Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁
Temp_Vars: M, N, O, P
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₅: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₅, X₃, X₃, X₃, X₅, X₅, X₀, X₁, X₈, X₉, X₁₀, X₁₁)
t₆: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₅, X₃, X₃, X₃, X₅, X₅, M, N, M, N, X₁₀, X₁₁)
t₉: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₀+1, X₁, X₃, X₃, X₅, X₅, X₀, X₁, X₈, X₉, X₁₀, X₁₁)
t₁₁: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₀, X₁+1, X₃, X₃, X₅, X₅, X₀, X₁, X₈, X₉, X₁₀, X₁₁)
t₁: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₂: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₇: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l3(O, P, X₃, M, X₅, N, X₀, X₁, M, N, O, P)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l2(X₀, X₁, X₃, X₃, X₅, X₅, X₀, X₁, X₈, X₉, X₁₀, X₁₁) :|: X₁+1 ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l2(X₀, X₁, X₃, X₃, X₅, X₅, X₀, X₁, X₈, X₉, X₁₀, X₁₁) :|: X₀+1 ≤ X₁
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l3(O, P, X₃, M, X₅, N, X₀, X₀, M, N, O, P) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁₀: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₀+1, X₁, X₃, X₃, X₅, X₅, X₀, X₁, X₈, X₉, X₁₀, X₁₁) :|: X₀+1 ≤ X₁
t₁₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₀, X₁+1, X₃, X₃, X₅, X₅, X₀, X₁, X₈, X₉, X₁₀, X₁₁) :|: X₁ ≤ X₀
Preprocessing
Eliminate variables {X₂,X₄,X₆,X₇,X₈,X₉,X₁₀,X₁₁} that do not contribute to the problem
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: M, N, O, P
Locations: l0, l1, l2, l3
Transitions:
t₁₉: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₂₀: l0(X₀, X₁, X₂, X₃) → l1(X₃, X₂, X₂, X₃)
t₂₁: l0(X₀, X₁, X₂, X₃) → l1(X₃, X₂, X₂, X₃)
t₂₂: l0(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃)
t₂₃: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃)
t₂₄: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂₅: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂₆: l0(X₀, X₁, X₂, X₃) → l3(O, P, M, N)
t₂₇: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₀
t₂₈: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁
t₂₉: l1(X₀, X₁, X₂, X₃) → l3(O, P, M, N) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₃₀: l2(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₀+1 ≤ X₁
t₃₁: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₁ ≤ X₀
MPRF for transition t₂₇: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₀ of depth 1:
new bound:
2⋅X₂+2⋅X₃+4⋅X₀+4⋅X₁+13 {O(n)}
MPRF for transition t₃₁: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₁ ≤ X₀ of depth 1:
new bound:
2⋅X₂+2⋅X₃+4⋅X₀+4⋅X₁+8 {O(n)}
MPRF for transition t₂₈: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁ of depth 1:
new bound:
16⋅X₂⋅X₃+32⋅X₀⋅X₀+32⋅X₀⋅X₂+32⋅X₀⋅X₃+32⋅X₁⋅X₁+32⋅X₁⋅X₂+32⋅X₁⋅X₃+64⋅X₀⋅X₁+8⋅X₂⋅X₂+8⋅X₃⋅X₃+116⋅X₀+116⋅X₁+58⋅X₂+58⋅X₃+109 {O(n^2)}
MPRF for transition t₃₀: l2(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₀+1 ≤ X₁ of depth 1:
new bound:
16⋅X₂⋅X₃+32⋅X₀⋅X₀+32⋅X₀⋅X₂+32⋅X₀⋅X₃+32⋅X₁⋅X₁+32⋅X₁⋅X₂+32⋅X₁⋅X₃+64⋅X₀⋅X₁+8⋅X₂⋅X₂+8⋅X₃⋅X₃+112⋅X₀+112⋅X₁+56⋅X₂+56⋅X₃+96 {O(n^2)}
Chain transitions t₃₁: l2→l1 and t₂₉: l1→l3 to t₁₁₁: l2→l3
Chain transitions t₃₀: l2→l1 and t₂₉: l1→l3 to t₁₁₂: l2→l3
Chain transitions t₃₀: l2→l1 and t₂₈: l1→l2 to t₁₁₃: l2→l2
Chain transitions t₃₁: l2→l1 and t₂₈: l1→l2 to t₁₁₄: l2→l2
Chain transitions t₂₃: l0→l1 and t₂₈: l1→l2 to t₁₁₅: l0→l2
Chain transitions t₂₃: l0→l1 and t₂₉: l1→l3 to t₁₁₆: l0→l3
Chain transitions t₂₃: l0→l1 and t₂₇: l1→l2 to t₁₁₇: l0→l2
Chain transitions t₃₀: l2→l1 and t₂₇: l1→l2 to t₁₁₈: l2→l2
Chain transitions t₃₁: l2→l1 and t₂₇: l1→l2 to t₁₁₉: l2→l2
Chain transitions t₂₂: l0→l1 and t₂₇: l1→l2 to t₁₂₀: l0→l2
Chain transitions t₂₂: l0→l1 and t₂₈: l1→l2 to t₁₂₁: l0→l2
Chain transitions t₂₂: l0→l1 and t₂₉: l1→l3 to t₁₂₂: l0→l3
Chain transitions t₂₁: l0→l1 and t₂₇: l1→l2 to t₁₂₃: l0→l2
Chain transitions t₂₁: l0→l1 and t₂₈: l1→l2 to t₁₂₄: l0→l2
Chain transitions t₂₁: l0→l1 and t₂₉: l1→l3 to t₁₂₅: l0→l3
Chain transitions t₂₀: l0→l1 and t₂₇: l1→l2 to t₁₂₆: l0→l2
Chain transitions t₂₀: l0→l1 and t₂₈: l1→l2 to t₁₂₇: l0→l2
Chain transitions t₂₀: l0→l1 and t₂₉: l1→l3 to t₁₂₈: l0→l3
Chain transitions t₁₉: l0→l1 and t₂₇: l1→l2 to t₁₂₉: l0→l2
Chain transitions t₁₉: l0→l1 and t₂₈: l1→l2 to t₁₃₀: l0→l2
Chain transitions t₁₉: l0→l1 and t₂₉: l1→l3 to t₁₃₁: l0→l3
Analysing control-flow refined program
Cut unsatisfiable transition t₁₁₈: l2→l2
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₁₄: l2(X₀, X₁, X₂, X₃) -{2}> l2(X₀, 1+X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁
MPRF for transition t₁₁₃: l2(X₀, X₁, X₂, X₃) -{2}> l2(1+X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁ ∧ 2+X₀ ≤ X₁ of depth 1:
new bound:
2⋅X₂+2⋅X₃+4⋅X₀+4⋅X₁+8 {O(n)}
MPRF for transition t₁₁₉: l2(X₀, X₁, X₂, X₃) -{2}> l2(X₀, 1+X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 2+X₁ ≤ X₀ of depth 1:
new bound:
2⋅X₂+2⋅X₃+4⋅X₀+4⋅X₁+8 {O(n)}
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Cut unsatisfiable transition t₃₃₂: n_l1___4→n_l2___5
Found invariant X₁ ≤ 1+X₀ for location n_l1___6
Found invariant 1+X₀ ≤ X₁ for location n_l2___7
Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___4
Found invariant X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ for location n_l2___5
Found invariant X₀ ≤ X₁ for location n_l1___3
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location n_l2___1
Found invariant X₃ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l2___2
Found invariant 1+X₁ ≤ X₀ for location n_l2___8
MPRF for transition t₃₃₁: n_l1___3(X₀, X₁, X₂, X₃) → n_l2___7(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₁ of depth 1:
new bound:
4⋅X₂+4⋅X₃+7⋅X₀+7⋅X₁+8 {O(n)}
MPRF for transition t₃₃₈: n_l2___7(X₀, X₁, X₂, X₃) → n_l1___3(X₀+1, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
4⋅X₂+4⋅X₃+7⋅X₀+7⋅X₁+6 {O(n)}
MPRF for transition t₃₃₄: n_l1___6(X₀, X₁, X₂, X₃) → n_l2___8(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ X₁ ≤ 1+X₀ of depth 1:
new bound:
4⋅X₂+4⋅X₃+7⋅X₀+7⋅X₁+11 {O(n)}
MPRF for transition t₃₃₉: n_l2___8(X₀, X₁, X₂, X₃) → n_l1___6(X₀, X₁+1, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
4⋅X₂+4⋅X₃+7⋅X₀+7⋅X₁+9 {O(n)}
CFR did not improve the program. Rolling back
CFR: Improvement to new bound with the following program:
new bound:
16⋅X₂+16⋅X₃+28⋅X₀+28⋅X₁+34 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: M, N, O, P
Locations: l0, l1, l2, l3, n_l1___3, n_l1___4, n_l1___6, n_l2___1, n_l2___2, n_l2___5, n_l2___7, n_l2___8
Transitions:
t₁₉: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₂₀: l0(X₀, X₁, X₂, X₃) → l1(X₃, X₂, X₂, X₃)
t₂₁: l0(X₀, X₁, X₂, X₃) → l1(X₃, X₂, X₂, X₃)
t₂₂: l0(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃)
t₂₃: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃)
t₂₄: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂₅: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂₆: l0(X₀, X₁, X₂, X₃) → l3(O, P, M, N)
t₂₉: l1(X₀, X₁, X₂, X₃) → l3(O, P, M, N) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₃₂₇: l1(X₀, X₁, X₂, X₃) → n_l2___1(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁
t₃₂₈: l1(X₀, X₁, X₂, X₃) → n_l2___2(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₁ ≤ X₀
t₃₂₉: l1(X₀, X₁, X₂, X₃) → n_l2___7(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁
t₃₃₀: l1(X₀, X₁, X₂, X₃) → n_l2___8(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀
t₃₄₀: l2(X₀, X₁, X₂, X₃) → n_l1___3(X₀+1, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁
t₃₄₁: l2(X₀, X₁, X₂, X₃) → n_l1___6(X₀, X₁+1, X₂, X₃) :|: X₁ ≤ X₀
t₃₅₂: n_l1___3(X₀, X₁, X₂, X₃) → l3(O, P, M, N) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₃₃₁: n_l1___3(X₀, X₁, X₂, X₃) → n_l2___7(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₁
t₃₅₃: n_l1___4(X₀, X₁, X₂, X₃) → l3(O, P, M, N) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₃₅₄: n_l1___6(X₀, X₁, X₂, X₃) → l3(O, P, M, N) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 1+X₀
t₃₃₃: n_l1___6(X₀, X₁, X₂, X₃) → n_l2___5(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀
t₃₃₄: n_l1___6(X₀, X₁, X₂, X₃) → n_l2___8(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ X₁ ≤ 1+X₀
t₃₃₅: n_l2___1(X₀, X₁, X₂, X₃) → n_l1___3(X₀+1, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
t₃₃₆: n_l2___2(X₀, X₁, X₂, X₃) → n_l1___6(X₀, X₁+1, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₃₃₇: n_l2___5(X₀, X₁, X₂, X₃) → n_l1___4(X₀+1, X₁, X₂, X₃) :|: X₀+1 ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
t₃₃₈: n_l2___7(X₀, X₁, X₂, X₃) → n_l1___3(X₀+1, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁
t₃₃₉: n_l2___8(X₀, X₁, X₂, X₃) → n_l1___6(X₀, X₁+1, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀
All Bounds
Timebounds
Overall timebound:16⋅X₂+16⋅X₃+28⋅X₀+28⋅X₁+56 {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₉: 1 {O(1)}
t₃₂₇: 1 {O(1)}
t₃₂₈: 1 {O(1)}
t₃₂₉: 1 {O(1)}
t₃₃₀: 1 {O(1)}
t₃₃₁: 4⋅X₂+4⋅X₃+7⋅X₀+7⋅X₁+8 {O(n)}
t₃₃₃: 1 {O(1)}
t₃₃₄: 4⋅X₂+4⋅X₃+7⋅X₀+7⋅X₁+11 {O(n)}
t₃₃₅: 1 {O(1)}
t₃₃₆: 1 {O(1)}
t₃₃₇: 1 {O(1)}
t₃₃₈: 4⋅X₂+4⋅X₃+7⋅X₀+7⋅X₁+6 {O(n)}
t₃₃₉: 4⋅X₂+4⋅X₃+7⋅X₀+7⋅X₁+9 {O(n)}
t₃₄₀: 1 {O(1)}
t₃₄₁: 1 {O(1)}
t₃₅₂: 1 {O(1)}
t₃₅₃: 1 {O(1)}
t₃₅₄: 1 {O(1)}
Costbounds
Overall costbound: 16⋅X₂+16⋅X₃+28⋅X₀+28⋅X₁+56 {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₉: 1 {O(1)}
t₃₂₇: 1 {O(1)}
t₃₂₈: 1 {O(1)}
t₃₂₉: 1 {O(1)}
t₃₃₀: 1 {O(1)}
t₃₃₁: 4⋅X₂+4⋅X₃+7⋅X₀+7⋅X₁+8 {O(n)}
t₃₃₃: 1 {O(1)}
t₃₃₄: 4⋅X₂+4⋅X₃+7⋅X₀+7⋅X₁+11 {O(n)}
t₃₃₅: 1 {O(1)}
t₃₃₆: 1 {O(1)}
t₃₃₇: 1 {O(1)}
t₃₃₈: 4⋅X₂+4⋅X₃+7⋅X₀+7⋅X₁+6 {O(n)}
t₃₃₉: 4⋅X₂+4⋅X₃+7⋅X₀+7⋅X₁+9 {O(n)}
t₃₄₀: 1 {O(1)}
t₃₄₁: 1 {O(1)}
t₃₅₂: 1 {O(1)}
t₃₅₃: 1 {O(1)}
t₃₅₄: 1 {O(1)}
Sizebounds
t₁₉, X₀: X₀ {O(n)}
t₁₉, X₁: X₁ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₂₀, X₀: X₃ {O(n)}
t₂₀, X₁: X₂ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₁, X₀: X₃ {O(n)}
t₂₁, X₁: X₂ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₂, X₀: X₀+1 {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₃, X₀: X₀ {O(n)}
t₂₃, X₁: X₁+1 {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₄, X₀: X₀ {O(n)}
t₂₄, X₁: X₁ {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₅, X₀: X₀ {O(n)}
t₂₅, X₁: X₁ {O(n)}
t₂₅, X₂: X₂ {O(n)}
t₂₅, X₃: X₃ {O(n)}
t₃₂₇, X₀: 2⋅X₃+3⋅X₀+1 {O(n)}
t₃₂₇, X₁: 2⋅X₂+3⋅X₁+1 {O(n)}
t₃₂₇, X₂: 5⋅X₂ {O(n)}
t₃₂₇, X₃: 5⋅X₃ {O(n)}
t₃₂₈, X₀: 2⋅X₃+3⋅X₀+1 {O(n)}
t₃₂₈, X₁: 2⋅X₂+3⋅X₁+1 {O(n)}
t₃₂₈, X₂: 5⋅X₂ {O(n)}
t₃₂₈, X₃: 5⋅X₃ {O(n)}
t₃₂₉, X₀: 2⋅X₃+3⋅X₀+1 {O(n)}
t₃₂₉, X₁: 2⋅X₂+3⋅X₁+1 {O(n)}
t₃₂₉, X₂: 5⋅X₂ {O(n)}
t₃₂₉, X₃: 5⋅X₃ {O(n)}
t₃₃₀, X₀: 2⋅X₃+3⋅X₀+1 {O(n)}
t₃₃₀, X₁: 2⋅X₂+3⋅X₁+1 {O(n)}
t₃₃₀, X₂: 5⋅X₂ {O(n)}
t₃₃₀, X₃: 5⋅X₃ {O(n)}
t₃₃₁, X₀: 14⋅X₀+4⋅X₂+7⋅X₁+8⋅X₃+10 {O(n)}
t₃₃₁, X₁: 4⋅X₂+7⋅X₁+2 {O(n)}
t₃₃₁, X₂: 11⋅X₂ {O(n)}
t₃₃₁, X₃: 11⋅X₃ {O(n)}
t₃₃₃, X₀: X₀ {O(n)}
t₃₃₃, X₁: X₁+1 {O(n)}
t₃₃₃, X₂: X₂ {O(n)}
t₃₃₃, X₃: X₃ {O(n)}
t₃₃₄, X₀: 4⋅X₃+7⋅X₀+2 {O(n)}
t₃₃₄, X₁: 14⋅X₁+4⋅X₃+7⋅X₀+8⋅X₂+13 {O(n)}
t₃₃₄, X₂: 11⋅X₂ {O(n)}
t₃₃₄, X₃: 11⋅X₃ {O(n)}
t₃₃₅, X₀: 2⋅X₃+3⋅X₀+2 {O(n)}
t₃₃₅, X₁: 2⋅X₂+3⋅X₁+1 {O(n)}
t₃₃₅, X₂: 5⋅X₂ {O(n)}
t₃₃₅, X₃: 5⋅X₃ {O(n)}
t₃₃₆, X₀: 2⋅X₃+3⋅X₀+1 {O(n)}
t₃₃₆, X₁: 2⋅X₂+3⋅X₁+2 {O(n)}
t₃₃₆, X₂: 5⋅X₂ {O(n)}
t₃₃₆, X₃: 5⋅X₃ {O(n)}
t₃₃₇, X₀: X₀+1 {O(n)}
t₃₃₇, X₁: X₁+1 {O(n)}
t₃₃₇, X₂: X₂ {O(n)}
t₃₃₇, X₃: X₃ {O(n)}
t₃₃₈, X₀: 14⋅X₀+4⋅X₂+7⋅X₁+8⋅X₃+10 {O(n)}
t₃₃₈, X₁: 4⋅X₂+7⋅X₁+2 {O(n)}
t₃₃₈, X₂: 11⋅X₂ {O(n)}
t₃₃₈, X₃: 11⋅X₃ {O(n)}
t₃₃₉, X₀: 4⋅X₃+7⋅X₀+2 {O(n)}
t₃₃₉, X₁: 14⋅X₁+4⋅X₃+7⋅X₀+8⋅X₂+13 {O(n)}
t₃₃₉, X₂: 11⋅X₂ {O(n)}
t₃₃₉, X₃: 11⋅X₃ {O(n)}
t₃₄₀, X₀: X₀+1 {O(n)}
t₃₄₀, X₁: X₁ {O(n)}
t₃₄₀, X₂: X₂ {O(n)}
t₃₄₀, X₃: X₃ {O(n)}
t₃₄₁, X₀: X₀ {O(n)}
t₃₄₁, X₁: X₁+1 {O(n)}
t₃₄₁, X₂: X₂ {O(n)}
t₃₄₁, X₃: X₃ {O(n)}