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 t₁₇₁: 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 [2⋅X₃+X₇-2⋅X₀-2⋅X₂-5 ]
n_l6___2 [X₇-2⋅X₀-1 ]
n_l4___1 [X₇-2⋅X₀-1 ]
MPRF for transition t₁₇₃: 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 [X₇-X₂ ]
n_l5___3 [X₇-X₂ ]
n_l6___2 [X₇-X₂ ]
n_l4___1 [X₇-X₂ ]
MPRF for transition t₁₇₅: 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 t₁₇₇: 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:
X₅+X₇+2 {O(n)}
MPRF:
n_l2___4 [X₇-X₂-2 ]
n_l5___3 [X₇-X₂-2 ]
n_l6___2 [X₁-X₂-2 ]
n_l4___1 [X₁-X₂-4 ]
CFR: Improvement to new bound with the following program:
new bound:
4⋅X₇+6⋅X₅+4 {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
t₁₇₂: 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)
t₁₈₆: 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
t₁₈₇: 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
t₁₈₈: 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
t₁₇₁: 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
t₁₇₃: 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
t₁₇₄: 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
t₁₇₅: 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
t₁₇₆: 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
t₁₇₇: 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
t₁₇₈: 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+6⋅X₅+17 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₁₇₂: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₁₇₁: 2⋅X₅+X₇+1 {O(n)}
t₁₈₆: 1 {O(1)}
t₁₈₇: 1 {O(1)}
t₁₈₈: 1 {O(1)}
t₁₇₃: X₅+X₇ {O(n)}
t₁₇₄: 1 {O(1)}
t₁₇₅: 2⋅X₅+X₇+1 {O(n)}
t₁₇₆: 1 {O(1)}
t₁₇₇: X₅+X₇+2 {O(n)}
t₁₇₈: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₇+6⋅X₅+17 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₁₇₂: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₁₇₁: 2⋅X₅+X₇+1 {O(n)}
t₁₈₆: 1 {O(1)}
t₁₈₇: 1 {O(1)}
t₁₈₈: 1 {O(1)}
t₁₇₃: X₅+X₇ {O(n)}
t₁₇₄: 1 {O(1)}
t₁₇₅: 2⋅X₅+X₇+1 {O(n)}
t₁₇₆: 1 {O(1)}
t₁₇₇: X₅+X₇+2 {O(n)}
t₁₇₈: 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)}
t₁₇₂, X₀: X₅ {O(n)}
t₁₇₂, X₁: X₆ {O(n)}
t₁₇₂, X₂: X₄ {O(n)}
t₁₇₂, X₃: X₃ {O(n)}
t₁₇₂, X₄: X₄ {O(n)}
t₁₇₂, X₅: X₅ {O(n)}
t₁₇₂, X₆: X₆ {O(n)}
t₁₇₂, 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)}
t₁₇₁, X₁: X₇ {O(n)}
t₁₇₁, X₄: X₄ {O(n)}
t₁₇₁, X₅: X₅ {O(n)}
t₁₇₁, X₆: X₆ {O(n)}
t₁₇₁, X₇: X₇ {O(n)}
t₁₈₆, X₁: 2⋅X₇ {O(n)}
t₁₈₆, X₄: 2⋅X₄ {O(n)}
t₁₈₆, X₅: 2⋅X₅ {O(n)}
t₁₈₆, X₆: 2⋅X₆ {O(n)}
t₁₈₆, X₇: 2⋅X₇ {O(n)}
t₁₈₇, X₁: 2⋅X₇ {O(n)}
t₁₈₇, X₄: 2⋅X₄ {O(n)}
t₁₈₇, X₅: 2⋅X₅ {O(n)}
t₁₈₇, X₆: 2⋅X₆ {O(n)}
t₁₈₇, X₇: 2⋅X₇ {O(n)}
t₁₈₈, X₁: 2⋅X₇ {O(n)}
t₁₈₈, X₄: 2⋅X₄ {O(n)}
t₁₈₈, X₅: 2⋅X₅ {O(n)}
t₁₈₈, X₆: 2⋅X₆ {O(n)}
t₁₈₈, X₇: 2⋅X₇ {O(n)}
t₁₇₃, X₁: X₇ {O(n)}
t₁₇₃, X₄: X₄ {O(n)}
t₁₇₃, X₅: X₅ {O(n)}
t₁₇₃, X₆: X₆ {O(n)}
t₁₇₃, X₇: X₇ {O(n)}
t₁₇₄, X₁: X₇ {O(n)}
t₁₇₄, X₂: X₅ {O(n)}
t₁₇₄, X₄: X₄ {O(n)}
t₁₇₄, X₅: X₅ {O(n)}
t₁₇₄, X₆: X₆ {O(n)}
t₁₇₄, X₇: X₇ {O(n)}
t₁₇₅, X₁: X₇ {O(n)}
t₁₇₅, X₄: X₄ {O(n)}
t₁₇₅, X₅: X₅ {O(n)}
t₁₇₅, X₆: X₆ {O(n)}
t₁₇₅, X₇: X₇ {O(n)}
t₁₇₆, X₀: X₅ {O(n)}
t₁₇₆, X₁: X₆ {O(n)}
t₁₇₆, X₂: X₄ {O(n)}
t₁₇₆, X₃: X₃ {O(n)}
t₁₇₆, X₄: X₄ {O(n)}
t₁₇₆, X₅: X₅ {O(n)}
t₁₇₆, X₆: X₆ {O(n)}
t₁₇₆, X₇: X₇ {O(n)}
t₁₇₇, X₁: X₇ {O(n)}
t₁₇₇, X₄: X₄ {O(n)}
t₁₇₇, X₅: X₅ {O(n)}
t₁₇₇, X₆: X₆ {O(n)}
t₁₇₇, X₇: X₇ {O(n)}
t₁₇₈, X₀: X₅ {O(n)}
t₁₇₈, X₁: X₆ {O(n)}
t₁₇₈, X₂: X₄ {O(n)}
t₁₇₈, X₄: X₄ {O(n)}
t₁₇₈, X₅: X₅ {O(n)}
t₁₇₈, X₆: X₆ {O(n)}
t₁₇₈, X₇: X₇ {O(n)}