Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₁, X₃, X₄, X₅, X₆) :|: X₀+(X₁)² ≤ 0
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₀+(X₁)²
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, (X₂)², X₄, X₅, X₆)
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₄, X₅, X₂, X₃, X₄, X₅, X₆) :|: X₆ < 0
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₅, X₃, X₄, X₅, X₆) :|: 0 ≤ X₆
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀+(X₁)²*X₆, X₁-2⋅(X₆)², X₂, X₃, X₄, X₅, X₆)
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₃
t₈: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 0
t₉: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆)
t₁₀: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

Preprocessing

Found invariant X₂ ≤ X₅ for location l2

Found invariant X₂ ≤ X₅ ∧ 1 ≤ X₃ for location l6

Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l7

Found invariant X₂ ≤ X₅ ∧ 0 ≤ X₃ for location l5

Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l8

Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location l1

Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₁, X₃, X₄, X₅, X₆) :|: X₀+(X₁)² ≤ 0 ∧ 1+X₆ ≤ 0 ∧ X₁ ≤ X₅
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₀+(X₁)² ∧ 1+X₆ ≤ 0 ∧ X₁ ≤ X₅
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, (X₂)², X₄, X₅, X₆) :|: X₂ ≤ X₅
t₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₄, X₅, X₂, X₃, X₄, X₅, X₆) :|: X₆ < 0
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₅, X₃, X₄, X₅, X₆) :|: 0 ≤ X₆
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀+(X₁)²*X₆, X₁-2⋅(X₆)², X₂, X₃, X₄, X₅, X₆) :|: 1+X₆ ≤ 0 ∧ X₁ ≤ X₅
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₃ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₃
t₈: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 0 ∧ X₂ ≤ X₅ ∧ 0 ≤ X₃
t₉: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆) :|: X₂ ≤ X₅ ∧ 1 ≤ X₃
t₁₀: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃

TWN: t₃: l1→l4

cycle: [t₃: l1→l4; t₅: l4→l1]
loop: (0 < X₀+(X₁)²,(X₀,X₁,X₆) -> (X₀+(X₁)²*X₆,X₁-2⋅(X₆)²,X₆)
order: [X₆; X₁; X₀]
closed-form:
X₆: X₆
X₁: X₁ + [[n != 0]] * -2⋅(X₆)² * n^1
X₀: X₀ + [[n != 0]] * (X₁)²*X₆ * n^1 + [[n != 0, n != 1]] * 4/3⋅(X₆)⁵ * n^3 + [[n != 0, n != 1]] * (-2⋅(X₆)⁵-2⋅X₁*(X₆)³) * n^2 + [[n != 0, n != 1]] * (2/3⋅(X₆)⁵+2⋅X₁*(X₆)³) * n^1

Termination: true
Formula:

0 < 4⋅(X₆)⁵
∨ 6⋅(X₆)⁵+6⋅X₁*(X₆)³ < 12⋅(X₆)⁴ ∧ 0 ≤ 4⋅(X₆)⁵ ∧ 4⋅(X₆)⁵ ≤ 0
∨ 12⋅X₁*(X₆)² < 3⋅(X₁)²*X₆+2⋅(X₆)⁵+6⋅X₁*(X₆)³ ∧ 0 ≤ 4⋅(X₆)⁵ ∧ 4⋅(X₆)⁵ ≤ 0 ∧ 6⋅(X₆)⁵+6⋅X₁*(X₆)³ ≤ 12⋅(X₆)⁴ ∧ 12⋅(X₆)⁴ ≤ 6⋅(X₆)⁵+6⋅X₁*(X₆)³
∨ 0 < 3⋅X₀+3⋅(X₁)² ∧ 0 ≤ 4⋅(X₆)⁵ ∧ 4⋅(X₆)⁵ ≤ 0 ∧ 6⋅(X₆)⁵+6⋅X₁*(X₆)³ ≤ 12⋅(X₆)⁴ ∧ 12⋅(X₆)⁴ ≤ 6⋅(X₆)⁵+6⋅X₁*(X₆)³ ∧ 12⋅X₁*(X₆)² ≤ 3⋅(X₁)²*X₆+2⋅(X₆)⁵+6⋅X₁*(X₆)³ ∧ 3⋅(X₁)²*X₆+2⋅(X₆)⁵+6⋅X₁*(X₆)³ ≤ 12⋅X₁*(X₆)²

Stabilization-Threshold for: 0 < X₀+(X₁)²
alphas_abs: 3⋅X₀+12⋅X₁*(X₆)²+6⋅X₁*(X₆)³+3⋅(X₁)²+3⋅(X₁)²*X₆+12⋅(X₆)⁴+6⋅(X₆)⁵
M: 0
N: 3
Bound: 12⋅X₆⋅X₆⋅X₆⋅X₆⋅X₆+12⋅X₁⋅X₆⋅X₆⋅X₆+24⋅X₆⋅X₆⋅X₆⋅X₆+24⋅X₁⋅X₆⋅X₆+6⋅X₁⋅X₁⋅X₆+6⋅X₁⋅X₁+6⋅X₀+4 {O(n^5)}

TWN - Lifting for t₃: l1→l4 of 12⋅X₆⋅X₆⋅X₆⋅X₆⋅X₆+12⋅X₁⋅X₆⋅X₆⋅X₆+24⋅X₆⋅X₆⋅X₆⋅X₆+24⋅X₁⋅X₆⋅X₆+6⋅X₁⋅X₁⋅X₆+6⋅X₁⋅X₁+6⋅X₀+6 {O(n^5)}

relevant size-bounds w.r.t. t₁:
X₀: X₄ {O(n)}
X₁: X₅ {O(n)}
X₆: X₆ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 12⋅X₆⋅X₆⋅X₆⋅X₆⋅X₆+12⋅X₅⋅X₆⋅X₆⋅X₆+24⋅X₆⋅X₆⋅X₆⋅X₆+24⋅X₅⋅X₆⋅X₆+6⋅X₅⋅X₅⋅X₆+6⋅X₅⋅X₅+6⋅X₄+6 {O(n^5)}

TWN: t₅: l4→l1

TWN - Lifting for t₅: l4→l1 of 12⋅X₆⋅X₆⋅X₆⋅X₆⋅X₆+12⋅X₁⋅X₆⋅X₆⋅X₆+24⋅X₆⋅X₆⋅X₆⋅X₆+24⋅X₁⋅X₆⋅X₆+6⋅X₁⋅X₁⋅X₆+6⋅X₁⋅X₁+6⋅X₀+6 {O(n^5)}

relevant size-bounds w.r.t. t₁:
X₀: X₄ {O(n)}
X₁: X₅ {O(n)}
X₆: X₆ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 12⋅X₆⋅X₆⋅X₆⋅X₆⋅X₆+12⋅X₅⋅X₆⋅X₆⋅X₆+24⋅X₆⋅X₆⋅X₆⋅X₆+24⋅X₅⋅X₆⋅X₆+6⋅X₅⋅X₅⋅X₆+6⋅X₅⋅X₅+6⋅X₄+6 {O(n^5)}

Chain transitions t₅: l4→l1 and t₃: l1→l4 to t₇₂: l4→l4

Chain transitions t₁: l3→l1 and t₃: l1→l4 to t₇₃: l3→l4

Chain transitions t₁: l3→l1 and t₄: l1→l2 to t₇₄: l3→l2

Chain transitions t₅: l4→l1 and t₄: l1→l2 to t₇₅: l4→l2

Analysing control-flow refined program

Found invariant X₂ ≤ X₅ for location l2

Found invariant X₂ ≤ X₅ ∧ 1 ≤ X₃ for location l6

Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l7

Found invariant X₂ ≤ X₅ ∧ 0 ≤ X₃ for location l5

Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l8

Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location l1

Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location l4

TWN: t₇₂: l4→l4

cycle: [t₇₂: l4→l4]
loop: (4⋅X₁*(X₆)² < X₀+(X₁)²*X₆+(X₁)²+4⋅(X₆)⁴,(X₀,X₁,X₆) -> (X₀+(X₁)²*X₆,X₁-2⋅(X₆)²,X₆)
order: [X₆; X₁; X₀]
closed-form:
X₆: X₆
X₁: X₁ + [[n != 0]] * -2⋅(X₆)² * n^1
X₀: X₀ + [[n != 0]] * (X₁)²*X₆ * n^1 + [[n != 0, n != 1]] * 4/3⋅(X₆)⁵ * n^3 + [[n != 0, n != 1]] * (-2⋅(X₆)⁵-2⋅X₁*(X₆)³) * n^2 + [[n != 0, n != 1]] * (2/3⋅(X₆)⁵+2⋅X₁*(X₆)³) * n^1

Termination: true
Formula:

0 < 4⋅(X₆)⁵
∨ 6⋅X₁*(X₆)³ < 6⋅(X₆)⁵+12⋅(X₆)⁴ ∧ 0 ≤ 4⋅(X₆)⁵ ∧ 4⋅(X₆)⁵ ≤ 0
∨ 6⋅X₁*(X₆)³+12⋅X₁*(X₆)² < 3⋅(X₁)²*X₆+2⋅(X₆)⁵+24⋅(X₆)⁴ ∧ 0 ≤ 4⋅(X₆)⁵ ∧ 4⋅(X₆)⁵ ≤ 0 ∧ 6⋅X₁*(X₆)³ ≤ 6⋅(X₆)⁵+12⋅(X₆)⁴ ∧ 6⋅(X₆)⁵+12⋅(X₆)⁴ ≤ 6⋅X₁*(X₆)³
∨ 12⋅X₁*(X₆)² < 3⋅X₀+3⋅(X₁)²*X₆+3⋅(X₁)²+12⋅(X₆)⁴ ∧ 0 ≤ 4⋅(X₆)⁵ ∧ 4⋅(X₆)⁵ ≤ 0 ∧ 6⋅X₁*(X₆)³ ≤ 6⋅(X₆)⁵+12⋅(X₆)⁴ ∧ 6⋅(X₆)⁵+12⋅(X₆)⁴ ≤ 6⋅X₁*(X₆)³ ∧ 6⋅X₁*(X₆)³+12⋅X₁*(X₆)² ≤ 3⋅(X₁)²*X₆+2⋅(X₆)⁵+24⋅(X₆)⁴ ∧ 3⋅(X₁)²*X₆+2⋅(X₆)⁵+24⋅(X₆)⁴ ≤ 6⋅X₁*(X₆)³+12⋅X₁*(X₆)²

Stabilization-Threshold for: 4⋅X₁*(X₆)² < X₀+(X₁)²*X₆+(X₁)²+4⋅(X₆)⁴
alphas_abs: 3⋅X₀+12⋅X₁*(X₆)²+6⋅X₁*(X₆)³+3⋅(X₁)²+3⋅(X₁)²*X₆+24⋅(X₆)⁴+6⋅(X₆)⁵
M: 0
N: 3
Bound: 12⋅X₆⋅X₆⋅X₆⋅X₆⋅X₆+12⋅X₁⋅X₆⋅X₆⋅X₆+48⋅X₆⋅X₆⋅X₆⋅X₆+24⋅X₁⋅X₆⋅X₆+6⋅X₁⋅X₁⋅X₆+6⋅X₁⋅X₁+6⋅X₀+4 {O(n^5)}

TWN - Lifting for t₇₂: l4→l4 of 12⋅X₆⋅X₆⋅X₆⋅X₆⋅X₆+12⋅X₁⋅X₆⋅X₆⋅X₆+48⋅X₆⋅X₆⋅X₆⋅X₆+24⋅X₁⋅X₆⋅X₆+6⋅X₁⋅X₁⋅X₆+6⋅X₁⋅X₁+6⋅X₀+6 {O(n^5)}

relevant size-bounds w.r.t. t₇₃:
X₀: X₄ {O(n)}
X₁: X₅ {O(n)}
X₆: X₆ {O(n)}
Runtime-bound of t₇₃: 1 {O(1)}
Results in: 12⋅X₆⋅X₆⋅X₆⋅X₆⋅X₆+12⋅X₅⋅X₆⋅X₆⋅X₆+48⋅X₆⋅X₆⋅X₆⋅X₆+24⋅X₅⋅X₆⋅X₆+6⋅X₅⋅X₅⋅X₆+6⋅X₅⋅X₅+6⋅X₄+6 {O(n^5)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant X₂ ≤ X₅ for location l2

Found invariant X₂ ≤ X₅ ∧ 1 ≤ X₃ for location l6

Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location n_l4___2

Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l7

Found invariant X₂ ≤ X₅ ∧ 0 ≤ X₃ for location l5

Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l8

Found invariant 1+X₆ ≤ 0 ∧ X₅ ≤ X₁ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₄ for location l1

Found invariant 1+X₆ ≤ 0 for location n_l1___1

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Chain transitions t₉: l6→l5 and t₈: l5→l7 to t₂₅₆: l6→l7

Chain transitions t₆: l2→l5 and t₈: l5→l7 to t₂₅₇: l2→l7

Chain transitions t₆: l2→l5 and t₇: l5→l6 to t₂₅₈: l2→l6

Chain transitions t₉: l6→l5 and t₇: l5→l6 to t₂₅₉: l6→l6

Analysing control-flow refined program

Found invariant X₂ ≤ X₅ for location l2

Found invariant X₂ ≤ X₅ ∧ 0 ≤ X₃ for location l6

Found invariant X₂ ≤ X₅ ∧ 0 ≤ X₃ for location l7

Found invariant X₂ ≤ X₅ ∧ 0 ≤ X₃ for location l5

Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l8

Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location l1

Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location l4

MPRF for transition t₂₅₉: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) -{2}> l6(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆) :|: 1 < X₃ ∧ X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ X₂ ≤ X₅ ∧ 0 ≤ X₃ of depth 1:

new bound:

2⋅X₅⋅X₅+1 {O(n^2)}

Analysing control-flow refined program

Found invariant X₂ ≤ X₅ for location l2

Found invariant X₂ ≤ X₅ ∧ 0 ≤ X₃ for location n_l5___1

Found invariant X₂ ≤ X₅ ∧ 1 ≤ X₃ for location n_l6___2

Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l7

Found invariant X₂ ≤ X₅ ∧ 0 ≤ X₃ for location l5

Found invariant X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location l8

Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location l1

Found invariant 1+X₆ ≤ 0 ∧ X₁ ≤ X₅ for location l4

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 12⋅X₆⋅X₆⋅X₆⋅X₆⋅X₆+12⋅X₅⋅X₆⋅X₆⋅X₆+24⋅X₆⋅X₆⋅X₆⋅X₆+24⋅X₅⋅X₆⋅X₆+6⋅X₅⋅X₅⋅X₆+6⋅X₅⋅X₅+6⋅X₄+6 {O(n^5)}
t₄: 1 {O(1)}
t₅: 12⋅X₆⋅X₆⋅X₆⋅X₆⋅X₆+12⋅X₅⋅X₆⋅X₆⋅X₆+24⋅X₆⋅X₆⋅X₆⋅X₆+24⋅X₅⋅X₆⋅X₆+6⋅X₅⋅X₅⋅X₆+6⋅X₅⋅X₅+6⋅X₄+6 {O(n^5)}
t₆: 1 {O(1)}
t₇: inf {Infinity}
t₈: 1 {O(1)}
t₉: inf {Infinity}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 12⋅X₆⋅X₆⋅X₆⋅X₆⋅X₆+12⋅X₅⋅X₆⋅X₆⋅X₆+24⋅X₆⋅X₆⋅X₆⋅X₆+24⋅X₅⋅X₆⋅X₆+6⋅X₅⋅X₅⋅X₆+6⋅X₅⋅X₅+6⋅X₄+6 {O(n^5)}
t₄: 1 {O(1)}
t₅: 12⋅X₆⋅X₆⋅X₆⋅X₆⋅X₆+12⋅X₅⋅X₆⋅X₆⋅X₆+24⋅X₆⋅X₆⋅X₆⋅X₆+24⋅X₅⋅X₆⋅X₆+6⋅X₅⋅X₅⋅X₆+6⋅X₅⋅X₅+6⋅X₄+6 {O(n^5)}
t₆: 1 {O(1)}
t₇: inf {Infinity}
t₈: 1 {O(1)}
t₉: inf {Infinity}
t₁₀: 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)}
t₁, X₀: X₄ {O(n)}
t₁, X₁: X₅ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₅ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₃, X₅: X₅ {O(n)}
t₃, X₆: X₆ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅X₅ {O(n)}
t₄, X₆: 2⋅X₆ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₆ {O(n)}
t₆, X₄: 3⋅X₄ {O(n)}
t₆, X₅: 3⋅X₅ {O(n)}
t₆, X₆: 3⋅X₆ {O(n)}
t₇, X₄: 3⋅X₄ {O(n)}
t₇, X₅: 3⋅X₅ {O(n)}
t₇, X₆: 3⋅X₆ {O(n)}
t₈, X₃: 0 {O(1)}
t₈, X₄: 6⋅X₄ {O(n)}
t₈, X₅: 6⋅X₅ {O(n)}
t₈, X₆: 6⋅X₆ {O(n)}
t₉, X₄: 3⋅X₄ {O(n)}
t₉, X₅: 3⋅X₅ {O(n)}
t₉, X₆: 3⋅X₆ {O(n)}
t₁₀, X₃: 0 {O(1)}
t₁₀, X₄: 6⋅X₄ {O(n)}
t₁₀, X₅: 6⋅X₅ {O(n)}
t₁₀, X₆: 6⋅X₆ {O(n)}