KoAT2 Proof Output

Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars:
Locations: l0, l1, l10, l11, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 0 < X₁ ∧ 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₁ ≤ 0
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₀ ≤ 0
t₁₇: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l6(X₀, X₁, X₂, X₃, X₄-X₁, X₅, X₆, X₇, X₈)
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l1(X₆, X₈, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₁ < 0
t₇: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 0 < X₁
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, X₀, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₁₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₃: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l1(X₁, X₃, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃ < X₁
t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₁ ≤ X₃
t₁₆: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l1(X₁, X₄, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 0 ≤ X₄
t₁₅: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₄ < 0
t₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, -X₀, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₁ < 0
t₉: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, X₀, X₃, X₄, X₅, X₆, X₇, X₈) :|: 0 ≤ X₁
t₁₀: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l5(X₀, X₁, X₂, X₂, X₄, X₅, X₆, X₇, X₈) :|: 0 < X₂
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l6(X₀, X₁, X₂, X₃, X₂, X₅, X₆, X₇, X₈) :|: X₂ ≤ 0
t₁₄: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l5(X₀, X₁, X₂, X₃-X₁, X₄, X₅, X₆, X₇, X₈)

Preprocessing

Cut unsatisfiable transition t₅: l3→l8

Cut unsatisfiable transition t₆: l3→l7

Eliminate variables {X₅,X₇} that do not contribute to the problem

Found invariant X₁ ≤ X₈ for location l11

Found invariant 1 ≤ 0 for location l6

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₁+X₈ ∧ X₁ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l7

Found invariant 1 ≤ X₈ ∧ 1 ≤ X₃+X₈ ∧ 2 ≤ X₂+X₈ ∧ 2 ≤ X₁+X₈ ∧ X₁ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ 2 ≤ X₁+X₈ ∧ X₁ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l8

Found invariant X₁ ≤ X₈ for location l1

Found invariant 1 ≤ 0 for location l10

Found invariant X₁ ≤ X₈ for location l4

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₃+X₈ ∧ 2 ≤ X₂+X₈ ∧ 2 ≤ X₁+X₈ ∧ X₁ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l9

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₁+X₈ ∧ X₁ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

Cut unsatisfiable transition t₄₃: l10→l6

Cut unsatisfiable transition t₄₉: l6→l10

Cut unsatisfiable transition t₅₀: l6→l1

Cut unsatisfiable transition t₅₁: l7→l8

Cut unsatisfiable transition t₅₄: l8→l6

Cut unreachable locations [l10; l6] from the program graph

Eliminate variables {X₄} that do not contribute to the problem

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₆, X₈
Temp_Vars:
Locations: l0, l1, l11, l2, l3, l4, l5, l7, l8, l9
Transitions:
t₇₉: l0(X₀, X₁, X₂, X₃, X₆, X₈) → l2(X₀, X₁, X₂, X₃, X₆, X₈)
t₈₀: l1(X₀, X₁, X₂, X₃, X₆, X₈) → l3(X₀, X₁, X₂, X₃, X₆, X₈) :|: 0 < X₁ ∧ 0 < X₀ ∧ X₁ ≤ X₈
t₈₁: l1(X₀, X₁, X₂, X₃, X₆, X₈) → l4(X₀, X₁, X₂, X₃, X₆, X₈) :|: X₁ ≤ 0 ∧ X₁ ≤ X₈
t₈₂: l1(X₀, X₁, X₂, X₃, X₆, X₈) → l4(X₀, X₁, X₂, X₃, X₆, X₈) :|: X₀ ≤ 0 ∧ X₁ ≤ X₈
t₈₃: l2(X₀, X₁, X₂, X₃, X₆, X₈) → l1(X₆, X₈, X₂, X₃, X₆, X₈)
t₈₄: l3(X₀, X₁, X₂, X₃, X₆, X₈) → l7(X₀, X₁, X₂, X₃, X₆, X₈) :|: 0 < X₁ ∧ 1 ≤ X₈ ∧ 2 ≤ X₁+X₈ ∧ X₁ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₅: l4(X₀, X₁, X₂, X₃, X₆, X₈) → l11(X₀, X₁, X₂, X₃, X₆, X₈) :|: X₁ ≤ X₈
t₈₇: l5(X₀, X₁, X₂, X₃, X₆, X₈) → l1(X₁, X₃, X₂, X₃, X₆, X₈) :|: X₃ < X₁ ∧ 1 ≤ X₈ ∧ 1 ≤ X₃+X₈ ∧ 2 ≤ X₂+X₈ ∧ 2 ≤ X₁+X₈ ∧ X₁ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₆: l5(X₀, X₁, X₂, X₃, X₆, X₈) → l9(X₀, X₁, X₂, X₃, X₆, X₈) :|: X₁ ≤ X₃ ∧ 1 ≤ X₈ ∧ 1 ≤ X₃+X₈ ∧ 2 ≤ X₂+X₈ ∧ 2 ≤ X₁+X₈ ∧ X₁ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₈: l7(X₀, X₁, X₂, X₃, X₆, X₈) → l8(X₀, X₁, X₀, X₃, X₆, X₈) :|: 0 ≤ X₁ ∧ 1 ≤ X₈ ∧ 2 ≤ X₁+X₈ ∧ X₁ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₉: l8(X₀, X₁, X₂, X₃, X₆, X₈) → l5(X₀, X₁, X₂, X₂, X₆, X₈) :|: 0 < X₂ ∧ 1 ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ 2 ≤ X₁+X₈ ∧ X₁ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₉₀: l9(X₀, X₁, X₂, X₃, X₆, X₈) → l5(X₀, X₁, X₂, X₃-X₁, X₆, X₈) :|: 1 ≤ X₈ ∧ 2 ≤ X₃+X₈ ∧ 2 ≤ X₂+X₈ ∧ 2 ≤ X₁+X₈ ∧ X₁ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₈₀: l1(X₀, X₁, X₂, X₃, X₆, X₈) → l3(X₀, X₁, X₂, X₃, X₆, X₈) :|: 0 < X₁ ∧ 0 < X₀ ∧ X₁ ≤ X₈ of depth 1:

new bound:

X₈+1 {O(n)}

MPRF:

l3 [X₁ ]
l1 [X₁+1 ]
l7 [X₁ ]
l8 [X₁ ]
l9 [X₁ ]
l5 [X₁ ]

MPRF for transition t₈₄: l3(X₀, X₁, X₂, X₃, X₆, X₈) → l7(X₀, X₁, X₂, X₃, X₆, X₈) :|: 0 < X₁ ∧ 1 ≤ X₈ ∧ 2 ≤ X₁+X₈ ∧ X₁ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₈ {O(n)}

MPRF:

l3 [X₁ ]
l1 [X₁ ]
l7 [X₁-1 ]
l8 [X₁-1 ]
l9 [X₁-1 ]
l5 [X₁-1 ]

MPRF for transition t₈₆: l5(X₀, X₁, X₂, X₃, X₆, X₈) → l9(X₀, X₁, X₂, X₃, X₆, X₈) :|: X₁ ≤ X₃ ∧ 1 ≤ X₈ ∧ 1 ≤ X₃+X₈ ∧ 2 ≤ X₂+X₈ ∧ 2 ≤ X₁+X₈ ∧ X₁ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₈+X₆+1 {O(n)}

MPRF:

l3 [X₀+X₁+X₈+1 ]
l1 [X₀+X₁+X₈+1 ]
l7 [X₀+X₁+X₈+1 ]
l8 [X₁+X₂+X₈+1 ]
l9 [X₁+X₃+X₈ ]
l5 [X₁+X₃+X₈+1 ]

MPRF for transition t₈₇: l5(X₀, X₁, X₂, X₃, X₆, X₈) → l1(X₁, X₃, X₂, X₃, X₆, X₈) :|: X₃ < X₁ ∧ 1 ≤ X₈ ∧ 1 ≤ X₃+X₈ ∧ 2 ≤ X₂+X₈ ∧ 2 ≤ X₁+X₈ ∧ X₁ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₈ {O(n)}

MPRF:

l3 [X₁ ]
l1 [X₁ ]
l7 [X₁ ]
l8 [X₁ ]
l9 [X₁ ]
l5 [X₁ ]

MPRF for transition t₈₈: l7(X₀, X₁, X₂, X₃, X₆, X₈) → l8(X₀, X₁, X₀, X₃, X₆, X₈) :|: 0 ≤ X₁ ∧ 1 ≤ X₈ ∧ 2 ≤ X₁+X₈ ∧ X₁ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₈+1 {O(n)}

MPRF:

l3 [X₁+1 ]
l1 [X₁+1 ]
l7 [X₁+1 ]
l8 [X₁ ]
l9 [X₁ ]
l5 [X₁ ]

MPRF for transition t₈₉: l8(X₀, X₁, X₂, X₃, X₆, X₈) → l5(X₀, X₁, X₂, X₂, X₆, X₈) :|: 0 < X₂ ∧ 1 ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ 2 ≤ X₁+X₈ ∧ X₁ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₈ {O(n)}

MPRF:

l3 [X₁ ]
l1 [X₁ ]
l7 [X₁ ]
l8 [X₁ ]
l9 [X₁-1 ]
l5 [X₁-1 ]

MPRF for transition t₉₀: l9(X₀, X₁, X₂, X₃, X₆, X₈) → l5(X₀, X₁, X₂, X₃-X₁, X₆, X₈) :|: 1 ≤ X₈ ∧ 2 ≤ X₃+X₈ ∧ 2 ≤ X₂+X₈ ∧ 2 ≤ X₁+X₈ ∧ X₁ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₆+X₈ {O(n)}

MPRF:

l3 [X₀+X₁ ]
l1 [X₀+X₁ ]
l7 [X₀+X₁ ]
l8 [X₀+X₁ ]
l9 [X₃+1 ]
l5 [X₁+X₃ ]

All Bounds

Timebounds

Overall timebound:2⋅X₆+8⋅X₈+8 {O(n)}
t₇₉: 1 {O(1)}
t₈₀: X₈+1 {O(n)}
t₈₁: 1 {O(1)}
t₈₂: 1 {O(1)}
t₈₃: 1 {O(1)}
t₈₄: X₈ {O(n)}
t₈₅: 1 {O(1)}
t₈₆: 2⋅X₈+X₆+1 {O(n)}
t₈₇: X₈ {O(n)}
t₈₈: X₈+1 {O(n)}
t₈₉: X₈ {O(n)}
t₉₀: X₆+X₈ {O(n)}

Costbounds

Overall costbound: 2⋅X₆+8⋅X₈+8 {O(n)}
t₇₉: 1 {O(1)}
t₈₀: X₈+1 {O(n)}
t₈₁: 1 {O(1)}
t₈₂: 1 {O(1)}
t₈₃: 1 {O(1)}
t₈₄: X₈ {O(n)}
t₈₅: 1 {O(1)}
t₈₆: 2⋅X₈+X₆+1 {O(n)}
t₈₇: X₈ {O(n)}
t₈₈: X₈+1 {O(n)}
t₈₉: X₈ {O(n)}
t₉₀: X₆+X₈ {O(n)}

Sizebounds

t₇₉, X₀: X₀ {O(n)}
t₇₉, X₁: X₁ {O(n)}
t₇₉, X₂: X₂ {O(n)}
t₇₉, X₃: X₃ {O(n)}
t₇₉, X₆: X₆ {O(n)}
t₇₉, X₈: X₈ {O(n)}
t₈₀, X₀: 2⋅X₈+X₆ {O(n)}
t₈₀, X₁: X₈ {O(n)}
t₈₀, X₂: 2⋅X₆+4⋅X₈+X₂ {O(n)}
t₈₀, X₃: 2⋅X₆+4⋅X₈+X₃ {O(n)}
t₈₀, X₆: X₆ {O(n)}
t₈₀, X₈: X₈ {O(n)}
t₈₁, X₀: 2⋅X₈+X₆ {O(n)}
t₈₁, X₁: 2⋅X₈ {O(n)}
t₈₁, X₂: 2⋅X₆+4⋅X₈+X₂ {O(n)}
t₈₁, X₃: 2⋅X₆+4⋅X₈+X₃ {O(n)}
t₈₁, X₆: 2⋅X₆ {O(n)}
t₈₁, X₈: 2⋅X₈ {O(n)}
t₈₂, X₀: X₆ {O(n)}
t₈₂, X₁: X₈ {O(n)}
t₈₂, X₂: X₂ {O(n)}
t₈₂, X₃: X₃ {O(n)}
t₈₂, X₆: X₆ {O(n)}
t₈₂, X₈: X₈ {O(n)}
t₈₃, X₀: X₆ {O(n)}
t₈₃, X₁: X₈ {O(n)}
t₈₃, X₂: X₂ {O(n)}
t₈₃, X₃: X₃ {O(n)}
t₈₃, X₆: X₆ {O(n)}
t₈₃, X₈: X₈ {O(n)}
t₈₄, X₀: 2⋅X₈+X₆ {O(n)}
t₈₄, X₁: X₈ {O(n)}
t₈₄, X₂: 2⋅X₆+4⋅X₈+X₂ {O(n)}
t₈₄, X₃: 2⋅X₆+4⋅X₈+X₃ {O(n)}
t₈₄, X₆: X₆ {O(n)}
t₈₄, X₈: X₈ {O(n)}
t₈₅, X₀: 2⋅X₆+2⋅X₈ {O(n)}
t₈₅, X₁: 3⋅X₈ {O(n)}
t₈₅, X₂: 2⋅X₂+2⋅X₆+4⋅X₈ {O(n)}
t₈₅, X₃: 2⋅X₃+2⋅X₆+4⋅X₈ {O(n)}
t₈₅, X₆: 3⋅X₆ {O(n)}
t₈₅, X₈: 3⋅X₈ {O(n)}
t₈₆, X₀: 2⋅X₈+X₆ {O(n)}
t₈₆, X₁: X₈ {O(n)}
t₈₆, X₂: 2⋅X₈+X₆ {O(n)}
t₈₆, X₃: 2⋅X₈+X₆ {O(n)}
t₈₆, X₆: X₆ {O(n)}
t₈₆, X₈: X₈ {O(n)}
t₈₇, X₀: 2⋅X₈ {O(n)}
t₈₇, X₁: X₈ {O(n)}
t₈₇, X₂: 2⋅X₆+4⋅X₈ {O(n)}
t₈₇, X₃: 2⋅X₆+4⋅X₈ {O(n)}
t₈₇, X₆: X₆ {O(n)}
t₈₇, X₈: X₈ {O(n)}
t₈₈, X₀: 2⋅X₈+X₆ {O(n)}
t₈₈, X₁: X₈ {O(n)}
t₈₈, X₂: 2⋅X₈+X₆ {O(n)}
t₈₈, X₃: 2⋅X₆+4⋅X₈+X₃ {O(n)}
t₈₈, X₆: X₆ {O(n)}
t₈₈, X₈: X₈ {O(n)}
t₈₉, X₀: 2⋅X₈+X₆ {O(n)}
t₈₉, X₁: X₈ {O(n)}
t₈₉, X₂: 2⋅X₈+X₆ {O(n)}
t₈₉, X₃: 2⋅X₈+X₆ {O(n)}
t₈₉, X₆: X₆ {O(n)}
t₈₉, X₈: X₈ {O(n)}
t₉₀, X₀: 2⋅X₈+X₆ {O(n)}
t₉₀, X₁: X₈ {O(n)}
t₉₀, X₂: 2⋅X₈+X₆ {O(n)}
t₉₀, X₃: 2⋅X₈+X₆ {O(n)}
t₉₀, X₆: X₆ {O(n)}
t₉₀, X₈: X₈ {O(n)}