Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₃, X₅, X₃) :|: 1 < X₃
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 1
t₁₀: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l11(X₀, X₁, X₆-X₁, X₃, X₄, X₅, X₆)
t₁₁: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ < X₁
t₇: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ ≤ X₅
t₁₈: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ < 0
t₁₉: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₆
t₂₀: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ 0 ∧ 0 ≤ X₆
t₉: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₁, X₂, X₃, X₄, X₅-X₁, X₆)
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₄-1, X₂, X₃, X₄, X₃, X₆) :|: 1 < X₄
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ ≤ 1
t₂₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₀)
t₁₅: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₆: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₂: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₂, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ ≤ 0 ∧ 0 ≤ X₅
t₁₃: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₆, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ < 0
t₁₄: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₆, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₅

Preprocessing

Found invariant 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ for location l11

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ for location l6

Found invariant 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 l12

Found invariant 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ for location l7

Found invariant X₄ ≤ 1 ∧ X₄ ≤ X₃ for location l13

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ for location l8

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

Found invariant X₄ ≤ X₃ for location l4

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

Found invariant 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 l14

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₃, X₅, X₃) :|: 1 < X₃
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 1
t₁₀: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l11(X₀, X₁, X₆-X₁, X₃, X₄, X₅, X₆) :|: 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃
t₁₁: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃
t₈: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ < X₁ ∧ 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
t₇: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ ≤ X₅ ∧ 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
t₁₈: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ < 0 ∧ X₄ ≤ 1 ∧ X₄ ≤ X₃
t₁₉: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₆ ∧ X₄ ≤ 1 ∧ X₄ ≤ X₃
t₂₀: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ 0 ∧ 0 ≤ X₆ ∧ X₄ ≤ 1 ∧ X₄ ≤ X₃
t₉: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₁, X₂, X₃, X₄, X₅-X₁, X₆) :|: 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) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₄-1, X₂, X₃, X₄, X₃, X₆) :|: 1 < X₄ ∧ X₄ ≤ X₃
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ ≤ 1 ∧ X₄ ≤ X₃
t₂₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₀) :|: X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃
t₁₅: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃
t₁₆: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃
t₁₂: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₂, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ ≤ 0 ∧ 0 ≤ X₅ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃
t₁₃: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₆, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ < 0 ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃
t₁₄: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₆, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₅ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃

Solv. Size Bound: t₅: l4→l12 for X₀

cycle: [t₅: l4→l12; t₈: l12→l10; t₁₀: l10→l11; t₁₁: l11→l9; t₁₃: l9→l7; t₁₄: l9→l7; t₁₅: l7→l8; t₁₆: l8→l6; t₁₇: l6→l4]
loop: (1 < X₄ ∧ X₃+1 < X₄ ∧ X₃ < 0 ∨ 1 < X₄ ∧ X₃+1 < X₄ ∧ 0 < X₃,(X₀,X₆) -> (X₆,X₆)
overappr. closed-form: 2⋅X₆ {O(n)}
runtime bound: X₄+1 {O(n)}

Solv. Size Bound - Lifting for t₅: l4→l12 and X₀: inf {Infinity}

Solv. Size Bound: t₈: l12→l10 for X₀

cycle: [t₈: l12→l10; t₁₀: l10→l11; t₁₁: l11→l9; t₁₃: l9→l7; t₁₄: l9→l7; t₁₅: l7→l8; t₁₆: l8→l6; t₁₇: l6→l4; t₅: l4→l12]
loop: (X₅ < X₁ ∧ X₅ < 0 ∧ 1 < X₁ ∨ X₅ < X₁ ∧ 0 < X₅ ∧ 1 < X₁,(X₀,X₆) -> (X₆,X₆)
overappr. closed-form: 2⋅X₆ {O(n)}
runtime bound: X₁+1 {O(n)}

Solv. Size Bound - Lifting for t₈: l12→l10 and X₀: inf {Infinity}

Solv. Size Bound: t₁₀: l10→l11 for X₀

Solv. Size Bound: t₁₀: l10→l11 for X₂

Solv. Size Bound: t₁₀: l10→l11 for X₆

cycle: [t₈: l12→l10; t₅: l4→l12; t₁₇: l6→l4; t₁₆: l8→l6; t₁₅: l7→l8; t₁₃: l9→l7; t₁₄: l9→l7; t₁₁: l11→l9; t₁₀: l10→l11]
loop: (X₅ < X₁ ∧ 1 < X₄ ∧ X₃ < 0 ∨ X₅ < X₁ ∧ 1 < X₄ ∧ 0 < X₃,(X₀,X₆) -> (X₀,X₀)
overappr. closed-form: 2⋅X₀ {O(n)}
runtime bound: X₄+1 {O(n)}

Solv. Size Bound - Lifting for t₁₀: l10→l11 and X₆: inf {Infinity}

Solv. Size Bound: t₁₁: l11→l9 for X₀

cycle: [t₁₁: l11→l9; t₁₃: l9→l7; t₁₄: l9→l7; t₁₅: l7→l8; t₁₆: l8→l6; t₁₇: l6→l4; t₅: l4→l12; t₈: l12→l10; t₁₀: l10→l11]
loop: (X₅ < 0 ∧ 1 < X₁ ∧ X₃+1 < X₁ ∨ 0 < X₅ ∧ 1 < X₁ ∧ X₃+1 < X₁,(X₀,X₆) -> (X₆,X₆)
overappr. closed-form: 2⋅X₆ {O(n)}
runtime bound: X₁+1 {O(n)}

Solv. Size Bound - Lifting for t₁₁: l11→l9 and X₀: inf {Infinity}

Solv. Size Bound: t₁₃: l9→l7 for X₀

cycle: [t₁₃: l9→l7; t₁₄: l9→l7; t₁₅: l7→l8; t₁₆: l8→l6; t₁₇: l6→l4; t₅: l4→l12; t₈: l12→l10; t₁₀: l10→l11; t₁₁: l11→l9]
loop: (X₅ < 0 ∧ 1 < X₁ ∧ X₃+1 < X₁ ∨ 0 < X₅ ∧ 1 < X₁ ∧ X₃+1 < X₁,(X₀,X₆) -> (X₆,X₆)
overappr. closed-form: 2⋅X₆ {O(n)}
runtime bound: X₁+1 {O(n)}

Solv. Size Bound - Lifting for t₁₃: l9→l7 and X₀: inf {Infinity}

Solv. Size Bound: t₁₄: l9→l7 for X₀

cycle: [t₁₃: l9→l7; t₁₄: l9→l7; t₁₅: l7→l8; t₁₆: l8→l6; t₁₇: l6→l4; t₅: l4→l12; t₈: l12→l10; t₁₀: l10→l11; t₁₁: l11→l9]
loop: (X₅ < 0 ∧ 1 < X₁ ∧ X₃+1 < X₁ ∨ 0 < X₅ ∧ 1 < X₁ ∧ X₃+1 < X₁,(X₀,X₆) -> (X₆,X₆)
overappr. closed-form: 2⋅X₆ {O(n)}
runtime bound: X₁+1 {O(n)}

Solv. Size Bound - Lifting for t₁₄: l9→l7 and X₀: inf {Infinity}

Solv. Size Bound: t₁₅: l7→l8 for X₀

Solv. Size Bound: t₁₅: l7→l8 for X₂

Solv. Size Bound: t₁₅: l7→l8 for X₆

cycle: [t₁₅: l7→l8; t₁₆: l8→l6; t₁₇: l6→l4; t₅: l4→l12; t₈: l12→l10; t₁₀: l10→l11; t₁₁: l11→l9; t₁₃: l9→l7; t₁₄: l9→l7]
loop: (1 < X₁ ∧ X₃+1 < X₁ ∧ X₃ < 0 ∨ 1 < X₁ ∧ X₃+1 < X₁ ∧ 0 < X₃,(X₀,X₆) -> (X₀,X₀)
overappr. closed-form: 2⋅X₀ {O(n)}
runtime bound: X₁+1 {O(n)}

Solv. Size Bound - Lifting for t₁₅: l7→l8 and X₆: inf {Infinity}

Solv. Size Bound: t₁₆: l8→l6 for X₀

Solv. Size Bound: t₁₆: l8→l6 for X₂

Solv. Size Bound: t₁₆: l8→l6 for X₆

cycle: [t₁₆: l8→l6; t₁₇: l6→l4; t₅: l4→l12; t₈: l12→l10; t₁₀: l10→l11; t₁₁: l11→l9; t₁₃: l9→l7; t₁₄: l9→l7; t₁₅: l7→l8]
loop: (1 < X₁ ∧ X₃+1 < X₁ ∧ X₃ < 0 ∨ 1 < X₁ ∧ X₃+1 < X₁ ∧ 0 < X₃,(X₀,X₆) -> (X₀,X₀)
overappr. closed-form: 2⋅X₀ {O(n)}
runtime bound: X₁+1 {O(n)}

Solv. Size Bound - Lifting for t₁₆: l8→l6 and X₆: inf {Infinity}

Solv. Size Bound: t₁₇: l6→l4 for X₀

Solv. Size Bound: t₁₇: l6→l4 for X₂

Solv. Size Bound: t₁₇: l6→l4 for X₆

cycle: [t₁₇: l6→l4; t₅: l4→l12; t₈: l12→l10; t₁₀: l10→l11; t₁₁: l11→l9; t₁₃: l9→l7; t₁₄: l9→l7; t₁₅: l7→l8; t₁₆: l8→l6]
loop: (1 < X₁ ∧ X₃+1 < X₁ ∧ X₃ < 0 ∨ 1 < X₁ ∧ X₃+1 < X₁ ∧ 0 < X₃,(X₀,X₆) -> (X₀,X₀)
overappr. closed-form: 2⋅X₀ {O(n)}
runtime bound: X₁+1 {O(n)}

Solv. Size Bound - Lifting for t₁₇: l6→l4 and X₆: inf {Infinity}

MPRF for transition t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₄-1, X₂, X₃, X₄, X₃, X₆) :|: 1 < X₄ ∧ X₄ ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF for transition t₈: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ < X₁ ∧ 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 for transition t₁₂: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₂, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ ≤ 0 ∧ 0 ≤ X₅ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF for transition t₁₄: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₆, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₅ ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ of depth 1:

new bound:

X₃+2 {O(n)}

knowledge_propagation leads to new time bound X₃ {O(n)} for transition t₁₀: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l11(X₀, X₁, X₆-X₁, X₃, X₄, X₅, X₆) :|: 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃

knowledge_propagation leads to new time bound X₃ {O(n)} for transition t₁₁: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃

knowledge_propagation leads to new time bound X₃ {O(n)} for transition t₁₃: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₆, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ < 0 ∧ 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃

knowledge_propagation leads to new time bound 3⋅X₃+3 {O(n)} for transition t₁₅: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃

knowledge_propagation leads to new time bound 3⋅X₃+3 {O(n)} for transition t₁₆: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃

knowledge_propagation leads to new time bound 3⋅X₃+3 {O(n)} for transition t₁₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₀) :|: X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃

MPRF for transition t₇: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ ≤ X₅ ∧ 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+8⋅X₃ {O(n^2)}

MPRF for transition t₉: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₁, X₂, X₃, X₄, X₅-X₁, X₆) :|: 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:

21⋅X₃⋅X₃+28⋅X₃ {O(n^2)}

Chain transitions t₈: l12→l10 and t₁₀: l10→l11 to t₅₃₂: l12→l11

Chain transitions t₅₃₂: l12→l11 and t₁₁: l11→l9 to t₅₃₃: l12→l9

Chain transitions t₅: l4→l12 and t₅₃₃: l12→l9 to t₅₃₄: l4→l9

Chain transitions t₉: l14→l12 and t₅₃₃: l12→l9 to t₅₃₅: l14→l9

Chain transitions t₉: l14→l12 and t₇: l12→l14 to t₅₃₆: l14→l14

Chain transitions t₅: l4→l12 and t₇: l12→l14 to t₅₃₇: l4→l14

Chain transitions t₉: l14→l12 and t₅₃₂: l12→l11 to t₅₃₈: l14→l11

Chain transitions t₅: l4→l12 and t₅₃₂: l12→l11 to t₅₃₉: l4→l11

Chain transitions t₉: l14→l12 and t₈: l12→l10 to t₅₄₀: l14→l10

Chain transitions t₅: l4→l12 and t₈: l12→l10 to t₅₄₁: l4→l10

Chain transitions t₁₇: l6→l4 and t₅₃₄: l4→l9 to t₅₄₂: l6→l9

Chain transitions t₄: l1→l4 and t₅₃₄: l4→l9 to t₅₄₃: l1→l9

Chain transitions t₄: l1→l4 and t₅₃₇: l4→l14 to t₅₄₄: l1→l14

Chain transitions t₁₇: l6→l4 and t₅₃₇: l4→l14 to t₅₄₅: l6→l14

Chain transitions t₄: l1→l4 and t₆: l4→l13 to t₅₄₆: l1→l13

Chain transitions t₁₇: l6→l4 and t₆: l4→l13 to t₅₄₇: l6→l13

Chain transitions t₄: l1→l4 and t₅: l4→l12 to t₅₄₈: l1→l12

Chain transitions t₁₇: l6→l4 and t₅: l4→l12 to t₅₄₉: l6→l12

Chain transitions t₄: l1→l4 and t₅₃₉: l4→l11 to t₅₅₀: l1→l11

Chain transitions t₁₇: l6→l4 and t₅₃₉: l4→l11 to t₅₅₁: l6→l11

Chain transitions t₄: l1→l4 and t₅₄₁: l4→l10 to t₅₅₂: l1→l10

Chain transitions t₁₇: l6→l4 and t₅₄₁: l4→l10 to t₅₅₃: l6→l10

Chain transitions t₁₆: l8→l6 and t₅₄₂: l6→l9 to t₅₅₄: l8→l9

Chain transitions t₁₆: l8→l6 and t₁₇: l6→l4 to t₅₅₅: l8→l4

Chain transitions t₁₆: l8→l6 and t₅₄₅: l6→l14 to t₅₅₆: l8→l14

Chain transitions t₁₆: l8→l6 and t₅₄₇: l6→l13 to t₅₅₇: l8→l13

Chain transitions t₁₆: l8→l6 and t₅₄₉: l6→l12 to t₅₅₈: l8→l12

Chain transitions t₁₆: l8→l6 and t₅₅₁: l6→l11 to t₅₅₉: l8→l11

Chain transitions t₁₆: l8→l6 and t₅₅₃: l6→l10 to t₅₆₀: l8→l10

Chain transitions t₁₄: l9→l7 and t₁₅: l7→l8 to t₅₆₁: l9→l8

Chain transitions t₁₃: l9→l7 and t₁₅: l7→l8 to t₅₆₂: l9→l8

Chain transitions t₁₂: l9→l7 and t₁₅: l7→l8 to t₅₆₃: l9→l8

Chain transitions t₅₆₃: l9→l8 and t₅₅₄: l8→l9 to t₅₆₄: l9→l9

Chain transitions t₅₆₂: l9→l8 and t₅₅₄: l8→l9 to t₅₆₅: l9→l9

Chain transitions t₅₆₂: l9→l8 and t₁₆: l8→l6 to t₅₆₆: l9→l6

Chain transitions t₅₆₃: l9→l8 and t₁₆: l8→l6 to t₅₆₇: l9→l6

Chain transitions t₅₆₁: l9→l8 and t₁₆: l8→l6 to t₅₆₈: l9→l6

Chain transitions t₅₆₁: l9→l8 and t₅₅₄: l8→l9 to t₅₆₉: l9→l9

Chain transitions t₅₆₁: l9→l8 and t₅₅₅: l8→l4 to t₅₇₀: l9→l4

Chain transitions t₅₆₂: l9→l8 and t₅₅₅: l8→l4 to t₅₇₁: l9→l4

Chain transitions t₅₆₃: l9→l8 and t₅₅₅: l8→l4 to t₅₇₂: l9→l4

Chain transitions t₅₆₁: l9→l8 and t₅₅₆: l8→l14 to t₅₇₃: l9→l14

Chain transitions t₅₆₂: l9→l8 and t₅₅₆: l8→l14 to t₅₇₄: l9→l14

Chain transitions t₅₆₃: l9→l8 and t₅₅₆: l8→l14 to t₅₇₅: l9→l14

Chain transitions t₅₆₁: l9→l8 and t₅₅₇: l8→l13 to t₅₇₆: l9→l13

Chain transitions t₅₆₂: l9→l8 and t₅₅₇: l8→l13 to t₅₇₇: l9→l13

Chain transitions t₅₆₃: l9→l8 and t₅₅₇: l8→l13 to t₅₇₈: l9→l13

Chain transitions t₅₆₁: l9→l8 and t₅₅₈: l8→l12 to t₅₇₉: l9→l12

Chain transitions t₅₆₂: l9→l8 and t₅₅₈: l8→l12 to t₅₈₀: l9→l12

Chain transitions t₅₆₃: l9→l8 and t₅₅₈: l8→l12 to t₅₈₁: l9→l12

Chain transitions t₅₆₁: l9→l8 and t₅₅₉: l8→l11 to t₅₈₂: l9→l11

Chain transitions t₅₆₂: l9→l8 and t₅₅₉: l8→l11 to t₅₈₃: l9→l11

Chain transitions t₅₆₃: l9→l8 and t₅₅₉: l8→l11 to t₅₈₄: l9→l11

Chain transitions t₅₆₁: l9→l8 and t₅₆₀: l8→l10 to t₅₈₅: l9→l10

Chain transitions t₅₆₂: l9→l8 and t₅₆₀: l8→l10 to t₅₈₆: l9→l10

Chain transitions t₅₆₃: l9→l8 and t₅₆₀: l8→l10 to t₅₈₇: l9→l10

Analysing control-flow refined program

Cut unsatisfiable transition t₁₃: l9→l7

Cut unsatisfiable transition t₅₄₃: l1→l9

Cut unsatisfiable transition t₅₄₆: l1→l13

Cut unsatisfiable transition t₅₅₀: l1→l11

Cut unsatisfiable transition t₅₅₂: l1→l10

Cut unsatisfiable transition t₅₆₂: l9→l8

Cut unsatisfiable transition t₅₆₄: l9→l9

Cut unsatisfiable transition t₅₆₅: l9→l9

Cut unsatisfiable transition t₅₆₆: l9→l6

Cut unsatisfiable transition t₅₆₉: l9→l9

Cut unsatisfiable transition t₅₇₁: l9→l4

Cut unsatisfiable transition t₅₇₄: l9→l14

Cut unsatisfiable transition t₅₇₆: l9→l13

Cut unsatisfiable transition t₅₇₇: l9→l13

Cut unsatisfiable transition t₅₈₀: l9→l12

Cut unsatisfiable transition t₅₈₂: l9→l11

Cut unsatisfiable transition t₅₈₃: l9→l11

Cut unsatisfiable transition t₅₈₄: l9→l11

Cut unsatisfiable transition t₅₈₅: l9→l10

Cut unsatisfiable transition t₅₈₆: l9→l10

Cut unsatisfiable transition t₅₈₇: l9→l10

Eliminate variables {X₀} that do not contribute to the problem

Found invariant X₅ ≤ X₂ ∧ 1+X₁ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l11

Found invariant X₅ ≤ X₂ ∧ 1+X₁ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l6

Found invariant X₅ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l12

Found invariant X₅ ≤ X₂ ∧ 1+X₁ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l7

Found invariant 1+X₅ ≤ X₂ ∧ X₅ ≤ X₁ ∧ X₁ ≤ X₅ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ X₃+X₄ ≤ 1 ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ X₀+X₄ ≤ 1 ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ X₃ ≤ 1 ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₀+X₃ ≤ 2 ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location l13

Found invariant X₅ ≤ X₂ ∧ 1+X₁ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l8

Found invariant X₅ ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l10

Found invariant X₅ ≤ X₂ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₂ for location l4

Found invariant X₅ ≤ X₂ ∧ 1+X₁ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l9

Found invariant X₅ ≤ X₂ ∧ X₄ ≤ X₂ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l14

MPRF for transition t₇₅₆: l14(X₀, X₁, X₂, X₃, X₄, X₅) -{4}> l9(X₀, X₅-X₀, X₂, X₃, X₄-X₀, X₅) :|: X₄ < 2⋅X₀ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₂ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₇₆₃: l9(X₀, X₁, X₂, X₃, X₄, X₅) -{6}> l14(X₀-1, X₁, X₂, X₀, X₂, X₅) :|: 0 < X₄ ∧ 1 < X₀ ∧ X₀ ≤ 1+X₂ ∧ X₅ ≤ X₂ ∧ 1+X₁ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₇₆₄: l9(X₀, X₁, X₂, X₃, X₄, X₅) -{6}> l14(X₀-1, X₁, X₂, X₀, X₂, X₁) :|: X₄ ≤ 0 ∧ 0 ≤ X₄ ∧ 1 < X₀ ∧ X₀ ≤ 1+X₂ ∧ X₅ ≤ X₂ ∧ 1+X₁ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₇₅₅: l14(X₀, X₁, X₂, X₃, X₄, X₅) -{2}> l14(X₀, X₁, X₂, X₃, X₄-X₀, X₅) :|: 2⋅X₀ ≤ X₄ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₂ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

12⋅X₂⋅X₂+20⋅X₂+3 {O(n^2)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Cut unsatisfiable transition t₈: l12→l10

Found invariant 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ for location l11

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ for location l6

Found invariant 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_l14___3

Found invariant 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_l12___2

Found invariant 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 l12

Found invariant 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ for location l7

Found invariant X₄ ≤ 1 ∧ X₄ ≤ X₃ for location l13

Found invariant 2+X₅ ≤ X₄ ∧ 2+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₃ for location l8

Found invariant 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 l10

Found invariant X₄ ≤ X₃ for location l4

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

Found invariant 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_l14___1

knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₈₆₄: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l14___3(X₀, X₁, X₂, X₃, X₁+1, X₅, X₆) :|: X₄ ≤ 1+X₅ ∧ X₁+1 ≤ X₄ ∧ X₁ ≤ X₅ ∧ X₁+1 ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 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+1 {O(n)} for transition t₈₆₆: n_l14___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l12___2(X₀, X₁, X₂, X₃, X₁+1, X₅-X₁, X₆) :|: X₁+1 ≤ X₄ ∧ X₁+1 ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ X₃ ∧ 2 ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₅ ∧ X₄ ≤ 1+X₁ ∧ 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 t₈₆₃: n_l12___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l14___1(X₀, X₁, X₂, X₃, X₁+1, X₅, X₆) :|: X₁+1 ≤ X₄ ∧ 0 ≤ X₅ ∧ X₄+X₅ ≤ 1+X₃ ∧ X₁ ≤ X₅ ∧ X₁+1 ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₃ ∧ 2 ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ 2 ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 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:

2⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}

MPRF for transition t₈₆₅: n_l14___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l12___2(X₀, X₁, X₂, X₃, X₁+1, X₅-X₁, X₆) :|: X₄+X₅ ≤ 1+X₃ ∧ X₁+1 ≤ X₄ ∧ X₁+1 ≤ X₄ ∧ X₄ ≤ 1+X₅ ∧ 2 ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₅ ∧ X₄ ≤ 1+X₁ ∧ 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:

3⋅X₃⋅X₃+5⋅X₃+1 {O(n^2)}

MPRF for transition t₈₇₀: n_l12___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₅ < X₁ ∧ 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 ∧ 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+1 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:27⋅X₃⋅X₃+52⋅X₃+23 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₃+1 {O(n)}
t₆: 1 {O(1)}
t₇: 6⋅X₃⋅X₃+8⋅X₃ {O(n^2)}
t₈: X₃ {O(n)}
t₉: 21⋅X₃⋅X₃+28⋅X₃ {O(n^2)}
t₁₀: X₃ {O(n)}
t₁₁: X₃ {O(n)}
t₁₂: X₃+1 {O(n)}
t₁₃: X₃ {O(n)}
t₁₄: X₃+2 {O(n)}
t₁₅: 3⋅X₃+3 {O(n)}
t₁₆: 3⋅X₃+3 {O(n)}
t₁₇: 3⋅X₃+3 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}

Costbounds

Overall costbound: 27⋅X₃⋅X₃+52⋅X₃+23 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₃+1 {O(n)}
t₆: 1 {O(1)}
t₇: 6⋅X₃⋅X₃+8⋅X₃ {O(n^2)}
t₈: X₃ {O(n)}
t₉: 21⋅X₃⋅X₃+28⋅X₃ {O(n^2)}
t₁₀: X₃ {O(n)}
t₁₁: X₃ {O(n)}
t₁₂: X₃+1 {O(n)}
t₁₃: X₃ {O(n)}
t₁₄: X₃+2 {O(n)}
t₁₅: 3⋅X₃+3 {O(n)}
t₁₆: 3⋅X₃+3 {O(n)}
t₁₇: 3⋅X₃+3 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 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)}
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)}
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)}
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)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₃ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₃ {O(n)}
t₅, X₀: X₃⋅X₃+2⋅X₃+X₀ {O(n^2)}
t₅, X₁: X₃ {O(n)}
t₅, X₂: 3⋅X₃⋅X₃+6⋅X₃+X₂ {O(n^2)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: 2⋅X₃ {O(n)}
t₅, X₅: 2⋅X₃ {O(n)}
t₅, X₆: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₆, X₀: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₆, X₁: X₃ {O(n)}
t₆, X₂: 3⋅X₃⋅X₃+6⋅X₃ {O(n^2)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₃ {O(n)}
t₆, X₅: 4⋅X₃ {O(n)}
t₆, X₆: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₇, X₀: X₃⋅X₃+2⋅X₃+X₀ {O(n^2)}
t₇, X₁: X₃ {O(n)}
t₇, X₂: 3⋅X₃⋅X₃+6⋅X₃+X₂ {O(n^2)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: 2⋅X₃ {O(n)}
t₇, X₅: 2⋅X₃ {O(n)}
t₇, X₆: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₈, X₀: X₃⋅X₃+2⋅X₃+X₀ {O(n^2)}
t₈, X₁: X₃ {O(n)}
t₈, X₂: 3⋅X₃⋅X₃+6⋅X₃+X₂ {O(n^2)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: 2⋅X₃ {O(n)}
t₈, X₅: 2⋅X₃ {O(n)}
t₈, X₆: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₉, X₀: X₃⋅X₃+2⋅X₃+X₀ {O(n^2)}
t₉, X₁: X₃ {O(n)}
t₉, X₂: 3⋅X₃⋅X₃+6⋅X₃+X₂ {O(n^2)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: 2⋅X₃ {O(n)}
t₉, X₅: 2⋅X₃ {O(n)}
t₉, X₆: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₀, X₀: X₃⋅X₃+2⋅X₃+X₀ {O(n^2)}
t₁₀, X₁: X₃ {O(n)}
t₁₀, X₂: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: 2⋅X₃ {O(n)}
t₁₀, X₅: 2⋅X₃ {O(n)}
t₁₀, X₆: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₁, X₀: X₃⋅X₃+2⋅X₃+X₀ {O(n^2)}
t₁₁, X₁: X₃ {O(n)}
t₁₁, X₂: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₁, X₃: X₃ {O(n)}
t₁₁, X₄: 2⋅X₃ {O(n)}
t₁₁, X₅: 2⋅X₃ {O(n)}
t₁₁, X₆: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₂, X₀: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₂, X₁: X₃ {O(n)}
t₁₂, X₂: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₂, X₃: X₃ {O(n)}
t₁₂, X₄: 2⋅X₃ {O(n)}
t₁₂, X₅: 0 {O(1)}
t₁₂, X₆: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₃, X₀: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₃, X₁: X₃ {O(n)}
t₁₃, X₂: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: 2⋅X₃ {O(n)}
t₁₃, X₅: 2⋅X₃ {O(n)}
t₁₃, X₆: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₄, X₀: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₄, X₁: X₃ {O(n)}
t₁₄, X₂: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: 2⋅X₃ {O(n)}
t₁₄, X₅: 2⋅X₃ {O(n)}
t₁₄, X₆: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₅, X₀: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₅, X₁: X₃ {O(n)}
t₁₅, X₂: 3⋅X₃⋅X₃+6⋅X₃ {O(n^2)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: 6⋅X₃ {O(n)}
t₁₅, X₅: 4⋅X₃ {O(n)}
t₁₅, X₆: 3⋅X₃⋅X₃+6⋅X₃ {O(n^2)}
t₁₆, X₀: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₆, X₁: X₃ {O(n)}
t₁₆, X₂: 3⋅X₃⋅X₃+6⋅X₃ {O(n^2)}
t₁₆, X₃: X₃ {O(n)}
t₁₆, X₄: 6⋅X₃ {O(n)}
t₁₆, X₅: 4⋅X₃ {O(n)}
t₁₆, X₆: 3⋅X₃⋅X₃+6⋅X₃ {O(n^2)}
t₁₇, X₀: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₇, X₁: X₃ {O(n)}
t₁₇, X₂: 3⋅X₃⋅X₃+6⋅X₃ {O(n^2)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: X₃ {O(n)}
t₁₇, X₅: 4⋅X₃ {O(n)}
t₁₇, X₆: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₈, X₀: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₈, X₁: X₃ {O(n)}
t₁₈, X₂: 3⋅X₃⋅X₃+6⋅X₃ {O(n^2)}
t₁₈, X₃: X₃ {O(n)}
t₁₈, X₄: X₃ {O(n)}
t₁₈, X₅: 4⋅X₃ {O(n)}
t₁₈, X₆: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₉, X₀: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₉, X₁: X₃ {O(n)}
t₁₉, X₂: 3⋅X₃⋅X₃+6⋅X₃ {O(n^2)}
t₁₉, X₃: X₃ {O(n)}
t₁₉, X₄: X₃ {O(n)}
t₁₉, X₅: 4⋅X₃ {O(n)}
t₁₉, X₆: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₂₀, X₀: X₃⋅X₃+2⋅X₃ {O(n^2)}
t₂₀, X₁: X₃ {O(n)}
t₂₀, X₂: 3⋅X₃⋅X₃+6⋅X₃ {O(n^2)}
t₂₀, X₃: X₃ {O(n)}
t₂₀, X₄: X₃ {O(n)}
t₂₀, X₅: 4⋅X₃ {O(n)}
t₂₀, X₆: 0 {O(1)}
t₂₁, X₀: 3⋅X₃⋅X₃+6⋅X₃+X₀ {O(n^2)}
t₂₁, X₁: 3⋅X₃+X₁ {O(n)}
t₂₁, X₂: 9⋅X₃⋅X₃+18⋅X₃+X₂ {O(n^2)}
t₂₁, X₃: 4⋅X₃ {O(n)}
t₂₁, X₄: 3⋅X₃+X₄ {O(n)}
t₂₁, X₅: 12⋅X₃+X₅ {O(n)}
t₂₁, X₆: 2⋅X₃⋅X₃+4⋅X₃+X₆ {O(n^2)}