Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₈: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₀, X₃, X₃, X₅, X₅, X₇, X₇)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₂, X₇) :|: X₂+1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₀: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, 1, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄-1, X₅, X₆, X₇) :|: X₂+1 ≤ X₄ ∧ X₄ ≤ X₀ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₂+1 ≤ X₆ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆, X₇) :|: X₄ ≤ X₀ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₄ ∧ X₄+1 ≤ X₆ ∧ X₂ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₄: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, 1+X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂+1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₆ ≤ X₀+1 ∧ X₀+1 ≤ X₆ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₆, X₇) :|: X₆ ≤ X₀ ∧ X₆ ≤ X₀+1 ∧ X₂+1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂+1 ≤ X₆ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
Preprocessing
Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l6
Found invariant X₆ ≤ 1+X₁ ∧ X₆ ≤ 1+X₀ ∧ 2 ≤ X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location l5
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l1
Found invariant X₆ ≤ X₁ ∧ X₆ ≤ X₀ ∧ 2 ≤ X₆ ∧ 3 ≤ X₄+X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location l4
Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₈: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₀, X₃, X₃, X₅, X₅, X₇, X₇)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₂, X₇) :|: X₂+1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₀: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, 1, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄-1, X₅, X₆, X₇) :|: X₂+1 ≤ X₄ ∧ X₄ ≤ X₀ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₂+1 ≤ X₆ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₆ ≤ X₁ ∧ X₆ ≤ X₀ ∧ 2 ≤ X₆ ∧ 3 ≤ X₄+X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆, X₇) :|: X₄ ≤ X₀ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₄ ∧ X₄+1 ≤ X₆ ∧ X₂ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₆ ≤ X₁ ∧ X₆ ≤ X₀ ∧ 2 ≤ X₆ ∧ 3 ≤ X₄+X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₄: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, 1+X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂+1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₆ ≤ X₀+1 ∧ X₀+1 ≤ X₆ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₆ ≤ 1+X₁ ∧ X₆ ≤ 1+X₀ ∧ 2 ≤ X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₆, X₇) :|: X₆ ≤ X₀ ∧ X₆ ≤ X₀+1 ∧ X₂+1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂+1 ≤ X₆ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₆ ≤ 1+X₁ ∧ X₆ ≤ 1+X₀ ∧ 2 ≤ X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₂, X₇) :|: X₂+1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF:
l1 [X₁+1-X₂ ]
l5 [X₁-X₂ ]
l4 [X₁-X₂ ]
MPRF for transition t₄: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, 1+X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂+1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₆ ≤ X₀+1 ∧ X₀+1 ≤ X₆ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₆ ≤ 1+X₁ ∧ X₆ ≤ 1+X₀ ∧ 2 ≤ X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF:
l1 [X₁+1-X₂ ]
l5 [X₁+1-X₂ ]
l4 [X₁+1-X₂ ]
MPRF for transition t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆, X₇) :|: X₄ ≤ X₀ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₄ ∧ X₄+1 ≤ X₆ ∧ X₂ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₆ ≤ X₁ ∧ X₆ ≤ X₀ ∧ 2 ≤ X₆ ∧ 3 ≤ X₄+X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₀⋅X₀+8⋅X₀+7 {O(n^2)}
MPRF:
l1 [X₁-X₂ ]
l5 [X₁+1-X₆ ]
l4 [X₁+1-X₆ ]
MPRF for transition t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₁, X₅, X₆, X₇) :|: X₆ ≤ X₀ ∧ X₆ ≤ X₀+1 ∧ X₂+1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂+1 ≤ X₆ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₆ ≤ 1+X₁ ∧ X₆ ≤ 1+X₀ ∧ 2 ≤ X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₀⋅X₀+9⋅X₀+10 {O(n^2)}
MPRF:
l1 [X₁+1-X₂ ]
l5 [X₁+2-X₆ ]
l4 [X₁+1-X₆ ]
MPRF for transition t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄-1, X₅, X₆, X₇) :|: X₂+1 ≤ X₄ ∧ X₄ ≤ X₀ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₂+1 ≤ X₆ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₆ ≤ X₁ ∧ X₆ ≤ X₀ ∧ 2 ≤ X₆ ∧ 3 ≤ X₄+X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
6⋅X₀⋅X₀⋅X₀+35⋅X₀⋅X₀+66⋅X₀+40 {O(n^3)}
MPRF:
l4 [X₄+1-X₂ ]
l5 [0 ]
l1 [0 ]
Analysing control-flow refined program
Cut unsatisfiable transition t₄: l5→l1
Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2
Found invariant X₆ ≤ 1+X₁ ∧ X₆ ≤ 1+X₀ ∧ 3 ≤ X₆ ∧ 4 ≤ X₄+X₆ ∧ 2+X₄ ≤ X₆ ∧ 4 ≤ X₂+X₆ ∧ 2+X₂ ≤ X₆ ∧ 5 ≤ X₁+X₆ ∧ 5 ≤ X₀+X₆ ∧ X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l5___1
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l6
Found invariant X₆ ≤ X₄ ∧ X₆ ≤ X₁ ∧ X₆ ≤ X₀ ∧ 2 ≤ X₆ ∧ 4 ≤ X₄+X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l4___3
Found invariant X₆ ≤ X₁ ∧ X₆ ≤ X₀ ∧ 2 ≤ X₆ ∧ 3 ≤ X₄+X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l4___2
Found invariant X₆ ≤ 1+X₂ ∧ X₆ ≤ X₁ ∧ X₆ ≤ X₀ ∧ 2 ≤ X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location l5
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l1
Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3
knowledge_propagation leads to new time bound X₀+2 {O(n)} for transition t₇₄: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l4___3(X₀, X₀, X₂, X₃, X₀, X₅, X₆, X₇) :|: X₆ ≤ X₀ ∧ 1+X₂ ≤ X₆ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₂ ≤ X₆ ∧ X₆ ≤ 1+X₂ ∧ 2 ≤ X₆ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₆ ≤ 1+X₂ ∧ X₆ ≤ X₁ ∧ X₆ ≤ X₀ ∧ 2 ≤ X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀
MPRF for transition t₇₁: n_l4___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l5___1(X₀, X₀, X₂, X₃, X₂, X₅, X₆+1, X₇) :|: X₆ ≤ X₀ ∧ X₄ ≤ X₀ ∧ 1+X₂ ≤ X₆ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₄ ∧ 1+X₂ ≤ X₆ ∧ 1+X₄ ≤ X₀ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₆ ≤ X₀ ∧ 1+X₂ ≤ X₆ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₄ ∧ X₄ ≤ X₂ ∧ X₆ ≤ X₁ ∧ X₆ ≤ X₀ ∧ 2 ≤ X₆ ∧ 3 ≤ X₄+X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₀⋅X₀+11⋅X₀+14 {O(n^2)}
MPRF:
l5 [0 ]
n_l4___2 [X₀+1-X₆ ]
n_l4___3 [X₀+1-X₆ ]
n_l5___1 [X₁+1-X₆ ]
l1 [0 ]
MPRF for transition t₇₂: n_l4___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l4___2(X₀, X₀, X₂, X₃, X₄-1, X₅, X₆, X₇) :|: X₆ ≤ X₀ ∧ X₄ ≤ X₀ ∧ 1+X₂ ≤ X₆ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 1+X₂ ≤ X₆ ∧ X₄ ≤ X₀ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₆ ≤ X₀ ∧ 1+X₂ ≤ X₄ ∧ 1+X₂ ≤ X₆ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₁ ∧ X₆ ≤ X₀ ∧ 2 ≤ X₆ ∧ 4 ≤ X₄+X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₀⋅X₀+13⋅X₀+14 {O(n^2)}
MPRF:
l5 [0 ]
n_l4___2 [X₀-X₆ ]
n_l4___3 [X₀+1-X₆ ]
n_l5___1 [X₀+1-X₆ ]
l1 [X₀-X₁ ]
MPRF for transition t₇₃: n_l5___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l4___3(X₀, X₀, X₂, X₃, X₀, X₅, X₆, X₇) :|: 1+X₂ ≤ X₆ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₄ ∧ X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2+X₄ ≤ X₆ ∧ X₆ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₆ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₆ ≤ 1+X₁ ∧ X₆ ≤ 1+X₀ ∧ 3 ≤ X₆ ∧ 4 ≤ X₄+X₆ ∧ 2+X₄ ≤ X₆ ∧ 4 ≤ X₂+X₆ ∧ 2+X₂ ≤ X₆ ∧ 5 ≤ X₁+X₆ ∧ 5 ≤ X₀+X₆ ∧ X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₀⋅X₀+10⋅X₀+12 {O(n^2)}
MPRF:
l5 [0 ]
n_l4___2 [X₀-X₆ ]
n_l4___3 [X₄-X₆ ]
n_l5___1 [X₁+1-X₆ ]
l1 [0 ]
MPRF for transition t₈₁: n_l5___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, 1+X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂+1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₆ ≤ X₀+1 ∧ X₀+1 ≤ X₆ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₆ ≤ 1+X₁ ∧ X₆ ≤ 1+X₀ ∧ 2 ≤ X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ ∧ X₆ ≤ 1+X₁ ∧ X₆ ≤ 1+X₀ ∧ 3 ≤ X₆ ∧ 4 ≤ X₄+X₆ ∧ 2+X₄ ≤ X₆ ∧ 4 ≤ X₂+X₆ ∧ 2+X₂ ≤ X₆ ∧ 5 ≤ X₁+X₆ ∧ 5 ≤ X₀+X₆ ∧ X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
l5 [X₀-X₂ ]
n_l4___2 [X₀-X₂ ]
n_l4___3 [X₀-X₂ ]
n_l5___1 [X₀-X₄ ]
l1 [X₁-X₂ ]
MPRF for transition t₇₀: n_l4___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l4___2(X₀, X₀, X₂, X₃, X₄-1, X₅, X₆, X₇) :|: X₆ ≤ X₀ ∧ X₄ ≤ X₀ ∧ 1+X₂ ≤ X₆ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₄ ∧ 1+X₂ ≤ X₆ ∧ 1+X₄ ≤ X₀ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₆ ≤ X₀ ∧ 1+X₂ ≤ X₄ ∧ 1+X₂ ≤ X₆ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₆ ≤ X₁ ∧ X₆ ≤ X₀ ∧ 2 ≤ X₆ ∧ 3 ≤ X₄+X₆ ∧ 3 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 4 ≤ X₁+X₆ ∧ 4 ≤ X₀+X₆ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
4⋅X₀⋅X₀⋅X₀⋅X₀+50⋅X₀⋅X₀⋅X₀+218⋅X₀⋅X₀+402⋅X₀+264 {O(n^4)}
MPRF:
l5 [2⋅X₁ ]
n_l4___3 [X₀+X₄+X₆-X₂-1 ]
n_l4___2 [X₀+X₄+X₆-X₂ ]
n_l5___1 [X₀+X₆-1 ]
l1 [2⋅X₁ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:6⋅X₀⋅X₀⋅X₀+39⋅X₀⋅X₀+85⋅X₀+65 {O(n^3)}
t₈: 1 {O(1)}
t₂: X₀+2 {O(n)}
t₃: 1 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₆: 6⋅X₀⋅X₀⋅X₀+35⋅X₀⋅X₀+66⋅X₀+40 {O(n^3)}
t₇: 2⋅X₀⋅X₀+8⋅X₀+7 {O(n^2)}
t₄: X₀+2 {O(n)}
t₅: 2⋅X₀⋅X₀+9⋅X₀+10 {O(n^2)}
Costbounds
Overall costbound: 6⋅X₀⋅X₀⋅X₀+39⋅X₀⋅X₀+85⋅X₀+65 {O(n^3)}
t₈: 1 {O(1)}
t₂: X₀+2 {O(n)}
t₃: 1 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₆: 6⋅X₀⋅X₀⋅X₀+35⋅X₀⋅X₀+66⋅X₀+40 {O(n^3)}
t₇: 2⋅X₀⋅X₀+8⋅X₀+7 {O(n^2)}
t₄: X₀+2 {O(n)}
t₅: 2⋅X₀⋅X₀+9⋅X₀+10 {O(n^2)}
Sizebounds
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₀ {O(n)}
t₈, X₂: X₃ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₅ {O(n)}
t₈, X₅: X₅ {O(n)}
t₈, X₆: X₇ {O(n)}
t₈, X₇: X₇ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₀ {O(n)}
t₂, X₂: X₀+3 {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: 2⋅X₀+X₅ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₀+6 {O(n)}
t₂, X₇: X₇ {O(n)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: 2⋅X₀ {O(n)}
t₃, X₂: X₀+4 {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₀+X₅ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₃, X₆: 2⋅X₀⋅X₀+9⋅X₀+X₇+13 {O(n^2)}
t₃, X₇: 2⋅X₇ {O(n)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₀ {O(n)}
t₀, X₂: X₃ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₅ {O(n)}
t₀, X₅: X₅ {O(n)}
t₀, X₆: X₇ {O(n)}
t₀, X₇: X₇ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: 1 {O(1)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₅ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₇ {O(n)}
t₁, X₇: X₇ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₀ {O(n)}
t₆, X₂: X₀+3 {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: 2⋅X₀ {O(n)}
t₆, X₅: X₅ {O(n)}
t₆, X₆: 2⋅X₀⋅X₀+9⋅X₀+13 {O(n^2)}
t₆, X₇: X₇ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₀ {O(n)}
t₇, X₂: X₀+3 {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: 2⋅X₀ {O(n)}
t₇, X₅: X₅ {O(n)}
t₇, X₆: 2⋅X₀⋅X₀+9⋅X₀+13 {O(n^2)}
t₇, X₇: X₇ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₀ {O(n)}
t₄, X₂: X₀+3 {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: 2⋅X₀ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: 2⋅X₀⋅X₀+9⋅X₀+13 {O(n^2)}
t₄, X₇: X₇ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₀ {O(n)}
t₅, X₂: X₀+3 {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: 2⋅X₀ {O(n)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: 2⋅X₀⋅X₀+9⋅X₀+13 {O(n^2)}
t₅, X₇: X₇ {O(n)}