Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef_0, nondef_1
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l18, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₁₉: l10(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₁, X₄)
t₉: l11(X₀, X₁, X₂, X₃, X₄) → l15(X₀, X₁, X₂, X₃, X₃) :|: X₃+1 < X₂
t₁₀: l11(X₀, X₁, X₂, X₃, X₄) → l16(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1+X₃
t₆: l12(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄)
t₇: l13(X₀, X₁, X₂, X₃, X₄) → l14(X₀, X₁, X₂, X₃, X₄)
t₈: l14(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, 0, X₄)
t₁₁: l15(X₀, X₁, X₂, X₃, X₄) → l17(X₄+1, X₁, X₂, X₃, X₄) :|: X₄+1 < X₂
t₁₂: l15(X₀, X₁, X₂, X₃, X₄) → l6(X₄+1, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₄+1
t₂₀: l16(X₀, X₁, X₂, X₃, X₄) → l18(X₀, X₁, X₂, X₃, X₄)
t₁₃: l17(X₀, X₁, X₂, X₃, X₄) → l15(X₀, X₁, X₂, X₃, X₀) :|: nondef_0 < nondef_1
t₁₄: l17(X₀, X₁, X₂, X₃, X₄) → l15(X₀, X₁, X₂, X₃, X₀) :|: nondef_1 ≤ nondef_0
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₁₇: l5(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₃+1, X₂, X₃, X₄)
t₁₅: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₁₆: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₅: l8(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄)
t₁₈: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Found invariant 0 ≤ X₃ for location l11

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

Found invariant 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂ for location l15

Found invariant 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l17

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

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₀ for location l5

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l10

Found invariant 0 ≤ X₃ ∧ X₂ ≤ 1+X₃ for location l16

Found invariant 0 ≤ X₃ ∧ X₂ ≤ 1+X₃ for location l18

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l9

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef_0, nondef_1
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l18, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₁₉: l10(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₁, X₄) :|: 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₉: l11(X₀, X₁, X₂, X₃, X₄) → l15(X₀, X₁, X₂, X₃, X₃) :|: X₃+1 < X₂ ∧ 0 ≤ X₃
t₁₀: l11(X₀, X₁, X₂, X₃, X₄) → l16(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1+X₃ ∧ 0 ≤ X₃
t₆: l12(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄)
t₇: l13(X₀, X₁, X₂, X₃, X₄) → l14(X₀, X₁, X₂, X₃, X₄)
t₈: l14(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, 0, X₄)
t₁₁: l15(X₀, X₁, X₂, X₃, X₄) → l17(X₄+1, X₁, X₂, X₃, X₄) :|: X₄+1 < X₂ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂
t₁₂: l15(X₀, X₁, X₂, X₃, X₄) → l6(X₄+1, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₄+1 ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂
t₂₀: l16(X₀, X₁, X₂, X₃, X₄) → l18(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃ ∧ X₂ ≤ 1+X₃
t₁₃: l17(X₀, X₁, X₂, X₃, X₄) → l15(X₀, X₁, X₂, X₃, X₀) :|: nondef_0 < nondef_1 ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀
t₁₄: l17(X₀, X₁, X₂, X₃, X₄) → l15(X₀, X₁, X₂, X₃, X₀) :|: nondef_1 ≤ nondef_0 ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₁₇: l5(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₃+1, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₀
t₁₅: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₀
t₁₆: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₀
t₅: l8(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄)
t₁₈: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀

MPRF for transition t₁₉: l10(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₁, X₄) :|: 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l11 [X₂-X₃-1 ]
l17 [X₂-X₃-1 ]
l15 [X₂-X₃-1 ]
l6 [X₂-X₃-1 ]
l7 [X₂-X₃-1 ]
l5 [X₀-X₃-1 ]
l9 [X₀-X₁ ]
l10 [X₄+1-X₁ ]

MPRF for transition t₉: l11(X₀, X₁, X₂, X₃, X₄) → l15(X₀, X₁, X₂, X₃, X₃) :|: X₃+1 < X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l11 [X₂-X₃-1 ]
l17 [X₂-X₃-2 ]
l15 [X₂-X₃-2 ]
l6 [X₂-X₃-2 ]
l7 [X₀-X₃-2 ]
l5 [X₀-X₃-2 ]
l9 [X₀-X₁-1 ]
l10 [X₂-X₁-1 ]

MPRF for transition t₁₂: l15(X₀, X₁, X₂, X₃, X₄) → l6(X₄+1, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₄+1 ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l11 [X₂+1-X₃ ]
l17 [X₂+1-X₃ ]
l15 [X₂+1-X₃ ]
l6 [X₂-X₃ ]
l7 [X₂-X₃ ]
l5 [X₀-X₃ ]
l9 [X₀-X₃ ]
l10 [X₀+1-X₁ ]

MPRF for transition t₁₇: l5(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₃+1, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l11 [X₂-X₃-1 ]
l17 [X₂-X₃-1 ]
l15 [X₂-X₃-1 ]
l6 [X₂+X₄-X₀-X₃ ]
l7 [X₄-X₃ ]
l5 [X₂-X₃-1 ]
l9 [X₀-X₃-2 ]
l10 [X₂-X₃-2 ]

MPRF for transition t₁₅: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l11 [X₂+1-X₃ ]
l17 [X₂+1-X₃ ]
l15 [X₂+1-X₃ ]
l6 [X₂+1-X₃ ]
l7 [X₂-X₃ ]
l5 [X₂-X₃ ]
l9 [X₂-X₃ ]
l10 [X₂+1-X₁ ]

MPRF for transition t₁₆: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l11 [X₂-X₃-1 ]
l17 [X₂-X₃-1 ]
l15 [X₂-X₃-1 ]
l6 [X₂-X₃-1 ]
l7 [X₂-X₃-1 ]
l5 [X₀-X₃-2 ]
l9 [X₀-X₁-1 ]
l10 [X₂-X₁-1 ]

MPRF for transition t₁₈: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l11 [X₂-X₃-1 ]
l17 [X₂-X₃-1 ]
l15 [X₂-X₃-1 ]
l6 [X₂-X₃-1 ]
l7 [X₀-X₃-1 ]
l5 [X₄-X₃ ]
l9 [X₄+1-X₁ ]
l10 [X₄-X₁ ]

MPRF for transition t₁₁: l15(X₀, X₁, X₂, X₃, X₄) → l17(X₄+1, X₁, X₂, X₃, X₄) :|: X₄+1 < X₂ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂ of depth 1:

new bound:

X₂⋅X₂+2⋅X₂ {O(n^2)}

MPRF:

l10 [X₂ ]
l11 [X₂ ]
l17 [X₂-X₀ ]
l15 [X₂-X₄ ]
l9 [0 ]
l6 [X₂-X₄ ]
l7 [X₂-X₀ ]
l5 [0 ]

MPRF for transition t₁₃: l17(X₀, X₁, X₂, X₃, X₄) → l15(X₀, X₁, X₂, X₃, X₀) :|: nondef_0 < nondef_1 ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}

MPRF:

l10 [2⋅X₂ ]
l11 [2⋅X₂ ]
l17 [2⋅X₂-X₄-3 ]
l15 [2⋅X₂-X₄-3 ]
l9 [X₂-4 ]
l6 [2⋅X₂-X₄-3 ]
l7 [2⋅X₄-X₂ ]
l5 [X₀-4 ]

MPRF for transition t₁₄: l17(X₀, X₁, X₂, X₃, X₄) → l15(X₀, X₁, X₂, X₃, X₀) :|: nondef_1 ≤ nondef_0 ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}

MPRF:

l10 [2⋅X₂ ]
l11 [2⋅X₂ ]
l17 [2⋅X₂-X₄-3 ]
l15 [2⋅X₂-X₄-3 ]
l9 [X₀-2 ]
l6 [2⋅X₂-X₄-3 ]
l7 [X₀+X₂-X₄-3 ]
l5 [X₀-2 ]

Analysing control-flow refined program

Cut unsatisfiable transition t₁₂: l15→l6

Found invariant 0 ≤ X₃ for location l11

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

Found invariant X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂ for location l15

Found invariant X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l17___3

Found invariant 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 3+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 3 ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₀ for location n_l17___1

Found invariant 1+X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l15___2

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

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₀ for location l5

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l10

Found invariant 0 ≤ X₃ ∧ X₂ ≤ 1+X₃ for location l16

Found invariant 0 ≤ X₃ ∧ X₂ ≤ 1+X₃ for location l18

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l9

knowledge_propagation leads to new time bound X₂+1 {O(n)} for transition t₁₃₂: l15(X₀, X₁, X₂, X₃, X₄) → n_l17___3(X₄+1, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₄ ∧ 0 ≤ X₃ ∧ 1+X₄ < X₂ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₄ < X₂ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂

knowledge_propagation leads to new time bound X₂+1 {O(n)} for transition t₁₃₅: n_l17___3(X₀, X₁, X₂, X₃, X₄) → n_l15___2(X₀, X₁, X₂, Arg3_P, X₀) :|: X₀ < X₂ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₄+1 ∧ 1+X₄ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+Arg3_P ≤ X₀ ∧ 0 ≤ Arg3_P ∧ X₀ ≤ X₄+1 ∧ 1+X₄ ≤ X₀ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₂+1 {O(n)} for transition t₁₃₆: n_l17___3(X₀, X₁, X₂, X₃, X₄) → n_l15___2(X₀, X₁, X₂, Arg3_P, X₀) :|: X₀ < X₂ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₄+1 ∧ 1+X₄ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+Arg3_P ≤ X₀ ∧ 0 ≤ Arg3_P ∧ X₀ ≤ X₄+1 ∧ 1+X₄ ≤ X₀ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀

MPRF for transition t₁₃₁: n_l15___2(X₀, X₁, X₂, X₃, X₄) → n_l17___1(X₄+1, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₄ ∧ 0 ≤ X₃ ∧ 2+X₃ ≤ X₂ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1+X₄ < X₂ ∧ X₃ ≤ X₄ ∧ 1+X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

6⋅X₂⋅X₂+13⋅X₂+6 {O(n^2)}

MPRF:

l11 [X₂ ]
l15 [X₂ ]
n_l17___3 [X₂ ]
l7 [X₀+X₂-X₄-1 ]
l5 [X₀+X₂-X₄-1 ]
l9 [2⋅X₂-X₄-1 ]
l10 [2⋅X₀-X₄-1 ]
l6 [X₀+X₂-X₄-1 ]
n_l17___1 [2⋅X₂-X₀-1 ]
n_l15___2 [2⋅X₂-X₀-1 ]

MPRF for transition t₁₄₃: n_l15___2(X₀, X₁, X₂, X₃, X₄) → l6(X₄+1, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₄+1 ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

l11 [X₂-X₃ ]
l15 [X₂-X₄ ]
l7 [X₂-X₃-1 ]
l5 [X₂-X₃-1 ]
l9 [X₂-X₁ ]
l10 [X₂-X₁ ]
l6 [X₂-X₃-1 ]
n_l17___1 [X₂-X₃ ]
n_l17___3 [X₂-X₄ ]
n_l15___2 [X₂-X₃ ]

MPRF for transition t₁₃₃: n_l17___1(X₀, X₁, X₂, X₃, X₄) → n_l15___2(X₀, X₁, X₂, Arg3_P, X₀) :|: X₀ < X₂ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₄+1 ∧ 1+X₄ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+Arg3_P ≤ X₀ ∧ 0 ≤ Arg3_P ∧ X₀ ≤ X₄+1 ∧ 1+X₄ ≤ X₀ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 3+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 3 ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₀ of depth 1:

new bound:

4⋅X₂⋅X₂+10⋅X₂+6 {O(n^2)}

MPRF:

l11 [0 ]
l15 [0 ]
n_l17___3 [0 ]
l7 [2⋅X₂-2⋅X₄-2 ]
l5 [2⋅X₀-2⋅X₄-2 ]
l9 [2⋅X₀-2⋅X₄-2 ]
l10 [2⋅X₂-2⋅X₄-2 ]
l6 [2⋅X₀-2⋅X₄-2 ]
n_l17___1 [X₂-X₄-1 ]
n_l15___2 [X₂-X₄-1 ]

MPRF for transition t₁₃₄: n_l17___1(X₀, X₁, X₂, X₃, X₄) → n_l15___2(X₀, X₁, X₂, Arg3_P, X₀) :|: X₀ < X₂ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₄+1 ∧ 1+X₄ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+Arg3_P ≤ X₀ ∧ 0 ≤ Arg3_P ∧ X₀ ≤ X₄+1 ∧ 1+X₄ ≤ X₀ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 3+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 3 ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₀ of depth 1:

new bound:

4⋅X₂⋅X₂+10⋅X₂+6 {O(n^2)}

MPRF:

l11 [0 ]
l15 [0 ]
n_l17___3 [0 ]
l7 [2⋅X₂-2⋅X₄-2 ]
l5 [2⋅X₀-2⋅X₄-2 ]
l9 [2⋅X₀-2⋅X₄-2 ]
l10 [2⋅X₂-2⋅X₄-2 ]
l6 [2⋅X₀-2⋅X₄-2 ]
n_l17___1 [X₂-X₄-1 ]
n_l15___2 [X₂-X₄-1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:5⋅X₂⋅X₂+17⋅X₂+18 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₉: X₂+1 {O(n)}
t₉: X₂+1 {O(n)}
t₁₀: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₁₁: X₂⋅X₂+2⋅X₂ {O(n^2)}
t₁₂: X₂+1 {O(n)}
t₂₀: 1 {O(1)}
t₁₃: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
t₁₄: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₁₇: X₂+1 {O(n)}
t₁₅: X₂+1 {O(n)}
t₁₆: X₂+1 {O(n)}
t₅: 1 {O(1)}
t₁₈: X₂+1 {O(n)}

Costbounds

Overall costbound: 5⋅X₂⋅X₂+17⋅X₂+18 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₉: X₂+1 {O(n)}
t₉: X₂+1 {O(n)}
t₁₀: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₁₁: X₂⋅X₂+2⋅X₂ {O(n^2)}
t₁₂: X₂+1 {O(n)}
t₂₀: 1 {O(1)}
t₁₃: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
t₁₄: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₁₇: X₂+1 {O(n)}
t₁₅: X₂+1 {O(n)}
t₁₆: X₂+1 {O(n)}
t₅: 1 {O(1)}
t₁₈: X₂+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)}
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)}
t₁₉, X₀: 2⋅X₂⋅X₂+6⋅X₂+4 {O(n^2)}
t₁₉, X₁: X₂+1 {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₂+1 {O(n)}
t₁₉, X₄: 2⋅X₂⋅X₂+6⋅X₂+2 {O(n^2)}
t₉, X₀: 2⋅X₂⋅X₂+6⋅X₂+X₀+4 {O(n^2)}
t₉, X₁: X₁+X₂+1 {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₂+1 {O(n)}
t₉, X₄: X₂+1 {O(n)}
t₁₀, X₀: 2⋅X₂⋅X₂+6⋅X₂+X₀+4 {O(n^2)}
t₁₀, X₁: X₁+X₂+1 {O(n)}
t₁₀, X₂: 2⋅X₂ {O(n)}
t₁₀, X₃: X₂+1 {O(n)}
t₁₀, X₄: 2⋅X₂⋅X₂+6⋅X₂+X₄+2 {O(n^2)}
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)}
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)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: 0 {O(1)}
t₈, X₄: X₄ {O(n)}
t₁₁, X₀: X₂⋅X₂+3⋅X₂+1 {O(n^2)}
t₁₁, X₁: X₁+X₂+1 {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₂+1 {O(n)}
t₁₁, X₄: 2⋅X₂⋅X₂+7⋅X₂+3 {O(n^2)}
t₁₂, X₀: 2⋅X₂⋅X₂+6⋅X₂+4 {O(n^2)}
t₁₂, X₁: 2⋅X₁+2⋅X₂+2 {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₂+1 {O(n)}
t₁₂, X₄: 2⋅X₂⋅X₂+6⋅X₂+2 {O(n^2)}
t₂₀, X₀: 2⋅X₂⋅X₂+6⋅X₂+X₀+4 {O(n^2)}
t₂₀, X₁: X₁+X₂+1 {O(n)}
t₂₀, X₂: 2⋅X₂ {O(n)}
t₂₀, X₃: X₂+1 {O(n)}
t₂₀, X₄: 2⋅X₂⋅X₂+6⋅X₂+X₄+2 {O(n^2)}
t₁₃, X₀: X₂⋅X₂+3⋅X₂+1 {O(n^2)}
t₁₃, X₁: X₁+X₂+1 {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₂+1 {O(n)}
t₁₃, X₄: X₂⋅X₂+3⋅X₂+1 {O(n^2)}
t₁₄, X₀: X₂⋅X₂+3⋅X₂+1 {O(n^2)}
t₁₄, X₁: X₁+X₂+1 {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₂+1 {O(n)}
t₁₄, X₄: X₂⋅X₂+3⋅X₂+1 {O(n^2)}
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)}
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)}
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)}
t₁₇, X₀: 2⋅X₂⋅X₂+6⋅X₂+4 {O(n^2)}
t₁₇, X₁: X₂+1 {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₂+1 {O(n)}
t₁₇, X₄: 2⋅X₂⋅X₂+6⋅X₂+2 {O(n^2)}
t₁₅, X₀: 2⋅X₂⋅X₂+6⋅X₂+4 {O(n^2)}
t₁₅, X₁: 2⋅X₁+2⋅X₂+2 {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₂+1 {O(n)}
t₁₅, X₄: 2⋅X₂⋅X₂+6⋅X₂+2 {O(n^2)}
t₁₆, X₀: 2⋅X₂⋅X₂+6⋅X₂+4 {O(n^2)}
t₁₆, X₁: 2⋅X₁+2⋅X₂+2 {O(n)}
t₁₆, X₂: X₂ {O(n)}
t₁₆, X₃: X₂+1 {O(n)}
t₁₆, X₄: 2⋅X₂⋅X₂+6⋅X₂+2 {O(n^2)}
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)}
t₁₈, X₀: 2⋅X₂⋅X₂+6⋅X₂+4 {O(n^2)}
t₁₈, X₁: X₂+1 {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₂+1 {O(n)}
t₁₈, X₄: 2⋅X₂⋅X₂+6⋅X₂+2 {O(n^2)}