Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁
Temp_Vars: nondef.0, nondef.1, nondef.2
Locations: l0, l1, l10, l11, l12, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₉: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₁₁: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l9(X₀, X₁, X₂, X₃, nondef.0, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₁₆: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l3(X₅, X₀, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₄ ≤ 0 ∧ 0 ≤ X₄
t₁₄: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₄ < 0
t₁₅: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 0 < X₄
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l3(X₁₀, X₈, X₁₁, X₉, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 0 ≤ X₁₀+X₁₁
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₁₀+X₁₁ < 0
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₀ ≤ X₇
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₇ < X₀
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 2⋅X₁+X₂ ≤ X₀ ∧ X₃+1 ≤ X₂ ∧ X₁+1 ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₀ < 2⋅X₁+X₂
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₂ < X₃+1
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₀ < X₁+1
t₂₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₂₀: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l3(X₅, X₀, X₆, X₂, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₁₇: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₁₉: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l6(X₀, X₁, X₂, X₃, X₄, X₅, nondef.2, X₇, X₈, X₉, X₁₀, X₁₁)
t₁₃: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l12(X₀, X₁, X₂, X₃, X₄, nondef.1, X₆, X₇, X₈, X₉, X₁₀, X₁₁)

Preprocessing

Found invariant X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ for location l11

Found invariant X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ for location l6

Found invariant X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ for location l12

Found invariant X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ for location l7

Found invariant X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ for location l8

Found invariant X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ for location l10

Found invariant X₉ ≤ X₃ ∧ X₈ ≤ X₁ ∧ X₀ ≤ X₇ ∧ 0 ≤ X₁₀+X₁₁ for location l4

Found invariant X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ for location l9

Found invariant X₉ ≤ X₃ ∧ X₈ ≤ X₁ ∧ 0 ≤ X₁₀+X₁₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁
Temp_Vars: nondef.0, nondef.1, nondef.2
Locations: l0, l1, l10, l11, l12, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₉: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀
t₁₁: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l9(X₀, X₁, X₂, X₃, nondef.0, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀
t₁₆: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l3(X₅, X₀, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₄ ≤ 0 ∧ 0 ≤ X₄ ∧ X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀
t₁₄: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₄ < 0 ∧ X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀
t₁₅: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 0 < X₄ ∧ X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l3(X₁₀, X₈, X₁₁, X₉, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 0 ≤ X₁₀+X₁₁
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₁₀+X₁₁ < 0
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₀ ≤ X₇ ∧ X₉ ≤ X₃ ∧ X₈ ≤ X₁ ∧ 0 ≤ X₁₀+X₁₁
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₇ < X₀ ∧ X₉ ≤ X₃ ∧ X₈ ≤ X₁ ∧ 0 ≤ X₁₀+X₁₁
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 2⋅X₁+X₂ ≤ X₀ ∧ X₃+1 ≤ X₂ ∧ X₁+1 ≤ X₀ ∧ X₉ ≤ X₃ ∧ X₈ ≤ X₁ ∧ X₀ ≤ X₇ ∧ 0 ≤ X₁₀+X₁₁
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₀ < 2⋅X₁+X₂ ∧ X₉ ≤ X₃ ∧ X₈ ≤ X₁ ∧ X₀ ≤ X₇ ∧ 0 ≤ X₁₀+X₁₁
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₂ < X₃+1 ∧ X₉ ≤ X₃ ∧ X₈ ≤ X₁ ∧ X₀ ≤ X₇ ∧ 0 ≤ X₁₀+X₁₁
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₀ < X₁+1 ∧ X₉ ≤ X₃ ∧ X₈ ≤ X₁ ∧ X₀ ≤ X₇ ∧ 0 ≤ X₁₀+X₁₁
t₂₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₂₀: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l3(X₅, X₀, X₆, X₂, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀
t₁₇: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀
t₁₉: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l6(X₀, X₁, X₂, X₃, X₄, X₅, nondef.2, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀
t₁₃: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l12(X₀, X₁, X₂, X₃, X₄, nondef.1, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀

MPRF for transition t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 2⋅X₁+X₂ ≤ X₀ ∧ X₃+1 ≤ X₂ ∧ X₁+1 ≤ X₀ ∧ X₉ ≤ X₃ ∧ X₈ ≤ X₁ ∧ X₀ ≤ X₇ ∧ 0 ≤ X₁₀+X₁₁ of depth 1:

new bound:

X₇+X₈ {O(n)}

MPRF for transition t₉: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₇+X₈ {O(n)}

MPRF for transition t₁₁: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l9(X₀, X₁, X₂, X₃, nondef.0, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₇+X₈ {O(n)}

MPRF for transition t₁₃: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l12(X₀, X₁, X₂, X₃, X₄, nondef.1, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₇+X₈ {O(n)}

MPRF for transition t₁₄: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₄ < 0 ∧ X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₇+X₈ {O(n)}

MPRF for transition t₁₅: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: 0 < X₄ ∧ X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₇+X₈ {O(n)}

MPRF for transition t₁₆: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l3(X₅, X₀, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₄ ≤ 0 ∧ 0 ≤ X₄ ∧ X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₇+X₈ {O(n)}

MPRF for transition t₁₇: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₇+X₈ {O(n)}

MPRF for transition t₁₉: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l6(X₀, X₁, X₂, X₃, X₄, X₅, nondef.2, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₇+X₈ {O(n)}

MPRF for transition t₂₀: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l3(X₅, X₀, X₆, X₂, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₉ ≤ X₃ ∧ 1+X₉ ≤ X₂ ∧ 1+X₈ ≤ X₇ ∧ X₈ ≤ X₁ ∧ 1+X₈ ≤ X₀ ∧ 1+X₁ ≤ X₇ ∧ X₀ ≤ X₇ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ X₁₀+X₁₁ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₇+X₈ {O(n)}

knowledge_propagation leads to new time bound 2⋅X₇+2⋅X₈+1 {O(n)} for transition t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) :|: X₀ ≤ X₇ ∧ X₉ ≤ X₃ ∧ X₈ ≤ X₁ ∧ 0 ≤ X₁₀+X₁₁

All Bounds

Timebounds

Overall timebound:12⋅X₇+12⋅X₈+9 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 2⋅X₇+2⋅X₈+1 {O(n)}
t₄: 1 {O(1)}
t₅: X₇+X₈ {O(n)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₇+X₈ {O(n)}
t₁₁: X₇+X₈ {O(n)}
t₁₃: X₇+X₈ {O(n)}
t₁₄: X₇+X₈ {O(n)}
t₁₅: X₇+X₈ {O(n)}
t₁₆: X₇+X₈ {O(n)}
t₁₇: X₇+X₈ {O(n)}
t₁₉: X₇+X₈ {O(n)}
t₂₀: X₇+X₈ {O(n)}
t₂₁: 1 {O(1)}

Costbounds

Overall costbound: 12⋅X₇+12⋅X₈+9 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 2⋅X₇+2⋅X₈+1 {O(n)}
t₄: 1 {O(1)}
t₅: X₇+X₈ {O(n)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₇+X₈ {O(n)}
t₁₁: X₇+X₈ {O(n)}
t₁₃: X₇+X₈ {O(n)}
t₁₄: X₇+X₈ {O(n)}
t₁₅: X₇+X₈ {O(n)}
t₁₆: X₇+X₈ {O(n)}
t₁₇: X₇+X₈ {O(n)}
t₁₉: X₇+X₈ {O(n)}
t₂₀: X₇+X₈ {O(n)}
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)}
t₀, X₇: X₇ {O(n)}
t₀, X₈: X₈ {O(n)}
t₀, X₉: X₉ {O(n)}
t₀, X₁₀: X₁₀ {O(n)}
t₀, X₁₁: X₁₁ {O(n)}
t₁, X₀: X₁₀ {O(n)}
t₁, X₁: X₈ {O(n)}
t₁, X₂: X₁₁ {O(n)}
t₁, X₃: X₉ {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)}
t₁, X₉: X₉ {O(n)}
t₁, X₁₀: X₁₀ {O(n)}
t₁, X₁₁: X₁₁ {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)}
t₂, X₉: X₉ {O(n)}
t₂, X₁₀: X₁₀ {O(n)}
t₂, X₁₁: X₁₁ {O(n)}
t₃, X₇: X₇ {O(n)}
t₃, X₈: X₈ {O(n)}
t₃, X₉: X₉ {O(n)}
t₃, X₁₀: X₁₀ {O(n)}
t₃, X₁₁: X₁₁ {O(n)}
t₄, X₇: 3⋅X₇ {O(n)}
t₄, X₈: 3⋅X₈ {O(n)}
t₄, X₉: 3⋅X₉ {O(n)}
t₄, X₁₀: 3⋅X₁₀ {O(n)}
t₄, X₁₁: 3⋅X₁₁ {O(n)}
t₅, X₇: X₇ {O(n)}
t₅, X₈: X₈ {O(n)}
t₅, X₉: X₉ {O(n)}
t₅, X₁₀: X₁₀ {O(n)}
t₅, X₁₁: X₁₁ {O(n)}
t₆, X₇: X₇ {O(n)}
t₆, X₈: X₈ {O(n)}
t₆, X₉: X₉ {O(n)}
t₆, X₁₀: X₁₀ {O(n)}
t₆, X₁₁: X₁₁ {O(n)}
t₇, X₇: X₇ {O(n)}
t₇, X₈: X₈ {O(n)}
t₇, X₉: X₉ {O(n)}
t₇, X₁₀: X₁₀ {O(n)}
t₇, X₁₁: X₁₁ {O(n)}
t₈, X₇: X₇ {O(n)}
t₈, X₈: X₈ {O(n)}
t₈, X₉: X₉ {O(n)}
t₈, X₁₀: X₁₀ {O(n)}
t₈, X₁₁: X₁₁ {O(n)}
t₉, X₇: X₇ {O(n)}
t₉, X₈: X₈ {O(n)}
t₉, X₉: X₉ {O(n)}
t₉, X₁₀: X₁₀ {O(n)}
t₉, X₁₁: X₁₁ {O(n)}
t₁₁, X₇: X₇ {O(n)}
t₁₁, X₈: X₈ {O(n)}
t₁₁, X₉: X₉ {O(n)}
t₁₁, X₁₀: X₁₀ {O(n)}
t₁₁, X₁₁: X₁₁ {O(n)}
t₁₃, X₇: X₇ {O(n)}
t₁₃, X₈: X₈ {O(n)}
t₁₃, X₉: X₉ {O(n)}
t₁₃, X₁₀: X₁₀ {O(n)}
t₁₃, X₁₁: X₁₁ {O(n)}
t₁₄, X₇: X₇ {O(n)}
t₁₄, X₈: X₈ {O(n)}
t₁₄, X₉: X₉ {O(n)}
t₁₄, X₁₀: X₁₀ {O(n)}
t₁₄, X₁₁: X₁₁ {O(n)}
t₁₅, X₇: X₇ {O(n)}
t₁₅, X₈: X₈ {O(n)}
t₁₅, X₉: X₉ {O(n)}
t₁₅, X₁₀: X₁₀ {O(n)}
t₁₅, X₁₁: X₁₁ {O(n)}
t₁₆, X₄: 0 {O(1)}
t₁₆, X₇: X₇ {O(n)}
t₁₆, X₈: X₈ {O(n)}
t₁₆, X₉: X₉ {O(n)}
t₁₆, X₁₀: X₁₀ {O(n)}
t₁₆, X₁₁: X₁₁ {O(n)}
t₁₇, X₇: X₇ {O(n)}
t₁₇, X₈: X₈ {O(n)}
t₁₇, X₉: X₉ {O(n)}
t₁₇, X₁₀: X₁₀ {O(n)}
t₁₇, X₁₁: X₁₁ {O(n)}
t₁₉, X₇: X₇ {O(n)}
t₁₉, X₈: X₈ {O(n)}
t₁₉, X₉: X₉ {O(n)}
t₁₉, X₁₀: X₁₀ {O(n)}
t₁₉, X₁₁: X₁₁ {O(n)}
t₂₀, X₇: X₇ {O(n)}
t₂₀, X₈: X₈ {O(n)}
t₂₀, X₉: X₉ {O(n)}
t₂₀, X₁₀: X₁₀ {O(n)}
t₂₀, X₁₁: X₁₁ {O(n)}
t₂₁, X₇: 7⋅X₇ {O(n)}
t₂₁, X₈: 7⋅X₈ {O(n)}
t₂₁, X₉: 7⋅X₉ {O(n)}
t₂₁, X₁₀: 7⋅X₁₀ {O(n)}
t₂₁, X₁₁: 7⋅X₁₁ {O(n)}