Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars: nondef_0
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, 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)
t₆: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₇: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, X₇, X₈, X₄, X₅, X₆, X₇, X₈)
t₁₅: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₀ ≤ 0
t₁₄: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 0 < X₀
t₁₂: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₃: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l12(nondef_0, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₆: l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l16(X₀, X₁, X₂, X₃, X₄+1, X₅, X₆, X₇, X₈)
t₁₀: l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₄ < X₅
t₁₁: l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₅ ≤ X₄
t₂₀: l17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l18(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)
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) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₉: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, X₁, X₄, X₄, X₅, X₆, X₇, X₈)
t₁₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l7(X₀, X₂+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₈: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l16(X₀, X₁, X₂, X₃, X₃, X₅, X₆, X₇, X₈) :|: X₂ < X₆
t₉: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₆ ≤ X₂
t₅: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)

Preprocessing

Found invariant X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ X₃ ≤ X₄ for location l6

Found invariant 1+X₈ ≤ X₅ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₀ ≤ 0 for location l15

Found invariant 1+X₈ ≤ X₅ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ X₄ for location l12

Found invariant X₈ ≤ X₃ ∧ X₇ ≤ X₂ ∧ X₆ ≤ X₂ for location l17

Found invariant X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₃ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ for location l7

Found invariant X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₃ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ for location l5

Found invariant 1+X₈ ≤ X₅ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ X₄ for location l13

Found invariant X₈ ≤ X₃ ∧ X₇ ≤ X₂ for location l8

Found invariant X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ X₃ ≤ X₄ for location l16

Found invariant X₈ ≤ X₃ ∧ X₇ ≤ X₂ ∧ X₆ ≤ X₂ for location l18

Found invariant 1+X₈ ≤ X₅ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ X₄ for location l14

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars: nondef_0
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, 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)
t₆: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₇: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, X₇, X₈, X₄, X₅, X₆, X₇, X₈)
t₁₅: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₀ ≤ 0 ∧ 1+X₈ ≤ X₅ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ X₄
t₁₄: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 0 < X₀ ∧ 1+X₈ ≤ X₅ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ X₄
t₁₂: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₈ ≤ X₅ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ X₄
t₁₃: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l12(nondef_0, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₈ ≤ X₅ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ X₄
t₁₆: l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l16(X₀, X₁, X₂, X₃, X₄+1, X₅, X₆, X₇, X₈) :|: 1+X₈ ≤ X₅ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₀ ≤ 0
t₁₀: l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₄ < X₅ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ X₃ ≤ X₄
t₁₁: l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₅ ≤ X₄ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ X₃ ≤ X₄
t₂₀: l17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l18(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₈ ≤ X₃ ∧ X₇ ≤ X₂ ∧ X₆ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
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) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₉: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, X₁, X₄, X₄, X₅, X₆, X₇, X₈) :|: X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₃ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂
t₁₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l7(X₀, X₂+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ X₃ ≤ X₄
t₁₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₃ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂
t₈: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l16(X₀, X₁, X₂, X₃, X₃, X₅, X₆, X₇, X₈) :|: X₂ < X₆ ∧ X₈ ≤ X₃ ∧ X₇ ≤ X₂
t₉: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₆ ≤ X₂ ∧ X₈ ≤ X₃ ∧ X₇ ≤ X₂
t₅: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)

MPRF for transition t₁₄: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 0 < X₀ ∧ 1+X₈ ≤ X₅ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ X₄ of depth 1:

new bound:

X₆+X₇+1 {O(n)}

MPRF:

l14 [X₆+1-X₂ ]
l12 [X₆+1-X₂ ]
l15 [X₆+1-X₂ ]
l13 [X₆+1-X₂ ]
l6 [X₆-X₂ ]
l7 [X₆-X₂ ]
l5 [X₆-X₂ ]
l8 [X₆+1-X₂ ]
l16 [X₆+1-X₂ ]

MPRF for transition t₁₅: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₀ ≤ 0 ∧ 1+X₈ ≤ X₅ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ X₄ of depth 1:

new bound:

X₅+X₈ {O(n)}

MPRF:

l14 [X₅-X₄ ]
l12 [X₅-X₄ ]
l15 [X₅-X₄-1 ]
l13 [X₅-X₄ ]
l6 [X₅-X₄ ]
l7 [X₅-X₄ ]
l5 [X₅-X₄ ]
l8 [X₅-X₃ ]
l16 [X₅-X₄ ]

MPRF for transition t₁₂: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₈ ≤ X₅ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ X₄ of depth 1:

new bound:

X₅+X₆+X₇+X₈+1 {O(n)}

MPRF:

l14 [X₅+X₆-X₂-X₄-2 ]
l12 [X₅+X₆-X₂-X₄-2 ]
l15 [X₅+X₆-X₂-X₄-2 ]
l13 [X₅+X₆-X₂-X₄-1 ]
l6 [X₅+X₆-X₂-X₄-2 ]
l7 [X₅+X₆-X₂-X₄-2 ]
l5 [X₅+X₆-X₁-X₄-1 ]
l8 [X₅+X₆-X₂-X₃-1 ]
l16 [X₅+X₆-X₂-X₄-1 ]

MPRF for transition t₁₃: l14(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l12(nondef_0, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₈ ≤ X₅ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ X₄ of depth 1:

new bound:

X₅+X₆+X₇+X₈ {O(n)}

MPRF:

l14 [X₅+X₆-X₂-X₄ ]
l12 [X₅+X₆-X₂-X₄-1 ]
l15 [X₅+X₆-X₂-X₄-1 ]
l13 [X₅+X₆-X₂-X₄ ]
l6 [X₅+X₆-X₂-X₄-1 ]
l7 [X₅+X₆-X₂-X₄-1 ]
l5 [X₅+X₆-X₂-X₄-1 ]
l8 [X₅+X₆-X₂-X₃ ]
l16 [X₅+X₆-X₂-X₄ ]

MPRF for transition t₁₆: l15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l16(X₀, X₁, X₂, X₃, X₄+1, X₅, X₆, X₇, X₈) :|: 1+X₈ ≤ X₅ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₀ ≤ 0 of depth 1:

new bound:

X₅+X₈+1 {O(n)}

MPRF:

l14 [X₅+1-X₄ ]
l12 [X₅+1-X₄ ]
l15 [X₅+1-X₄ ]
l13 [X₅+1-X₄ ]
l6 [X₅+1-X₄ ]
l7 [X₅+1-X₄ ]
l5 [X₅+1-X₄ ]
l8 [X₅+1-X₃ ]
l16 [X₅+1-X₄ ]

MPRF for transition t₁₀: l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₄ < X₅ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ X₃ ≤ X₄ of depth 1:

new bound:

X₅+X₆+X₇+X₈+1 {O(n)}

MPRF:

l14 [X₅+X₆-X₂-X₄-2 ]
l12 [X₅+X₆-X₂-X₄-2 ]
l15 [X₅+X₆-X₂-X₄-2 ]
l13 [X₅+X₆-X₂-X₄-2 ]
l6 [X₅+X₆-X₂-X₄-2 ]
l7 [X₅+X₆-X₂-X₄-2 ]
l5 [X₅+X₆-X₂-X₄-2 ]
l8 [X₅+X₆-X₂-X₃-1 ]
l16 [X₅+X₆-X₂-X₄-1 ]

MPRF for transition t₁₁: l16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₅ ≤ X₄ ∧ X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ X₃ ≤ X₄ of depth 1:

new bound:

X₆+X₇ {O(n)}

MPRF:

l14 [X₆-X₂ ]
l12 [X₆-X₂ ]
l15 [X₆-X₂ ]
l13 [X₆-X₂ ]
l6 [X₆-X₂-1 ]
l7 [X₆-X₁ ]
l5 [X₆-X₁ ]
l8 [X₆-X₂ ]
l16 [X₆-X₂ ]

MPRF for transition t₁₉: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, X₁, X₄, X₄, X₅, X₆, X₇, X₈) :|: X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₃ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ of depth 1:

new bound:

X₆+X₇+1 {O(n)}

MPRF:

l14 [X₆+1-X₂ ]
l12 [X₆+1-X₂ ]
l15 [X₆+1-X₂ ]
l13 [X₆+1-X₂ ]
l6 [X₆+1-X₂ ]
l7 [X₆+2-X₁ ]
l5 [X₆+2-X₁ ]
l8 [X₆+1-X₂ ]
l16 [X₆+1-X₂ ]

MPRF for transition t₁₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l7(X₀, X₂+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ X₃ ≤ X₄ of depth 1:

new bound:

X₆+X₇ {O(n)}

MPRF:

l14 [X₆-X₂ ]
l12 [X₆-X₂ ]
l15 [X₆-X₂ ]
l13 [X₆-X₂ ]
l6 [X₆-X₂ ]
l7 [X₆-X₂-1 ]
l5 [X₆-X₁ ]
l8 [X₆-X₂ ]
l16 [X₆-X₂ ]

MPRF for transition t₁₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₈ ≤ X₄ ∧ X₈ ≤ X₃ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₃ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂ of depth 1:

new bound:

X₆+X₇ {O(n)}

MPRF:

l14 [X₆-X₂ ]
l12 [X₆-X₂ ]
l15 [X₆-X₂ ]
l13 [X₆-X₂ ]
l6 [X₆-X₂ ]
l7 [X₆+1-X₁ ]
l5 [X₆-X₁ ]
l8 [X₆-X₂ ]
l16 [X₆-X₂ ]

MPRF for transition t₈: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l16(X₀, X₁, X₂, X₃, X₃, X₅, X₆, X₇, X₈) :|: X₂ < X₆ ∧ X₈ ≤ X₃ ∧ X₇ ≤ X₂ of depth 1:

new bound:

X₆+X₇ {O(n)}

MPRF:

l14 [X₆-X₂-1 ]
l12 [X₆-X₂-1 ]
l15 [X₆-X₂-1 ]
l13 [X₆-X₂-1 ]
l6 [X₆-X₂-1 ]
l7 [X₆-X₁ ]
l5 [X₆-X₁ ]
l8 [X₆-X₂ ]
l16 [X₆-X₂-1 ]

All Bounds

Timebounds

Overall timebound:5⋅X₅+5⋅X₈+9⋅X₆+9⋅X₇+15 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₁₄: X₆+X₇+1 {O(n)}
t₁₅: X₅+X₈ {O(n)}
t₁₂: X₅+X₆+X₇+X₈+1 {O(n)}
t₁₃: X₅+X₆+X₇+X₈ {O(n)}
t₁₆: X₅+X₈+1 {O(n)}
t₁₀: X₅+X₆+X₇+X₈+1 {O(n)}
t₁₁: X₆+X₇ {O(n)}
t₂₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₁₉: X₆+X₇+1 {O(n)}
t₁₇: X₆+X₇ {O(n)}
t₁₈: X₆+X₇ {O(n)}
t₈: X₆+X₇ {O(n)}
t₉: 1 {O(1)}
t₅: 1 {O(1)}

Costbounds

Overall costbound: 5⋅X₅+5⋅X₈+9⋅X₆+9⋅X₇+15 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₁₄: X₆+X₇+1 {O(n)}
t₁₅: X₅+X₈ {O(n)}
t₁₂: X₅+X₆+X₇+X₈+1 {O(n)}
t₁₃: X₅+X₆+X₇+X₈ {O(n)}
t₁₆: X₅+X₈+1 {O(n)}
t₁₀: X₅+X₆+X₇+X₈+1 {O(n)}
t₁₁: X₆+X₇ {O(n)}
t₂₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₁₉: X₆+X₇+1 {O(n)}
t₁₇: X₆+X₇ {O(n)}
t₁₈: X₆+X₇ {O(n)}
t₈: X₆+X₇ {O(n)}
t₉: 1 {O(1)}
t₅: 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)}
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)}
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: X₇ {O(n)}
t₇, X₃: X₈ {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)}
t₁₄, X₁: 2⋅X₇+X₁+X₆ {O(n)}
t₁₄, X₂: 2⋅X₇+X₆ {O(n)}
t₁₄, X₃: 3⋅X₈+X₅+1 {O(n)}
t₁₄, X₄: 2⋅X₈+X₅+1 {O(n)}
t₁₄, X₅: X₅ {O(n)}
t₁₄, X₆: X₆ {O(n)}
t₁₄, X₇: X₇ {O(n)}
t₁₄, X₈: X₈ {O(n)}
t₁₅, X₁: 2⋅X₇+X₁+X₆ {O(n)}
t₁₅, X₂: 2⋅X₇+X₆ {O(n)}
t₁₅, X₃: 3⋅X₈+X₅+1 {O(n)}
t₁₅, X₄: 2⋅X₈+X₅+1 {O(n)}
t₁₅, X₅: X₅ {O(n)}
t₁₅, X₆: X₆ {O(n)}
t₁₅, X₇: X₇ {O(n)}
t₁₅, X₈: X₈ {O(n)}
t₁₂, X₁: 2⋅X₇+X₁+X₆ {O(n)}
t₁₂, X₂: 2⋅X₇+X₆ {O(n)}
t₁₂, X₃: 3⋅X₈+X₅+1 {O(n)}
t₁₂, X₄: 2⋅X₈+X₅+1 {O(n)}
t₁₂, X₅: X₅ {O(n)}
t₁₂, X₆: X₆ {O(n)}
t₁₂, X₇: X₇ {O(n)}
t₁₂, X₈: X₈ {O(n)}
t₁₃, X₁: 2⋅X₇+X₁+X₆ {O(n)}
t₁₃, X₂: 2⋅X₇+X₆ {O(n)}
t₁₃, X₃: 3⋅X₈+X₅+1 {O(n)}
t₁₃, X₄: 2⋅X₈+X₅+1 {O(n)}
t₁₃, X₅: X₅ {O(n)}
t₁₃, X₆: X₆ {O(n)}
t₁₃, X₇: X₇ {O(n)}
t₁₃, X₈: X₈ {O(n)}
t₁₆, X₁: 2⋅X₇+X₁+X₆ {O(n)}
t₁₆, X₂: 2⋅X₇+X₆ {O(n)}
t₁₆, X₃: 3⋅X₈+X₅+1 {O(n)}
t₁₆, X₄: 2⋅X₈+X₅+1 {O(n)}
t₁₆, X₅: X₅ {O(n)}
t₁₆, X₆: X₆ {O(n)}
t₁₆, X₇: X₇ {O(n)}
t₁₆, X₈: X₈ {O(n)}
t₁₀, X₁: 2⋅X₇+X₁+X₆ {O(n)}
t₁₀, X₂: 2⋅X₇+X₆ {O(n)}
t₁₀, X₃: 3⋅X₈+X₅+1 {O(n)}
t₁₀, X₄: 2⋅X₈+X₅+1 {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₀, X₆: X₆ {O(n)}
t₁₀, X₇: X₇ {O(n)}
t₁₀, X₈: X₈ {O(n)}
t₁₁, X₁: 2⋅X₁+2⋅X₆+4⋅X₇ {O(n)}
t₁₁, X₂: 2⋅X₇+X₆ {O(n)}
t₁₁, X₃: 2⋅X₅+6⋅X₈+2 {O(n)}
t₁₁, X₄: 2⋅X₈+X₅+1 {O(n)}
t₁₁, X₅: X₅ {O(n)}
t₁₁, X₆: X₆ {O(n)}
t₁₁, X₇: X₇ {O(n)}
t₁₁, X₈: X₈ {O(n)}
t₂₀, X₁: 2⋅X₇+X₁+X₆ {O(n)}
t₂₀, X₂: 3⋅X₇+X₆ {O(n)}
t₂₀, X₃: 3⋅X₈+X₅+1 {O(n)}
t₂₀, X₄: 2⋅X₈+X₄+X₅+1 {O(n)}
t₂₀, X₅: 2⋅X₅ {O(n)}
t₂₀, X₆: 2⋅X₆ {O(n)}
t₂₀, X₇: 2⋅X₇ {O(n)}
t₂₀, X₈: 2⋅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)}
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)}
t₁₉, X₁: 2⋅X₇+X₆ {O(n)}
t₁₉, X₂: 2⋅X₇+X₆ {O(n)}
t₁₉, X₃: 2⋅X₈+X₅+1 {O(n)}
t₁₉, X₄: 2⋅X₈+X₅+1 {O(n)}
t₁₉, X₅: X₅ {O(n)}
t₁₉, X₆: X₆ {O(n)}
t₁₉, X₇: X₇ {O(n)}
t₁₉, X₈: X₈ {O(n)}
t₁₇, X₁: 2⋅X₇+X₆ {O(n)}
t₁₇, X₂: 2⋅X₆+4⋅X₇ {O(n)}
t₁₇, X₃: 3⋅X₅+9⋅X₈+3 {O(n)}
t₁₇, X₄: 2⋅X₈+X₅+1 {O(n)}
t₁₇, X₅: X₅ {O(n)}
t₁₇, X₆: X₆ {O(n)}
t₁₇, X₇: X₇ {O(n)}
t₁₇, X₈: X₈ {O(n)}
t₁₈, X₁: 2⋅X₇+X₆ {O(n)}
t₁₈, X₂: 2⋅X₆+4⋅X₇ {O(n)}
t₁₈, X₃: 3⋅X₅+9⋅X₈+3 {O(n)}
t₁₈, X₄: 2⋅X₈+X₅+1 {O(n)}
t₁₈, X₅: X₅ {O(n)}
t₁₈, X₆: X₆ {O(n)}
t₁₈, X₇: X₇ {O(n)}
t₁₈, X₈: X₈ {O(n)}
t₈, X₁: 2⋅X₇+X₁+X₆ {O(n)}
t₈, X₂: 2⋅X₇+X₆ {O(n)}
t₈, X₃: 3⋅X₈+X₅+1 {O(n)}
t₈, X₄: 2⋅X₈+X₅+1 {O(n)}
t₈, X₅: X₅ {O(n)}
t₈, X₆: X₆ {O(n)}
t₈, X₇: X₇ {O(n)}
t₈, X₈: X₈ {O(n)}
t₉, X₁: 2⋅X₇+X₁+X₆ {O(n)}
t₉, X₂: 3⋅X₇+X₆ {O(n)}
t₉, X₃: 3⋅X₈+X₅+1 {O(n)}
t₉, X₄: 2⋅X₈+X₄+X₅+1 {O(n)}
t₉, X₅: 2⋅X₅ {O(n)}
t₉, X₆: 2⋅X₆ {O(n)}
t₉, X₇: 2⋅X₇ {O(n)}
t₉, X₈: 2⋅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)}