8→l9 and t₂₄: l9→l13 to t₂₆₇: l8→l13
Analysing control-flow refined program
Eliminate variables {X₀,X₁} that do not contribute to the problem
Found invariant 1+X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location l11
Found invariant 1+X₄ ≤ X₆ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location l6
Found invariant 1+X₁ ≤ X₄ ∧ X₀ ≤ X₄ for location l19
Found invariant 1+X₁ ≤ X₄ ∧ X₀ ≤ X₄ for location l23
Found invariant 1+X₄ ≤ X₆ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location l7
Found invariant X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location l20
Found invariant X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location l21
Found invariant 1+X₄ ≤ X₆ ∧ 1+X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location l5
Found invariant X₀ ≤ X₄ for location l13
Found invariant X₅ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location l22
Found invariant X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location l8
Found invariant 1+X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location l10
Found invariant 1+X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location l9
MPRF for transition t₃₃₂: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) -{5}> l8(X₀, X₁, X₂, X₃, 1+X₄, X₂, X₆) :|: X₃ < X₅ ∧ 1+X₄ ≤ X₁ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
TWN: t₃₃₁: l8→l8
cycle: [t₃₃₁: l8→l8]
loop: (X₅ ≤ X₃ ∧ 2⋅X₅ < 0,(X₃,X₅) -> (X₃,1+X₅)
order: [X₃; X₅]
closed-form:
X₃: X₃
X₅: X₅ + [[n != 0]] * n^1
Termination: true
Formula:
2 < 0 ∧ 1 < 0
∨ 2 < 0 ∧ X₅ < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₅ ≤ X₃ ∧ X₃ ≤ X₅
∨ 2⋅X₅ < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 < 0
∨ 2⋅X₅ < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ X₅ < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₅ < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₅ ≤ X₃ ∧ X₃ ≤ X₅
Stabilization-Threshold for: 2⋅X₅ < 0
alphas_abs: 2⋅X₅
M: 0
N: 1
Bound: 4⋅X₅+2 {O(n)}
Stabilization-Threshold for: X₅ ≤ X₃
alphas_abs: X₅+X₃
M: 0
N: 1
Bound: 2⋅X₃+2⋅X₅+2 {O(n)}
loop: (X₅ ≤ X₃ ∧ 2⋅X₅ < 0,(X₃,X₅) -> (X₃,1+X₅)
order: [X₃; X₅]
closed-form:
X₃: X₃
X₅: X₅ + [[n != 0]] * n^1
Termination: true
Formula:
2 < 0 ∧ 1 < 0
∨ 2 < 0 ∧ X₅ < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₅ ≤ X₃ ∧ X₃ ≤ X₅
∨ 2⋅X₅ < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 < 0
∨ 2⋅X₅ < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ X₅ < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₅ < 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₅ ≤ X₃ ∧ X₃ ≤ X₅
Stabilization-Threshold for: 2⋅X₅ < 0
alphas_abs: 2⋅X₅
M: 0
N: 1
Bound: 4⋅X₅+2 {O(n)}
Stabilization-Threshold for: X₅ ≤ X₃
alphas_abs: X₅+X₃
M: 0
N: 1
Bound: 2⋅X₃+2⋅X₅+2 {O(n)}
TWN - Lifting for t₃₃₁: l8→l8 of 2⋅X₃+6⋅X₅+6 {O(n)}
relevant size-bounds w.r.t. t₃₃₂:
X₃: X₃ {O(n)}
X₅: 4⋅X₂ {O(n)}
Runtime-bound of t₃₃₂: X₀+X₁+1 {O(n)}
Results in: 2⋅X₀⋅X₃+2⋅X₁⋅X₃+24⋅X₀⋅X₂+24⋅X₁⋅X₂+2⋅X₃+24⋅X₂+6⋅X₀+6⋅X₁+6 {O(n^2)}
TWN - Lifting for t₃₃₁: l8→l8 of 2⋅X₃+6⋅X₅+6 {O(n)}
relevant size-bounds w.r.t. t₃₁₀:
X₃: X₃ {O(n)}
X₅: X₂ {O(n)}
Runtime-bound of t₃₁₀: 1 {O(1)}
Results in: 2⋅X₃+6⋅X₂+6 {O(n)}
MPRF for transition t₃₁₈: l22(X₀, X₁, X₂, X₃, X₄, X₅, X₆) -{5}> l8(X₀, X₁, X₂, X₃, X₄, 1+X₅, 1+X₆) :|: X₄+X₅ < X₆+1 ∧ X₅ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ of depth 1:
new bound:
4⋅X₀⋅X₂+4⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₃+5⋅X₂+X₀+X₁+2 {O(n^2)}
MPRF for transition t₃₂₇: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) -{3}> l22(X₀, X₁, X₂, X₃, X₄, X₅, X₄-X₅) :|: X₅ ≤ X₃ ∧ 0 ≤ 2⋅X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ of depth 1:
new bound:
4⋅X₀⋅X₂+4⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₃+5⋅X₂+X₀+X₁+2 {O(n^2)}
MPRF for transition t₃₁₄: l22(X₀, X₁, X₂, X₃, X₄, X₅, X₆) -{2}> l22(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆) :|: 1+X₆ ≤ X₄+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ of depth 1:
new bound:
16⋅X₀⋅X₀⋅X₂⋅X₃+16⋅X₁⋅X₁⋅X₂⋅X₃+2⋅X₀⋅X₀⋅X₃⋅X₃+2⋅X₁⋅X₁⋅X₃⋅X₃+32⋅X₀⋅X₀⋅X₂⋅X₂+32⋅X₀⋅X₁⋅X₂⋅X₃+32⋅X₁⋅X₁⋅X₂⋅X₂+4⋅X₀⋅X₁⋅X₃⋅X₃+64⋅X₀⋅X₁⋅X₂⋅X₂+102⋅X₀⋅X₂⋅X₃+102⋅X₁⋅X₂⋅X₃+12⋅X₁⋅X₁⋅X₃+196⋅X₀⋅X₀⋅X₂+25⋅X₀⋅X₀⋅X₃+276⋅X₀⋅X₁⋅X₂+37⋅X₀⋅X₁⋅X₃+440⋅X₀⋅X₂⋅X₂+440⋅X₁⋅X₂⋅X₂+8⋅X₀⋅X₃⋅X₃+8⋅X₁⋅X₃⋅X₃+80⋅X₁⋅X₁⋅X₂+140⋅X₂⋅X₃+18⋅X₁⋅X₁+310⋅X₁⋅X₂+42⋅X₁⋅X₃+455⋅X₀⋅X₂+47⋅X₀⋅X₀+500⋅X₂⋅X₂+65⋅X₀⋅X₁+68⋅X₀⋅X₃+8⋅X₃⋅X₃+121⋅X₀+330⋅X₂+36⋅X₃+62⋅X₁+X₆+53 {O(n^4)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Found invariant 1+X₅ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ 1+X₆ ≤ X₁ ∧ X₂ ≤ X₆ ∧ X₁ ≤ 1+X₆ ∧ X₂ ≤ X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ for location l11
Found invariant 1+X₆ ≤ X₈ ∧ 1+X₂ ≤ X₈ ∧ 1+X₇ ≤ 0 ∧ X₇ ≤ X₅ ∧ 2+X₄+X₇ ≤ 0 ∧ 1+X₇ ≤ X₀ ∧ 1+X₀+X₇ ≤ 0 ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1+X₀+X₄ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₀ ≤ 0 for location n_l5___1
Found invariant X₇ ≤ X₅ ∧ 1+X₇ ≤ X₀ ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ for location n_l5___5
Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location n_l21___12
Found invariant 1+X₃ ≤ X₆ ∧ X₂ ≤ X₆ for location l19
Found invariant X₇ ≤ X₅ ∧ X₇ ≤ X₄ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location n_l20___13
Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location n_l6___10
Found invariant X₇ ≤ X₅ ∧ 1+X₇ ≤ X₀ ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ for location n_l7___6
Found invariant 1+X₃ ≤ X₆ ∧ X₂ ≤ X₆ for location l23
Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location n_l22___8
Found invariant 1+X₇ ≤ 0 ∧ X₇ ≤ X₅ ∧ 2+X₄+X₇ ≤ 0 ∧ 1+X₇ ≤ X₀ ∧ 1+X₀+X₇ ≤ 0 ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1+X₀+X₄ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₀ ≤ 0 for location n_l7___2
Found invariant X₇ ≤ X₅ ∧ X₇ ≤ X₀ ∧ 1+X₄ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ for location n_l20___3
Found invariant X₂ ≤ X₆ for location l13
Found invariant X₇ ≤ X₄ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₃ for location l8
Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location n_l21___9
Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location n_l6___7
Found invariant X₇ ≤ 1+X₅ ∧ X₇ ≤ X₀ ∧ 1+X₄ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ for location n_l8___4
Found invariant 1+X₅ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₃ for location l10
Found invariant 1+X₅ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ 1+X₆ ≤ X₁ ∧ X₂ ≤ X₆ ∧ X₁ ≤ 1+X₆ ∧ X₂ ≤ X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ for location l9
Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location n_l22___11
Solv. Size Bound: t₄₉₃: n_l21___12→n_l22___11 for X₀
Solv. Size Bound: t₄₉₃: n_l21___12→n_l22___11 for X₇
cycle: [t₄₉₃: n_l21___12→n_l22___11; t₄₉₇: n_l22___11→n_l21___9; t₄₉₆: n_l21___9→n_l6___7; t₅₀₂: n_l6___7→n_l7___6; t₅₀₄: n_l7___6→n_l5___5; t₅₀₀: n_l5___5→n_l8___4; t₅₁₈: n_l8___4→l10; t₂₂: l10→l11; t₂₃: l11→l9; t₂₄: l9→l13; t₁₁: l13→l8; t₅₀₅: l8→n_l20___13; t₄₉₁: n_l20___13→n_l21___12]
loop: (X₆ ≤ X₇+X₈ ∧ X₇+X₈ ≤ X₆ ∧ X₄+X₈ ≤ X₆ ∧ X₆ ≤ X₅+X₈ ∧ X₈ ≤ X₆+X₇ ∧ X₄+X₈ ≤ X₆ ∧ X₆ ≤ X₅+X₈ ∧ X₈ ≤ X₆ ∧ X₆ ≤ X₇+X₈ ∧ X₇+X₈ ≤ X₆ ∧ X₆+X₇ < X₈+1 ∧ X₆+X₇ < 1+X₈ ∧ X₇+X₆ < 1+X₈ ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ X₇+X₆ < 1+X₈ ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ X₅ < 1+X₇ ∧ 1+X₆ ≤ X₃ ∧ 0 ≤ 0 ∧ X₄ ≤ X₅ ∧ 0 ≤ 0,(X₄,X₇) -> (X₄,X₄)
overappr. closed-form: 2⋅X₄ {O(n)}
runtime bound: X₃+X₆+1 {O(n)}
Solv. Size Bound - Lifting for t₄₉₃: n_l21___12→n_l22___11 and X₇: 8⋅X₄ {O(n)}
Solv. Size Bound: t₄₉₄: n_l21___12→n_l6___10 for X₀
Solv. Size Bound: t₄₉₄: n_l21___12→n_l6___10 for X₇
cycle: [t₄₉₄: n_l21___12→n_l6___10; t₅₀₁: n_l6___10→n_l7___2; t₅₀₃: n_l7___2→n_l5___1; t₄₉₉: n_l5___1→n_l8___4; t₅₁₈: n_l8___4→l10; t₂₂: l10→l11; t₂₃: l11→l9; t₂₄: l9→l13; t₁₁: l13→l8; t₅₀₅: l8→n_l20___13; t₄₉₁: n_l20___13→n_l21___12]
loop: (X₆ ≤ X₇+X₈ ∧ X₇+X₈ ≤ X₆ ∧ X₄+X₈ ≤ X₆ ∧ X₆ ≤ X₅+X₈ ∧ X₆+X₇ < X₈ ∧ 2⋅X₇ < 0 ∧ X₆ ≤ X₇+X₈ ∧ X₇+X₈ ≤ X₆ ∧ X₇ < 0 ∧ 0 ≤ 0 ∧ X₇+X₈ ≤ X₆ ∧ X₆ ≤ X₇+X₈ ∧ 0 ≤ 0 ∧ X₇ < 0 ∧ 0 ≤ 0 ∧ X₇+X₈ ≤ X₆ ∧ X₆ ≤ X₇+X₈ ∧ 0 ≤ 0 ∧ X₅ < 1+X₇ ∧ 1+X₆ ≤ X₃ ∧ 0 ≤ 0 ∧ X₄ ≤ X₅ ∧ 0 ≤ 0,(X₄,X₇) -> (X₄,X₄)
overappr. closed-form: 2⋅X₄ {O(n)}
runtime bound: X₃+X₅+X₈+1 {O(n)}
Solv. Size Bound - Lifting for t₄₉₄: n_l21___12→n_l6___10 and X₇: 8⋅X₄ {O(n)}
Solv. Size Bound: t₄₉₉: n_l5___1→n_l8___4 for X₀
Solv. Size Bound: t₄₉₉: n_l5___1→n_l8___4 for X₇
cycle: [t₅₀₃: n_l7___2→n_l5___1; t₅₀₁: n_l6___10→n_l7___2; t₄₉₄: n_l21___12→n_l6___10; t₄₉₁: n_l20___13→n_l21___12; t₅₀₅: l8→n_l20___13; t₁₁: l13→l8; t₂₄: l9→l13; t₂₃: l11→l9; t₂₂: l10→l11; t₅₁₈: n_l8___4→l10; t₄₉₉: n_l5___1→n_l8___4]
loop: (X₀ < 1 ∧ X₀ ≤ X₇+1 ∧ X₀+X₈ ≤ X₆+1 ∧ 1+X₆ ≤ X₀+X₈ ∧ X₀ ≤ X₇+1 ∧ X₀ < 1 ∧ 0 ≤ 1 ∧ X₀+X₈ ≤ X₆+1 ∧ 1+X₆ ≤ X₀+X₈ ∧ 0 ≤ 1 ∧ 2⋅X₀ < 2 ∧ X₆+1 ≤ X₀+X₈ ∧ X₀+X₈ ≤ X₆+1 ∧ X₆+1 ≤ X₀+X₈ ∧ X₀+X₈ ≤ X₆+1 ∧ X₄+X₈ ≤ X₆ ∧ X₆ ≤ X₅+X₈ ∧ X₆+X₀ < 1+X₈ ∧ X₀ ≤ X₄+1 ∧ X₀ ≤ X₄+1 ∧ X₀ ≤ X₅+1 ∧ X₆ ≤ X₃ ∧ X₅ < X₄,(X₄,X₇) -> (X₄,X₄)
overappr. closed-form: 2⋅X₄ {O(n)}
runtime bound: 2 {O(1)}
Solv. Size Bound - Lifting for t₄₉₉: n_l5___1→n_l8___4 and X₇: 8⋅X₄ {O(n)}
Solv. Size Bound: t₅₀₀: n_l5___5→n_l8___4 for X₀
Solv. Size Bound: t₅₀₀: n_l5___5→n_l8___4 for X₇
cycle: [t₅₀₀: n_l5___5→n_l8___4; t₅₁₈: n_l8___4→l10; t₂₂: l10→l11; t₂₃: l11→l9; t₂₄: l9→l13; t₁₁: l13→l8; t₅₀₅: l8→n_l20___13; t₄₉₁: n_l20___13→n_l21___12; t₄₉₃: n_l21___12→n_l22___11; t₄₉₇: n_l22___11→n_l21___9; t₄₉₆: n_l21___9→n_l6___7; t₅₀₂: n_l6___7→n_l7___6; t₅₀₄: n_l7___6→n_l5___5]
loop: (X₀+X₆ < 1+X₈ ∧ X₀ ≤ X₇+1 ∧ X₀ ≤ X₇+1 ∧ X₅ < X₀ ∧ 1+X₆ ≤ X₃ ∧ 0 ≤ 0 ∧ X₄ ≤ X₅ ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ X₄ ≤ X₅ ∧ 0 ≤ 2⋅X₄ ∧ 0 ≤ 0 ∧ X₄ ≤ X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2⋅X₄ < 1 ∧ 2⋅X₄ < 1 ∧ 2⋅X₄ < 1 ∧ 0 ≤ 0 ∧ 0 ≤ 0,(X₄,X₇) -> (X₄,X₄)
overappr. closed-form: 2⋅X₄ {O(n)}
runtime bound: X₃+X₆+1 {O(n)}
Solv. Size Bound - Lifting for t₅₀₀: n_l5___5→n_l8___4 and X₇: 8⋅X₄ {O(n)}
Solv. Size Bound: t₅₀₁: n_l6___10→n_l7___2 for X₀
Solv. Size Bound: t₅₀₁: n_l6___10→n_l7___2 for X₇
Solv. Size Bound: t₅₀₁: n_l6___10→n_l7___2 for X₈
cycle: [t₄₉₄: n_l21___12→n_l6___10; t₄₉₂: n_l20___3→n_l21___12; t₅₀₆: n_l8___4→n_l20___3; t₄₉₉: n_l5___1→n_l8___4; t₅₀₃: n_l7___2→n_l5___1; t₅₀₁: n_l6___10→n_l7___2]
loop: (2⋅X₇ < 0 ∧ X₆ ≤ X₇+X₈ ∧ X₇+X₈ ≤ X₆ ∧ X₆ ≤ X₇+X₈ ∧ X₇+X₈ ≤ X₆ ∧ X₄+X₈ ≤ X₆ ∧ X₆ ≤ X₅+X₈ ∧ X₆+X₇ < X₈ ∧ 1+X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₇ < 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ X₇ < 0 ∧ 0 ≤ 1 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 1,(X₆,X₇,X₈) -> (X₆,X₇,X₆-X₇)
overappr. closed-form: 2⋅X₆+2⋅X₇ {O(n)}
runtime bound: 1 {O(1)}
Solv. Size Bound - Lifting for t₅₀₁: n_l6___10→n_l7___2 and X₈: 20⋅X₄+4⋅X₃+8⋅X₂+4 {O(n)}
Solv. Size Bound: t₅₀₂: n_l6___7→n_l7___6 for X₀
Solv. Size Bound: t₅₀₂: n_l6___7→n_l7___6 for X₇
Solv. Size Bound: t₅₀₂: n_l6___7→n_l7___6 for X₈
cycle: [t₄₉₆: n_l21___9→n_l6___7; t₄₉₇: n_l22___11→n_l21___9; t₄₉₃: n_l21___12→n_l22___11; t₄₉₂: n_l20___3→n_l21___12; t₅₀₆: n_l8___4→n_l20___3; t₅₀₀: n_l5___5→n_l8___4; t₅₀₄: n_l7___6→n_l5___5; t₅₀₂: n_l6___7→n_l7___6]
loop: (X₆+X₇ < X₈ ∧ X₆+X₇ < X₈ ∧ X₄+X₈ ≤ X₆ ∧ X₆ ≤ X₅+X₈ ∧ X₈ ≤ X₆ ∧ X₆ ≤ X₇+X₈ ∧ X₇+X₈ ≤ X₆ ∧ X₆ ≤ X₇+X₈+1 ∧ X₇+X₈+1 ≤ X₆ ∧ X₄+X₈+1 ≤ X₆ ∧ X₆ ≤ X₅+X₈+1 ∧ X₈+1 ≤ X₆+X₇ ∧ 1+X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ 2⋅X₇ < 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2⋅X₇ < 0 ∧ 0 ≤ 1 ∧ 0 ≤ 1,(X₆,X₇,X₈) -> (X₆,X₇,X₆-X₇)
overappr. closed-form: 2⋅X₆+2⋅X₇ {O(n)}
runtime bound: 2 {O(1)}
Solv. Size Bound - Lifting for t₅₀₂: n_l6___7→n_l7___6 and X₈: inf {Infinity}
Solv. Size Bound: t₅₀₃: n_l7___2→n_l5___1 for X₀
Solv. Size Bound: t₅₀₃: n_l7___2→n_l5___1 for X₇
cycle: [t₅₀₁: n_l6___10→n_l7___2; t₄₉₄: n_l21___12→n_l6___10; t₄₉₁: n_l20___13→n_l21___12; t₅₀₅: l8→n_l20___13; t₁₁: l13→l8; t₂₄: l9→l13; t₂₃: l11→l9; t₂₂: l10→l11; t₅₁₈: n_l8___4→l10; t₄₉₉: n_l5___1→n_l8___4; t₅₀₃: n_l7___2→n_l5___1]
loop: (X₀ < 1 ∧ X₀ ≤ X₇+1 ∧ X₀+X₈ ≤ X₆+1 ∧ 1+X₆ ≤ X₀+X₈ ∧ X₀ ≤ X₇+1 ∧ 2⋅X₀ < 2 ∧ X₆+1 ≤ X₀+X₈ ∧ X₀+X₈ ≤ X₆+1 ∧ X₆+1 ≤ X₀+X₈ ∧ X₀+X₈ ≤ X₆+1 ∧ X₄+X₈ ≤ X₆ ∧ X₆ ≤ X₅+X₈ ∧ X₆+X₀ < 1+X₈ ∧ X₀ ≤ X₄+1 ∧ X₀ ≤ X₄+1 ∧ X₀ ≤ X₅+1 ∧ X₆ ≤ X₃ ∧ X₅ < X₄ ∧ X₀ < 1 ∧ X₀ ≤ X₄+1 ∧ X₆ ≤ X₁ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₄+1,(X₀,X₇) -> (X₀,X₀)
overappr. closed-form: 2⋅X₀ {O(n)}
runtime bound: X₁+X₃+2 {O(n)}
Solv. Size Bound - Lifting for t₅₀₃: n_l7___2→n_l5___1 and X₇: inf {Infinity}
Solv. Size Bound: t₅₀₄: n_l7___6→n_l5___5 for X₀
Solv. Size Bound: t₅₀₄: n_l7___6→n_l5___5 for X₇
cycle: [t₅₀₄: n_l7___6→n_l5___5; t₅₀₀: n_l5___5→n_l8___4; t₅₁₈: n_l8___4→l10; t₂₂: l10→l11; t₂₃: l11→l9; t₂₄: l9→l13; t₁₁: l13→l8; t₅₀₅: l8→n_l20___13; t₄₉₁: n_l20___13→n_l21___12; t₄₉₃: n_l21___12→n_l22___11; t₄₉₇: n_l22___11→n_l21___9; t₄₉₆: n_l21___9→n_l6___7; t₅₀₂: n_l6___7→n_l7___6]
loop: (X₀+X₆ < 1+X₈ ∧ X₀ ≤ X₇+1 ∧ X₀ ≤ X₇+1 ∧ X₀+X₆ < 1+X₈ ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ X₅ < X₀ ∧ 1+X₆ ≤ X₃ ∧ 0 ≤ 0 ∧ X₄ ≤ X₅ ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ X₄ ≤ X₅ ∧ 0 ≤ 2⋅X₄ ∧ 0 ≤ 0 ∧ X₄ ≤ X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2⋅X₄ < 1 ∧ 2⋅X₄ < 1,(X₄,X₇) -> (X₄,X₄)
overappr. closed-form: 2⋅X₄ {O(n)}
runtime bound: X₃+X₆+1 {O(n)}
Solv. Size Bound - Lifting for t₅₀₄: n_l7___6→n_l5___5 and X₇: 8⋅X₄ {O(n)}
Solv. Size Bound: t₅₁₈: n_l8___4→l10 for X₀
Solv. Size Bound: t₅₁₈: n_l8___4→l10 for X₇
cycle: [t₄₉₉: n_l5___1→n_l8___4; t₅₀₃: n_l7___2→n_l5___1; t₅₀₁: n_l6___10→n_l7___2; t₄₉₄: n_l21___12→n_l6___10; t₄₉₁: n_l20___13→n_l21___12; t₅₀₅: l8→n_l20___13; t₁₁: l13→l8; t₂₄: l9→l13; t₂₃: l11→l9; t₂₂: l10→l11; t₅₁₈: n_l8___4→l10]
loop: (X₅ < X₇ ∧ X₀ < 1 ∧ X₀ ≤ X₇+1 ∧ X₀+X₈ ≤ X₆+1 ∧ 1+X₆ ≤ X₀+X₈ ∧ X₀ ≤ X₇+1 ∧ X₀ < 1 ∧ 0 ≤ 1 ∧ X₀+X₈ ≤ X₆+1 ∧ 1+X₆ ≤ X₀+X₈ ∧ 0 ≤ 1 ∧ 2⋅X₀ < 2 ∧ X₆+1 ≤ X₀+X₈ ∧ X₀+X₈ ≤ X₆+1 ∧ X₆+1 ≤ X₀+X₈ ∧ X₀+X₈ ≤ X₆+1 ∧ X₄+X₈ ≤ X₆ ∧ X₆ ≤ X₅+X₈ ∧ X₆+X₀ < 1+X₈ ∧ X₀ ≤ X₄+1 ∧ X₀ ≤ X₄+1 ∧ X₀ ≤ X₅+1 ∧ X₆ ≤ X₃,(X₄,X₇) -> (X₄,X₄)
overappr. closed-form: 2⋅X₄ {O(n)}
runtime bound: X₀+X₇+3 {O(n)}
Solv. Size Bound - Lifting for t₅₁₈: n_l8___4→l10 and X₇: 8⋅X₄ {O(n)}
knowledge_propagation leads to new time bound X₂+X₃+1 {O(n)} for transition t₅₀₅: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → n_l20___13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₇ ≤ X₄ ∧ X₇ ≤ X₅ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₇ ≤ X₄ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₃
knowledge_propagation leads to new time bound X₂+X₃+1 {O(n)} for transition t₄₉₁: n_l20___13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → n_l21___12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₆-X₇) :|: X₇ ≤ X₄ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₄ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃
MPRF for transition t₄₉₂: n_l20___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → n_l21___12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₆-X₇) :|: X₀ ≤ X₅ ∧ 1+X₄ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₀ ∧ 1+X₄ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ of depth 1:
new bound:
2⋅X₂⋅X₄+2⋅X₃⋅X₄+X₂⋅X₅+X₃⋅X₅+2⋅X₄+2⋅X₅+X₀ {O(n^2)}
MPRF for transition t₄₉₃: n_l21___12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → n_l22___11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₆ ≤ X₇+X₈ ∧ X₇+X₈ ≤ X₆ ∧ X₄+X₈ ≤ X₆ ∧ X₆ ≤ X₅+X₈ ∧ X₈ ≤ X₆+X₇ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₂ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ of depth 1:
new bound:
2⋅X₂⋅X₄+2⋅X₃⋅X₄+X₂⋅X₅+X₃⋅X₅+2⋅X₄+X₂+X₃+X₅+1 {O(n^2)}
MPRF for transition t₄₉₄: n_l21___12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → n_l6___10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₆ ≤ X₇+X₈ ∧ X₇+X₈ ≤ X₆ ∧ X₄+X₈ ≤ X₆ ∧ X₆ ≤ X₅+X₈ ∧ X₆+X₇ < X₈ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₂ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ of depth 1:
new bound:
2⋅X₂⋅X₄+2⋅X₃⋅X₄+X₂⋅X₅+X₃⋅X₅+2⋅X₄+X₂+X₃+X₅+1 {O(n^2)}
MPRF for transition t₄₉₆: n_l21___9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → n_l6___7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₆+X₇ < X₈ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₂ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ of depth 1:
new bound:
2⋅X₂⋅X₄+2⋅X₃⋅X₄+X₂⋅X₅+X₃⋅X₅+2⋅X₄+X₂+X₃+X₅+1 {O(n^2)}
MPRF for transition t₄₉₇: n_l22___11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → n_l21___9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈+1) :|: X₄+X₈ ≤ X₆ ∧ X₆ ≤ X₅+X₈ ∧ X₈ ≤ X₆ ∧ X₆ ≤ X₇+X₈ ∧ X₇+X₈ ≤ X₆ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ of depth 1:
new bound:
2⋅X₂⋅X₄+2⋅X₃⋅X₄+X₂⋅X₅+X₃⋅X₅+2⋅X₄+X₂+X₃+X₅+1 {O(n^2)}
MPRF for transition t₄₉₉: n_l5___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → n_l8___4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₀, X₈) :|: X₀ < 1 ∧ X₀ ≤ X₇+1 ∧ X₀+X₈ ≤ X₆+1 ∧ 1+X₆ ≤ X₀+X₈ ∧ X₀ ≤ X₇+1 ∧ X₂ ≤ X₆ ∧ 1+X₄ ≤ X₀ ∧ X₀ ≤ 1+X₅ ∧ X₆ ≤ X₃ ∧ 1+X₇ ≤ X₀ ∧ X₆ ≤ X₃ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₆ ∧ X₀ ≤ 1+X₅ ∧ 1+X₇ ≤ X₀ ∧ 1+X₆ ≤ X₈ ∧ 1+X₂ ≤ X₈ ∧ 1+X₇ ≤ 0 ∧ X₇ ≤ X₅ ∧ 2+X₄+X₇ ≤ 0 ∧ 1+X₇ ≤ X₀ ∧ 1+X₀+X₇ ≤ 0 ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1+X₀+X₄ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₀ ≤ 0 of depth 1:
new bound:
2⋅X₂⋅X₄+2⋅X₃⋅X₄+2⋅X₄+X₅+1 {O(n^2)}
MPRF for transition t₅₀₀: n_l5___5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → n_l8___4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₀, X₈) :|: X₀+X₆ < 1+X₈ ∧ X₀ ≤ X₇+1 ∧ X₀ ≤ X₇+1 ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ 1+X₄ ≤ X₀ ∧ X₀ ≤ 1+X₅ ∧ 1+X₇ ≤ X₀ ∧ X₆ ≤ X₃ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₆ ∧ X₀ ≤ 1+X₅ ∧ 1+X₇ ≤ X₀ ∧ X₇ ≤ X₅ ∧ 1+X₇ ≤ X₀ ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ of depth 1:
new bound:
2⋅X₂⋅X₄+2⋅X₃⋅X₄+X₂⋅X₅+X₃⋅X₅+2⋅X₄+2⋅X₅+X₀+X₂+X₃+2 {O(n^2)}
MPRF for transition t₅₀₁: n_l6___10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → n_l7___2(X₇+1, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 2⋅X₇ < 0 ∧ X₆ ≤ X₇+X₈ ∧ X₇+X₈ ≤ X₆ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₆ ≤ X₃ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ of depth 1:
new bound:
2⋅X₂⋅X₄+2⋅X₃⋅X₄+X₂⋅X₅+X₃⋅X₅+2⋅X₄+X₂+X₃+X₅+1 {O(n^2)}
MPRF for transition t₅₀₂: n_l6___7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → n_l7___6(X₇+1, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₆+X₇ < X₈ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ of depth 1:
new bound:
2⋅X₂⋅X₄+2⋅X₃⋅X₄+X₂⋅X₅+X₃⋅X₅+2⋅X₄+2⋅X₅+X₀+X₂+X₃+2 {O(n^2)}
MPRF for transition t₅₀₃: n_l7___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → n_l5___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₀-1, X₈) :|: X₀ < 1 ∧ X₀ ≤ X₇+1 ∧ X₀+X₈ ≤ X₆+1 ∧ 1+X₆ ≤ X₀+X₈ ∧ X₀ ≤ X₇+1 ∧ X₂ ≤ X₆ ∧ 1+X₄ ≤ X₀ ∧ X₀ ≤ 1+X₅ ∧ X₆ ≤ X₃ ∧ 1+X₇ ≤ X₀ ∧ X₆ ≤ X₃ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₆ ∧ X₀ ≤ 1+X₅ ∧ 1+X₇ ≤ X₀ ∧ 1+X₇ ≤ 0 ∧ X₇ ≤ X₅ ∧ 2+X₄+X₇ ≤ 0 ∧ 1+X₇ ≤ X₀ ∧ 1+X₀+X₇ ≤ 0 ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1+X₀+X₄ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₀ ≤ 0 of depth 1:
new bound:
2⋅X₂⋅X₄+2⋅X₃⋅X₄+2⋅X₄+X₀+X₂+X₃+2 {O(n^2)}
MPRF for transition t₅₀₄: n_l7___6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → n_l5___5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₀-1, X₈) :|: X₀+X₆ < 1+X₈ ∧ X₀ ≤ X₇+1 ∧ X₀ ≤ X₇+1 ∧ X₀ ≤ 1+X₅ ∧ X₂ ≤ X₆ ∧ 1+X₄ ≤ X₀ ∧ X₆ ≤ X₃ ∧ 1+X₇ ≤ X₀ ∧ X₆ ≤ X₃ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₆ ∧ X₀ ≤ 1+X₅ ∧ 1+X₇ ≤ X₀ ∧ X₇ ≤ X₅ ∧ 1+X₇ ≤ X₀ ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ of depth 1:
new bound:
2⋅X₂⋅X₄+2⋅X₃⋅X₄+X₂⋅X₅+X₃⋅X₅+2⋅X₄+X₂+X₃+X₅+1 {O(n^2)}
MPRF for transition t₅₀₆: n_l8___4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → n_l20___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₀ ≤ X₇ ∧ X₇ ≤ X₀ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₇ ≤ X₅ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₇ ≤ 1+X₅ ∧ X₇ ≤ X₀ ∧ 1+X₄ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ of depth 1:
new bound:
2⋅X₂⋅X₄+2⋅X₃⋅X₄+X₂⋅X₅+X₃⋅X₅+2⋅X₄+2⋅X₅+X₀ {O(n^2)}
MPRF for transition t₅₁₈: n_l8___4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₅ < X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₃ ∧ X₇ ≤ 1+X₅ ∧ X₇ ≤ X₀ ∧ 1+X₄ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ of depth 1:
new bound:
X₂+X₃+1 {O(n)}
Solv. Size Bound - Lifting for t₅₀₂: n_l6___7→n_l7___6 and X₈: 2⋅X₂⋅X₅+2⋅X₃⋅X₅+4⋅X₂⋅X₄+4⋅X₃⋅X₄+14⋅X₂+2⋅X₀+28⋅X₄+4⋅X₅+8⋅X₃+10 {O(n^2)}
MPRF for transition t₄₉₅: n_l21___9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → n_l22___8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₈ ≤ X₆+X₇ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₂ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ of depth 1:
new bound:
2⋅X₂⋅X₂⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₃⋅X₅+2⋅X₃⋅X₅⋅X₅+4⋅X₂⋅X₂⋅X₄+4⋅X₂⋅X₃⋅X₅+4⋅X₂⋅X₄⋅X₅+4⋅X₃⋅X₃⋅X₄+4⋅X₃⋅X₄⋅X₅+8⋅X₂⋅X₃⋅X₄+2⋅X₀⋅X₂+2⋅X₀⋅X₃+2⋅X₀⋅X₅+2⋅X₂⋅X₂+2⋅X₃⋅X₃+4⋅X₂⋅X₃+4⋅X₄⋅X₅+4⋅X₅⋅X₅+6⋅X₂⋅X₄+6⋅X₃⋅X₄+7⋅X₂⋅X₅+7⋅X₃⋅X₅+2⋅X₄+4⋅X₂+4⋅X₃+6⋅X₅+X₀+1 {O(n^3)}
MPRF for transition t₄₉₈: n_l22___8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → n_l21___9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈+1) :|: X₈ ≤ X₆+X₇ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ of depth 1:
new bound:
2⋅X₂⋅X₃⋅X₅⋅X₅+4⋅X₂⋅X₂⋅X₄⋅X₄+4⋅X₂⋅X₂⋅X₄⋅X₅+4⋅X₃⋅X₃⋅X₄⋅X₄+4⋅X₃⋅X₃⋅X₄⋅X₅+8⋅X₂⋅X₃⋅X₄⋅X₄+8⋅X₂⋅X₃⋅X₄⋅X₅+X₂⋅X₂⋅X₅⋅X₅+X₃⋅X₃⋅X₅⋅X₅+12⋅X₂⋅X₄⋅X₄+12⋅X₃⋅X₄⋅X₄+16⋅X₂⋅X₄⋅X₅+16⋅X₃⋅X₄⋅X₅+2⋅X₀⋅X₂⋅X₅+2⋅X₀⋅X₃⋅X₅+2⋅X₂⋅X₂⋅X₄+2⋅X₂⋅X₃⋅X₅+2⋅X₃⋅X₃⋅X₄+4⋅X₀⋅X₂⋅X₄+4⋅X₀⋅X₃⋅X₄+4⋅X₂⋅X₃⋅X₄+5⋅X₂⋅X₅⋅X₅+5⋅X₃⋅X₅⋅X₅+X₂⋅X₂⋅X₅+X₃⋅X₃⋅X₅+14⋅X₄⋅X₅+5⋅X₀⋅X₅+5⋅X₂⋅X₅+5⋅X₃⋅X₅+6⋅X₀⋅X₄+6⋅X₅⋅X₅+7⋅X₂⋅X₄+7⋅X₃⋅X₄+8⋅X₄⋅X₄+X₀⋅X₀+X₀⋅X₂+X₀⋅X₃+2⋅X₀+6⋅X₄+6⋅X₅ {O(n^4)}
knowledge_propagation leads to new time bound 2⋅X₂⋅X₂⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₃⋅X₅+2⋅X₃⋅X₅⋅X₅+4⋅X₂⋅X₂⋅X₄+4⋅X₂⋅X₃⋅X₅+4⋅X₂⋅X₄⋅X₅+4⋅X₃⋅X₃⋅X₄+4⋅X₃⋅X₄⋅X₅+8⋅X₂⋅X₃⋅X₄+2⋅X₀⋅X₂+2⋅X₀⋅X₃+2⋅X₀⋅X₅+2⋅X₂⋅X₂+2⋅X₃⋅X₃+4⋅X₂⋅X₃+4⋅X₄⋅X₅+4⋅X₅⋅X₅+6⋅X₂⋅X₄+6⋅X₃⋅X₄+7⋅X₂⋅X₅+7⋅X₃⋅X₅+2⋅X₄+4⋅X₂+4⋅X₃+6⋅X₅+X₀+1 {O(n^3)} for transition t₄₉₈: n_l22___8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → n_l21___9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈+1) :|: X₈ ≤ X₆+X₇ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:4⋅X₂⋅X₄⋅X₅+4⋅X₂⋅X₅⋅X₅+4⋅X₃⋅X₄⋅X₅+4⋅X₃⋅X₅⋅X₅+12⋅X₂⋅X₅+12⋅X₃⋅X₅+8⋅X₂⋅X₄+8⋅X₃⋅X₄+8⋅X₄⋅X₅+8⋅X₅⋅X₅+13⋅X₂+13⋅X₃+16⋅X₄+28⋅X₅+36 {O(n^3)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: X₂+X₃+1 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₁₄: X₂+X₃+1 {O(n)}
t₁₅: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₁₆: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₅+3⋅X₃⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+X₂⋅X₄+X₃⋅X₄+2⋅X₄+8⋅X₅+X₂+X₃+3 {O(n^3)}
t₁₇: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₁₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₅+3⋅X₃⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+X₂⋅X₄+X₃⋅X₄+2⋅X₄+8⋅X₅+X₂+X₃+3 {O(n^3)}
t₁₉: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₂₀: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₂₁: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₂₂: X₂+X₃+1 {O(n)}
t₂₃: X₂+X₃+1 {O(n)}
t₂₄: X₂+X₃+1 {O(n)}
t₂₅: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₂⋅X₄⋅X₅+4⋅X₂⋅X₅⋅X₅+4⋅X₃⋅X₄⋅X₅+4⋅X₃⋅X₅⋅X₅+12⋅X₂⋅X₅+12⋅X₃⋅X₅+8⋅X₂⋅X₄+8⋅X₃⋅X₄+8⋅X₄⋅X₅+8⋅X₅⋅X₅+13⋅X₂+13⋅X₃+16⋅X₄+28⋅X₅+36 {O(n^3)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: X₂+X₃+1 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₁₄: X₂+X₃+1 {O(n)}
t₁₅: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₁₆: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₅+3⋅X₃⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+X₂⋅X₄+X₃⋅X₄+2⋅X₄+8⋅X₅+X₂+X₃+3 {O(n^3)}
t₁₇: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₁₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₅+3⋅X₃⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+X₂⋅X₄+X₃⋅X₄+2⋅X₄+8⋅X₅+X₂+X₃+3 {O(n^3)}
t₁₉: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₂₀: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₂₁: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₂₂: X₂+X₃+1 {O(n)}
t₂₃: X₂+X₃+1 {O(n)}
t₂₄: X₂+X₃+1 {O(n)}
t₂₅: 1 {O(1)}
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)}
t₀, X₈: X₈ {O(n)}
t₁, X₀: X₀ {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)}
t₁, X₈: X₈ {O(n)}
t₂, X₀: X₀ {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)}
t₂, X₈: X₈ {O(n)}
t₃, X₀: X₀ {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)}
t₃, X₈: X₈ {O(n)}
t₄, X₀: X₀ {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)}
t₄, X₇: X₇ {O(n)}
t₄, X₈: X₈ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₆ {O(n)}
t₅, X₇: X₇ {O(n)}
t₅, X₈: X₈ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₆, X₆: X₆ {O(n)}
t₆, X₇: X₇ {O(n)}
t₆, X₈: X₈ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₅ {O(n)}
t₇, X₆: X₆ {O(n)}
t₇, X₇: X₇ {O(n)}
t₇, X₈: X₈ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₈, X₆: X₆ {O(n)}
t₈, X₇: X₇ {O(n)}
t₈, X₈: X₈ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: X₅ {O(n)}
t₉, X₆: X₆ {O(n)}
t₉, X₇: X₇ {O(n)}
t₉, X₈: X₈ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₀, X₆: X₂ {O(n)}
t₁₀, X₇: X₇ {O(n)}
t₁₀, X₈: X₈ {O(n)}
t₁₁, X₀: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₅+4⋅X₄+X₀+X₂+X₃+2 {O(n^2)}
t₁₁, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₁₁, X₅: X₅ {O(n)}
t₁₁, X₆: 2⋅X₂+X₃+1 {O(n)}
t₁₁, X₇: 2⋅X₄ {O(n)}
t₁₁, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₄+3⋅X₃⋅X₄+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₅+5⋅X₃⋅X₅+10⋅X₄+12⋅X₅+5⋅X₃+7⋅X₂+X₈+9 {O(n^3)}
t₁₂, X₀: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₀+2⋅X₅+4⋅X₄+X₂+X₃+2 {O(n^2)}
t₁₂, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₁₂, X₂: 2⋅X₂ {O(n)}
t₁₂, X₃: 2⋅X₃ {O(n)}
t₁₂, X₄: 2⋅X₄ {O(n)}
t₁₂, X₅: 2⋅X₅ {O(n)}
t₁₂, X₆: 3⋅X₂+X₃+1 {O(n)}
t₁₂, X₇: 4⋅X₄+X₇ {O(n)}
t₁₂, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₄+3⋅X₃⋅X₄+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₅+5⋅X₃⋅X₅+10⋅X₄+12⋅X₅+2⋅X₈+5⋅X₃+7⋅X₂+9 {O(n^3)}
t₁₃, X₀: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+2⋅X₂+2⋅X₃+4⋅X₅+8⋅X₄+X₀+4 {O(n^2)}
t₁₃, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₃, X₅: X₅ {O(n)}
t₁₃, X₆: 2⋅X₂+X₃+1 {O(n)}
t₁₃, X₇: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₅+4⋅X₄+X₂+X₃+2 {O(n^2)}
t₁₃, X₈: 4⋅X₂⋅X₄⋅X₅+4⋅X₂⋅X₅⋅X₅+4⋅X₃⋅X₄⋅X₅+4⋅X₃⋅X₅⋅X₅+10⋅X₂⋅X₅+10⋅X₃⋅X₅+6⋅X₂⋅X₄+6⋅X₃⋅X₄+8⋅X₄⋅X₅+8⋅X₅⋅X₅+10⋅X₃+14⋅X₂+20⋅X₄+24⋅X₅+X₈+18 {O(n^3)}
t₁₄, X₀: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₅+4⋅X₄+X₀+X₂+X₃+2 {O(n^2)}
t₁₄, X₁: 2⋅X₁+2⋅X₃+4⋅X₂+2 {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₄, X₅: X₅ {O(n)}
t₁₄, X₆: 2⋅X₂+X₃+1 {O(n)}
t₁₄, X₇: 4⋅X₄ {O(n)}
t₁₄, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₄+3⋅X₃⋅X₄+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₅+5⋅X₃⋅X₅+10⋅X₄+12⋅X₅+5⋅X₃+7⋅X₂+X₈+9 {O(n^3)}
t₁₅, X₀: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+2⋅X₂+2⋅X₃+4⋅X₅+8⋅X₄+X₀+4 {O(n^2)}
t₁₅, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₅, X₅: X₅ {O(n)}
t₁₅, X₆: 2⋅X₂+X₃+1 {O(n)}
t₁₅, X₇: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₅+4⋅X₄+X₂+X₃+2 {O(n^2)}
t₁₅, X₈: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₃+2⋅X₅+3⋅X₂+4⋅X₄+3 {O(n^2)}
t₁₆, X₀: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+2⋅X₂+2⋅X₃+4⋅X₅+8⋅X₄+X₀+4 {O(n^2)}
t₁₆, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₁₆, X₂: X₂ {O(n)}
t₁₆, X₃: X₃ {O(n)}
t₁₆, X₄: X₄ {O(n)}
t₁₆, X₅: X₅ {O(n)}
t₁₆, X₆: 2⋅X₂+X₃+1 {O(n)}
t₁₆, X₇: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₅+4⋅X₄+X₂+X₃+2 {O(n^2)}
t₁₆, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+2⋅X₂⋅X₄+2⋅X₃⋅X₄+4⋅X₂⋅X₅+4⋅X₃⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+10⋅X₅+3⋅X₃+4⋅X₂+6⋅X₄+6 {O(n^3)}
t₁₇, X₀: 4⋅X₂⋅X₄+4⋅X₂⋅X₅+4⋅X₃⋅X₄+4⋅X₃⋅X₅+16⋅X₄+2⋅X₀+4⋅X₂+4⋅X₃+8⋅X₅+8 {O(n^2)}
t₁₇, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: X₄ {O(n)}
t₁₇, X₅: X₅ {O(n)}
t₁₇, X₆: 2⋅X₂+X₃+1 {O(n)}
t₁₇, X₇: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₅+4⋅X₄+X₂+X₃+2 {O(n^2)}
t₁₇, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₄+3⋅X₃⋅X₄+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₅+5⋅X₃⋅X₅+10⋅X₄+12⋅X₅+5⋅X₃+7⋅X₂+9 {O(n^3)}
t₁₈, X₀: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+2⋅X₂+2⋅X₃+4⋅X₅+8⋅X₄+X₀+4 {O(n^2)}
t₁₈, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₈, X₅: X₅ {O(n)}
t₁₈, X₆: 2⋅X₂+X₃+1 {O(n)}
t₁₈, X₇: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₅+4⋅X₄+X₂+X₃+2 {O(n^2)}
t₁₈, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+2⋅X₂⋅X₄+2⋅X₃⋅X₄+4⋅X₂⋅X₅+4⋅X₃⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+10⋅X₅+3⋅X₃+4⋅X₂+6⋅X₄+6 {O(n^3)}
t₁₉, X₀: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₅+4⋅X₄+X₂+X₃+2 {O(n^2)}
t₁₉, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₁₉, X₅: X₅ {O(n)}
t₁₉, X₆: 2⋅X₂+X₃+1 {O(n)}
t₁₉, X₇: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₅+4⋅X₄+X₂+X₃+2 {O(n^2)}
t₁₉, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₄+3⋅X₃⋅X₄+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₅+5⋅X₃⋅X₅+10⋅X₄+12⋅X₅+5⋅X₃+7⋅X₂+9 {O(n^3)}
t₂₀, X₀: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₅+4⋅X₄+X₂+X₃+2 {O(n^2)}
t₂₀, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₀, X₄: X₄ {O(n)}
t₂₀, X₅: X₅ {O(n)}
t₂₀, X₆: 2⋅X₂+X₃+1 {O(n)}
t₂₀, X₇: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₅+4⋅X₄+X₂+X₃+2 {O(n^2)}
t₂₀, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₄+3⋅X₃⋅X₄+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₅+5⋅X₃⋅X₅+10⋅X₄+12⋅X₅+5⋅X₃+7⋅X₂+9 {O(n^3)}
t₂₁, X₀: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₅+4⋅X₄+X₂+X₃+2 {O(n^2)}
t₂₁, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₁, X₄: X₄ {O(n)}
t₂₁, X₅: X₅ {O(n)}
t₂₁, X₆: 2⋅X₂+X₃+1 {O(n)}
t₂₁, X₇: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₅+4⋅X₄+X₂+X₃+2 {O(n^2)}
t₂₁, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₄+3⋅X₃⋅X₄+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₅+5⋅X₃⋅X₅+10⋅X₄+12⋅X₅+5⋅X₃+7⋅X₂+9 {O(n^3)}
t₂₂, X₀: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₅+4⋅X₄+X₀+X₂+X₃+2 {O(n^2)}
t₂₂, X₁: 2⋅X₂+X₃+1 {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₂, X₅: X₅ {O(n)}
t₂₂, X₆: 2⋅X₂+X₃+1 {O(n)}
t₂₂, X₇: 4⋅X₄ {O(n)}
t₂₂, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₄+3⋅X₃⋅X₄+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₅+5⋅X₃⋅X₅+10⋅X₄+12⋅X₅+5⋅X₃+7⋅X₂+X₈+9 {O(n^3)}
t₂₃, X₀: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₅+4⋅X₄+X₀+X₂+X₃+2 {O(n^2)}
t₂₃, X₁: 2⋅X₂+X₃+1 {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₃, X₅: X₅ {O(n)}
t₂₃, X₆: 2⋅X₂+X₃+1 {O(n)}
t₂₃, X₇: 4⋅X₄ {O(n)}
t₂₃, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₄+3⋅X₃⋅X₄+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₅+5⋅X₃⋅X₅+10⋅X₄+12⋅X₅+5⋅X₃+7⋅X₂+X₈+9 {O(n^3)}
t₂₄, X₀: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₅+4⋅X₄+X₀+X₂+X₃+2 {O(n^2)}
t₂₄, X₁: 2⋅X₂+X₃+1 {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₄, X₄: X₄ {O(n)}
t₂₄, X₅: X₅ {O(n)}
t₂₄, X₆: 2⋅X₂+X₃+1 {O(n)}
t₂₄, X₇: 4⋅X₄ {O(n)}
t₂₄, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₄+3⋅X₃⋅X₄+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₅+5⋅X₃⋅X₅+10⋅X₄+12⋅X₅+5⋅X₃+7⋅X₂+X₈+9 {O(n^3)}
t₂₅, X₀: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₀+2⋅X₅+4⋅X₄+X₂+X₃+2 {O(n^2)}
t₂₅, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₂₅, X₂: 2⋅X₂ {O(n)}
t₂₅, X₃: 2⋅X₃ {O(n)}
t₂₅, X₄: 2⋅X₄ {O(n)}
t₂₅, X₅: 2⋅X₅ {O(n)}
t₂₅, X₆: 3⋅X₂+X₃+1 {O(n)}
t₂₅, X₇: 4⋅X₄+X₇ {O(n)}
t₂₅, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₄+3⋅X₃⋅X₄+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₅+5⋅X₃⋅X₅+10⋅X₄+12⋅X₅+2⋅X₈+5⋅X₃+7⋅X₂+9 {O(n^3)}