KoAT2 Proof Output

Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars: K, L
Locations: f0, f17, f27, f37, f45, f55, f65, f75, f83, f93
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f17(0, K, L, 0, X₄, X₅, X₆, X₇, X₈, X₉)
t₁: f17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f17(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1+X₃ ≤ X₄
t₁₆: f17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f27(X₀, X₁, X₂, X₃, X₄, 0, X₆, X₇, X₈, X₉) :|: X₄ ≤ X₃
t₂: f27(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f27(X₀, X₁, X₂, X₃, X₄, 1+X₅, X₆, X₇, X₈, X₉) :|: 1+X₅ ≤ X₄
t₁₅: f27(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f37(X₀, X₁, X₂, X₃, X₄, X₅, 0, X₇, X₈, X₉) :|: X₄ ≤ X₅
t₃: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f37(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆, X₇, X₈, X₉) :|: 1+X₆ ≤ X₄
t₁₄: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f45(0, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₄ ≤ X₆
t₄: f45(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f45(1+X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1+X₀ ≤ X₄
t₁₃: f45(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f55(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 0, X₈, X₉) :|: X₄ ≤ X₀
t₅: f55(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f55(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 1+X₇, X₈, X₉) :|: 1+X₇ ≤ X₄
t₁₂: f55(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f65(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, 0, X₉) :|: X₄ ≤ X₇
t₆: f65(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f65(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, 1+X₈, X₉) :|: 1+X₈ ≤ X₄
t₁₁: f65(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f75(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, 0) :|: X₄ ≤ X₈
t₇: f75(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f75(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, 1+X₉) :|: 1+X₉ ≤ X₄
t₁₀: f75(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f83(0, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₄ ≤ X₉
t₈: f83(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f83(1+X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1+X₀ ≤ X₄
t₉: f83(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f93(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₄ ≤ X₀

Preprocessing

Eliminate variables [K; L; X₁; X₂] that do not contribute to the problem

Found invariant X₆ ≤ X₅ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₁ ∧ X₆ ≤ X₀ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ 0 ≤ X₄+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₁+X₆ ∧ 0 ≤ X₀+X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location f65

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location f45

Found invariant X₅ ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location f55

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location f37

Found invariant X₇ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₄ ∧ X₇ ≤ X₃ ∧ X₇ ≤ X₁ ∧ 0 ≤ X₇ ∧ 0 ≤ X₆+X₇ ∧ 0 ≤ X₅+X₇ ∧ 0 ≤ X₄+X₇ ∧ 0 ≤ X₃+X₇ ∧ X₂ ≤ X₇ ∧ 0 ≤ X₁+X₇ ∧ 0 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₁ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ 0 ≤ X₄+X₆ ∧ 0 ≤ X₃+X₆ ∧ X₂ ≤ X₆ ∧ 0 ≤ X₁+X₆ ∧ 0 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location f83

Found invariant X₇ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₄ ∧ X₇ ≤ X₃ ∧ X₇ ≤ X₁ ∧ X₇ ≤ X₀ ∧ 0 ≤ X₇ ∧ 0 ≤ X₆+X₇ ∧ 0 ≤ X₅+X₇ ∧ 0 ≤ X₄+X₇ ∧ 0 ≤ X₃+X₇ ∧ 0 ≤ X₁+X₇ ∧ 0 ≤ X₀+X₇ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₁ ∧ X₆ ≤ X₀ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ 0 ≤ X₄+X₆ ∧ 0 ≤ X₃+X₆ ∧ X₂ ≤ X₆ ∧ 0 ≤ X₁+X₆ ∧ 0 ≤ X₀+X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location f75

Found invariant X₇ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₄ ∧ X₇ ≤ X₃ ∧ X₇ ≤ X₁ ∧ 0 ≤ X₇ ∧ 0 ≤ X₆+X₇ ∧ 0 ≤ X₅+X₇ ∧ 0 ≤ X₄+X₇ ∧ 0 ≤ X₃+X₇ ∧ X₂ ≤ X₇ ∧ 0 ≤ X₁+X₇ ∧ 0 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₁ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ 0 ≤ X₄+X₆ ∧ 0 ≤ X₃+X₆ ∧ X₂ ≤ X₆ ∧ 0 ≤ X₁+X₆ ∧ 0 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location f93

Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location f17

Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location f27

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: f0, f17, f27, f37, f45, f55, f65, f75, f83, f93
Transitions:
t₄₁: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f17(0, 0, X₂, X₃, X₄, X₅, X₆, X₇)
t₄₂: f17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f17(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₁ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₄₃: f17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f27(X₀, X₁, X₂, 0, X₄, X₅, X₆, X₇) :|: X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₄₄: f27(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f27(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, X₇) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃
t₄₅: f27(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f37(X₀, X₁, X₂, X₃, 0, X₅, X₆, X₇) :|: X₂ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃
t₄₆: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f37(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, X₇) :|: 1+X₄ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄
t₄₇: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f45(0, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂ ≤ X₄ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄
t₄₈: f45(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f45(1+X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄
t₄₉: f45(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f55(X₀, X₁, X₂, X₃, X₄, 0, X₆, X₇) :|: X₂ ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄
t₅₀: f55(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f55(X₀, X₁, X₂, X₃, X₄, 1+X₅, X₆, X₇) :|: 1+X₅ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ X₅ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₅
t₅₁: f55(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f65(X₀, X₁, X₂, X₃, X₄, X₅, 0, X₇) :|: X₂ ≤ X₅ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ X₅ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₅
t₅₂: f65(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f65(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆, X₇) :|: 1+X₆ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₀+X₆ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₁+X₆ ∧ X₆ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₄+X₆ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆
t₅₃: f65(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f75(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 0) :|: X₂ ≤ X₆ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₀+X₆ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₁+X₆ ∧ X₆ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₄+X₆ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆
t₅₄: f75(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f75(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 1+X₇) :|: 1+X₇ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₀+X₆ ∧ X₆ ≤ X₀ ∧ 0 ≤ X₀+X₇ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₁+X₆ ∧ X₆ ≤ X₁ ∧ 0 ≤ X₁+X₇ ∧ X₇ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₅ ∧ X₂ ≤ X₆ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₄+X₆ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₄+X₇ ∧ X₇ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₅+X₇ ∧ X₇ ≤ X₅ ∧ 0 ≤ X₆ ∧ 0 ≤ X₆+X₇ ∧ X₇ ≤ X₆ ∧ 0 ≤ X₇
t₅₅: f75(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f83(0, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂ ≤ X₇ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₀+X₆ ∧ X₆ ≤ X₀ ∧ 0 ≤ X₀+X₇ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₁+X₆ ∧ X₆ ≤ X₁ ∧ 0 ≤ X₁+X₇ ∧ X₇ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₅ ∧ X₂ ≤ X₆ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₄+X₆ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₄+X₇ ∧ X₇ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₅+X₇ ∧ X₇ ≤ X₅ ∧ 0 ≤ X₆ ∧ 0 ≤ X₆+X₇ ∧ X₇ ≤ X₆ ∧ 0 ≤ X₇
t₅₆: f83(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f83(1+X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀+X₆ ∧ 0 ≤ X₀+X₇ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₅ ∧ X₀ ≤ X₆ ∧ X₀ ≤ X₇ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₁+X₆ ∧ X₆ ≤ X₁ ∧ 0 ≤ X₁+X₇ ∧ X₇ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₅ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₇ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₄+X₆ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₄+X₇ ∧ X₇ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₅+X₇ ∧ X₇ ≤ X₅ ∧ 0 ≤ X₆ ∧ 0 ≤ X₆+X₇ ∧ X₇ ≤ X₆ ∧ 0 ≤ X₇
t₅₇: f83(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f93(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂ ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀+X₆ ∧ 0 ≤ X₀+X₇ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₅ ∧ X₀ ≤ X₆ ∧ X₀ ≤ X₇ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₁+X₆ ∧ X₆ ≤ X₁ ∧ 0 ≤ X₁+X₇ ∧ X₇ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₅ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₇ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₄+X₆ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₄+X₇ ∧ X₇ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₅+X₇ ∧ X₇ ≤ X₅ ∧ 0 ≤ X₆ ∧ 0 ≤ X₆+X₇ ∧ X₇ ≤ X₆ ∧ 0 ≤ X₇

MPRF for transition t₄₂: f17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f17(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₁ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

• f17: [X₂-X₁]

MPRF for transition t₄₄: f27(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f27(X₀, X₁, X₂, 1+X₃, X₄, X₅, X₆, X₇) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• f27: [1+X₁-X₃]

MPRF for transition t₄₆: f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f37(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, X₇) :|: 1+X₄ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ of depth 1:

new bound:

2⋅X₂+1 {O(n)}

MPRF:

• f37: [1+X₁-X₄]

MPRF for transition t₄₈: f45(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f45(1+X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ of depth 1:

new bound:

2⋅X₂+2 {O(n)}

MPRF:

• f45: [1+X₄-X₀]

MPRF for transition t₅₀: f55(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f55(X₀, X₁, X₂, X₃, X₄, 1+X₅, X₆, X₇) :|: 1+X₅ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ X₅ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₅ of depth 1:

new bound:

4⋅X₂+5 {O(n)}

MPRF:

• f55: [1+X₃-X₅]

MPRF for transition t₅₂: f65(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f65(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆, X₇) :|: 1+X₆ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₀+X₆ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₁+X₆ ∧ X₆ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₄+X₆ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆ of depth 1:

new bound:

8⋅X₂+5 {O(n)}

MPRF:

• f65: [1+X₄-X₆]

MPRF for transition t₅₄: f75(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f75(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 1+X₇) :|: 1+X₇ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ X₅ ≤ X₀ ∧ 0 ≤ X₀+X₆ ∧ X₆ ≤ X₀ ∧ 0 ≤ X₀+X₇ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₁+X₆ ∧ X₆ ≤ X₁ ∧ 0 ≤ X₁+X₇ ∧ X₇ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₅ ∧ X₂ ≤ X₆ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₄+X₆ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₄+X₇ ∧ X₇ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₅+X₇ ∧ X₇ ≤ X₅ ∧ 0 ≤ X₆ ∧ 0 ≤ X₆+X₇ ∧ X₇ ≤ X₆ ∧ 0 ≤ X₇ of depth 1:

new bound:

8⋅X₂+6 {O(n)}

MPRF:

• f75: [1+X₆-X₇]

MPRF for transition t₅₆: f83(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f83(1+X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀+X₆ ∧ 0 ≤ X₀+X₇ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₅ ∧ X₀ ≤ X₆ ∧ X₀ ≤ X₇ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₁+X₅ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₁+X₆ ∧ X₆ ≤ X₁ ∧ 0 ≤ X₁+X₇ ∧ X₇ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₄ ∧ X₂ ≤ X₅ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₇ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₄+X₆ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₄+X₇ ∧ X₇ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₅+X₇ ∧ X₇ ≤ X₅ ∧ 0 ≤ X₆ ∧ 0 ≤ X₆+X₇ ∧ X₇ ≤ X₆ ∧ 0 ≤ X₇ of depth 1:

new bound:

32⋅X₂+33 {O(n)}

MPRF:

• f83: [1+X₃-X₀]

All Bounds

Timebounds

Overall timebound:58⋅X₂+62 {O(n)}
t₄₁: 1 {O(1)}
t₄₂: X₂ {O(n)}
t₄₃: 1 {O(1)}
t₄₄: X₂+1 {O(n)}
t₄₅: 1 {O(1)}
t₄₆: 2⋅X₂+1 {O(n)}
t₄₇: 1 {O(1)}
t₄₈: 2⋅X₂+2 {O(n)}
t₄₉: 1 {O(1)}
t₅₀: 4⋅X₂+5 {O(n)}
t₅₁: 1 {O(1)}
t₅₂: 8⋅X₂+5 {O(n)}
t₅₃: 1 {O(1)}
t₅₄: 8⋅X₂+6 {O(n)}
t₅₅: 1 {O(1)}
t₅₆: 32⋅X₂+33 {O(n)}
t₅₇: 1 {O(1)}

Costbounds

Overall costbound: 58⋅X₂+62 {O(n)}
t₄₁: 1 {O(1)}
t₄₂: X₂ {O(n)}
t₄₃: 1 {O(1)}
t₄₄: X₂+1 {O(n)}
t₄₅: 1 {O(1)}
t₄₆: 2⋅X₂+1 {O(n)}
t₄₇: 1 {O(1)}
t₄₈: 2⋅X₂+2 {O(n)}
t₄₉: 1 {O(1)}
t₅₀: 4⋅X₂+5 {O(n)}
t₅₁: 1 {O(1)}
t₅₂: 8⋅X₂+5 {O(n)}
t₅₃: 1 {O(1)}
t₅₄: 8⋅X₂+6 {O(n)}
t₅₅: 1 {O(1)}
t₅₆: 32⋅X₂+33 {O(n)}
t₅₇: 1 {O(1)}

Sizebounds

t₄₁, X₀: 0 {O(1)}
t₄₁, X₁: 0 {O(1)}
t₄₁, X₂: X₂ {O(n)}
t₄₁, X₃: X₃ {O(n)}
t₄₁, X₄: X₄ {O(n)}
t₄₁, X₅: X₅ {O(n)}
t₄₁, X₆: X₆ {O(n)}
t₄₁, X₇: X₇ {O(n)}
t₄₂, X₀: 0 {O(1)}
t₄₂, X₁: X₂ {O(n)}
t₄₂, X₂: X₂ {O(n)}
t₄₂, X₃: X₃ {O(n)}
t₄₂, X₄: X₄ {O(n)}
t₄₂, X₅: X₅ {O(n)}
t₄₂, X₆: X₆ {O(n)}
t₄₂, X₇: X₇ {O(n)}
t₄₃, X₀: 0 {O(1)}
t₄₃, X₁: X₂ {O(n)}
t₄₃, X₂: 2⋅X₂ {O(n)}
t₄₃, X₃: 0 {O(1)}
t₄₃, X₄: 2⋅X₄ {O(n)}
t₄₃, X₅: 2⋅X₅ {O(n)}
t₄₃, X₆: 2⋅X₆ {O(n)}
t₄₃, X₇: 2⋅X₇ {O(n)}
t₄₄, X₀: 0 {O(1)}
t₄₄, X₁: X₂ {O(n)}
t₄₄, X₂: 2⋅X₂ {O(n)}
t₄₄, X₃: X₂+1 {O(n)}
t₄₄, X₄: 2⋅X₄ {O(n)}
t₄₄, X₅: 2⋅X₅ {O(n)}
t₄₄, X₆: 2⋅X₆ {O(n)}
t₄₄, X₇: 2⋅X₇ {O(n)}
t₄₅, X₀: 0 {O(1)}
t₄₅, X₁: 2⋅X₂ {O(n)}
t₄₅, X₂: 4⋅X₂ {O(n)}
t₄₅, X₃: X₂+1 {O(n)}
t₄₅, X₄: 0 {O(1)}
t₄₅, X₅: 4⋅X₅ {O(n)}
t₄₅, X₆: 4⋅X₆ {O(n)}
t₄₅, X₇: 4⋅X₇ {O(n)}
t₄₆, X₀: 0 {O(1)}
t₄₆, X₁: 2⋅X₂ {O(n)}
t₄₆, X₂: 4⋅X₂ {O(n)}
t₄₆, X₃: X₂+1 {O(n)}
t₄₆, X₄: 2⋅X₂+1 {O(n)}
t₄₆, X₅: 4⋅X₅ {O(n)}
t₄₆, X₆: 4⋅X₆ {O(n)}
t₄₆, X₇: 4⋅X₇ {O(n)}
t₄₇, X₀: 0 {O(1)}
t₄₇, X₁: 4⋅X₂ {O(n)}
t₄₇, X₂: 8⋅X₂ {O(n)}
t₄₇, X₃: 2⋅X₂+2 {O(n)}
t₄₇, X₄: 2⋅X₂+1 {O(n)}
t₄₇, X₅: 8⋅X₅ {O(n)}
t₄₇, X₆: 8⋅X₆ {O(n)}
t₄₇, X₇: 8⋅X₇ {O(n)}
t₄₈, X₀: 2⋅X₂+2 {O(n)}
t₄₈, X₁: 4⋅X₂ {O(n)}
t₄₈, X₂: 8⋅X₂ {O(n)}
t₄₈, X₃: 2⋅X₂+2 {O(n)}
t₄₈, X₄: 2⋅X₂+1 {O(n)}
t₄₈, X₅: 8⋅X₅ {O(n)}
t₄₈, X₆: 8⋅X₆ {O(n)}
t₄₈, X₇: 8⋅X₇ {O(n)}
t₄₉, X₀: 2⋅X₂+2 {O(n)}
t₄₉, X₁: 8⋅X₂ {O(n)}
t₄₉, X₂: 16⋅X₂ {O(n)}
t₄₉, X₃: 4⋅X₂+4 {O(n)}
t₄₉, X₄: 4⋅X₂+2 {O(n)}
t₄₉, X₅: 0 {O(1)}
t₄₉, X₆: 16⋅X₆ {O(n)}
t₄₉, X₇: 16⋅X₇ {O(n)}
t₅₀, X₀: 2⋅X₂+2 {O(n)}
t₅₀, X₁: 8⋅X₂ {O(n)}
t₅₀, X₂: 16⋅X₂ {O(n)}
t₅₀, X₃: 4⋅X₂+4 {O(n)}
t₅₀, X₄: 4⋅X₂+2 {O(n)}
t₅₀, X₅: 4⋅X₂+5 {O(n)}
t₅₀, X₆: 16⋅X₆ {O(n)}
t₅₀, X₇: 16⋅X₇ {O(n)}
t₅₁, X₀: 4⋅X₂+4 {O(n)}
t₅₁, X₁: 16⋅X₂ {O(n)}
t₅₁, X₂: 32⋅X₂ {O(n)}
t₅₁, X₃: 8⋅X₂+8 {O(n)}
t₅₁, X₄: 8⋅X₂+4 {O(n)}
t₅₁, X₅: 4⋅X₂+5 {O(n)}
t₅₁, X₆: 0 {O(1)}
t₅₁, X₇: 32⋅X₇ {O(n)}
t₅₂, X₀: 4⋅X₂+4 {O(n)}
t₅₂, X₁: 16⋅X₂ {O(n)}
t₅₂, X₂: 32⋅X₂ {O(n)}
t₅₂, X₃: 8⋅X₂+8 {O(n)}
t₅₂, X₄: 8⋅X₂+4 {O(n)}
t₅₂, X₅: 4⋅X₂+5 {O(n)}
t₅₂, X₆: 8⋅X₂+5 {O(n)}
t₅₂, X₇: 32⋅X₇ {O(n)}
t₅₃, X₀: 8⋅X₂+8 {O(n)}
t₅₃, X₁: 32⋅X₂ {O(n)}
t₅₃, X₂: 64⋅X₂ {O(n)}
t₅₃, X₃: 16⋅X₂+16 {O(n)}
t₅₃, X₄: 16⋅X₂+8 {O(n)}
t₅₃, X₅: 8⋅X₂+10 {O(n)}
t₅₃, X₆: 8⋅X₂+5 {O(n)}
t₅₃, X₇: 0 {O(1)}
t₅₄, X₀: 8⋅X₂+8 {O(n)}
t₅₄, X₁: 32⋅X₂ {O(n)}
t₅₄, X₂: 64⋅X₂ {O(n)}
t₅₄, X₃: 16⋅X₂+16 {O(n)}
t₅₄, X₄: 16⋅X₂+8 {O(n)}
t₅₄, X₅: 8⋅X₂+10 {O(n)}
t₅₄, X₆: 8⋅X₂+5 {O(n)}
t₅₄, X₇: 8⋅X₂+6 {O(n)}
t₅₅, X₀: 0 {O(1)}
t₅₅, X₁: 64⋅X₂ {O(n)}
t₅₅, X₂: 128⋅X₂ {O(n)}
t₅₅, X₃: 32⋅X₂+32 {O(n)}
t₅₅, X₄: 32⋅X₂+16 {O(n)}
t₅₅, X₅: 16⋅X₂+20 {O(n)}
t₅₅, X₆: 16⋅X₂+10 {O(n)}
t₅₅, X₇: 8⋅X₂+6 {O(n)}
t₅₆, X₀: 32⋅X₂+33 {O(n)}
t₅₆, X₁: 64⋅X₂ {O(n)}
t₅₆, X₂: 128⋅X₂ {O(n)}
t₅₆, X₃: 32⋅X₂+32 {O(n)}
t₅₆, X₄: 32⋅X₂+16 {O(n)}
t₅₆, X₅: 16⋅X₂+20 {O(n)}
t₅₆, X₆: 16⋅X₂+10 {O(n)}
t₅₆, X₇: 8⋅X₂+6 {O(n)}
t₅₇, X₀: 32⋅X₂+33 {O(n)}
t₅₇, X₁: 128⋅X₂ {O(n)}
t₅₇, X₂: 256⋅X₂ {O(n)}
t₅₇, X₃: 64⋅X₂+64 {O(n)}
t₅₇, X₄: 64⋅X₂+32 {O(n)}
t₅₇, X₅: 32⋅X₂+40 {O(n)}
t₅₇, X₆: 32⋅X₂+20 {O(n)}
t₅₇, X₇: 16⋅X₂+12 {O(n)}