KoAT2 Proof Output

Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: I
Locations: f0, f10, f18, f22, f34, f43
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f10(I, 0, X₂, X₃, X₄, X₅, X₆, X₇)
t₁: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f10(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₁ ≤ X₂
t₉: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f18(X₀, X₁, X₂, X₂, 0, X₅, X₆, X₇) :|: X₂ ≤ X₁
t₂: f18(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f22(X₀, X₁, X₂, X₃, X₄, X₄, 1+X₄, X₇) :|: 2+X₄ ≤ X₃
t₈: f18(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f34(X₀, X₁, X₂, X₃, 0, X₅, X₆, X₇) :|: X₃ ≤ 1+X₄
t₇: f22(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f18(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, I) :|: X₃ ≤ X₆
t₃: f22(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f22(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆, X₇) :|: 1+X₆ ≤ X₃
t₄: f22(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f22(X₀, X₁, X₂, X₃, X₄, X₆, 1+X₆, X₇) :|: 1+X₆ ≤ X₃
t₅: f34(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f34(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, X₇) :|: 2+X₄ ≤ X₃
t₆: f34(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → f43(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₃ ≤ 1+X₄

Preprocessing

Eliminate variables [I; X₀; X₅; X₇] that do not contribute to the problem

Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location f18

Found invariant 0 ≤ X₀ for location f10

Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₂ ≤ 1+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location f43

Found invariant X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f22

Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location f34

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: f0, f10, f18, f22, f34, f43
Transitions:
t₂₂: f0(X₀, X₁, X₂, X₃, X₄) → f10(0, X₁, X₂, X₃, X₄)
t₂₃: f10(X₀, X₁, X₂, X₃, X₄) → f10(1+X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂₄: f10(X₀, X₁, X₂, X₃, X₄) → f18(X₀, X₁, X₁, 0, X₄) :|: X₁ ≤ X₀ ∧ 0 ≤ X₀
t₂₅: f18(X₀, X₁, X₂, X₃, X₄) → f22(X₀, X₁, X₂, X₃, 1+X₃) :|: 2+X₃ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₃
t₂₆: f18(X₀, X₁, X₂, X₃, X₄) → f34(X₀, X₁, X₂, 0, X₄) :|: X₂ ≤ 1+X₃ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₃
t₂₇: f22(X₀, X₁, X₂, X₃, X₄) → f18(X₀, X₁, X₂, 1+X₃, X₄) :|: X₂ ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 2+X₃ ≤ X₁ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₃
t₂₈: f22(X₀, X₁, X₂, X₃, X₄) → f22(X₀, X₁, X₂, X₃, 1+X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 2+X₃ ≤ X₁ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₃
t₂₉: f22(X₀, X₁, X₂, X₃, X₄) → f22(X₀, X₁, X₂, X₃, 1+X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 2+X₃ ≤ X₁ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₃
t₃₀: f34(X₀, X₁, X₂, X₃, X₄) → f34(X₀, X₁, X₂, 1+X₃, X₄) :|: 2+X₃ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₃
t₃₁: f34(X₀, X₁, X₂, X₃, X₄) → f43(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1+X₃ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₃

MPRF for transition t₂₃: f10(X₀, X₁, X₂, X₃, X₄) → f10(1+X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

• f10: [X₁-X₀]

MPRF for transition t₂₅: f18(X₀, X₁, X₂, X₃, X₄) → f22(X₀, X₁, X₂, X₃, 1+X₃) :|: 2+X₃ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

• f18: [X₀-1-X₃]
• f22: [X₀-2-X₃]

MPRF for transition t₂₇: f22(X₀, X₁, X₂, X₃, X₄) → f18(X₀, X₁, X₂, 1+X₃, X₄) :|: X₂ ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 2+X₃ ≤ X₁ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

2⋅X₁+1 {O(n)}

MPRF:

• f18: [X₂-1-X₃]
• f22: [X₂-1-X₃]

MPRF for transition t₂₈: f22(X₀, X₁, X₂, X₃, X₄) → f22(X₀, X₁, X₂, X₃, 1+X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 2+X₃ ≤ X₁ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

8⋅X₁⋅X₁+8⋅X₁+1 {O(n^2)}

MPRF:

• f18: [X₂-X₃]
• f22: [1+X₂-X₄]

MPRF for transition t₂₉: f22(X₀, X₁, X₂, X₃, X₄) → f22(X₀, X₁, X₂, X₃, 1+X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 2+X₃ ≤ X₁ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

4⋅X₁⋅X₁+4⋅X₁ {O(n^2)}

MPRF:

• f18: [X₂]
• f22: [1+X₂-X₄]

Cut unsatisfiable transition [t₂₇: f22→f18; t₆₃: f22→f18]

Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location f18

Found invariant 0 ≤ X₀ for location f10

Found invariant X₄ ≤ 1+X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f22

Found invariant X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 2 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 4 ≤ X₁+X₄ ∧ 4 ≤ X₀+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f22_v1

Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location f34

MPRF for transition t₃₀: f34(X₀, X₁, X₂, X₃, X₄) → f34(X₀, X₁, X₂, 1+X₃, X₄) :|: 2+X₃ ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

2⋅X₁+1 {O(n)}

MPRF:

• f34: [1+X₀-X₃]

All Bounds

Timebounds

Overall timebound:12⋅X₁⋅X₁+18⋅X₁+8 {O(n^2)}
t₂₂: 1 {O(1)}
t₂₃: X₁ {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₁+1 {O(n)}
t₂₆: 1 {O(1)}
t₂₇: 2⋅X₁+1 {O(n)}
t₂₈: 8⋅X₁⋅X₁+8⋅X₁+1 {O(n^2)}
t₂₉: 4⋅X₁⋅X₁+4⋅X₁ {O(n^2)}
t₃₀: 2⋅X₁+1 {O(n)}
t₃₁: 1 {O(1)}

Costbounds

Overall costbound: 12⋅X₁⋅X₁+18⋅X₁+8 {O(n^2)}
t₂₂: 1 {O(1)}
t₂₃: X₁ {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₁+1 {O(n)}
t₂₆: 1 {O(1)}
t₂₇: 2⋅X₁+1 {O(n)}
t₂₈: 8⋅X₁⋅X₁+8⋅X₁+1 {O(n^2)}
t₂₉: 4⋅X₁⋅X₁+4⋅X₁ {O(n^2)}
t₃₀: 2⋅X₁+1 {O(n)}
t₃₁: 1 {O(1)}

Sizebounds

t₂₂, X₀: 0 {O(1)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₃, X₀: X₁ {O(n)}
t₂₃, X₁: X₁ {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₄, X₀: X₁ {O(n)}
t₂₄, X₁: 2⋅X₁ {O(n)}
t₂₄, X₂: 2⋅X₁ {O(n)}
t₂₄, X₃: 0 {O(1)}
t₂₄, X₄: 2⋅X₄ {O(n)}
t₂₅, X₀: X₁ {O(n)}
t₂₅, X₁: 2⋅X₁ {O(n)}
t₂₅, X₂: 2⋅X₁ {O(n)}
t₂₅, X₃: 2⋅X₁+1 {O(n)}
t₂₅, X₄: 2⋅X₁+3 {O(n)}
t₂₆, X₀: 2⋅X₁ {O(n)}
t₂₆, X₁: 4⋅X₁ {O(n)}
t₂₆, X₂: 4⋅X₁ {O(n)}
t₂₆, X₃: 0 {O(1)}
t₂₆, X₄: 24⋅X₁⋅X₁+2⋅X₄+28⋅X₁+8 {O(n^2)}
t₂₇, X₀: X₁ {O(n)}
t₂₇, X₁: 2⋅X₁ {O(n)}
t₂₇, X₂: 2⋅X₁ {O(n)}
t₂₇, X₃: 2⋅X₁+1 {O(n)}
t₂₇, X₄: 24⋅X₁⋅X₁+28⋅X₁+8 {O(n^2)}
t₂₈, X₀: X₁ {O(n)}
t₂₈, X₁: 2⋅X₁ {O(n)}
t₂₈, X₂: 2⋅X₁ {O(n)}
t₂₈, X₃: 2⋅X₁+1 {O(n)}
t₂₈, X₄: 12⋅X₁⋅X₁+14⋅X₁+4 {O(n^2)}
t₂₉, X₀: X₁ {O(n)}
t₂₉, X₁: 2⋅X₁ {O(n)}
t₂₉, X₂: 2⋅X₁ {O(n)}
t₂₉, X₃: 2⋅X₁+1 {O(n)}
t₂₉, X₄: 12⋅X₁⋅X₁+14⋅X₁+4 {O(n^2)}
t₃₀, X₀: 2⋅X₁ {O(n)}
t₃₀, X₁: 4⋅X₁ {O(n)}
t₃₀, X₂: 4⋅X₁ {O(n)}
t₃₀, X₃: 2⋅X₁+1 {O(n)}
t₃₀, X₄: 24⋅X₁⋅X₁+2⋅X₄+28⋅X₁+8 {O(n^2)}
t₃₁, X₀: 4⋅X₁ {O(n)}
t₃₁, X₁: 8⋅X₁ {O(n)}
t₃₁, X₂: 8⋅X₁ {O(n)}
t₃₁, X₃: 2⋅X₁+1 {O(n)}
t₃₁, X₄: 48⋅X₁⋅X₁+4⋅X₄+56⋅X₁+16 {O(n^2)}