Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ X₀
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 2⋅X₂
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₀ ∧ X₀ < X₁ ∧ 2⋅X₂ < X₀
t₁₀: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₃, X₇, X₀, X₃, X₄, X₅, X₆, X₇)
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, nondef.0, X₄, X₅, X₆, X₇)
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₅, X₆, X₄, X₃, X₄, X₅, X₆, X₇)
Preprocessing
Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l6
Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l5
Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ X₀
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 2⋅X₂
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₀ ∧ X₀ < X₁ ∧ 2⋅X₂ < X₀
t₁₀: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₃, X₇, X₀, X₃, X₄, X₅, X₆, X₇) :|: 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, nondef.0, X₄, X₅, X₆, X₇) :|: 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₅, X₆, X₄, X₃, X₄, X₅, X₆, X₇)
Analysing control-flow refined program
Found invariant X₆ ≤ X₁ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 3 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₆ ∧ 1+X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l6___6
Found invariant X₆ ≤ X₁ ∧ X₁ ≤ X₆ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ for location l2
Found invariant X₇ ≤ X₁ ∧ 4 ≤ X₇ ∧ 6 ≤ X₆+X₇ ∧ 5 ≤ X₅+X₇ ∧ 3+X₅ ≤ X₇ ∧ 7 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ 5 ≤ X₂+X₇ ∧ 3+X₂ ≤ X₇ ∧ 8 ≤ X₁+X₇ ∧ X₁ ≤ X₇ ∧ 7 ≤ X₀+X₇ ∧ 1+X₀ ≤ X₇ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 5 ≤ X₃+X₆ ∧ 3 ≤ X₂+X₆ ∧ 6 ≤ X₁+X₆ ∧ 5 ≤ X₀+X₆ ∧ 2+X₅ ≤ X₃ ∧ X₅ ≤ X₂ ∧ 3+X₅ ≤ X₁ ∧ 2+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 5 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 7 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 3 ≤ X₀ for location n_l6___2
Found invariant X₆ ≤ X₁ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 3 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₆ ∧ 1+X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___5
Found invariant X₇ ≤ X₁ ∧ 4 ≤ X₇ ∧ 6 ≤ X₆+X₇ ∧ 5 ≤ X₅+X₇ ∧ 3+X₅ ≤ X₇ ∧ 5 ≤ X₂+X₇ ∧ 3+X₂ ≤ X₇ ∧ 8 ≤ X₁+X₇ ∧ X₁ ≤ X₇ ∧ 7 ≤ X₀+X₇ ∧ 1+X₀ ≤ X₇ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 3 ≤ X₂+X₆ ∧ 6 ≤ X₁+X₆ ∧ 5 ≤ X₀+X₆ ∧ X₅ ≤ X₂ ∧ 3+X₅ ≤ X₁ ∧ 2+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 5 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 3 ≤ X₀ for location n_l4___1
Found invariant X₆ ≤ X₁ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 3 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₆ ∧ 1+X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l5___7
Found invariant X₇ ≤ X₁ ∧ X₁ ≤ X₇ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 3 ≤ X₂+X₆ ∧ X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ for location n_l2___4
Found invariant X₇ ≤ X₁ ∧ 4 ≤ X₇ ∧ 6 ≤ X₆+X₇ ∧ 5 ≤ X₅+X₇ ∧ 3+X₅ ≤ X₇ ∧ 7 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ 5 ≤ X₂+X₇ ∧ 3+X₂ ≤ X₇ ∧ 8 ≤ X₁+X₇ ∧ X₁ ≤ X₇ ∧ 7 ≤ X₀+X₇ ∧ 1+X₀ ≤ X₇ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 5 ≤ X₃+X₆ ∧ 3 ≤ X₂+X₆ ∧ 6 ≤ X₁+X₆ ∧ 5 ≤ X₀+X₆ ∧ 2+X₅ ≤ X₃ ∧ X₅ ≤ X₂ ∧ 3+X₅ ≤ X₁ ∧ 2+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 5 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 7 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 3 ≤ X₀ for location n_l5___3
MPRF for transition t₆₇: n_l2___4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l5___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ X₇ ∧ X₇ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 0 < X₀ ∧ 2⋅X₂ < X₀ ∧ X₀ < X₁ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₇ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 3 ≤ X₂+X₆ ∧ X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ of depth 1:
new bound:
2⋅X₅+X₇+1 {O(n)}
MPRF:
n_l2___4 [X₇-2⋅X₂-1 ]
n_l5___3 [X₇-2⋅X₂-5 ]
n_l6___2 [X₇-2⋅X₂-5 ]
n_l4___1 [X₁-2⋅X₀-1 ]
MPRF for transition t₆₉: n_l4___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l2___4(X₃, X₇, X₀, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₁ ∧ 2⋅X₂ < X₀ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₇ ∧ X₇ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₇ ≤ X₁ ∧ 4 ≤ X₇ ∧ 6 ≤ X₆+X₇ ∧ 5 ≤ X₅+X₇ ∧ 3+X₅ ≤ X₇ ∧ 5 ≤ X₂+X₇ ∧ 3+X₂ ≤ X₇ ∧ 8 ≤ X₁+X₇ ∧ X₁ ≤ X₇ ∧ 7 ≤ X₀+X₇ ∧ 1+X₀ ≤ X₇ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 3 ≤ X₂+X₆ ∧ 6 ≤ X₁+X₆ ∧ 5 ≤ X₀+X₆ ∧ X₅ ≤ X₂ ∧ 3+X₅ ≤ X₁ ∧ 2+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 5 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 3 ≤ X₀ of depth 1:
new bound:
X₅+X₇ {O(n)}
MPRF:
n_l2___4 [X₁-X₂ ]
n_l5___3 [X₇-X₂ ]
n_l6___2 [X₇-X₂ ]
n_l4___1 [X₇-X₂ ]
MPRF for transition t₇₁: n_l5___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l6___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ < X₁ ∧ 2⋅X₂ < X₀ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₇ ∧ X₇ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₇ ≤ X₁ ∧ 4 ≤ X₇ ∧ 6 ≤ X₆+X₇ ∧ 5 ≤ X₅+X₇ ∧ 3+X₅ ≤ X₇ ∧ 7 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ 5 ≤ X₂+X₇ ∧ 3+X₂ ≤ X₇ ∧ 8 ≤ X₁+X₇ ∧ X₁ ≤ X₇ ∧ 7 ≤ X₀+X₇ ∧ 1+X₀ ≤ X₇ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 5 ≤ X₃+X₆ ∧ 3 ≤ X₂+X₆ ∧ 6 ≤ X₁+X₆ ∧ 5 ≤ X₀+X₆ ∧ 2+X₅ ≤ X₃ ∧ X₅ ≤ X₂ ∧ 3+X₅ ≤ X₁ ∧ 2+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 5 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 7 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 3 ≤ X₀ of depth 1:
new bound:
2⋅X₅+X₇+1 {O(n)}
MPRF:
n_l2___4 [X₇-2⋅X₂-1 ]
n_l5___3 [X₁-2⋅X₂-1 ]
n_l6___2 [X₇-2⋅X₂-5 ]
n_l4___1 [X₇-2⋅X₀-1 ]
MPRF for transition t₇₃: n_l6___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l4___1(X₀, X₁, X₂, NoDet0, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₁ ∧ 2⋅X₂ < X₀ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₇ ∧ X₇ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₇ ≤ X₁ ∧ 4 ≤ X₇ ∧ 6 ≤ X₆+X₇ ∧ 5 ≤ X₅+X₇ ∧ 3+X₅ ≤ X₇ ∧ 7 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ 5 ≤ X₂+X₇ ∧ 3+X₂ ≤ X₇ ∧ 8 ≤ X₁+X₇ ∧ X₁ ≤ X₇ ∧ 7 ≤ X₀+X₇ ∧ 1+X₀ ≤ X₇ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 5 ≤ X₃+X₆ ∧ 3 ≤ X₂+X₆ ∧ 6 ≤ X₁+X₆ ∧ 5 ≤ X₀+X₆ ∧ 2+X₅ ≤ X₃ ∧ X₅ ≤ X₂ ∧ 3+X₅ ≤ X₁ ∧ 2+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 5 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 7 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 3 ≤ X₀ of depth 1:
new bound:
2⋅X₅+X₇+3 {O(n)}
MPRF:
n_l2___4 [X₁+X₅-X₂-3 ]
n_l5___3 [X₁-X₂-2 ]
n_l6___2 [X₁-X₂-2 ]
n_l4___1 [X₁+X₅-2⋅X₂-4 ]
CFR: Improvement to new bound with the following program:
new bound:
4⋅X₇+7⋅X₅+5 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: NoDet0
Locations: l0, l1, l2, l3, l7, n_l2___4, n_l4___1, n_l4___5, n_l5___3, n_l5___7, n_l6___2, n_l6___6
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0 ∧ X₆ ≤ X₁ ∧ X₁ ≤ X₆ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ X₀ ∧ X₆ ≤ X₁ ∧ X₁ ≤ X₆ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 2⋅X₂ ∧ X₆ ≤ X₁ ∧ X₁ ≤ X₆ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄
t₆₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l5___7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₆ ∧ X₆ ≤ X₁ ∧ X₂ ≤ X₄ ∧ X₄ ≤ X₂ ∧ 0 < X₀ ∧ 2⋅X₂ < X₀ ∧ X₀ < X₁ ∧ X₆ ≤ X₁ ∧ X₁ ≤ X₆ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄
t₁₀: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₅, X₆, X₄, X₃, X₄, X₅, X₆, X₇)
t₈₂: n_l2___4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0 ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₇ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 3 ≤ X₂+X₆ ∧ X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂
t₈₃: n_l2___4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₇ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 3 ≤ X₂+X₆ ∧ X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂
t₈₄: n_l2___4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 2⋅X₂ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₇ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 3 ≤ X₂+X₆ ∧ X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂
t₆₇: n_l2___4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l5___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ X₇ ∧ X₇ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 0 < X₀ ∧ 2⋅X₂ < X₀ ∧ X₀ < X₁ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₇ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 3 ≤ X₂+X₆ ∧ X₅ ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂
t₆₉: n_l4___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l2___4(X₃, X₇, X₀, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₁ ∧ 2⋅X₂ < X₀ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₇ ∧ X₇ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₇ ≤ X₁ ∧ 4 ≤ X₇ ∧ 6 ≤ X₆+X₇ ∧ 5 ≤ X₅+X₇ ∧ 3+X₅ ≤ X₇ ∧ 5 ≤ X₂+X₇ ∧ 3+X₂ ≤ X₇ ∧ 8 ≤ X₁+X₇ ∧ X₁ ≤ X₇ ∧ 7 ≤ X₀+X₇ ∧ 1+X₀ ≤ X₇ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 3 ≤ X₂+X₆ ∧ 6 ≤ X₁+X₆ ∧ 5 ≤ X₀+X₆ ∧ X₅ ≤ X₂ ∧ 3+X₅ ≤ X₁ ∧ 2+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 5 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 3 ≤ X₀
t₇₀: n_l4___5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l2___4(X₃, X₇, X₀, X₃, X₄, X₅, X₆, X₇) :|: 2⋅X₂ < X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₆ ∧ X₆ ≤ X₁ ∧ X₂ ≤ X₄ ∧ X₄ ≤ X₂ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₆ ≤ X₁ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 3 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₆ ∧ 1+X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₇₁: n_l5___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l6___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ < X₁ ∧ 2⋅X₂ < X₀ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₇ ∧ X₇ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₇ ≤ X₁ ∧ 4 ≤ X₇ ∧ 6 ≤ X₆+X₇ ∧ 5 ≤ X₅+X₇ ∧ 3+X₅ ≤ X₇ ∧ 7 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ 5 ≤ X₂+X₇ ∧ 3+X₂ ≤ X₇ ∧ 8 ≤ X₁+X₇ ∧ X₁ ≤ X₇ ∧ 7 ≤ X₀+X₇ ∧ 1+X₀ ≤ X₇ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 5 ≤ X₃+X₆ ∧ 3 ≤ X₂+X₆ ∧ 6 ≤ X₁+X₆ ∧ 5 ≤ X₀+X₆ ∧ 2+X₅ ≤ X₃ ∧ X₅ ≤ X₂ ∧ 3+X₅ ≤ X₁ ∧ 2+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 5 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 7 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 3 ≤ X₀
t₇₂: n_l5___7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l6___6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 2⋅X₂ < X₅ ∧ X₅ < X₁ ∧ 0 < X₅ ∧ X₂ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₆ ∧ X₆ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₆ ≤ X₁ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 3 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₆ ∧ 1+X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₇₃: n_l6___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l4___1(X₀, X₁, X₂, NoDet0, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₁ ∧ 2⋅X₂ < X₀ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₇ ∧ X₇ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₇ ≤ X₁ ∧ 4 ≤ X₇ ∧ 6 ≤ X₆+X₇ ∧ 5 ≤ X₅+X₇ ∧ 3+X₅ ≤ X₇ ∧ 7 ≤ X₃+X₇ ∧ 1+X₃ ≤ X₇ ∧ 5 ≤ X₂+X₇ ∧ 3+X₂ ≤ X₇ ∧ 8 ≤ X₁+X₇ ∧ X₁ ≤ X₇ ∧ 7 ≤ X₀+X₇ ∧ 1+X₀ ≤ X₇ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 5 ≤ X₃+X₆ ∧ 3 ≤ X₂+X₆ ∧ 6 ≤ X₁+X₆ ∧ 5 ≤ X₀+X₆ ∧ 2+X₅ ≤ X₃ ∧ X₅ ≤ X₂ ∧ 3+X₅ ≤ X₁ ∧ 2+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 5 ≤ X₁+X₅ ∧ 4 ≤ X₀+X₅ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 7 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 3 ≤ X₀
t₇₄: n_l6___6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l4___5(X₀, X₁, X₂, NoDet0, X₄, X₅, X₆, X₇) :|: 2⋅X₂ < X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₆ ∧ X₆ ≤ X₁ ∧ X₂ ≤ X₄ ∧ X₄ ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₆ ≤ X₁ ∧ 2 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ 3 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₆ ∧ 1+X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
All Bounds
Timebounds
Overall timebound:4⋅X₇+7⋅X₅+18 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆₈: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₆₇: 2⋅X₅+X₇+1 {O(n)}
t₈₂: 1 {O(1)}
t₈₃: 1 {O(1)}
t₈₄: 1 {O(1)}
t₆₉: X₅+X₇ {O(n)}
t₇₀: 1 {O(1)}
t₇₁: 2⋅X₅+X₇+1 {O(n)}
t₇₂: 1 {O(1)}
t₇₃: 2⋅X₅+X₇+3 {O(n)}
t₇₄: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₇+7⋅X₅+18 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆₈: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₆₇: 2⋅X₅+X₇+1 {O(n)}
t₈₂: 1 {O(1)}
t₈₃: 1 {O(1)}
t₈₄: 1 {O(1)}
t₆₉: X₅+X₇ {O(n)}
t₇₀: 1 {O(1)}
t₇₁: 2⋅X₅+X₇+1 {O(n)}
t₇₂: 1 {O(1)}
t₇₃: 2⋅X₅+X₇+3 {O(n)}
t₇₄: 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)}
t₃, X₀: X₅ {O(n)}
t₃, X₁: X₆ {O(n)}
t₃, X₂: X₄ {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)}
t₄, X₀: X₅ {O(n)}
t₄, X₁: X₆ {O(n)}
t₄, X₂: X₄ {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)}
t₅, X₀: X₅ {O(n)}
t₅, X₁: X₆ {O(n)}
t₅, X₂: X₄ {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)}
t₆₈, X₀: X₅ {O(n)}
t₆₈, X₁: X₆ {O(n)}
t₆₈, X₂: X₄ {O(n)}
t₆₈, X₃: X₃ {O(n)}
t₆₈, X₄: X₄ {O(n)}
t₆₈, X₅: X₅ {O(n)}
t₆₈, X₆: X₆ {O(n)}
t₆₈, X₇: X₇ {O(n)}
t₁₀, X₁: 3⋅X₆+6⋅X₇ {O(n)}
t₁₀, X₄: 9⋅X₄ {O(n)}
t₁₀, X₅: 9⋅X₅ {O(n)}
t₁₀, X₆: 9⋅X₆ {O(n)}
t₁₀, X₇: 9⋅X₇ {O(n)}
t₁, X₀: X₅ {O(n)}
t₁, X₁: X₆ {O(n)}
t₁, X₂: X₄ {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)}
t₆₇, X₁: X₇ {O(n)}
t₆₇, X₄: X₄ {O(n)}
t₆₇, X₅: X₅ {O(n)}
t₆₇, X₆: X₆ {O(n)}
t₆₇, X₇: X₇ {O(n)}
t₈₂, X₁: 2⋅X₇ {O(n)}
t₈₂, X₄: 2⋅X₄ {O(n)}
t₈₂, X₅: 2⋅X₅ {O(n)}
t₈₂, X₆: 2⋅X₆ {O(n)}
t₈₂, X₇: 2⋅X₇ {O(n)}
t₈₃, X₁: 2⋅X₇ {O(n)}
t₈₃, X₄: 2⋅X₄ {O(n)}
t₈₃, X₅: 2⋅X₅ {O(n)}
t₈₃, X₆: 2⋅X₆ {O(n)}
t₈₃, X₇: 2⋅X₇ {O(n)}
t₈₄, X₁: 2⋅X₇ {O(n)}
t₈₄, X₄: 2⋅X₄ {O(n)}
t₈₄, X₅: 2⋅X₅ {O(n)}
t₈₄, X₆: 2⋅X₆ {O(n)}
t₈₄, X₇: 2⋅X₇ {O(n)}
t₆₉, X₁: X₇ {O(n)}
t₆₉, X₄: X₄ {O(n)}
t₆₉, X₅: X₅ {O(n)}
t₆₉, X₆: X₆ {O(n)}
t₆₉, X₇: X₇ {O(n)}
t₇₀, X₁: X₇ {O(n)}
t₇₀, X₂: X₅ {O(n)}
t₇₀, X₄: X₄ {O(n)}
t₇₀, X₅: X₅ {O(n)}
t₇₀, X₆: X₆ {O(n)}
t₇₀, X₇: X₇ {O(n)}
t₇₁, X₁: X₇ {O(n)}
t₇₁, X₄: X₄ {O(n)}
t₇₁, X₅: X₅ {O(n)}
t₇₁, X₆: X₆ {O(n)}
t₇₁, X₇: X₇ {O(n)}
t₇₂, X₀: X₅ {O(n)}
t₇₂, X₁: X₆ {O(n)}
t₇₂, X₂: X₄ {O(n)}
t₇₂, X₃: X₃ {O(n)}
t₇₂, X₄: X₄ {O(n)}
t₇₂, X₅: X₅ {O(n)}
t₇₂, X₆: X₆ {O(n)}
t₇₂, X₇: X₇ {O(n)}
t₇₃, X₁: X₇ {O(n)}
t₇₃, X₄: X₄ {O(n)}
t₇₃, X₅: X₅ {O(n)}
t₇₃, X₆: X₆ {O(n)}
t₇₃, X₇: X₇ {O(n)}
t₇₄, X₀: X₅ {O(n)}
t₇₄, X₁: X₆ {O(n)}
t₇₄, X₂: X₄ {O(n)}
t₇₄, X₄: X₄ {O(n)}
t₇₄, X₅: X₅ {O(n)}
t₇₄, X₆: X₆ {O(n)}
t₇₄, X₇: X₇ {O(n)}