Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef_0
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l18, l19, l2, l20, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅)
t₂₀: l10(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅)
t₉: l11(X₀, X₁, X₂, X₃, X₄, X₅) → l18(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ < X₅
t₁₀: l11(X₀, X₁, X₂, X₃, X₄, X₅) → l19(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₂
t₅: l12(X₀, X₁, X₂, X₃, X₄, X₅) → l13(X₀, X₁, X₂, X₃, X₄, X₅)
t₆: l13(X₀, X₁, X₂, X₃, X₄, X₅) → l14(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l14(X₀, X₁, X₂, X₃, X₄, X₅) → l15(X₀, X₁, X₂, X₃, X₄, X₅)
t₈: l15(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, 0, X₃, X₄, X₅)
t₁₄: l16(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₂: l17(X₀, X₁, X₂, X₃, X₄, X₅) → l16(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < X₅
t₁₃: l17(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₃
t₁₁: l18(X₀, X₁, X₂, X₃, X₄, X₅) → l17(X₀, X₁, X₂, X₂+1, 0, X₅)
t₂₃: l19(X₀, X₁, X₂, X₃, X₄, X₅) → l20(X₀, X₁, X₂, X₃, X₄, X₅)
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l12(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₉: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₃-1, X₂, X₃, X₄, X₅)
t₁₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l17(X₀, X₁, X₂, X₃+1, X₄+1, X₅)
t₁₅: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(nondef_0, X₁, X₂, X₃, X₄, X₅)
t₁₇: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0
t₁₆: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀
t₂₁: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₁, X₃, X₄, X₅) :|: 0 < X₄
t₂₂: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₃, X₃, X₄, X₅) :|: X₄ ≤ 0

Preprocessing

Found invariant 0 ≤ X₂ for location l11

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

Found invariant X₅ ≤ X₂ ∧ 0 ≤ X₂ for location l19

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l17

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

Found invariant X₅ ≤ X₂ ∧ 0 ≤ X₂ for location l20

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l5

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

Found invariant 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l10

Found invariant 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l16

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 0 ≤ X₂ for location l18

Found invariant 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l9

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef_0
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l18, l19, l2, l20, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅)
t₂₀: l10(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₉: l11(X₀, X₁, X₂, X₃, X₄, X₅) → l18(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ < X₅ ∧ 0 ≤ X₂
t₁₀: l11(X₀, X₁, X₂, X₃, X₄, X₅) → l19(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₂ ∧ 0 ≤ X₂
t₅: l12(X₀, X₁, X₂, X₃, X₄, X₅) → l13(X₀, X₁, X₂, X₃, X₄, X₅)
t₆: l13(X₀, X₁, X₂, X₃, X₄, X₅) → l14(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l14(X₀, X₁, X₂, X₃, X₄, X₅) → l15(X₀, X₁, X₂, X₃, X₄, X₅)
t₈: l15(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, 0, X₃, X₄, X₅)
t₁₄: l16(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₂: l17(X₀, X₁, X₂, X₃, X₄, X₅) → l16(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < X₅ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₃: l17(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₁: l18(X₀, X₁, X₂, X₃, X₄, X₅) → l17(X₀, X₁, X₂, X₂+1, 0, X₅) :|: 1 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 0 ≤ X₂
t₂₃: l19(X₀, X₁, X₂, X₃, X₄, X₅) → l20(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₂ ∧ 0 ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l12(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₉: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₃-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l17(X₀, X₁, X₂, X₃+1, X₄+1, X₅) :|: 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₁₅: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(nondef_0, X₁, X₂, X₃, X₄, X₅) :|: 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₇: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₆: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀ ∧ 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂
t₂₁: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₁, X₃, X₄, X₅) :|: 0 < X₄ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₂₂: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₃, X₃, X₄, X₅) :|: X₄ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁

MPRF for transition t₉: l11(X₀, X₁, X₂, X₃, X₄, X₅) → l18(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ < X₅ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₅ {O(n)}

MPRF for transition t₁₁: l18(X₀, X₁, X₂, X₃, X₄, X₅) → l17(X₀, X₁, X₂, X₂+1, 0, X₅) :|: 1 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₅ {O(n)}

MPRF for transition t₁₂: l17(X₀, X₁, X₂, X₃, X₄, X₅) → l16(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < X₅ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:

new bound:

3⋅X₅+2 {O(n)}

MPRF for transition t₁₃: l17(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₅ {O(n)}

MPRF for transition t₁₄: l16(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:

new bound:

2⋅X₅+2 {O(n)}

MPRF for transition t₁₅: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(nondef_0, X₁, X₂, X₃, X₄, X₅) :|: 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:

new bound:

3⋅X₅+1 {O(n)}

MPRF for transition t₁₆: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀ ∧ 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF for transition t₁₇: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:

new bound:

2⋅X₅+2 {O(n)}

MPRF for transition t₁₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l17(X₀, X₁, X₂, X₃+1, X₄+1, X₅) :|: 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF for transition t₁₉: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₃-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:

new bound:

2⋅X₅+1 {O(n)}

knowledge_propagation leads to new time bound 2⋅X₅+1 {O(n)} for transition t₂₀: l10(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁

knowledge_propagation leads to new time bound 2⋅X₅+1 {O(n)} for transition t₂₁: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₁, X₃, X₄, X₅) :|: 0 < X₄ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁

knowledge_propagation leads to new time bound 2⋅X₅+1 {O(n)} for transition t₂₂: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₃, X₃, X₄, X₅) :|: X₄ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁

All Bounds

Timebounds

Overall timebound:23⋅X₅+24 {O(n)}
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: X₅ {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₅ {O(n)}
t₁₂: 3⋅X₅+2 {O(n)}
t₁₃: X₅ {O(n)}
t₁₄: 2⋅X₅+2 {O(n)}
t₁₅: 3⋅X₅+1 {O(n)}
t₁₆: X₅+1 {O(n)}
t₁₇: 2⋅X₅+2 {O(n)}
t₁₈: X₅+1 {O(n)}
t₁₉: 2⋅X₅+1 {O(n)}
t₂₀: 2⋅X₅+1 {O(n)}
t₂₁: 2⋅X₅+1 {O(n)}
t₂₂: 2⋅X₅+1 {O(n)}
t₂₃: 1 {O(1)}

Costbounds

Overall costbound: 23⋅X₅+24 {O(n)}
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: X₅ {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₅ {O(n)}
t₁₂: 3⋅X₅+2 {O(n)}
t₁₃: X₅ {O(n)}
t₁₄: 2⋅X₅+2 {O(n)}
t₁₅: 3⋅X₅+1 {O(n)}
t₁₆: X₅+1 {O(n)}
t₁₇: 2⋅X₅+2 {O(n)}
t₁₈: X₅+1 {O(n)}
t₁₉: 2⋅X₅+1 {O(n)}
t₂₀: 2⋅X₅+1 {O(n)}
t₂₁: 2⋅X₅+1 {O(n)}
t₂₂: 2⋅X₅+1 {O(n)}
t₂₃: 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)}
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)}
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)}
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)}
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)}
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)}
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)}
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)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: 0 {O(1)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₉, X₁: 4⋅X₅+X₁+2 {O(n)}
t₉, X₂: 2⋅X₅+1 {O(n)}
t₉, X₃: 4⋅X₅+X₃+2 {O(n)}
t₉, X₄: 2⋅X₅+X₄+2 {O(n)}
t₉, X₅: X₅ {O(n)}
t₁₀, X₁: 4⋅X₅+X₁+2 {O(n)}
t₁₀, X₂: 4⋅X₅+2 {O(n)}
t₁₀, X₃: 4⋅X₅+X₃+2 {O(n)}
t₁₀, X₄: 2⋅X₅+X₄+2 {O(n)}
t₁₀, X₅: 3⋅X₅ {O(n)}
t₁₁, X₁: 4⋅X₅+X₁+2 {O(n)}
t₁₁, X₂: 2⋅X₅+1 {O(n)}
t₁₁, X₃: 2⋅X₅+1 {O(n)}
t₁₁, X₄: 0 {O(1)}
t₁₁, X₅: X₅ {O(n)}
t₁₂, X₁: 4⋅X₅+X₁+2 {O(n)}
t₁₂, X₂: 2⋅X₅+1 {O(n)}
t₁₂, X₃: 2⋅X₅+1 {O(n)}
t₁₂, X₄: X₅+1 {O(n)}
t₁₂, X₅: X₅ {O(n)}
t₁₃, X₁: 2⋅X₁+8⋅X₅+4 {O(n)}
t₁₃, X₂: 4⋅X₅+2 {O(n)}
t₁₃, X₃: 2⋅X₅+1 {O(n)}
t₁₃, X₄: X₅+1 {O(n)}
t₁₃, X₅: X₅ {O(n)}
t₁₄, X₁: 4⋅X₅+X₁+2 {O(n)}
t₁₄, X₂: 2⋅X₅+1 {O(n)}
t₁₄, X₃: 2⋅X₅+1 {O(n)}
t₁₄, X₄: X₅+1 {O(n)}
t₁₄, X₅: X₅ {O(n)}
t₁₅, X₁: 4⋅X₅+X₁+2 {O(n)}
t₁₅, X₂: 2⋅X₅+1 {O(n)}
t₁₅, X₃: 2⋅X₅+1 {O(n)}
t₁₅, X₄: X₅+1 {O(n)}
t₁₅, X₅: X₅ {O(n)}
t₁₆, X₁: 4⋅X₅+X₁+2 {O(n)}
t₁₆, X₂: 2⋅X₅+1 {O(n)}
t₁₆, X₃: 2⋅X₅+1 {O(n)}
t₁₆, X₄: X₅+1 {O(n)}
t₁₆, X₅: X₅ {O(n)}
t₁₇, X₁: 4⋅X₅+X₁+2 {O(n)}
t₁₇, X₂: 2⋅X₅+1 {O(n)}
t₁₇, X₃: 2⋅X₅+1 {O(n)}
t₁₇, X₄: X₅+1 {O(n)}
t₁₇, X₅: X₅ {O(n)}
t₁₈, X₁: 4⋅X₅+X₁+2 {O(n)}
t₁₈, X₂: 2⋅X₅+1 {O(n)}
t₁₈, X₃: 2⋅X₅+1 {O(n)}
t₁₈, X₄: X₅+1 {O(n)}
t₁₈, X₅: X₅ {O(n)}
t₁₉, X₁: 2⋅X₅+1 {O(n)}
t₁₉, X₂: 6⋅X₅+3 {O(n)}
t₁₉, X₃: 2⋅X₅+1 {O(n)}
t₁₉, X₄: 2⋅X₅+2 {O(n)}
t₁₉, X₅: X₅ {O(n)}
t₂₀, X₁: 2⋅X₅+1 {O(n)}
t₂₀, X₂: 6⋅X₅+3 {O(n)}
t₂₀, X₃: 2⋅X₅+1 {O(n)}
t₂₀, X₄: 2⋅X₅+2 {O(n)}
t₂₀, X₅: X₅ {O(n)}
t₂₁, X₁: 2⋅X₅+1 {O(n)}
t₂₁, X₂: 2⋅X₅+1 {O(n)}
t₂₁, X₃: 2⋅X₅+1 {O(n)}
t₂₁, X₄: 2⋅X₅+2 {O(n)}
t₂₁, X₅: X₅ {O(n)}
t₂₂, X₁: 2⋅X₅+1 {O(n)}
t₂₂, X₂: 2⋅X₅+1 {O(n)}
t₂₂, X₃: 2⋅X₅+1 {O(n)}
t₂₂, X₄: 0 {O(1)}
t₂₂, X₅: X₅ {O(n)}
t₂₃, X₁: 4⋅X₅+X₁+2 {O(n)}
t₂₃, X₂: 4⋅X₅+2 {O(n)}
t₂₃, X₃: 4⋅X₅+X₃+2 {O(n)}
t₂₃, X₄: 2⋅X₅+X₄+2 {O(n)}
t₂₃, X₅: 3⋅X₅ {O(n)}