Initial Problem

Start: f2
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀
Temp_Vars: L, M
Locations: f1, f2, f23, f26, f30, f40, f44, f5, f59, f69, f71, f74, f9
Transitions:
t₂: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀)
t₂₆: f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₃
t₆: f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f26(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₃ ≤ X₀
t₇: f26(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f30(X₀, X₁, X₂, X₃, X₄, X₅, L, X₇, X₈, X₉, X₁₀) :|: 1+X₁ ≤ X₃
t₂₅: f26(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f40(X₀, X₁, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₃ ≤ X₁
t₂₄: f30(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f26(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₁ ≤ X₇
t₈: f30(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f30(X₀, X₁, X₂, X₃, X₄, X₅, L, 1+X₇, X₈, X₉, X₁₀) :|: 1+X₇ ≤ X₁
t₉: f40(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f44(X₀, X₁, X₂, X₃, X₄, X₅, L, X₇, X₈, X₉, X₁₀) :|: X₁ ≤ X₀
t₂₁: f40(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f59(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁₀
t₂₂: f40(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f59(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₁ ∧ 1+X₁₀ ≤ X₃
t₂₃: f40(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₃) :|: 1+X₀ ≤ X₁ ∧ X₁₀ ≤ X₃ ∧ X₃ ≤ X₁₀
t₁₉: f44(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f40(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇, M, L, X₁₀) :|: 1+M ≤ X₂ ∧ X₃ ≤ X₇
t₂₀: f44(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f40(X₀, 1+X₁, L, X₃, X₄, X₅, X₆, X₇, L, M, X₁) :|: X₂ ≤ L ∧ X₃ ≤ X₇
t₁₀: f44(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f44(X₀, X₁, X₂, X₃, X₄, X₅, L, 1+X₇, X₈, X₉, X₁₀) :|: 1+X₇ ≤ X₃
t₃₀: f5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₁
t₃: f5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f9(X₀, X₁, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₁ ≤ X₀
t₁₁: f59(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f59(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 1+X₇, L, X₉, X₁₀) :|: X₇ ≤ X₀
t₁₈: f59(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₇
t₀: f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+L ≤ 0
t₁: f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1 ≤ L
t₁₂: f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀)
t₁₆: f71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f23(X₀, X₁, X₂, 1+X₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁₃: f71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f74(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, L, X₉, X₁₀) :|: 1+X₃ ≤ X₀
t₁₄: f71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f74(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, L, X₉, X₁₀) :|: 1+X₀ ≤ X₃
t₁₇: f74(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f23(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₁
t₁₅: f74(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f74(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₁ ≤ X₀
t₂₇: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f5(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0
t₂₈: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f5(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₃ ∧ 1 ≤ X₂
t₂₉: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f5(X₀, 1+X₁, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₄: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f9(X₀, X₁, X₂, 1+X₃, L, L, X₆, X₇, X₈, X₉, X₁₀) :|: L ≤ X₂ ∧ X₃ ≤ X₀
t₅: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f9(X₀, X₁, L, 1+X₃, L, L, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₂ ≤ L ∧ X₃ ≤ X₀

Preprocessing

Eliminate variables [X₄; X₅; X₆; X₈; X₉] that do not contribute to the problem

Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location f74

Found invariant 1 ≤ 0 for location f44

Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location f40

Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location f71

Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location f59

Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location f69

Found invariant 1+X₀ ≤ X₁ for location f23

Found invariant 1 ≤ 0 for location f30

Found invariant 0 ≤ X₂ ∧ X₁ ≤ X₀ for location f9

Found invariant 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ for location f1

Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location f26

Cut unsatisfiable transition [t₆₉: f26→f30; t₇₁: f30→f26; t₇₂: f30→f30; t₇₃: f40→f44; t₇₇: f44→f40; t₇₈: f44→f40; t₇₉: f44→f44; t₈₉: f71→f74; t₉₁: f74→f74; t₉₂: f9→f5]

Cut unreachable locations [f30; f44] from the program graph

Problem after Preprocessing

Start: f2
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: L
Locations: f1, f2, f23, f26, f40, f5, f59, f69, f71, f74, f9
Transitions:
t₆₆: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f5(X₀, X₁, X₂, X₃, X₄, X₅)
t₆₇: f23(X₀, X₁, X₂, X₃, X₄, X₅) → f1(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁
t₆₈: f23(X₀, X₁, X₂, X₃, X₄, X₅) → f26(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁
t₇₀: f26(X₀, X₁, X₂, X₃, X₄, X₅) → f40(X₀, X₁, 0, X₃, X₄, X₅) :|: X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀
t₇₄: f40(X₀, X₁, X₂, X₃, X₄, X₅) → f59(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₇₅: f40(X₀, X₁, X₂, X₃, X₄, X₅) → f59(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₅ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₇₆: f40(X₀, X₁, X₂, X₃, X₄, X₅) → f69(X₀, X₁, X₂, X₃, X₄, X₃) :|: 1+X₀ ≤ X₁ ∧ X₅ ≤ X₃ ∧ X₃ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈₀: f5(X₀, X₁, X₂, X₃, X₄, X₅) → f23(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁
t₈₁: f5(X₀, X₁, X₂, X₃, X₄, X₅) → f9(X₀, X₁, 0, X₃, X₄, X₅) :|: X₁ ≤ X₀
t₈₂: f59(X₀, X₁, X₂, X₃, X₄, X₅) → f59(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₄ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈₃: f59(X₀, X₁, X₂, X₃, X₄, X₅) → f69(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈₄: f69(X₀, X₁, X₂, X₃, X₄, X₅) → f71(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+L ≤ 0 ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈₅: f69(X₀, X₁, X₂, X₃, X₄, X₅) → f71(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ L ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈₆: f69(X₀, X₁, X₂, X₃, X₄, X₅) → f71(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈₇: f71(X₀, X₁, X₂, X₃, X₄, X₅) → f23(X₀, X₁, X₂, 1+X₀, X₄, X₅) :|: X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈₈: f71(X₀, X₁, X₂, X₃, X₄, X₅) → f74(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₉₀: f74(X₀, X₁, X₂, X₃, X₄, X₅) → f23(X₀, X₁, X₂, 1+X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 2+X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₉₃: f9(X₀, X₁, X₂, X₃, X₄, X₅) → f5(X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂
t₉₄: f9(X₀, X₁, X₂, X₃, X₄, X₅) → f5(X₀, 1+X₁, 0, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₁ ≤ X₀
t₉₅: f9(X₀, X₁, X₂, X₃, X₄, X₅) → f9(X₀, X₁, X₂, 1+X₃, X₄, X₅) :|: L ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂
t₉₆: f9(X₀, X₁, X₂, X₃, X₄, X₅) → f9(X₀, X₁, L, 1+X₃, X₄, X₅) :|: 1+X₂ ≤ L ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂

MPRF for transition t₈₁: f5(X₀, X₁, X₂, X₃, X₄, X₅) → f9(X₀, X₁, 0, X₃, X₄, X₅) :|: X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• f5: [1+X₀-X₁]
• f9: [X₀-X₁]

MPRF for transition t₉₃: f9(X₀, X₁, X₂, X₃, X₄, X₅) → f5(X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• f5: [1+X₀-X₁]
• f9: [1+X₀-X₁]

MPRF for transition t₉₄: f9(X₀, X₁, X₂, X₃, X₄, X₅) → f5(X₀, 1+X₁, 0, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• f5: [1+X₀-X₁]
• f9: [1+X₀-X₁]

MPRF for transition t₉₅: f9(X₀, X₁, X₂, X₃, X₄, X₅) → f9(X₀, X₁, X₂, 1+X₃, X₄, X₅) :|: L ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₀+X₃+1 {O(n)}

• f5: [1+X₀-X₃]
• f9: [1+X₀-X₃]

MPRF for transition t₉₆: f9(X₀, X₁, X₂, X₃, X₄, X₅) → f9(X₀, X₁, L, 1+X₃, X₄, X₅) :|: 1+X₂ ≤ L ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₀+X₃+1 {O(n)}

• f5: [1+X₀-X₃]
• f9: [1+X₀-X₃]

MPRF for transition t₆₈: f23(X₀, X₁, X₂, X₃, X₄, X₅) → f26(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ of depth 1:

new bound:

7⋅X₀+7⋅X₃+5 {O(n)}

• f23: [1+X₀-X₃]
• f26: [X₀-X₃]
• f40: [X₀-X₃]
• f59: [X₀-X₃]
• f69: [X₀-X₃]
• f71: [X₀-X₃]
• f74: [X₀-X₃]

MPRF for transition t₇₀: f26(X₀, X₁, X₂, X₃, X₄, X₅) → f40(X₀, X₁, 0, X₃, X₄, X₅) :|: X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ of depth 1:

new bound:

7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}

• f23: [X₁-X₃]
• f26: [X₁-X₃]
• f40: [X₁-1-X₃]
• f59: [X₁-1-X₃]
• f69: [X₁-1-X₃]
• f71: [X₁-1-X₃]
• f74: [X₁-1-X₃]

MPRF for transition t₇₄: f40(X₀, X₁, X₂, X₃, X₄, X₅) → f59(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

7⋅X₀+7⋅X₃+5 {O(n)}

• f23: [1+X₀-X₃]
• f26: [1+X₀-X₃]
• f40: [1+X₀-X₃]
• f59: [X₀-X₃]
• f69: [X₀-X₃]
• f71: [X₀-X₃]
• f74: [X₀-X₃]

MPRF for transition t₇₅: f40(X₀, X₁, X₂, X₃, X₄, X₅) → f59(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₅ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

7⋅X₀+7⋅X₃+5 {O(n)}

• f23: [1+X₀-X₃]
• f26: [1+X₀-X₃]
• f40: [1+X₀-X₃]
• f59: [X₀-X₃]
• f69: [X₀-X₃]
• f71: [X₀-X₃]
• f74: [X₀-X₃]

MPRF for transition t₇₆: f40(X₀, X₁, X₂, X₃, X₄, X₅) → f69(X₀, X₁, X₂, X₃, X₄, X₃) :|: 1+X₀ ≤ X₁ ∧ X₅ ≤ X₃ ∧ X₃ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}

• f23: [X₁-X₃]
• f26: [X₁-X₃]
• f40: [X₁-X₃]
• f59: [X₁-X₃]
• f69: [X₁-1-X₃]
• f71: [X₁-1-X₃]
• f74: [X₁-1-X₃]

MPRF for transition t₈₂: f59(X₀, X₁, X₂, X₃, X₄, X₅) → f59(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₄ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

3⋅X₀+3⋅X₄+1 {O(n)}

• f23: [1+X₀-X₄]
• f26: [1+X₀-X₄]
• f40: [1+X₀-X₄]
• f59: [1+X₀-X₄]
• f69: [1+X₀-X₄]
• f71: [1+X₀-X₄]
• f74: [1+X₀-X₄]

MPRF for transition t₈₃: f59(X₀, X₁, X₂, X₃, X₄, X₅) → f69(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

7⋅X₁+7⋅X₃+8⋅X₀+9 {O(n)}

• f23: [1+X₁-X₃]
• f26: [1+X₁-X₃]
• f40: [1+X₁-X₃]
• f59: [1+X₁-X₃]
• f69: [X₁-X₃]
• f71: [X₁-X₃]
• f74: [X₁-X₃]

MPRF for transition t₈₄: f69(X₀, X₁, X₂, X₃, X₄, X₅) → f71(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+L ≤ 0 ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

7⋅X₀+7⋅X₃+5 {O(n)}

• f23: [1+X₀-X₃]
• f26: [1+X₀-X₃]
• f40: [1+X₀-X₃]
• f59: [1+X₀-X₃]
• f69: [1+X₀-X₃]
• f71: [X₀-X₃]
• f74: [X₀-X₃]

MPRF for transition t₈₅: f69(X₀, X₁, X₂, X₃, X₄, X₅) → f71(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ L ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

7⋅X₀+7⋅X₃+5 {O(n)}

• f23: [1+X₀-X₃]
• f26: [1+X₀-X₃]
• f40: [1+X₀-X₃]
• f59: [1+X₀-X₃]
• f69: [1+X₀-X₃]
• f71: [X₀-X₃]
• f74: [X₀-X₃]

MPRF for transition t₈₆: f69(X₀, X₁, X₂, X₃, X₄, X₅) → f71(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}

• f23: [X₁-X₃]
• f26: [X₁-X₃]
• f40: [X₁-X₃]
• f59: [X₁-X₃]
• f69: [X₁-X₃]
• f71: [X₁-1-X₃]
• f74: [X₁-1-X₃]

MPRF for transition t₈₇: f71(X₀, X₁, X₂, X₃, X₄, X₅) → f23(X₀, X₁, X₂, 1+X₀, X₄, X₅) :|: X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}

• f23: [X₁-X₃]
• f26: [X₁-X₃]
• f40: [X₁-X₃]
• f59: [X₁-X₃]
• f69: [X₁-X₃]
• f71: [X₁-X₃]
• f74: [X₁-X₃]

MPRF for transition t₈₈: f71(X₀, X₁, X₂, X₃, X₄, X₅) → f74(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

7⋅X₀+7⋅X₃+4 {O(n)}

• f23: [X₀-X₃]
• f26: [X₀-X₃]
• f40: [X₀-X₃]
• f59: [X₀-X₃]
• f69: [X₀-X₃]
• f71: [X₀-X₃]
• f74: [X₀-1-X₃]

MPRF for transition t₉₀: f74(X₀, X₁, X₂, X₃, X₄, X₅) → f23(X₀, X₁, X₂, 1+X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 2+X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

7⋅X₀+7⋅X₃+4 {O(n)}

• f23: [X₀-X₃]
• f26: [X₀-X₃]
• f40: [X₀-X₃]
• f59: [X₀-X₃]
• f69: [X₀-X₃]
• f71: [X₀-X₃]
• f74: [X₀-X₃]

All Bounds

Timebounds

Overall timebound:3⋅X₄+38⋅X₁+86⋅X₃+97⋅X₀+83 {O(n)}
t₆₆: 1 {O(1)}
t₆₇: 1 {O(1)}
t₆₈: 7⋅X₀+7⋅X₃+5 {O(n)}
t₇₀: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₇₄: 7⋅X₀+7⋅X₃+5 {O(n)}
t₇₅: 7⋅X₀+7⋅X₃+5 {O(n)}
t₇₆: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₈₀: 1 {O(1)}
t₈₁: X₀+X₁+1 {O(n)}
t₈₂: 3⋅X₀+3⋅X₄+1 {O(n)}
t₈₃: 7⋅X₁+7⋅X₃+8⋅X₀+9 {O(n)}
t₈₄: 7⋅X₀+7⋅X₃+5 {O(n)}
t₈₅: 7⋅X₀+7⋅X₃+5 {O(n)}
t₈₆: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₈₇: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₈₈: 7⋅X₀+7⋅X₃+4 {O(n)}
t₉₀: 7⋅X₀+7⋅X₃+4 {O(n)}
t₉₃: X₀+X₁+1 {O(n)}
t₉₄: X₀+X₁+1 {O(n)}
t₉₅: X₀+X₃+1 {O(n)}
t₉₆: X₀+X₃+1 {O(n)}

Costbounds

Overall costbound: 3⋅X₄+38⋅X₁+86⋅X₃+97⋅X₀+83 {O(n)}
t₆₆: 1 {O(1)}
t₆₇: 1 {O(1)}
t₆₈: 7⋅X₀+7⋅X₃+5 {O(n)}
t₇₀: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₇₄: 7⋅X₀+7⋅X₃+5 {O(n)}
t₇₅: 7⋅X₀+7⋅X₃+5 {O(n)}
t₇₆: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₈₀: 1 {O(1)}
t₈₁: X₀+X₁+1 {O(n)}
t₈₂: 3⋅X₀+3⋅X₄+1 {O(n)}
t₈₃: 7⋅X₁+7⋅X₃+8⋅X₀+9 {O(n)}
t₈₄: 7⋅X₀+7⋅X₃+5 {O(n)}
t₈₅: 7⋅X₀+7⋅X₃+5 {O(n)}
t₈₆: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₈₇: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₈₈: 7⋅X₀+7⋅X₃+4 {O(n)}
t₉₀: 7⋅X₀+7⋅X₃+4 {O(n)}
t₉₃: X₀+X₁+1 {O(n)}
t₉₄: X₀+X₁+1 {O(n)}
t₉₅: X₀+X₃+1 {O(n)}
t₉₆: X₀+X₃+1 {O(n)}

Sizebounds

t₆₆, X₀: X₀ {O(n)}
t₆₆, X₁: X₁ {O(n)}
t₆₆, X₂: X₂ {O(n)}
t₆₆, X₃: X₃ {O(n)}
t₆₆, X₄: X₄ {O(n)}
t₆₆, X₅: X₅ {O(n)}
t₆₇, X₀: 12⋅X₀ {O(n)}
t₆₇, X₁: 16⋅X₀+28⋅X₁+16 {O(n)}
t₆₇, X₃: 13⋅X₀+7⋅X₃+7 {O(n)}
t₆₇, X₄: 21⋅X₄+9⋅X₀+3 {O(n)}
t₆₇, X₅: 12⋅X₅+33⋅X₀+42⋅X₃+24 {O(n)}
t₆₈, X₀: 3⋅X₀ {O(n)}
t₆₈, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₆₈, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₆₈, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₆₈, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₇₀, X₀: 3⋅X₀ {O(n)}
t₇₀, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₇₀, X₂: 0 {O(1)}
t₇₀, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₇₀, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₇₀, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₇₄, X₀: 3⋅X₀ {O(n)}
t₇₄, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₇₄, X₂: 0 {O(1)}
t₇₄, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₇₄, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₇₄, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₇₅, X₀: 3⋅X₀ {O(n)}
t₇₅, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₇₅, X₂: 0 {O(1)}
t₇₅, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₇₅, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₇₅, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₇₆, X₀: 3⋅X₀ {O(n)}
t₇₆, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₇₆, X₂: 0 {O(1)}
t₇₆, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₇₆, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₇₆, X₅: 11⋅X₀+14⋅X₃+8 {O(n)}
t₈₀, X₀: 3⋅X₀ {O(n)}
t₈₀, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₀, X₃: 4⋅X₀+7⋅X₃+4 {O(n)}
t₈₀, X₄: 3⋅X₄ {O(n)}
t₈₀, X₅: 3⋅X₅ {O(n)}
t₈₁, X₀: X₀ {O(n)}
t₈₁, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₈₁, X₂: 0 {O(1)}
t₈₁, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₈₁, X₄: X₄ {O(n)}
t₈₁, X₅: X₅ {O(n)}
t₈₂, X₀: 3⋅X₀ {O(n)}
t₈₂, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₂, X₂: 0 {O(1)}
t₈₂, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₈₂, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₈₂, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₈₃, X₀: 3⋅X₀ {O(n)}
t₈₃, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₃, X₂: 0 {O(1)}
t₈₃, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₈₃, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₈₃, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₈₄, X₀: 3⋅X₀ {O(n)}
t₈₄, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₄, X₂: 0 {O(1)}
t₈₄, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₈₄, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₈₄, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₈₅, X₀: 3⋅X₀ {O(n)}
t₈₅, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₅, X₂: 0 {O(1)}
t₈₅, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₈₅, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₈₅, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₈₆, X₀: 3⋅X₀ {O(n)}
t₈₆, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₆, X₂: 0 {O(1)}
t₈₆, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₈₆, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₈₆, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₈₇, X₀: 9⋅X₀ {O(n)}
t₈₇, X₁: 12⋅X₀+21⋅X₁+12 {O(n)}
t₈₇, X₂: 0 {O(1)}
t₈₇, X₃: 9⋅X₀+3 {O(n)}
t₈₇, X₄: 18⋅X₄+9⋅X₀+3 {O(n)}
t₈₇, X₅: 33⋅X₀+42⋅X₃+9⋅X₅+24 {O(n)}
t₈₈, X₀: 3⋅X₀ {O(n)}
t₈₈, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₈, X₂: 0 {O(1)}
t₈₈, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₈₈, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₈₈, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₉₀, X₀: 3⋅X₀ {O(n)}
t₉₀, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₉₀, X₂: 0 {O(1)}
t₉₀, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₉₀, X₄: 3⋅X₀+6⋅X₄+1 {O(n)}
t₉₀, X₅: 11⋅X₀+14⋅X₃+3⋅X₅+8 {O(n)}
t₉₃, X₀: X₀ {O(n)}
t₉₃, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₉₃, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₉₃, X₄: X₄ {O(n)}
t₉₃, X₅: X₅ {O(n)}
t₉₄, X₀: X₀ {O(n)}
t₉₄, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₉₄, X₂: 0 {O(1)}
t₉₄, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₉₄, X₄: X₄ {O(n)}
t₉₄, X₅: X₅ {O(n)}
t₉₅, X₀: X₀ {O(n)}
t₉₅, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₉₅, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₉₅, X₄: X₄ {O(n)}
t₉₅, X₅: X₅ {O(n)}
t₉₆, X₀: X₀ {O(n)}
t₉₆, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₉₆, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₉₆, X₄: X₄ {O(n)}
t₉₆, X₅: X₅ {O(n)}