KoAT2 Proof Output

Initial Problem

Start: f3
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃
Temp_Vars: A1, B1, C1, D1, E1, F1, G1, H1, Y, Z
Locations: f1, f10, f3, f4, f9
Transitions:
t₀: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f1(X₀, 1+X₁, X₃, B1, Y, Z, A1, C1, D1, E1, X₃, F1, X₁, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁
t₁₂: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f10(Y, 1+X₂₀, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₂, X₁₁, X₁₂, X₂, X₂₀, 0, X₂, 0, X₂, X₂, X₂₀, X₂₁, X₂₂, X₂₃) :|: 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ Y ∧ Y ≤ Z ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₁₃: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f10(Y, 1+X₂₀, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₂, X₁₁, X₁₂, X₂, X₂₀, 0, X₂, 0, X₂, X₂, X₂₀, X₂₁, X₂₂, X₂₃) :|: 1 ≤ X₂ ∧ 2 ≤ Y ∧ Y ≤ Z ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₁₄: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f10(Y, 1+X₂₀, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₂, X₁₁, X₁₂, X₂, X₂₀, 0, X₂, 0, X₂, X₂, X₂₀, X₂₁, X₂₂, X₂₃) :|: 1+X₂ ≤ 0 ∧ 2 ≤ Y ∧ Y ≤ Z ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₁₅: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f10(Y, 1+X₂₀, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₂, X₁₁, X₁₂, X₂, X₂₀, 0, X₂, 0, X₂, X₂, X₂₀, X₂₁, X₂₂, X₂₃) :|: 1 ≤ X₂ ∧ 1+X₂ ≤ 0 ∧ 2 ≤ Y ∧ Y ≤ Z ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₇: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f10(A1, Z, Y, X₃, X₄, X₅, X₆, X₇, X₈, X₉, Y, X₁₁, X₁₂, X₁₃, X₁₄, 0, Y, 0, Y, X₁₃, X₂₀-1, B1, X₂₀-1, X₂₃) :|: 1+X₁₃ ≤ C1 ∧ 1+C1 ≤ Y ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ 0 ≤ X₁₅ ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₂₀
t₈: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f10(A1, Z, Y, X₃, X₄, X₅, X₆, X₇, X₈, X₉, Y, X₁₁, X₁₂, X₁₃, X₁₄, 0, Y, 0, Y, X₁₃, X₂₀-1, B1, X₂₀-1, X₂₃) :|: 1+Y ≤ C1 ∧ 1+X₁₃ ≤ C1 ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ 0 ≤ X₁₅ ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₂₀
t₉: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f10(A1, Z, Y, X₃, X₄, X₅, X₆, X₇, X₈, X₉, Y, X₁₁, X₁₂, X₁₃, X₁₄, 0, Y, 0, Y, X₁₃, X₂₀-1, B1, X₂₀-1, X₂₃) :|: 1+C1 ≤ Y ∧ 1+C1 ≤ X₁₃ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ 0 ≤ X₁₅ ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₂₀
t₁₀: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f10(A1, Z, Y, X₃, X₄, X₅, X₆, X₇, X₈, X₉, Y, X₁₁, X₁₂, X₁₃, X₁₄, 0, Y, 0, Y, X₁₃, X₂₀-1, B1, X₂₀-1, X₂₃) :|: 1+Y ≤ C1 ∧ 1+C1 ≤ X₁₃ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ 0 ≤ X₁₅ ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₂₀
t₁₁: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f4(D1, X₁, X₂, X₃, X₄, X₅, X₆, X₇, E1, X₉, X₁₀, X₁₁, X₁₂, C1, X₁₄, B1, Y, Z, A1, F1, X₂₀, X₂₁, X₂₂, X₂₃) :|: 2 ≤ D1 ∧ X₁₅ ≤ X₁₃ ∧ X₁₃ ≤ X₁₅ ∧ 0 ≤ X₂₀
t₁₇: f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f1(X₀, 2, Y, C1, Z, A1, B1, D1, E1, F1, Y, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, G1) :|: 2 ≤ X₀
t₁₆: f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f4(D1, 0, 0, X₃, X₄, X₅, X₆, X₇, E1, X₉, X₁₀, X₁₁, X₁₂, C1, X₁₄, B1, Y, Z, A1, F1, X₂₀, X₂₁, X₂₂, X₂₃) :|: D1 ≤ 0 ∧ X₀ ≤ 0
t₁: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f10(A1, Z, Y, X₃, X₄, X₅, X₆, X₇, X₈, X₉, Y, X₁₁, X₁₂, X₁₃, X₁₄, 0, Y, 0, Y, X₁₃, X₂₀, X₂₁, X₂₂, X₂₃) :|: 1+X₁₃ ≤ B1 ∧ 1+B1 ≤ Y ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ 0 ≤ X₁₄ ∧ 0 ≤ X₁₅ ∧ X₁₅ ≤ 0
t₂: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f10(A1, Z, Y, X₃, X₄, X₅, X₆, X₇, X₈, X₉, Y, X₁₁, X₁₂, X₁₃, X₁₄, 0, Y, 0, Y, X₁₃, X₂₀, X₂₁, X₂₂, X₂₃) :|: 1+Y ≤ B1 ∧ 1+X₁₃ ≤ B1 ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ 0 ≤ X₁₄ ∧ 0 ≤ X₁₅ ∧ X₁₅ ≤ 0
t₃: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f10(A1, Z, Y, X₃, X₄, X₅, X₆, X₇, X₈, X₉, Y, X₁₁, X₁₂, X₁₃, X₁₄, 0, Y, 0, Y, X₁₃, X₂₀, X₂₁, X₂₂, X₂₃) :|: 1+B1 ≤ Y ∧ 1+B1 ≤ X₁₃ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ 0 ≤ X₁₄ ∧ 0 ≤ X₁₅ ∧ X₁₅ ≤ 0
t₄: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f10(A1, Z, Y, X₃, X₄, X₅, X₆, X₇, X₈, X₉, Y, X₁₁, X₁₂, X₁₃, X₁₄, 0, Y, 0, Y, X₁₃, X₂₀, X₂₁, X₂₂, X₂₃) :|: 1+Y ≤ B1 ∧ 1+B1 ≤ X₁₃ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ 0 ≤ X₁₄ ∧ 0 ≤ X₁₅ ∧ X₁₅ ≤ 0
t₅: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f4(E1, D1, F1, X₃, X₄, X₅, X₆, X₇, G1, X₉, X₁₀, X₁₁, X₁₂, C1, X₁₄, B1, Y, Z, A1, H1, X₂₀, X₂₁, X₂₂, X₂₃) :|: 1+F1 ≤ 0 ∧ 2 ≤ E1 ∧ E1 ≤ D1 ∧ X₁₅ ≤ X₁₃ ∧ X₁₃ ≤ X₁₅ ∧ 0 ≤ X₁₄
t₆: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → f4(E1, D1, F1, X₃, X₄, X₅, X₆, X₇, G1, X₉, X₁₀, X₁₁, X₁₂, C1, X₁₄, B1, Y, Z, A1, H1, X₂₀, X₂₁, X₂₂, X₂₃) :|: 1 ≤ F1 ∧ 2 ≤ E1 ∧ E1 ≤ D1 ∧ X₁₅ ≤ X₁₃ ∧ X₁₃ ≤ X₁₅ ∧ 0 ≤ X₁₄

Preprocessing

Cut unreachable locations [f9] from the program graph

Cut unsatisfiable transition [t₁₂: f1→f10; t₁₅: f1→f10]

Eliminate variables [E1; F1; G1; X₄; X₅; X₆; X₇; X₈; X₉; X₁₀; X₁₁; X₁₂; X₁₄; X₁₆; X₁₇; X₁₈; X₁₉; X₂₁; X₂₂; X₂₃] that do not contribute to the problem

Found invariant X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f1

Found invariant X₅ ≤ 0 ∧ 2+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₀ for location f10

Problem after Preprocessing

Start: f3
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: A1, B1, C1, D1, Y, Z
Locations: f1, f10, f3, f4
Transitions:
t₃₁: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f1(X₀, 1+X₁, X₃, B1, X₄, X₅, X₆) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀
t₃₂: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f10(Y, 1+X₆, X₂, X₃, X₂, 0, X₆) :|: 1 ≤ X₂ ∧ 2 ≤ Y ∧ Y ≤ Z ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀
t₃₃: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f10(Y, 1+X₆, X₂, X₃, X₂, 0, X₆) :|: 1+X₂ ≤ 0 ∧ 2 ≤ Y ∧ Y ≤ Z ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀
t₃₄: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f10(A1, Z, Y, X₃, X₄, 0, X₆-1) :|: 1+X₄ ≤ C1 ∧ 1+C1 ≤ Y ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ 0 ≤ X₆ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₅ ∧ 2+X₅ ≤ X₀
t₃₅: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f10(A1, Z, Y, X₃, X₄, 0, X₆-1) :|: 1+Y ≤ C1 ∧ 1+X₄ ≤ C1 ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ 0 ≤ X₆ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₅ ∧ 2+X₅ ≤ X₀
t₃₆: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f10(A1, Z, Y, X₃, X₄, 0, X₆-1) :|: 1+C1 ≤ Y ∧ 1+C1 ≤ X₄ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ 0 ≤ X₆ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₅ ∧ 2+X₅ ≤ X₀
t₃₇: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f10(A1, Z, Y, X₃, X₄, 0, X₆-1) :|: 1+Y ≤ C1 ∧ 1+C1 ≤ X₄ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ 0 ≤ X₆ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₅ ∧ 2+X₅ ≤ X₀
t₃₈: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f4(D1, X₁, X₂, X₃, C1, B1, X₆) :|: 2 ≤ D1 ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ 0 ≤ X₆ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₅ ∧ 2+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₅ ≤ 0
t₃₉: f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f1(X₀, 2, Y, C1, X₄, X₅, X₆) :|: 2 ≤ X₀
t₄₀: f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f4(D1, 0, 0, X₃, C1, B1, X₆) :|: D1 ≤ 0 ∧ X₀ ≤ 0

MPRF for transition t₃₁: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f1(X₀, 1+X₁, X₃, B1, X₄, X₅, X₆) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₀+3 {O(n)}

MPRF:

• f1: [1+X₀-X₁]

MPRF for transition t₃₄: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f10(A1, Z, Y, X₃, X₄, 0, X₆-1) :|: 1+X₄ ≤ C1 ∧ 1+C1 ≤ Y ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ 0 ≤ X₆ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₅ ∧ 2+X₅ ≤ X₀ of depth 1:

new bound:

4⋅X₆+2 {O(n)}

MPRF:

• f10: [1+X₆]

MPRF for transition t₃₅: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f10(A1, Z, Y, X₃, X₄, 0, X₆-1) :|: 1+Y ≤ C1 ∧ 1+X₄ ≤ C1 ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ 0 ≤ X₆ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₅ ∧ 2+X₅ ≤ X₀ of depth 1:

new bound:

4⋅X₆+2 {O(n)}

MPRF:

• f10: [1+X₆]

MPRF for transition t₃₆: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f10(A1, Z, Y, X₃, X₄, 0, X₆-1) :|: 1+C1 ≤ Y ∧ 1+C1 ≤ X₄ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ 0 ≤ X₆ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₅ ∧ 2+X₅ ≤ X₀ of depth 1:

new bound:

4⋅X₆+2 {O(n)}

MPRF:

• f10: [1+X₆]

MPRF for transition t₃₇: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f10(A1, Z, Y, X₃, X₄, 0, X₆-1) :|: 1+Y ≤ C1 ∧ 1+C1 ≤ X₄ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ 0 ≤ X₆ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₅ ∧ 2+X₅ ≤ X₀ of depth 1:

new bound:

4⋅X₆+2 {O(n)}

MPRF:

• f10: [1+X₆]

All Bounds

Timebounds

Overall timebound:16⋅X₆+X₀+16 {O(n)}
t₃₁: X₀+3 {O(n)}
t₃₂: 1 {O(1)}
t₃₃: 1 {O(1)}
t₃₄: 4⋅X₆+2 {O(n)}
t₃₅: 4⋅X₆+2 {O(n)}
t₃₆: 4⋅X₆+2 {O(n)}
t₃₇: 4⋅X₆+2 {O(n)}
t₃₈: 1 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 1 {O(1)}

Costbounds

Overall costbound: 16⋅X₆+X₀+16 {O(n)}
t₃₁: X₀+3 {O(n)}
t₃₂: 1 {O(1)}
t₃₃: 1 {O(1)}
t₃₄: 4⋅X₆+2 {O(n)}
t₃₅: 4⋅X₆+2 {O(n)}
t₃₆: 4⋅X₆+2 {O(n)}
t₃₇: 4⋅X₆+2 {O(n)}
t₃₈: 1 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 1 {O(1)}

Sizebounds

t₃₁, X₀: X₀ {O(n)}
t₃₁, X₁: X₀+5 {O(n)}
t₃₁, X₄: X₄ {O(n)}
t₃₁, X₅: X₅ {O(n)}
t₃₁, X₆: X₆ {O(n)}
t₃₂, X₁: 2⋅X₆+2 {O(n)}
t₃₂, X₅: 0 {O(1)}
t₃₂, X₆: 2⋅X₆ {O(n)}
t₃₃, X₁: 2⋅X₆+2 {O(n)}
t₃₃, X₅: 0 {O(1)}
t₃₃, X₆: 2⋅X₆ {O(n)}
t₃₄, X₅: 0 {O(1)}
t₃₄, X₆: 4⋅X₆+1 {O(n)}
t₃₅, X₅: 0 {O(1)}
t₃₅, X₆: 4⋅X₆+1 {O(n)}
t₃₆, X₅: 0 {O(1)}
t₃₆, X₆: 4⋅X₆+1 {O(n)}
t₃₇, X₅: 0 {O(1)}
t₃₇, X₆: 4⋅X₆+1 {O(n)}
t₃₈, X₆: 16⋅X₆+4 {O(n)}
t₃₉, X₀: X₀ {O(n)}
t₃₉, X₁: 2 {O(1)}
t₃₉, X₄: X₄ {O(n)}
t₃₉, X₅: X₅ {O(n)}
t₃₉, X₆: X₆ {O(n)}
t₄₀, X₁: 0 {O(1)}
t₄₀, X₂: 0 {O(1)}
t₄₀, X₃: X₃ {O(n)}
t₄₀, X₆: X₆ {O(n)}