KoAT2 Proof Output

Initial Problem

Start: start
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, X₂₄, X₂₅, X₂₆
Temp_Vars: B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1, O1, P1, Q1, R1
Locations: f1, f10, f19, f2, f23, f26, f41, f53, f63, f66, f69, start
Transitions:
t₂₀: 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, X₂₄, X₂₅, X₂₆) → 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, X₂₄, X₂₅, X₂₆) :|: X₁ ≤ 0
t₁: 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, X₂₄, X₂₅, X₂₆) → f19(X₀, X₁, X₂, X₃, B1, Q1, D1, G1, L1, 1, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 1+B1*X₃ ≤ 2⋅B1*F1+F1 ∧ 1+B1*X₃ ≤ 2⋅B1*H1+H1 ∧ 1+X₂ ≤ B1*I1*X₃+I1 ∧ 1+B1*I1*X₃ ≤ 2⋅B1*J1*K1+K1 ∧ 1+X₂ ≤ B1*J1*X₃+J1 ∧ 1+X₂ ≤ B1*M1*X₃+M1 ∧ 1+B1*M1*X₃ ≤ 2⋅B1*N1*O1+O1 ∧ 1+X₂ ≤ B1*N1*X₃+N1 ∧ 1+X₂ ≤ B1*P1*X₃+P1 ∧ 1+X₂ ≤ B1*R1*X₃+R1 ∧ 1+X₃ ≤ 3⋅C1 ∧ 1+X₃ ≤ 3⋅E1 ∧ 1 ≤ X₁ ∧ 2⋅B1*F1 ≤ B1*X₃ ∧ 2⋅B1*H1 ≤ B1*X₃ ∧ 2⋅B1*J1*K1 ≤ B1*I1*X₃ ∧ B1*I1*X₃ ≤ X₂ ∧ B1*J1*X₃ ≤ X₂ ∧ 2⋅B1*N1*O1 ≤ B1*M1*X₃ ∧ B1*M1*X₃ ≤ X₂ ∧ B1*N1*X₃ ≤ X₂ ∧ B1*P1*X₃ ≤ X₂ ∧ B1*R1*X₃ ≤ X₂ ∧ D1 ≤ C1 ∧ 2⋅C1 ≤ X₃ ∧ E1 ≤ D1 ∧ 2⋅E1 ≤ X₃ ∧ G1 ≤ F1 ∧ H1 ≤ G1 ∧ L1 ≤ K1 ∧ O1 ≤ L1 ∧ Q1 ≤ P1 ∧ R1 ≤ Q1
t₂: f19(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 1+X₁₀ ≤ X₉ ∧ X₁₀ ≤ X₇
t₅: f19(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f41(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, B1, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 1+X₇ ≤ 3⋅D1 ∧ 1+X₇ ≤ 3⋅Q1 ∧ D1 ≤ B1 ∧ B1 ≤ Q1 ∧ 2⋅D1 ≤ X₇ ∧ 2⋅Q1 ≤ X₇ ∧ X₁₀ ≤ X₇ ∧ X₉ ≤ X₁₀
t₁₉: f19(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f53(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 1+X₇ ≤ X₁₀
t₂₁: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f10(X₀, X₁, X₂, 1, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 1+X₀ ≤ X₁
t₀: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f2(X₀, 1+X₁, B1*X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: X₁ ≤ X₀
t₃: f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f26(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 2+X₁₁ ≤ X₆+X₁₀
t₁₈: f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f41(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, B1, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: X₆+X₁₀ ≤ 1+X₁₁ ∧ 1+X₇ ≤ 3⋅D1 ∧ 1+X₇ ≤ 3⋅Q1 ∧ D1 ≤ B1 ∧ B1 ≤ Q1 ∧ 2⋅D1 ≤ X₇ ∧ 2⋅Q1 ≤ X₇
t₁₇: f26(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, 2+X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 1+X₈ ≤ X₁₂
t₄: f26(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f26(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₇+X₁₂, X₉+X₁₂-X₁₀, B1, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: X₁₂ ≤ X₈
t₁₅: f41(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f19(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉+X₁₅, X₆+X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: X₆ ≤ X₁₅ ∧ X₉ ≤ X₁₅
t₁₆: f41(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f19(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉+X₁₅, X₆+X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 1+X₁₅ ≤ X₆
t₆: f41(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f41(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉-X₁₅, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, B1, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 1+X₁₅ ≤ 3⋅D1 ∧ 1+X₁₅ ≤ 3⋅Q1 ∧ 1+X₁₅ ≤ X₉ ∧ D1 ≤ B1 ∧ B1 ≤ Q1 ∧ 2⋅D1 ≤ X₁₅ ∧ 2⋅Q1 ≤ X₁₅ ∧ X₆ ≤ X₁₅
t₁₄: f53(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f10(X₀, X₁-1, X₂, X₃*X₄, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: X₇ ≤ X₁₆
t₇: f53(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f63(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, 2⋅X₁₆, B1, Q1, D1, G1, 1, 0, X₂₄, X₂₅, X₂₆) :|: 1+X₁₆ ≤ X₇
t₁₃: f63(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f53(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₇, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 1+X₁₆ ≤ X₁₂
t₈: f63(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f66(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: X₁₂ ≤ X₁₆
t₁₂: f66(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f63(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₆+X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₂₂, X₂₀, X₂₁, X₂₀*X₂₂+X₂₂-X₂₁*X₂₃, X₂₀*X₂₃+X₂₁*X₂₂+X₂₃, X₂₄, X₂₅, X₂₆) :|: X₆+X₁₂ ≤ 1+X₁₁
t₉: f66(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 2+X₁₁ ≤ X₆+X₁₂
t₁₁: f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f66(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, 2+X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 1+X₈ ≤ X₁₀
t₁₀: f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f69(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀+X₁₇, X₁₁, X₁₂, X₁₃, B1*X₂₂-Q1*X₂₃, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₁₀, X₁₀+X₁₆, D1*X₂₂+G1*X₂₃) :|: X₁₀ ≤ X₈
t₂₂: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) → f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆)

Preprocessing

Eliminate variables [X₅; X₁₃; X₁₄; X₁₈; X₁₉; X₂₀; X₂₁; X₂₂; X₂₃; X₂₄; X₂₅; X₂₆] that do not contribute to the problem

Found invariant 1 ≤ 0 for location f19

Found invariant 1 ≤ 0 for location f66

Found invariant 1 ≤ 0 for location f41

Found invariant 1 ≤ 0 for location f63

Found invariant 1 ≤ 0 for location f69

Found invariant 1 ≤ 0 for location f23

Found invariant X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ 1+X₀ ≤ X₁ for location f10

Found invariant X₃ ≤ 1 ∧ X₁+X₃ ≤ 1 ∧ X₀+X₃ ≤ 0 ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ X₁ ≤ 0 ∧ 1+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location f1

Found invariant 1 ≤ 0 for location f53

Found invariant 1 ≤ 0 for location f26

Cut unsatisfiable transition [t₄₉: f10→f19; t₅₀: f19→f23; t₅₁: f19→f41; t₅₂: f19→f53; t₅₅: f23→f26; t₅₆: f23→f41; t₅₇: f26→f23; t₅₈: f26→f26; t₅₉: f41→f19; t₆₀: f41→f19; t₆₁: f41→f41; t₆₂: f53→f10; t₆₃: f53→f63; t₆₄: f63→f53; t₆₅: f63→f66; t₆₆: f66→f63; t₆₇: f66→f69; t₆₈: f69→f66; t₆₉: f69→f69]

Cut unreachable locations [f19; f23; f26; f41; f53; f63; f66; f69] from the program graph

Eliminate variables [B1; X₂; X₄; X₅; X₆; X₇; X₈; X₉; X₁₀; X₁₁; X₁₂; X₁₃; X₁₄] that do not contribute to the problem

Problem after Preprocessing

Start: start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: f1, f10, f2, start
Transitions:
t₁₁₉: f10(X₀, X₁, X₂) → f1(X₀, X₁, X₂) :|: X₁ ≤ 0
t₁₂₀: f2(X₀, X₁, X₂) → f10(X₀, X₁, 1) :|: 1+X₀ ≤ X₁
t₁₂₁: f2(X₀, X₁, X₂) → f2(X₀, 1+X₁, X₂) :|: X₁ ≤ X₀
t₁₂₂: start(X₀, X₁, X₂) → f2(X₀, X₁, X₂)

MPRF for transition t₁₂₁: f2(X₀, X₁, X₂) → f2(X₀, 1+X₁, X₂) :|: X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

• f2: [1+X₀-X₁]

All Bounds

Timebounds

Overall timebound:X₀+X₁+4 {O(n)}
t₁₁₉: 1 {O(1)}
t₁₂₀: 1 {O(1)}
t₁₂₁: X₀+X₁+1 {O(n)}
t₁₂₂: 1 {O(1)}

Costbounds

Overall costbound: X₀+X₁+4 {O(n)}
t₁₁₉: 1 {O(1)}
t₁₂₀: 1 {O(1)}
t₁₂₁: X₀+X₁+1 {O(n)}
t₁₂₂: 1 {O(1)}

Sizebounds

t₁₁₉, X₀: 2⋅X₀ {O(n)}
t₁₁₉, X₁: 3⋅X₁+X₀+1 {O(n)}
t₁₁₉, X₂: 1 {O(1)}
t₁₂₀, X₀: 2⋅X₀ {O(n)}
t₁₂₀, X₁: 3⋅X₁+X₀+1 {O(n)}
t₁₂₀, X₂: 1 {O(1)}
t₁₂₁, X₀: X₀ {O(n)}
t₁₂₁, X₁: 2⋅X₁+X₀+1 {O(n)}
t₁₂₁, X₂: X₂ {O(n)}
t₁₂₂, X₀: X₀ {O(n)}
t₁₂₂, X₁: X₁ {O(n)}
t₁₂₂, X₂: X₂ {O(n)}