Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l4(X₀, X₁, X₂, X₃, X₁, X₂, X₃, X₇, X₈, X₉, X₁₀) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l1(X₇, X₈, X₉, X₁₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l1(X₀-1, 3⋅X₁+2⋅X₂, -5⋅X₁-3⋅X₂, (X₀)²+X₃+1-2⋅X₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 0 < X₄+X₅+X₆
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₄+X₅+X₆ ≤ 0
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l4(X₀, X₁, X₂, X₃, X₄-1, X₅-1, X₆-1, X₇, X₈, X₉, X₁₀)
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀)
Preprocessing
Found invariant X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l6
Found invariant X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l7
Found invariant X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l5
Found invariant X₀ ≤ X₇ for location l1
Found invariant X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 0 < X₀ ∧ X₀ ≤ X₇
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l4(X₀, X₁, X₂, X₃, X₁, X₂, X₃, X₇, X₈, X₉, X₁₀) :|: X₀ ≤ 0 ∧ X₀ ≤ X₇
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l1(X₇, X₈, X₉, X₁₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l1(X₀-1, 3⋅X₁+2⋅X₂, -5⋅X₁-3⋅X₂, (X₀)²+X₃+1-2⋅X₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 0 < X₄+X₅+X₆ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₄+X₅+X₆ ≤ 0 ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l4(X₀, X₁, X₂, X₃, X₄-1, X₅-1, X₆-1, X₇, X₈, X₉, X₁₀) :|: X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0
TWN. Size Bound: t₄: l3→l1 for X₃
cycle: [t₄: l3→l1; t₂: l1→l3]
loop: (1 < X₀,(X₀,X₃) -> (X₀-1,1+(X₀)²+X₃-2⋅X₀)
closed-form: X₃ + [[n != 0]] * (1+(X₀)²-2⋅X₀) * n^1 + [[n != 0, n != 1]] * 1/3 * n^3 + [[n != 0, n != 1]] * 1/2-X₀ * n^2 + [[n != 0, n != 1]] * X₀-5/6 * n^1
runtime bound: X₀+1 {O(n)}
TWN Size Bound - Lifting for t₄: l3→l1 and X₃: 3⋅X₇⋅X₇⋅X₇+10⋅X₇⋅X₇+11⋅X₇+X₁₀+4 {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+2⋅X₂,-5⋅X₁-3⋅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⋅X₉+6⋅X₈ {O(n)}
Solv. Size Bound: t₂: l1→l3 for X₂
cycle: [t₂: l1→l3; t₄: l3→l1]
loop: (0 < X₀,(X₁,X₂) -> (3⋅X₁+2⋅X₂,-5⋅X₁-3⋅X₂)
overappr. closed-form: 6⋅X₁+6⋅X₂ {O(n)}
runtime bound: X₀+1 {O(n)}
Solv. Size Bound - Lifting for t₂: l1→l3 and X₂: 6⋅X₈+6⋅X₉ {O(n)}
Solv. Size Bound: t₄: l3→l1 for X₁
cycle: [t₄: l3→l1; t₂: l1→l3]
loop: (1 < X₀,(X₁,X₂) -> (3⋅X₁+2⋅X₂,-5⋅X₁-3⋅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⋅X₉+6⋅X₈ {O(n)}
Solv. Size Bound: t₄: l3→l1 for X₂
cycle: [t₄: l3→l1; t₂: l1→l3]
loop: (1 < X₀,(X₁,X₂) -> (3⋅X₁+2⋅X₂,-5⋅X₁-3⋅X₂)
overappr. closed-form: 6⋅X₁+6⋅X₂ {O(n)}
runtime bound: X₀+1 {O(n)}
Solv. Size Bound - Lifting for t₄: l3→l1 and X₂: 6⋅X₈+6⋅X₉ {O(n)}
MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 0 < X₀ ∧ X₀ ≤ X₇ of depth 1:
new bound:
X₇ {O(n)}
MPRF for transition t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l1(X₀-1, 3⋅X₁+2⋅X₂, -5⋅X₁-3⋅X₂, Temp_Int₇₉₇+X₃+Temp_Int₇₉₈-2⋅X₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 0 < Temp_Int₇₉₇ ∧ X₀ ≤ Temp_Int₇₉₇ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₇ {O(n)}
MPRF for transition t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 0 < X₄+X₅+X₆ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
3⋅X₇⋅X₇⋅X₇+10⋅X₇⋅X₇+11⋅X₇+13⋅X₈+2⋅X₁₀+9⋅X₉+4 {O(n^3)}
TWN: t₇: l5→l4
cycle: [t₇: l5→l4; t₅: l4→l5]
loop: (0 < X₄+X₅+X₆,(X₄,X₅,X₆) -> (X₄-1,X₅-1,X₆-1)
order: [X₄; X₅; X₆]
closed-form:
X₄: X₄ + [[n != 0]] * -1 * n^1
X₅: X₅ + [[n != 0]] * -1 * n^1
X₆: X₆ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
3 < 0
∨ 0 < X₄+X₅+X₆ ∧ 3 ≤ 0 ∧ 0 ≤ 3
Stabilization-Threshold for: 0 < X₄+X₅+X₆
alphas_abs: X₄+X₅+X₆
M: 0
N: 1
Bound: 2⋅X₄+2⋅X₅+2⋅X₆+2 {O(n)}
TWN - Lifting for t₇: l5→l4 of 2⋅X₄+2⋅X₅+2⋅X₆+4 {O(n)}
relevant size-bounds w.r.t. t₃:
X₄: 2⋅X₉+7⋅X₈ {O(n)}
X₅: 6⋅X₈+7⋅X₉ {O(n)}
X₆: 3⋅X₇⋅X₇⋅X₇+10⋅X₇⋅X₇+11⋅X₇+2⋅X₁₀+4 {O(n^3)}
Runtime-bound of t₃: 1 {O(1)}
Results in: 6⋅X₇⋅X₇⋅X₇+20⋅X₇⋅X₇+18⋅X₉+22⋅X₇+26⋅X₈+4⋅X₁₀+12 {O(n^3)}
Chain transitions t₇: l5→l4 and t₆: l4→l6 to t₉₂: l5→l6
Chain transitions t₃: l1→l4 and t₆: l4→l6 to t₉₃: l1→l6
Chain transitions t₃: l1→l4 and t₅: l4→l5 to t₉₄: l1→l5
Chain transitions t₇: l5→l4 and t₅: l4→l5 to t₉₅: l5→l5
Analysing control-flow refined program
Found invariant X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l6
Found invariant X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l7
Found invariant X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l5
Found invariant X₀ ≤ X₇ for location l1
Found invariant X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₀ for location l3
MPRF for transition t₉₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) -{2}> l5(X₀, X₁, X₂, X₃, X₄-1, X₅-1, X₆-1, X₇, X₈, X₉, X₁₀) :|: 3 < X₄+X₅+X₆ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₃+1 ∧ X₅ ≤ X₂+1 ∧ X₄ ≤ X₁+1 ∧ X₀ ≤ 0 ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
3⋅X₇⋅X₇⋅X₇+10⋅X₇⋅X₇+11⋅X₇+13⋅X₈+2⋅X₁₀+9⋅X₉+4 {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 ≤ X₇ ∧ 1+X₆ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ X₀ ≤ 0 for location n_l5___1
Found invariant X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l6
Found invariant X₀ ≤ X₇ ∧ 1+X₆ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ X₀ ≤ 0 for location n_l4___2
Found invariant X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ 0 for location l7
Found invariant X₀ ≤ X₇ for location l1
Found invariant X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₀ for location l3
Found invariant X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₀ ≤ 0 for location n_l5___3
MPRF for transition t₁₄₆: n_l4___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → n_l5___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₄ ≤ X₁ ∧ 1+X₅ ≤ X₂ ∧ 1+X₆ ≤ X₃ ∧ 0 < X₄+X₅+X₆ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₇ ∧ X₀ ≤ 0 ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₂ ∧ X₆ ≤ X₃ ∧ X₀ ≤ X₇ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₇ ∧ 1+X₆ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
3⋅X₇⋅X₇⋅X₇+10⋅X₇⋅X₇+11⋅X₇+13⋅X₈+2⋅X₁₀+9⋅X₉+7 {O(n^3)}
MPRF for transition t₁₄₈: n_l5___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → n_l4___2(X₀, X₁, X₂, X₃, X₄-1, X₅-1, X₆-1, X₇, X₈, X₉, X₁₀) :|: 1+X₆ ≤ X₃ ∧ 0 < X₄+X₅+X₆ ∧ 1+X₅ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₇ ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₂ ∧ X₆ ≤ X₃ ∧ X₀ ≤ X₇ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₇ ∧ 1+X₆ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
3⋅X₇⋅X₇⋅X₇+10⋅X₇⋅X₇+11⋅X₇+13⋅X₈+2⋅X₁₀+9⋅X₉+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:9⋅X₇⋅X₇⋅X₇+30⋅X₇⋅X₇+27⋅X₉+35⋅X₇+39⋅X₈+6⋅X₁₀+21 {O(n^3)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₇ {O(n)}
t₃: 1 {O(1)}
t₄: X₇ {O(n)}
t₅: 3⋅X₇⋅X₇⋅X₇+10⋅X₇⋅X₇+11⋅X₇+13⋅X₈+2⋅X₁₀+9⋅X₉+4 {O(n^3)}
t₆: 1 {O(1)}
t₇: 6⋅X₇⋅X₇⋅X₇+20⋅X₇⋅X₇+18⋅X₉+22⋅X₇+26⋅X₈+4⋅X₁₀+12 {O(n^3)}
t₈: 1 {O(1)}
Costbounds
Overall costbound: 9⋅X₇⋅X₇⋅X₇+30⋅X₇⋅X₇+27⋅X₉+35⋅X₇+39⋅X₈+6⋅X₁₀+21 {O(n^3)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₇ {O(n)}
t₃: 1 {O(1)}
t₄: X₇ {O(n)}
t₅: 3⋅X₇⋅X₇⋅X₇+10⋅X₇⋅X₇+11⋅X₇+13⋅X₈+2⋅X₁₀+9⋅X₉+4 {O(n^3)}
t₆: 1 {O(1)}
t₇: 6⋅X₇⋅X₇⋅X₇+20⋅X₇⋅X₇+18⋅X₉+22⋅X₇+26⋅X₈+4⋅X₁₀+12 {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)}
t₀, X₁₀: X₁₀ {O(n)}
t₁, X₀: X₇ {O(n)}
t₁, X₁: X₈ {O(n)}
t₁, X₂: X₉ {O(n)}
t₁, X₃: X₁₀ {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)}
t₁, X₁₀: X₁₀ {O(n)}
t₂, X₀: X₇ {O(n)}
t₂, X₁: 2⋅X₉+6⋅X₈ {O(n)}
t₂, X₂: 6⋅X₈+6⋅X₉ {O(n)}
t₂, X₃: 3⋅X₇⋅X₇⋅X₇+10⋅X₇⋅X₇+11⋅X₇+2⋅X₁₀+4 {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)}
t₂, X₁₀: X₁₀ {O(n)}
t₃, X₀: 2⋅X₇ {O(n)}
t₃, X₁: 2⋅X₉+7⋅X₈ {O(n)}
t₃, X₂: 6⋅X₈+7⋅X₉ {O(n)}
t₃, X₃: 3⋅X₇⋅X₇⋅X₇+10⋅X₇⋅X₇+11⋅X₇+2⋅X₁₀+4 {O(n^3)}
t₃, X₄: 2⋅X₉+7⋅X₈ {O(n)}
t₃, X₅: 6⋅X₈+7⋅X₉ {O(n)}
t₃, X₆: 3⋅X₇⋅X₇⋅X₇+10⋅X₇⋅X₇+11⋅X₇+2⋅X₁₀+4 {O(n^3)}
t₃, X₇: 2⋅X₇ {O(n)}
t₃, X₈: 2⋅X₈ {O(n)}
t₃, X₉: 2⋅X₉ {O(n)}
t₃, X₁₀: 2⋅X₁₀ {O(n)}
t₄, X₀: X₇ {O(n)}
t₄, X₁: 2⋅X₉+6⋅X₈ {O(n)}
t₄, X₂: 6⋅X₈+6⋅X₉ {O(n)}
t₄, X₃: 3⋅X₇⋅X₇⋅X₇+10⋅X₇⋅X₇+11⋅X₇+X₁₀+4 {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)}
t₄, X₁₀: X₁₀ {O(n)}
t₅, X₀: 2⋅X₇ {O(n)}
t₅, X₁: 2⋅X₉+7⋅X₈ {O(n)}
t₅, X₂: 6⋅X₈+7⋅X₉ {O(n)}
t₅, X₃: 3⋅X₇⋅X₇⋅X₇+10⋅X₇⋅X₇+11⋅X₇+2⋅X₁₀+4 {O(n^3)}
t₅, X₄: 6⋅X₇⋅X₇⋅X₇+20⋅X₇⋅X₇+20⋅X₉+22⋅X₇+33⋅X₈+4⋅X₁₀+12 {O(n^3)}
t₅, X₅: 6⋅X₇⋅X₇⋅X₇+20⋅X₇⋅X₇+22⋅X₇+25⋅X₉+32⋅X₈+4⋅X₁₀+12 {O(n^3)}
t₅, X₆: 9⋅X₇⋅X₇⋅X₇+30⋅X₇⋅X₇+18⋅X₉+26⋅X₈+33⋅X₇+6⋅X₁₀+16 {O(n^3)}
t₅, X₇: 2⋅X₇ {O(n)}
t₅, X₈: 2⋅X₈ {O(n)}
t₅, X₉: 2⋅X₉ {O(n)}
t₅, X₁₀: 2⋅X₁₀ {O(n)}
t₆, X₀: 4⋅X₇ {O(n)}
t₆, X₁: 14⋅X₈+4⋅X₉ {O(n)}
t₆, X₂: 12⋅X₈+14⋅X₉ {O(n)}
t₆, X₃: 6⋅X₇⋅X₇⋅X₇+20⋅X₇⋅X₇+22⋅X₇+4⋅X₁₀+8 {O(n^3)}
t₆, X₄: 6⋅X₇⋅X₇⋅X₇+20⋅X₇⋅X₇+22⋅X₇+22⋅X₉+4⋅X₁₀+40⋅X₈+12 {O(n^3)}
t₆, X₅: 6⋅X₇⋅X₇⋅X₇+20⋅X₇⋅X₇+22⋅X₇+32⋅X₉+38⋅X₈+4⋅X₁₀+12 {O(n^3)}
t₆, X₆: 12⋅X₇⋅X₇⋅X₇+40⋅X₇⋅X₇+18⋅X₉+26⋅X₈+44⋅X₇+8⋅X₁₀+20 {O(n^3)}
t₆, X₇: 4⋅X₇ {O(n)}
t₆, X₈: 4⋅X₈ {O(n)}
t₆, X₉: 4⋅X₉ {O(n)}
t₆, X₁₀: 4⋅X₁₀ {O(n)}
t₇, X₀: 2⋅X₇ {O(n)}
t₇, X₁: 2⋅X₉+7⋅X₈ {O(n)}
t₇, X₂: 6⋅X₈+7⋅X₉ {O(n)}
t₇, X₃: 3⋅X₇⋅X₇⋅X₇+10⋅X₇⋅X₇+11⋅X₇+2⋅X₁₀+4 {O(n^3)}
t₇, X₄: 6⋅X₇⋅X₇⋅X₇+20⋅X₇⋅X₇+20⋅X₉+22⋅X₇+33⋅X₈+4⋅X₁₀+12 {O(n^3)}
t₇, X₅: 6⋅X₇⋅X₇⋅X₇+20⋅X₇⋅X₇+22⋅X₇+25⋅X₉+32⋅X₈+4⋅X₁₀+12 {O(n^3)}
t₇, X₆: 9⋅X₇⋅X₇⋅X₇+30⋅X₇⋅X₇+18⋅X₉+26⋅X₈+33⋅X₇+6⋅X₁₀+16 {O(n^3)}
t₇, X₇: 2⋅X₇ {O(n)}
t₇, X₈: 2⋅X₈ {O(n)}
t₇, X₉: 2⋅X₉ {O(n)}
t₇, X₁₀: 2⋅X₁₀ {O(n)}
t₈, X₀: 4⋅X₇ {O(n)}
t₈, X₁: 14⋅X₈+4⋅X₉ {O(n)}
t₈, X₂: 12⋅X₈+14⋅X₉ {O(n)}
t₈, X₃: 6⋅X₇⋅X₇⋅X₇+20⋅X₇⋅X₇+22⋅X₇+4⋅X₁₀+8 {O(n^3)}
t₈, X₄: 6⋅X₇⋅X₇⋅X₇+20⋅X₇⋅X₇+22⋅X₇+22⋅X₉+4⋅X₁₀+40⋅X₈+12 {O(n^3)}
t₈, X₅: 6⋅X₇⋅X₇⋅X₇+20⋅X₇⋅X₇+22⋅X₇+32⋅X₉+38⋅X₈+4⋅X₁₀+12 {O(n^3)}
t₈, X₆: 12⋅X₇⋅X₇⋅X₇+40⋅X₇⋅X₇+18⋅X₉+26⋅X₈+44⋅X₇+8⋅X₁₀+20 {O(n^3)}
t₈, X₇: 4⋅X₇ {O(n)}
t₈, X₈: 4⋅X₈ {O(n)}
t₈, X₉: 4⋅X₉ {O(n)}
t₈, X₁₀: 4⋅X₁₀ {O(n)}