Initial Problem

Start: l0
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: l0, l1, l2, l3, l4
Transitions:
t₁₇: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l1(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: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l3(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
t₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l1(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) :|: X₁+1 ≤ X₀ ∧ 0 ≤ X₁
t₁₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l2(Y, X₂₀+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₂, X₁₁, X₁₂, X₂, X₂₀, 0, X₂, 0, X₂, X₂, X₂₀, X₂₁, X₂₂, X₂₃) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ Y ≤ Z ∧ 2 ≤ Y ∧ 1 ≤ X₂ ∧ X₂+1 ≤ 0
t₁₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l2(Y, X₂₀+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₂, X₁₁, X₁₂, X₂, X₂₀, 0, X₂, 0, X₂, X₂, X₂₀, X₂₁, X₂₂, X₂₃) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ Y ≤ Z ∧ 2 ≤ Y ∧ 1 ≤ X₂
t₁₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l2(Y, X₂₀+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₂, X₁₁, X₁₂, X₂, X₂₀, 0, X₂, 0, X₂, X₂, X₂₀, X₂₁, X₂₂, X₂₃) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ Y ≤ Z ∧ 2 ≤ Y ∧ X₂+1 ≤ 0
t₁₅: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l2(Y, X₂₀+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₂, X₁₁, X₁₂, X₂, X₂₀, 0, X₂, 0, X₂, X₂, X₂₀, X₂₁, X₂₂, X₂₃) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ Y ≤ Z ∧ 2 ≤ Y ∧ X₂+1 ≤ 0 ∧ 1 ≤ X₂
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l2(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) :|: X₁₃+1 ≤ C1 ∧ 0 ≤ X₂₀ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ C1+1 ≤ Y ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₁₅
t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l2(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) :|: X₁₃+1 ≤ C1 ∧ 0 ≤ X₂₀ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ Y+1 ≤ C1 ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₁₅
t₉: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l2(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) :|: C1+1 ≤ X₁₃ ∧ 0 ≤ X₂₀ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ C1+1 ≤ Y ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₁₅
t₁₀: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l2(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) :|: C1+1 ≤ X₁₃ ∧ 0 ≤ X₂₀ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ Y+1 ≤ C1 ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₁₅
t₁₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l3(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 ∧ 0 ≤ X₂₀ ∧ X₁₅ ≤ X₁₃ ∧ X₁₃ ≤ X₁₅
t₁: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l2(A1, Z, Y, X₃, X₄, X₅, X₆, X₇, X₈, X₉, Y, X₁₁, X₁₂, X₁₃, X₁₄, 0, Y, 0, Y, X₁₃, X₂₀, X₂₁, X₂₂, X₂₃) :|: X₁₃+1 ≤ B1 ∧ 0 ≤ X₁₄ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ B1+1 ≤ Y ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₁₅
t₂: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l2(A1, Z, Y, X₃, X₄, X₅, X₆, X₇, X₈, X₉, Y, X₁₁, X₁₂, X₁₃, X₁₄, 0, Y, 0, Y, X₁₃, X₂₀, X₂₁, X₂₂, X₂₃) :|: X₁₃+1 ≤ B1 ∧ 0 ≤ X₁₄ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ Y+1 ≤ B1 ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₁₅
t₃: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l2(A1, Z, Y, X₃, X₄, X₅, X₆, X₇, X₈, X₉, Y, X₁₁, X₁₂, X₁₃, X₁₄, 0, Y, 0, Y, X₁₃, X₂₀, X₂₁, X₂₂, X₂₃) :|: B1+1 ≤ X₁₃ ∧ 0 ≤ X₁₄ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ B1+1 ≤ Y ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₁₅
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l2(A1, Z, Y, X₃, X₄, X₅, X₆, X₇, X₈, X₉, Y, X₁₁, X₁₂, X₁₃, X₁₄, 0, Y, 0, Y, X₁₃, X₂₀, X₂₁, X₂₂, X₂₃) :|: B1+1 ≤ X₁₃ ∧ 0 ≤ X₁₄ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ Y+1 ≤ B1 ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₁₅
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l3(E1, D1, F1, X₃, X₄, X₅, X₆, X₇, G1, X₉, X₁₀, X₁₁, X₁₂, C1, X₁₄, B1, Y, Z, A1, H1, X₂₀, X₂₁, X₂₂, X₂₃) :|: 0 ≤ X₁₄ ∧ 2 ≤ E1 ∧ E1 ≤ D1 ∧ F1+1 ≤ 0 ∧ X₁₅ ≤ X₁₃ ∧ X₁₃ ≤ X₁₅
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃) → l3(E1, D1, F1, X₃, X₄, X₅, X₆, X₇, G1, X₉, X₁₀, X₁₁, X₁₂, C1, X₁₄, B1, Y, Z, A1, H1, X₂₀, X₂₁, X₂₂, X₂₃) :|: 0 ≤ X₁₄ ∧ 2 ≤ E1 ∧ E1 ≤ D1 ∧ 1 ≤ F1 ∧ X₁₅ ≤ X₁₃ ∧ X₁₃ ≤ X₁₅

Preprocessing

Cut unreachable locations [l4] from the program graph

Cut unsatisfiable transition t₁₂: l1→l2

Cut unsatisfiable transition t₁₅: l1→l2

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 X₁₅ ≤ 0 ∧ 2+X₁₅ ≤ X₀ ∧ 0 ≤ X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₀ for location l2

Found invariant X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₁₃, X₁₅, X₂₀
Temp_Vars: A1, B1, C1, D1, Y, Z
Locations: l0, l1, l2, l3
Transitions:
t₃₄: l0(X₀, X₁, X₂, X₃, X₁₃, X₁₅, X₂₀) → l1(X₀, 2, Y, C1, X₁₃, X₁₅, X₂₀) :|: 2 ≤ X₀
t₃₃: l0(X₀, X₁, X₂, X₃, X₁₃, X₁₅, X₂₀) → l3(D1, 0, 0, X₃, C1, B1, X₂₀) :|: D1 ≤ 0 ∧ X₀ ≤ 0
t₃₅: l1(X₀, X₁, X₂, X₃, X₁₃, X₁₅, X₂₀) → l1(X₀, 1+X₁, X₃, B1, X₁₃, X₁₅, X₂₀) :|: X₁+1 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₆: l1(X₀, X₁, X₂, X₃, X₁₃, X₁₅, X₂₀) → l2(Y, X₂₀+1, X₂, X₃, X₂, 0, X₂₀) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ Y ≤ Z ∧ 2 ≤ Y ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₇: l1(X₀, X₁, X₂, X₃, X₁₃, X₁₅, X₂₀) → l2(Y, X₂₀+1, X₂, X₃, X₂, 0, X₂₀) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ Y ≤ Z ∧ 2 ≤ Y ∧ X₂+1 ≤ 0 ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₃₈: l2(X₀, X₁, X₂, X₃, X₁₃, X₁₅, X₂₀) → l2(A1, Z, Y, X₃, X₁₃, 0, X₂₀-1) :|: X₁₃+1 ≤ C1 ∧ 0 ≤ X₂₀ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ C1+1 ≤ Y ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₁₅ ∧ X₁₅ ≤ 0 ∧ 2+X₁₅ ≤ X₀ ∧ 0 ≤ X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₀
t₃₉: l2(X₀, X₁, X₂, X₃, X₁₃, X₁₅, X₂₀) → l2(A1, Z, Y, X₃, X₁₃, 0, X₂₀-1) :|: X₁₃+1 ≤ C1 ∧ 0 ≤ X₂₀ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ Y+1 ≤ C1 ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₁₅ ∧ X₁₅ ≤ 0 ∧ 2+X₁₅ ≤ X₀ ∧ 0 ≤ X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₀
t₄₀: l2(X₀, X₁, X₂, X₃, X₁₃, X₁₅, X₂₀) → l2(A1, Z, Y, X₃, X₁₃, 0, X₂₀-1) :|: C1+1 ≤ X₁₃ ∧ 0 ≤ X₂₀ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ C1+1 ≤ Y ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₁₅ ∧ X₁₅ ≤ 0 ∧ 2+X₁₅ ≤ X₀ ∧ 0 ≤ X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₀
t₄₁: l2(X₀, X₁, X₂, X₃, X₁₃, X₁₅, X₂₀) → l2(A1, Z, Y, X₃, X₁₃, 0, X₂₀-1) :|: C1+1 ≤ X₁₃ ∧ 0 ≤ X₂₀ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ Y+1 ≤ C1 ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₁₅ ∧ X₁₅ ≤ 0 ∧ 2+X₁₅ ≤ X₀ ∧ 0 ≤ X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₀
t₄₂: l2(X₀, X₁, X₂, X₃, X₁₃, X₁₅, X₂₀) → l3(D1, X₁, X₂, X₃, C1, B1, X₂₀) :|: 2 ≤ D1 ∧ 0 ≤ X₂₀ ∧ X₁₅ ≤ X₁₃ ∧ X₁₃ ≤ X₁₅ ∧ X₁₅ ≤ 0 ∧ 2+X₁₅ ≤ X₀ ∧ 0 ≤ X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₀

MPRF for transition t₃₅: l1(X₀, X₁, X₂, X₃, X₁₃, X₁₅, X₂₀) → l1(X₀, 1+X₁, X₃, B1, X₁₃, X₁₅, X₂₀) :|: X₁+1 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+3 {O(n)}

MPRF:

l1 [X₀+1-X₁ ]

MPRF for transition t₃₈: l2(X₀, X₁, X₂, X₃, X₁₃, X₁₅, X₂₀) → l2(A1, Z, Y, X₃, X₁₃, 0, X₂₀-1) :|: X₁₃+1 ≤ C1 ∧ 0 ≤ X₂₀ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ C1+1 ≤ Y ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₁₅ ∧ X₁₅ ≤ 0 ∧ 2+X₁₅ ≤ X₀ ∧ 0 ≤ X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₀ of depth 1:

new bound:

4⋅X₂₀+2 {O(n)}

MPRF:

l2 [X₂₀+1 ]

MPRF for transition t₃₉: l2(X₀, X₁, X₂, X₃, X₁₃, X₁₅, X₂₀) → l2(A1, Z, Y, X₃, X₁₃, 0, X₂₀-1) :|: X₁₃+1 ≤ C1 ∧ 0 ≤ X₂₀ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ Y+1 ≤ C1 ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₁₅ ∧ X₁₅ ≤ 0 ∧ 2+X₁₅ ≤ X₀ ∧ 0 ≤ X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₀ of depth 1:

new bound:

4⋅X₂₀+2 {O(n)}

MPRF:

l2 [X₂₀+1 ]

MPRF for transition t₄₀: l2(X₀, X₁, X₂, X₃, X₁₃, X₁₅, X₂₀) → l2(A1, Z, Y, X₃, X₁₃, 0, X₂₀-1) :|: C1+1 ≤ X₁₃ ∧ 0 ≤ X₂₀ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ C1+1 ≤ Y ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₁₅ ∧ X₁₅ ≤ 0 ∧ 2+X₁₅ ≤ X₀ ∧ 0 ≤ X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₀ of depth 1:

new bound:

4⋅X₂₀+2 {O(n)}

MPRF:

l2 [X₂₀+1 ]

MPRF for transition t₄₁: l2(X₀, X₁, X₂, X₃, X₁₃, X₁₅, X₂₀) → l2(A1, Z, Y, X₃, X₁₃, 0, X₂₀-1) :|: C1+1 ≤ X₁₃ ∧ 0 ≤ X₂₀ ∧ 2 ≤ A1 ∧ A1 ≤ Z ∧ Y+1 ≤ C1 ∧ X₁₅ ≤ 0 ∧ 0 ≤ X₁₅ ∧ X₁₅ ≤ 0 ∧ 2+X₁₅ ≤ X₀ ∧ 0 ≤ X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₀ of depth 1:

new bound:

4⋅X₂₀+2 {O(n)}

MPRF:

l2 [X₂₀+1 ]

All Bounds

Timebounds

Overall timebound:16⋅X₂₀+X₀+16 {O(n)}
t₃₃: 1 {O(1)}
t₃₄: 1 {O(1)}
t₃₅: X₀+3 {O(n)}
t₃₆: 1 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 4⋅X₂₀+2 {O(n)}
t₃₉: 4⋅X₂₀+2 {O(n)}
t₄₀: 4⋅X₂₀+2 {O(n)}
t₄₁: 4⋅X₂₀+2 {O(n)}
t₄₂: 1 {O(1)}

Costbounds

Overall costbound: 16⋅X₂₀+X₀+16 {O(n)}
t₃₃: 1 {O(1)}
t₃₄: 1 {O(1)}
t₃₅: X₀+3 {O(n)}
t₃₆: 1 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 4⋅X₂₀+2 {O(n)}
t₃₉: 4⋅X₂₀+2 {O(n)}
t₄₀: 4⋅X₂₀+2 {O(n)}
t₄₁: 4⋅X₂₀+2 {O(n)}
t₄₂: 1 {O(1)}

Sizebounds

t₃₃, X₁: 0 {O(1)}
t₃₃, X₂: 0 {O(1)}
t₃₃, X₃: X₃ {O(n)}
t₃₃, X₂₀: X₂₀ {O(n)}
t₃₄, X₀: X₀ {O(n)}
t₃₄, X₁: 2 {O(1)}
t₃₄, X₁₃: X₁₃ {O(n)}
t₃₄, X₁₅: X₁₅ {O(n)}
t₃₄, X₂₀: X₂₀ {O(n)}
t₃₅, X₀: X₀ {O(n)}
t₃₅, X₁: X₀+5 {O(n)}
t₃₅, X₁₃: X₁₃ {O(n)}
t₃₅, X₁₅: X₁₅ {O(n)}
t₃₅, X₂₀: X₂₀ {O(n)}
t₃₆, X₁: 2⋅X₂₀+2 {O(n)}
t₃₆, X₁₅: 0 {O(1)}
t₃₆, X₂₀: 2⋅X₂₀ {O(n)}
t₃₇, X₁: 2⋅X₂₀+2 {O(n)}
t₃₇, X₁₅: 0 {O(1)}
t₃₇, X₂₀: 2⋅X₂₀ {O(n)}
t₃₈, X₁₅: 0 {O(1)}
t₃₈, X₂₀: 16⋅X₂₀+1 {O(n)}
t₃₉, X₁₅: 0 {O(1)}
t₃₉, X₂₀: 16⋅X₂₀+1 {O(n)}
t₄₀, X₁₅: 0 {O(1)}
t₄₀, X₂₀: 16⋅X₂₀+1 {O(n)}
t₄₁, X₁₅: 0 {O(1)}
t₄₁, X₂₀: 16⋅X₂₀+1 {O(n)}
t₄₂, X₂₀: 64⋅X₂₀+4 {O(n)}