Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₃, X₁, X₃, X₆, X₇, X₈, X₉) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₆, X₇, X₈, X₉, X₄, X₅, X₆, X₇, X₈, X₉)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀-1, 3⋅X₁+X₂, -6⋅X₁-2⋅X₂, X₃+2⋅(X₀)²+2-4⋅X₀, X₄, X₅, X₆, X₇, X₈, X₉)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 < X₄+X₅
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₄+X₅ ≤ 0
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₃, X₄-1, X₅-1, X₆, X₇, X₈, X₉)
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
Preprocessing
Found invariant X₀ ≤ X₆ ∧ X₄+X₅ ≤ 0 ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l6
Found invariant X₀ ≤ X₆ ∧ X₄+X₅ ≤ 0 ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l7
Found invariant X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ 0 for location l5
Found invariant X₀ ≤ X₆ for location l1
Found invariant X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 < X₀ ∧ X₀ ≤ X₆
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₃, X₁, X₃, X₆, X₇, X₈, X₉) :|: X₀ ≤ 0 ∧ X₀ ≤ X₆
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₆, X₇, X₈, X₉, X₄, X₅, X₆, X₇, X₈, X₉)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀-1, 3⋅X₁+X₂, -6⋅X₁-2⋅X₂, X₃+2⋅(X₀)²+2-4⋅X₀, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 < X₄+X₅ ∧ X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₄+X₅ ≤ 0 ∧ X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₃, X₄-1, X₅-1, X₆, X₇, X₈, X₉) :|: X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ 0
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₀ ≤ X₆ ∧ X₄+X₅ ≤ 0 ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0
TWN. Size Bound: t₄: l3→l1 for X₃
cycle: [t₄: l3→l1; t₂: l1→l3]
loop: (1 < X₀,(X₀,X₃) -> (X₀-1,2+X₃+2⋅(X₀)²-4⋅X₀)
closed-form: X₃ + [[n != 0]] * (2+2⋅(X₀)²-4⋅X₀) * n^1 + [[n != 0, n != 1]] * 2/3 * n^3 + [[n != 0, n != 1]] * 1-2⋅X₀ * n^2 + [[n != 0, n != 1]] * 2⋅X₀-5/3 * n^1
runtime bound: X₀+1 {O(n)}
TWN Size Bound - Lifting for t₄: l3→l1 and X₃: 5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+X₉+6 {O(n^3)}
Solv. Size Bound: t₂: l1→l3 for X₁
cycle: [t₂: l1→l3; t₄: l3→l1]
loop: (0 < X₀,(X₁,X₂) -> (3⋅X₁+X₂,-6⋅X₁-2⋅X₂)
overappr. closed-form: 2⋅X₂+6⋅X₁ {O(n)}
runtime bound: X₀+1 {O(n)}
Solv. Size Bound - Lifting for t₂: l1→l3 and X₁: 2⋅X₈+6⋅X₇ {O(n)}
Solv. Size Bound: t₂: l1→l3 for X₂
cycle: [t₂: l1→l3; t₄: l3→l1]
loop: (0 < X₀,(X₁,X₂) -> (3⋅X₁+X₂,-6⋅X₁-2⋅X₂)
overappr. closed-form: 12⋅X₁+4⋅X₂ {O(n)}
runtime bound: X₀+1 {O(n)}
Solv. Size Bound - Lifting for t₂: l1→l3 and X₂: 12⋅X₇+4⋅X₈ {O(n)}
Solv. Size Bound: t₄: l3→l1 for X₁
cycle: [t₄: l3→l1; t₂: l1→l3]
loop: (1 < X₀,(X₁,X₂) -> (3⋅X₁+X₂,-6⋅X₁-2⋅X₂)
overappr. closed-form: 2⋅X₂+6⋅X₁ {O(n)}
runtime bound: X₀+1 {O(n)}
Solv. Size Bound - Lifting for t₄: l3→l1 and X₁: 2⋅X₈+6⋅X₇ {O(n)}
Solv. Size Bound: t₄: l3→l1 for X₂
cycle: [t₄: l3→l1; t₂: l1→l3]
loop: (1 < X₀,(X₁,X₂) -> (3⋅X₁+X₂,-6⋅X₁-2⋅X₂)
overappr. closed-form: 12⋅X₁+4⋅X₂ {O(n)}
runtime bound: X₀+1 {O(n)}
Solv. Size Bound - Lifting for t₄: l3→l1 and X₂: 12⋅X₇+4⋅X₈ {O(n)}
MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 < X₀ ∧ X₀ ≤ X₆ of depth 1:
new bound:
X₆ {O(n)}
MPRF for transition t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀-1, 3⋅X₁+X₂, -6⋅X₁-2⋅X₂, X₃+2⋅Temp_Int₇₂₈+2⋅Temp_Int₇₂₉-4⋅X₀, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 < Temp_Int₇₂₈ ∧ X₀ ≤ Temp_Int₇₂₈ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₆ {O(n)}
MPRF for transition t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 < X₄+X₅ ∧ X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+2⋅X₈+2⋅X₉+7⋅X₇+6 {O(n^3)}
MPRF for transition t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₃, X₄-1, X₅-1, X₆, X₇, X₈, X₉) :|: X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ 0 of depth 1:
new bound:
5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+2⋅X₈+2⋅X₉+7⋅X₇+6 {O(n^3)}
Chain transitions t₇: l5→l4 and t₆: l4→l6 to t₈₅: l5→l6
Chain transitions t₃: l1→l4 and t₆: l4→l6 to t₈₆: l1→l6
Chain transitions t₃: l1→l4 and t₅: l4→l5 to t₈₇: l1→l5
Chain transitions t₇: l5→l4 and t₅: l4→l5 to t₈₈: l5→l5
Analysing control-flow refined program
Found invariant X₀ ≤ X₆ ∧ X₄+X₅ ≤ 0 ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l6
Found invariant X₀ ≤ X₆ ∧ X₄+X₅ ≤ 0 ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l7
Found invariant X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ 0 for location l5
Found invariant X₀ ≤ X₆ for location l1
Found invariant X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₀ for location l3
MPRF for transition t₈₈: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) -{2}> l5(X₀, X₁, X₂, X₃, X₄-1, X₅-1, X₆, X₇, X₈, X₉) :|: 2 < X₄+X₅ ∧ X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₆ ∧ X₅ ≤ X₃+1 ∧ X₄ ≤ X₁+1 ∧ X₀ ≤ 0 ∧ X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ 0 of depth 1:
new bound:
5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+2⋅X₈+2⋅X₉+7⋅X₇+6 {O(n^3)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Found invariant X₀ ≤ X₆ ∧ 1+X₅ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₁+X₅ ∧ 1+X₄ ≤ X₁ ∧ 2 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₃ ∧ X₀ ≤ 0 for location n_l5___1
Found invariant X₀ ≤ X₆ ∧ X₄+X₅ ≤ 0 ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l6
Found invariant X₀ ≤ X₆ ∧ 1+X₅ ≤ X₃ ∧ 0 ≤ 1+X₄+X₅ ∧ 0 ≤ X₁+X₅ ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ 0 for location n_l4___2
Found invariant X₀ ≤ X₆ ∧ X₄+X₅ ≤ 0 ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l7
Found invariant X₀ ≤ X₆ for location l1
Found invariant X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ X₃ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ 1 ≤ X₀ for location l3
Found invariant X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₃+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ 0 for location n_l5___3
MPRF for transition t₁₃₉: n_l4___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → n_l5___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 ≤ 1+X₄+X₅ ∧ 1+X₄ ≤ X₁ ∧ 1+X₅ ≤ X₃ ∧ 0 < X₄+X₅ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₆ ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₆ ∧ X₀ ≤ 0 ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₃ ∧ X₀ ≤ X₆ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₆ ∧ 1+X₅ ≤ X₃ ∧ 0 ≤ 1+X₄+X₅ ∧ 0 ≤ X₁+X₅ ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ 0 of depth 1:
new bound:
5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+2⋅X₈+2⋅X₉+7⋅X₇+8 {O(n^3)}
MPRF for transition t₁₄₁: n_l5___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → n_l4___2(X₀, X₁, X₂, X₃, X₄-1, X₅-1, X₆, X₇, X₈, X₉) :|: 1+X₅ ≤ X₃ ∧ 0 < X₄+X₅ ∧ 1+X₄ ≤ X₁ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₆ ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ X₀ ≤ X₆ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₆ ∧ 1+X₅ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₁+X₅ ∧ 1+X₄ ≤ X₁ ∧ 2 ≤ X₃+X₄ ∧ 3 ≤ X₁+X₃ ∧ X₀ ≤ 0 of depth 1:
new bound:
5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+2⋅X₈+2⋅X₉+7⋅X₇+7 {O(n^3)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:10⋅X₆⋅X₆⋅X₆+32⋅X₆⋅X₆+14⋅X₇+36⋅X₆+4⋅X₈+4⋅X₉+17 {O(n^3)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₆ {O(n)}
t₃: 1 {O(1)}
t₄: X₆ {O(n)}
t₅: 5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+2⋅X₈+2⋅X₉+7⋅X₇+6 {O(n^3)}
t₆: 1 {O(1)}
t₇: 5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+2⋅X₈+2⋅X₉+7⋅X₇+6 {O(n^3)}
t₈: 1 {O(1)}
Costbounds
Overall costbound: 10⋅X₆⋅X₆⋅X₆+32⋅X₆⋅X₆+14⋅X₇+36⋅X₆+4⋅X₈+4⋅X₉+17 {O(n^3)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₆ {O(n)}
t₃: 1 {O(1)}
t₄: X₆ {O(n)}
t₅: 5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+2⋅X₈+2⋅X₉+7⋅X₇+6 {O(n^3)}
t₆: 1 {O(1)}
t₇: 5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+2⋅X₈+2⋅X₉+7⋅X₇+6 {O(n^3)}
t₈: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₀, X₆: X₆ {O(n)}
t₀, X₇: X₇ {O(n)}
t₀, X₈: X₈ {O(n)}
t₀, X₉: X₉ {O(n)}
t₁, X₀: X₆ {O(n)}
t₁, X₁: X₇ {O(n)}
t₁, X₂: X₈ {O(n)}
t₁, X₃: X₉ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₁, X₇: X₇ {O(n)}
t₁, X₈: X₈ {O(n)}
t₁, X₉: X₉ {O(n)}
t₂, X₀: X₆ {O(n)}
t₂, X₁: 2⋅X₈+6⋅X₇ {O(n)}
t₂, X₂: 12⋅X₇+4⋅X₈ {O(n)}
t₂, X₃: 5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+2⋅X₉+6 {O(n^3)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₂, X₇: X₇ {O(n)}
t₂, X₈: X₈ {O(n)}
t₂, X₉: X₉ {O(n)}
t₃, X₀: 2⋅X₆ {O(n)}
t₃, X₁: 2⋅X₈+7⋅X₇ {O(n)}
t₃, X₂: 12⋅X₇+5⋅X₈ {O(n)}
t₃, X₃: 5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+2⋅X₉+6 {O(n^3)}
t₃, X₄: 2⋅X₈+7⋅X₇ {O(n)}
t₃, X₅: 5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+2⋅X₉+6 {O(n^3)}
t₃, X₆: 2⋅X₆ {O(n)}
t₃, X₇: 2⋅X₇ {O(n)}
t₃, X₈: 2⋅X₈ {O(n)}
t₃, X₉: 2⋅X₉ {O(n)}
t₄, X₀: X₆ {O(n)}
t₄, X₁: 2⋅X₈+6⋅X₇ {O(n)}
t₄, X₂: 12⋅X₇+4⋅X₈ {O(n)}
t₄, X₃: 5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+X₉+6 {O(n^3)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {O(n)}
t₄, X₇: X₇ {O(n)}
t₄, X₈: X₈ {O(n)}
t₄, X₉: X₉ {O(n)}
t₅, X₀: 2⋅X₆ {O(n)}
t₅, X₁: 2⋅X₈+7⋅X₇ {O(n)}
t₅, X₂: 12⋅X₇+5⋅X₈ {O(n)}
t₅, X₃: 5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+2⋅X₉+6 {O(n^3)}
t₅, X₄: 5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+14⋅X₇+17⋅X₆+2⋅X₉+4⋅X₈+6 {O(n^3)}
t₅, X₅: 10⋅X₆⋅X₆⋅X₆+32⋅X₆⋅X₆+2⋅X₈+34⋅X₆+4⋅X₉+7⋅X₇+12 {O(n^3)}
t₅, X₆: 2⋅X₆ {O(n)}
t₅, X₇: 2⋅X₇ {O(n)}
t₅, X₈: 2⋅X₈ {O(n)}
t₅, X₉: 2⋅X₉ {O(n)}
t₆, X₀: 4⋅X₆ {O(n)}
t₆, X₁: 14⋅X₇+4⋅X₈ {O(n)}
t₆, X₂: 10⋅X₈+24⋅X₇ {O(n)}
t₆, X₃: 10⋅X₆⋅X₆⋅X₆+32⋅X₆⋅X₆+34⋅X₆+4⋅X₉+12 {O(n^3)}
t₆, X₄: 5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+2⋅X₉+21⋅X₇+6⋅X₈+6 {O(n^3)}
t₆, X₅: 15⋅X₆⋅X₆⋅X₆+48⋅X₆⋅X₆+2⋅X₈+51⋅X₆+6⋅X₉+7⋅X₇+18 {O(n^3)}
t₆, X₆: 4⋅X₆ {O(n)}
t₆, X₇: 4⋅X₇ {O(n)}
t₆, X₈: 4⋅X₈ {O(n)}
t₆, X₉: 4⋅X₉ {O(n)}
t₇, X₀: 2⋅X₆ {O(n)}
t₇, X₁: 2⋅X₈+7⋅X₇ {O(n)}
t₇, X₂: 12⋅X₇+5⋅X₈ {O(n)}
t₇, X₃: 5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+2⋅X₉+6 {O(n^3)}
t₇, X₄: 5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+14⋅X₇+17⋅X₆+2⋅X₉+4⋅X₈+6 {O(n^3)}
t₇, X₅: 10⋅X₆⋅X₆⋅X₆+32⋅X₆⋅X₆+2⋅X₈+34⋅X₆+4⋅X₉+7⋅X₇+12 {O(n^3)}
t₇, X₆: 2⋅X₆ {O(n)}
t₇, X₇: 2⋅X₇ {O(n)}
t₇, X₈: 2⋅X₈ {O(n)}
t₇, X₉: 2⋅X₉ {O(n)}
t₈, X₀: 4⋅X₆ {O(n)}
t₈, X₁: 14⋅X₇+4⋅X₈ {O(n)}
t₈, X₂: 10⋅X₈+24⋅X₇ {O(n)}
t₈, X₃: 10⋅X₆⋅X₆⋅X₆+32⋅X₆⋅X₆+34⋅X₆+4⋅X₉+12 {O(n^3)}
t₈, X₄: 5⋅X₆⋅X₆⋅X₆+16⋅X₆⋅X₆+17⋅X₆+2⋅X₉+21⋅X₇+6⋅X₈+6 {O(n^3)}
t₈, X₅: 15⋅X₆⋅X₆⋅X₆+48⋅X₆⋅X₆+2⋅X₈+51⋅X₆+6⋅X₉+7⋅X₇+18 {O(n^3)}
t₈, X₆: 4⋅X₆ {O(n)}
t₈, X₇: 4⋅X₇ {O(n)}
t₈, X₈: 4⋅X₈ {O(n)}
t₈, X₉: 4⋅X₉ {O(n)}