KoAT2 Proof Output

Initial Problem

Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars:
Locations: lbl71, lbl81, start, start0, stop
Transitions:
t₅: lbl71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → lbl71(X₀, X₁, X₂, X₃+X₄, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₃ ≤ 1+X₂ ∧ X₄ ≤ 1 ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₄ ∧ X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₃ ≤ X₂ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈
t₆: lbl71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → lbl81(X₀, X₁, X₂, X₃-X₄, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₃ ≤ 1+X₂ ∧ X₄ ≤ 1 ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₄ ∧ X₉ ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₉ ∧ X₃ ≤ X₂ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈
t₄: lbl71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₃ ≤ 1+X₂ ∧ X₄ ≤ 1 ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₄ ∧ X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₁ ≤ X₂ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈
t₈: lbl81(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → lbl71(X₀, X₁, X₂, X₃+X₄, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₃ ≤ 1+X₂ ∧ 0 ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 1+X₄ ≤ 0 ∧ X₉ ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₉ ∧ X₃ ≤ X₂ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈
t₉: lbl81(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → lbl81(X₀, X₁, X₂, X₃-X₄, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₃ ≤ 1+X₂ ∧ 0 ≤ 1+X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₄ ≤ 0 ∧ X₉ ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₉ ∧ X₃ ≤ X₂ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈
t₇: lbl81(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₃ ≤ 1+X₂ ∧ 0 ≤ 1+X₄ ∧ 1+X₂ ≤ X₃ ∧ 1+X₄ ≤ 0 ∧ X₉ ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₉ ∧ X₁ ≤ X₂ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈
t₁: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → lbl71(X₀, X₁, X₂, 1+X₃, 1, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈
t₃: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → lbl81(X₀, X₁, X₂, 1+X₃, -1, X₅, X₆, X₇, X₈, X₉) :|: X₉ ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₉ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈
t₀: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → stop(X₀, X₁, X₂, X₃, 1, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈
t₂: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → stop(X₀, X₁, X₂, X₃, -1, X₅, X₆, X₇, X₈, X₉) :|: 1+X₂ ≤ X₁ ∧ X₉ ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₉ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈
t₁₀: start0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → start(X₀, X₁, X₂, X₁, X₅, X₅, X₂, X₈, X₈, X₀)

Preprocessing

Cut unsatisfiable transition [t₆: lbl71→lbl81; t₈: lbl81→lbl71]

Found invariant X₉ ≤ 0 ∧ X₉ ≤ 1+X₄ ∧ 1+X₄+X₉ ≤ 0 ∧ X₉ ≤ X₀ ∧ X₀+X₉ ≤ 0 ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈ ∧ X₆ ≤ X₂ ∧ X₃ ≤ 1+X₆ ∧ X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ 1+X₄ ≤ 0 ∧ 1+X₀+X₄ ≤ 0 ∧ 0 ≤ 1+X₄ ∧ X₀ ≤ 1+X₄ ∧ X₃ ≤ 1+X₂ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 0 for location lbl81

Found invariant X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈ ∧ 1+X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₄ ≤ 1 ∧ 0 ≤ 1+X₄ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ for location stop

Found invariant X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ for location start

Found invariant X₉ ≤ X₀ ∧ 1 ≤ X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₉ ∧ 2 ≤ X₀+X₉ ∧ X₀ ≤ X₉ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈ ∧ X₆ ≤ X₂ ∧ X₃ ≤ 1+X₆ ∧ X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₄ ≤ 1 ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ 1+X₂ ∧ 1+X₁ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ for location lbl71

Problem after Preprocessing

Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars:
Locations: lbl71, lbl81, start, start0, stop
Transitions:
t₅: lbl71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → lbl71(X₀, X₁, X₂, X₃+X₄, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₃ ≤ 1+X₂ ∧ X₄ ≤ 1 ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₄ ∧ X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₃ ≤ X₂ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈ ∧ X₃ ≤ 1+X₆ ∧ 1 ≤ X₉ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₆ ∧ X₄ ≤ X₉
t₄: lbl71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₃ ≤ 1+X₂ ∧ X₄ ≤ 1 ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₄ ∧ X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₁ ≤ X₂ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈ ∧ X₃ ≤ 1+X₆ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₉ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₀ ∧ X₁ ≤ X₆ ∧ X₄ ≤ X₉
t₉: lbl81(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → lbl81(X₀, X₁, X₂, X₃-X₄, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₃ ≤ 1+X₂ ∧ 0 ≤ 1+X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₄ ≤ 0 ∧ X₉ ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₉ ∧ X₃ ≤ X₂ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈ ∧ X₀ ≤ 1+X₄ ∧ X₃ ≤ 1+X₆ ∧ X₉ ≤ 1+X₄ ∧ 1+X₀+X₄ ≤ 0 ∧ 1+X₄+X₉ ≤ 0 ∧ X₀+X₉ ≤ 0 ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₆ ∧ X₉ ≤ 0
t₇: lbl81(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₃ ≤ 1+X₂ ∧ 0 ≤ 1+X₄ ∧ 1+X₂ ≤ X₃ ∧ 1+X₄ ≤ 0 ∧ X₉ ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₉ ∧ X₁ ≤ X₂ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈ ∧ X₀ ≤ 1+X₄ ∧ X₃ ≤ 1+X₆ ∧ X₉ ≤ 1+X₄ ∧ 1+X₀+X₄ ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ 1+X₄+X₉ ≤ 0 ∧ X₀+X₉ ≤ 0 ∧ X₁ ≤ X₆ ∧ X₉ ≤ 0
t₁: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → lbl71(X₀, X₁, X₂, 1+X₃, 1, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈
t₃: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → lbl81(X₀, X₁, X₂, 1+X₃, -1, X₅, X₆, X₇, X₈, X₉) :|: X₉ ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₉ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈
t₀: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → stop(X₀, X₁, X₂, X₃, 1, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈
t₂: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → stop(X₀, X₁, X₂, X₃, -1, X₅, X₆, X₇, X₈, X₉) :|: 1+X₂ ≤ X₁ ∧ X₉ ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₉ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈
t₁₀: start0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → start(X₀, X₁, X₂, X₁, X₅, X₅, X₂, X₈, X₈, X₀)

MPRF for transition t₉: lbl81(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → lbl81(X₀, X₁, X₂, X₃-X₄, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₃ ≤ 1+X₂ ∧ 0 ≤ 1+X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₄ ≤ 0 ∧ X₉ ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₉ ∧ X₃ ≤ X₂ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈ ∧ X₀ ≤ 1+X₄ ∧ X₃ ≤ 1+X₆ ∧ X₉ ≤ 1+X₄ ∧ 1+X₀+X₄ ≤ 0 ∧ 1+X₄+X₉ ≤ 0 ∧ X₀+X₉ ≤ 0 ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₆ ∧ X₉ ≤ 0 of depth 1:

new bound:

X₁+X₂+2 {O(n)}

MPRF:

• lbl81: [1+X₂-X₃]

MPRF for transition t₅: lbl71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → lbl71(X₀, X₁, X₂, X₃+X₄, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₃ ≤ 1+X₂ ∧ X₄ ≤ 1 ∧ 1 ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₄ ∧ X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₃ ≤ X₂ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₈ ≤ X₇ ∧ X₇ ≤ X₈ ∧ X₃ ≤ 1+X₆ ∧ 1 ≤ X₉ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₆ ∧ X₄ ≤ X₉ of depth 1:

new bound:

X₁+X₂+2 {O(n)}

MPRF:

• lbl71: [1+X₂-X₃]

All Bounds

Timebounds

Overall timebound:2⋅X₁+2⋅X₂+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₁+X₂+2 {O(n)}
t₇: 1 {O(1)}
t₉: X₁+X₂+2 {O(n)}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₁+2⋅X₂+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₁+X₂+2 {O(n)}
t₇: 1 {O(1)}
t₉: X₁+X₂+2 {O(n)}
t₁₀: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₁ {O(n)}
t₀, X₄: 1 {O(1)}
t₀, X₅: X₅ {O(n)}
t₀, X₆: X₂ {O(n)}
t₀, X₇: X₈ {O(n)}
t₀, X₈: X₈ {O(n)}
t₀, X₉: X₀ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₁+1 {O(n)}
t₁, X₄: 1 {O(1)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₂ {O(n)}
t₁, X₇: X₈ {O(n)}
t₁, X₈: X₈ {O(n)}
t₁, X₉: X₀ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₁ {O(n)}
t₂, X₄: 1 {O(1)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₂ {O(n)}
t₂, X₇: X₈ {O(n)}
t₂, X₈: X₈ {O(n)}
t₂, X₉: X₀ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₁+1 {O(n)}
t₃, X₄: 1 {O(1)}
t₃, X₅: X₅ {O(n)}
t₃, X₆: X₂ {O(n)}
t₃, X₇: X₈ {O(n)}
t₃, X₈: X₈ {O(n)}
t₃, X₉: X₀ {O(n)}
t₄, X₀: 2⋅X₀ {O(n)}
t₄, X₁: 2⋅X₁ {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 3⋅X₁+X₂+4 {O(n)}
t₄, X₄: 1 {O(1)}
t₄, X₅: 2⋅X₅ {O(n)}
t₄, X₆: 2⋅X₂ {O(n)}
t₄, X₇: 2⋅X₈ {O(n)}
t₄, X₈: 2⋅X₈ {O(n)}
t₄, X₉: 2⋅X₀ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: 2⋅X₁+X₂+3 {O(n)}
t₅, X₄: 1 {O(1)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₂ {O(n)}
t₅, X₇: X₈ {O(n)}
t₅, X₈: X₈ {O(n)}
t₅, X₉: X₀ {O(n)}
t₇, X₀: 2⋅X₀ {O(n)}
t₇, X₁: 2⋅X₁ {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₇, X₃: 3⋅X₁+X₂+4 {O(n)}
t₇, X₄: 1 {O(1)}
t₇, X₅: 2⋅X₅ {O(n)}
t₇, X₆: 2⋅X₂ {O(n)}
t₇, X₇: 2⋅X₈ {O(n)}
t₇, X₈: 2⋅X₈ {O(n)}
t₇, X₉: 2⋅X₀ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: 2⋅X₁+X₂+3 {O(n)}
t₉, X₄: 1 {O(1)}
t₉, X₅: X₅ {O(n)}
t₉, X₆: X₂ {O(n)}
t₉, X₇: X₈ {O(n)}
t₉, X₈: X₈ {O(n)}
t₉, X₉: X₀ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₁ {O(n)}
t₁₀, X₄: X₅ {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₀, X₆: X₂ {O(n)}
t₁₀, X₇: X₈ {O(n)}
t₁₀, X₈: X₈ {O(n)}
t₁₀, X₉: X₀ {O(n)}