KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ X₁ ≤ X₂ for location eval_speedNestedMultiple_bb3_in

Found invariant X₇ ≤ X₁ ∧ X₆ ≤ X₀ ∧ X₅ ≤ X₀ for location eval_speedNestedMultiple_bb5_in

Found invariant 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ X₁ ≤ X₂ for location eval_speedNestedMultiple_0

Found invariant 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ X₁ ≤ X₂ for location eval_speedNestedMultiple_1

Found invariant X₇ ≤ X₁ ∧ X₆ ≤ X₀ for location eval_speedNestedMultiple_bb1_in

Found invariant X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ X₁ ≤ X₂ for location eval_speedNestedMultiple_.critedge_in

Found invariant X₇ ≤ X₁ ∧ X₆ ≤ X₀ ∧ X₅ ≤ X₀ for location eval_speedNestedMultiple_stop

Found invariant 1+X₇ ≤ X₄ ∧ X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₁ ≤ X₂ for location eval_speedNestedMultiple_bb4_in

Found invariant X₇ ≤ X₂ ∧ X₇ ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ 1+X₀ ≤ X₅ ∧ X₁ ≤ X₂ for location eval_speedNestedMultiple_bb2_in

Problem after Preprocessing

Start: eval_speedNestedMultiple_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: nondef.0
Locations: eval_speedNestedMultiple_.critedge_in, eval_speedNestedMultiple_0, eval_speedNestedMultiple_1, eval_speedNestedMultiple_bb0_in, eval_speedNestedMultiple_bb1_in, eval_speedNestedMultiple_bb2_in, eval_speedNestedMultiple_bb3_in, eval_speedNestedMultiple_bb4_in, eval_speedNestedMultiple_bb5_in, eval_speedNestedMultiple_start, eval_speedNestedMultiple_stop
Transitions:
t₁₂: eval_speedNestedMultiple_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_bb1_in(1+X₀, X₂, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₅ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂
t₈: eval_speedNestedMultiple_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_1(X₀, X₁, X₂, nondef.0, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₅ ∧ 1+X₁ ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₇ ≤ X₄ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂
t₁₀: eval_speedNestedMultiple_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₃ ≤ 0 ∧ 1+X₀ ≤ X₅ ∧ 1+X₁ ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₇ ≤ X₄ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂
t₉: eval_speedNestedMultiple_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₃ ∧ 1+X₀ ≤ X₅ ∧ 1+X₁ ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₇ ≤ X₄ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂
t₁: eval_speedNestedMultiple_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_bb1_in(X₆, X₇, X₂, X₃, X₄, X₅, X₆, X₇)
t₂: eval_speedNestedMultiple_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_bb2_in(X₀, X₁, X₁, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁
t₃: eval_speedNestedMultiple_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ ≤ X₀ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁
t₅: eval_speedNestedMultiple_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₄ ≤ X₂ ∧ 1+X₀ ≤ X₅ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂
t₄: eval_speedNestedMultiple_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₂ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂
t₆: eval_speedNestedMultiple_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₅ ∧ 1+X₁ ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₇ ≤ X₄ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂
t₁₁: eval_speedNestedMultiple_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_bb2_in(X₀, X₁, 1+X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₅ ∧ 1+X₁ ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₇ ≤ X₄ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂
t₁₃: eval_speedNestedMultiple_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ ≤ X₀ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁
t₀: eval_speedNestedMultiple_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)

MPRF for transition t₂: eval_speedNestedMultiple_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_bb2_in(X₀, X₁, X₁, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁ of depth 1:

new bound:

X₅+X₆ {O(n)}

MPRF:

• eval_speedNestedMultiple_.critedge_in: [X₅-1-X₀]
• eval_speedNestedMultiple_0: [X₅-1-X₀]
• eval_speedNestedMultiple_1: [X₅-1-X₀]
• eval_speedNestedMultiple_bb1_in: [X₅-X₀]
• eval_speedNestedMultiple_bb2_in: [X₅-1-X₀]
• eval_speedNestedMultiple_bb3_in: [X₅-1-X₀]
• eval_speedNestedMultiple_bb4_in: [X₅-1-X₀]

MPRF for transition t₄: eval_speedNestedMultiple_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₂ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂ of depth 1:

new bound:

X₄+X₅+X₆+X₇+1 {O(n)}

MPRF:

• eval_speedNestedMultiple_.critedge_in: [X₄+X₅-2-X₀-X₂]
• eval_speedNestedMultiple_0: [X₄+X₅-2-X₀-X₂]
• eval_speedNestedMultiple_1: [X₄+X₅-2-X₀-X₂]
• eval_speedNestedMultiple_bb1_in: [X₄+X₅-1-X₀-X₁]
• eval_speedNestedMultiple_bb2_in: [X₄+X₅-1-X₀-X₂]
• eval_speedNestedMultiple_bb3_in: [X₄+X₅-2-X₀-X₂]
• eval_speedNestedMultiple_bb4_in: [X₄+X₅-2-X₀-X₂]

MPRF for transition t₅: eval_speedNestedMultiple_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₄ ≤ X₂ ∧ 1+X₀ ≤ X₅ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂ of depth 1:

new bound:

X₅+X₆ {O(n)}

MPRF:

• eval_speedNestedMultiple_.critedge_in: [X₅-1-X₀]
• eval_speedNestedMultiple_0: [X₅-X₀]
• eval_speedNestedMultiple_1: [X₅-X₀]
• eval_speedNestedMultiple_bb1_in: [X₅-X₀]
• eval_speedNestedMultiple_bb2_in: [X₅-X₀]
• eval_speedNestedMultiple_bb3_in: [X₅-X₀]
• eval_speedNestedMultiple_bb4_in: [X₅-X₀]

MPRF for transition t₆: eval_speedNestedMultiple_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₅ ∧ 1+X₁ ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₇ ≤ X₄ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂ of depth 1:

new bound:

X₄+X₅+X₆+X₇+1 {O(n)}

MPRF:

• eval_speedNestedMultiple_.critedge_in: [X₄+X₅-X₀-X₂]
• eval_speedNestedMultiple_0: [X₄+X₅-X₀-X₂]
• eval_speedNestedMultiple_1: [X₄+X₅-X₀-X₂]
• eval_speedNestedMultiple_bb1_in: [1+X₄+X₅-X₀-X₁]
• eval_speedNestedMultiple_bb2_in: [1+X₄+X₅-X₀-X₂]
• eval_speedNestedMultiple_bb3_in: [1+X₄+X₅-X₀-X₂]
• eval_speedNestedMultiple_bb4_in: [X₄+X₅-X₀-X₂]

MPRF for transition t₈: eval_speedNestedMultiple_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_1(X₀, X₁, X₂, nondef.0, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₅ ∧ 1+X₁ ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₇ ≤ X₄ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂ of depth 1:

new bound:

X₄+X₅+X₆+X₇+1 {O(n)}

MPRF:

• eval_speedNestedMultiple_.critedge_in: [X₄+X₅-X₀-X₂]
• eval_speedNestedMultiple_0: [1+X₄+X₅-X₀-X₂]
• eval_speedNestedMultiple_1: [X₄+X₅-X₀-X₂]
• eval_speedNestedMultiple_bb1_in: [1+X₄+X₅-X₀-X₁]
• eval_speedNestedMultiple_bb2_in: [1+X₄+X₅-X₀-X₂]
• eval_speedNestedMultiple_bb3_in: [1+X₄+X₅-X₀-X₂]
• eval_speedNestedMultiple_bb4_in: [X₄+X₅-X₀-X₂]

MPRF for transition t₉: eval_speedNestedMultiple_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₃ ∧ 1+X₀ ≤ X₅ ∧ 1+X₁ ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₇ ≤ X₄ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂ of depth 1:

new bound:

X₄+X₇+1 {O(n)}

MPRF:

• eval_speedNestedMultiple_.critedge_in: [1+X₄-X₂]
• eval_speedNestedMultiple_0: [1+X₄-X₂]
• eval_speedNestedMultiple_1: [1+X₄-X₂]
• eval_speedNestedMultiple_bb1_in: [1+X₄-X₁]
• eval_speedNestedMultiple_bb2_in: [1+X₄-X₂]
• eval_speedNestedMultiple_bb3_in: [1+X₄-X₂]
• eval_speedNestedMultiple_bb4_in: [X₄-X₂]

MPRF for transition t₁₀: eval_speedNestedMultiple_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₃ ≤ 0 ∧ 1+X₀ ≤ X₅ ∧ 1+X₁ ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 1+X₇ ≤ X₄ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂ of depth 1:

new bound:

X₅+X₆ {O(n)}

MPRF:

MPRF for transition t₁₁: eval_speedNestedMultiple_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_bb2_in(X₀, X₁, 1+X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₅ ∧ 1+X₁ ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₇ ≤ X₄ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂ of depth 1:

new bound:

X₄+X₇ {O(n)}

MPRF:

• eval_speedNestedMultiple_.critedge_in: [X₄-X₂]
• eval_speedNestedMultiple_0: [X₄-X₂]
• eval_speedNestedMultiple_1: [X₄-X₂]
• eval_speedNestedMultiple_bb1_in: [X₄-X₁]
• eval_speedNestedMultiple_bb2_in: [X₄-X₂]
• eval_speedNestedMultiple_bb3_in: [X₄-X₂]
• eval_speedNestedMultiple_bb4_in: [X₄-X₂]

MPRF for transition t₁₂: eval_speedNestedMultiple_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_speedNestedMultiple_bb1_in(1+X₀, X₂, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ X₅ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₇ ≤ X₂ of depth 1:

new bound:

X₅+X₆ {O(n)}

MPRF:

• eval_speedNestedMultiple_.critedge_in: [X₅-X₀]
• eval_speedNestedMultiple_0: [X₅-X₀]
• eval_speedNestedMultiple_1: [X₅-X₀]
• eval_speedNestedMultiple_bb1_in: [X₅-X₀]
• eval_speedNestedMultiple_bb2_in: [X₅-X₀]
• eval_speedNestedMultiple_bb3_in: [X₅-X₀]
• eval_speedNestedMultiple_bb4_in: [X₅-X₀]

All Bounds

Timebounds

Overall timebound:5⋅X₄+5⋅X₇+7⋅X₅+7⋅X₆+8 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₅+X₆ {O(n)}
t₃: 1 {O(1)}
t₄: X₄+X₅+X₆+X₇+1 {O(n)}
t₅: X₅+X₆ {O(n)}
t₆: X₄+X₅+X₆+X₇+1 {O(n)}
t₈: X₄+X₅+X₆+X₇+1 {O(n)}
t₉: X₄+X₇+1 {O(n)}
t₁₀: X₅+X₆ {O(n)}
t₁₁: X₄+X₇ {O(n)}
t₁₂: X₅+X₆ {O(n)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 5⋅X₄+5⋅X₇+7⋅X₅+7⋅X₆+8 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₅+X₆ {O(n)}
t₃: 1 {O(1)}
t₄: X₄+X₅+X₆+X₇+1 {O(n)}
t₅: X₅+X₆ {O(n)}
t₆: X₄+X₅+X₆+X₇+1 {O(n)}
t₈: X₄+X₅+X₆+X₇+1 {O(n)}
t₉: X₄+X₇+1 {O(n)}
t₁₀: X₅+X₆ {O(n)}
t₁₁: X₄+X₇ {O(n)}
t₁₂: X₅+X₆ {O(n)}
t₁₃: 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)}
t₁, X₀: X₆ {O(n)}
t₁, X₁: X₇ {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)}
t₁, X₇: X₇ {O(n)}
t₂, X₀: 2⋅X₆+X₅ {O(n)}
t₂, X₁: 3⋅X₇+X₄ {O(n)}
t₂, X₂: 2⋅X₇+X₄ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₂, X₇: X₇ {O(n)}
t₃, X₀: 3⋅X₆+X₅ {O(n)}
t₃, X₁: 3⋅X₇+X₄ {O(n)}
t₃, X₂: 2⋅X₄+4⋅X₇+X₂ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₃, X₆: 2⋅X₆ {O(n)}
t₃, X₇: 2⋅X₇ {O(n)}
t₄, X₀: 2⋅X₆+X₅ {O(n)}
t₄, X₁: 3⋅X₇+X₄ {O(n)}
t₄, X₂: 2⋅X₇+X₄ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {O(n)}
t₄, X₇: X₇ {O(n)}
t₅, X₀: 2⋅X₆+X₅ {O(n)}
t₅, X₁: 2⋅X₄+6⋅X₇ {O(n)}
t₅, X₂: 2⋅X₇+X₄ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₆ {O(n)}
t₅, X₇: X₇ {O(n)}
t₆, X₀: 2⋅X₆+X₅ {O(n)}
t₆, X₁: 3⋅X₇+X₄ {O(n)}
t₆, X₂: 2⋅X₇+X₄ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₆, X₆: X₆ {O(n)}
t₆, X₇: X₇ {O(n)}
t₈, X₀: 2⋅X₆+X₅ {O(n)}
t₈, X₁: 3⋅X₇+X₄ {O(n)}
t₈, X₂: 2⋅X₇+X₄ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₈, X₆: X₆ {O(n)}
t₈, X₇: X₇ {O(n)}
t₉, X₀: 2⋅X₆+X₅ {O(n)}
t₉, X₁: 3⋅X₇+X₄ {O(n)}
t₉, X₂: 2⋅X₇+X₄ {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: X₅ {O(n)}
t₉, X₆: X₆ {O(n)}
t₉, X₇: X₇ {O(n)}
t₁₀, X₀: 2⋅X₆+X₅ {O(n)}
t₁₀, X₁: 3⋅X₇+X₄ {O(n)}
t₁₀, X₂: 2⋅X₇+X₄ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₀, X₆: X₆ {O(n)}
t₁₀, X₇: X₇ {O(n)}
t₁₁, X₀: 2⋅X₆+X₅ {O(n)}
t₁₁, X₁: 3⋅X₇+X₄ {O(n)}
t₁₁, X₂: 2⋅X₇+X₄ {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₁₁, X₅: X₅ {O(n)}
t₁₁, X₆: X₆ {O(n)}
t₁₁, X₇: X₇ {O(n)}
t₁₂, X₀: 2⋅X₆+X₅ {O(n)}
t₁₂, X₁: 2⋅X₇+X₄ {O(n)}
t₁₂, X₂: 2⋅X₄+4⋅X₇ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₂, X₅: X₅ {O(n)}
t₁₂, X₆: X₆ {O(n)}
t₁₂, X₇: X₇ {O(n)}
t₁₃, X₀: 3⋅X₆+X₅ {O(n)}
t₁₃, X₁: 3⋅X₇+X₄ {O(n)}
t₁₃, X₂: 2⋅X₄+4⋅X₇+X₂ {O(n)}
t₁₃, X₄: 2⋅X₄ {O(n)}
t₁₃, X₅: 2⋅X₅ {O(n)}
t₁₃, X₆: 2⋅X₆ {O(n)}
t₁₃, X₇: 2⋅X₇ {O(n)}