KoAT2 Proof Output

Initial Problem

Start: eval_abc_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: eval_abc_0, eval_abc_1, eval_abc_11, eval_abc_12, eval_abc_2, eval_abc_3, eval_abc_4, eval_abc_5, eval_abc_6, eval_abc_7, eval_abc_bb0_in, eval_abc_bb1_in, eval_abc_bb2_in, eval_abc_bb3_in, eval_abc_bb4_in, eval_abc_bb5_in, eval_abc_start, eval_abc_stop
Transitions:
t₂: eval_abc_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: eval_abc_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₆: eval_abc_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₇: eval_abc_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₀, X₆)
t₄: eval_abc_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₅: eval_abc_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₆: eval_abc_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₇: eval_abc_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: eval_abc_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₉: eval_abc_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₁, X₆)
t₁: eval_abc_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₀: eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₃) :|: X₅ ≤ X₂
t₁₁: eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₂ ≤ X₅
t₁₂: eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₄
t₁₃: eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄ ≤ X₆
t₁₄: eval_abc_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆)
t₁₅: eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_11(1+X₅, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₈: eval_abc_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₀: eval_abc_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

Preprocessing

Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ for location eval_abc_11

Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ for location eval_abc_bb4_in

Found invariant X₁ ≤ X₅ for location eval_abc_bb1_in

Found invariant 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅ for location eval_abc_bb5_in

Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ for location eval_abc_12

Found invariant X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ for location eval_abc_bb2_in

Found invariant 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅ for location eval_abc_stop

Found invariant X₆ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂ for location eval_abc_bb3_in

Problem after Preprocessing

Start: eval_abc_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: eval_abc_0, eval_abc_1, eval_abc_11, eval_abc_12, eval_abc_2, eval_abc_3, eval_abc_4, eval_abc_5, eval_abc_6, eval_abc_7, eval_abc_bb0_in, eval_abc_bb1_in, eval_abc_bb2_in, eval_abc_bb3_in, eval_abc_bb4_in, eval_abc_bb5_in, eval_abc_start, eval_abc_stop
Transitions:
t₂: eval_abc_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: eval_abc_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₆: eval_abc_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₅ ∧ 1+X₁ ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1+X₄ ≤ X₆ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆
t₁₇: eval_abc_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₀, X₆) :|: X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₅ ∧ 1+X₁ ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1+X₄ ≤ X₆ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆
t₄: eval_abc_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₅: eval_abc_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₆: eval_abc_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₇: eval_abc_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: eval_abc_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₉: eval_abc_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₁, X₆)
t₁: eval_abc_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₀: eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₃) :|: X₅ ≤ X₂ ∧ X₁ ≤ X₅
t₁₁: eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅
t₁₂: eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₄ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆
t₁₃: eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄ ≤ X₆ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆
t₁₄: eval_abc_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆) :|: X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₄
t₁₅: eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_11(1+X₅, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄ ≤ X₆ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆
t₁₈: eval_abc_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅
t₀: eval_abc_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

MPRF for transition t₁₀: eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₃) :|: X₅ ≤ X₂ ∧ X₁ ≤ X₅ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF:

• eval_abc_11: [X₂-X₅]
• eval_abc_12: [1+X₂-X₀]
• eval_abc_bb1_in: [1+X₂-X₅]
• eval_abc_bb2_in: [X₂-X₅]
• eval_abc_bb3_in: [X₂-X₅]
• eval_abc_bb4_in: [X₂-X₅]

MPRF for transition t₁₃: eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄ ≤ X₆ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF:

• eval_abc_11: [1+X₂-X₀]
• eval_abc_12: [1+X₂-X₀]
• eval_abc_bb1_in: [1+X₂-X₅]
• eval_abc_bb2_in: [1+X₂-X₅]
• eval_abc_bb3_in: [1+X₂-X₅]
• eval_abc_bb4_in: [X₂-X₅]

MPRF for transition t₁₅: eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_11(1+X₅, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₄ ≤ X₆ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF:

• eval_abc_11: [1+X₂-X₀]
• eval_abc_12: [1+X₂-X₀]
• eval_abc_bb1_in: [1+X₂-X₅]
• eval_abc_bb2_in: [1+X₂-X₅]
• eval_abc_bb3_in: [1+X₂-X₅]
• eval_abc_bb4_in: [1+X₂-X₅]

MPRF for transition t₁₆: eval_abc_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₅ ∧ 1+X₁ ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1+X₄ ≤ X₆ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF:

• eval_abc_11: [2+X₂-X₀]
• eval_abc_12: [X₂-X₅]
• eval_abc_bb1_in: [1+X₂-X₅]
• eval_abc_bb2_in: [1+X₂-X₅]
• eval_abc_bb3_in: [1+X₂-X₅]
• eval_abc_bb4_in: [1+X₂-X₅]

MPRF for transition t₁₇: eval_abc_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₀, X₆) :|: X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₅ ∧ 1+X₁ ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1+X₄ ≤ X₆ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF:

• eval_abc_11: [1+X₂-X₅]
• eval_abc_12: [1+X₂-X₅]
• eval_abc_bb1_in: [1+X₂-X₅]
• eval_abc_bb2_in: [1+X₂-X₅]
• eval_abc_bb3_in: [1+X₂-X₅]
• eval_abc_bb4_in: [1+X₂-X₅]

MPRF for transition t₁₂: eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₄ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₆ of depth 1:

new bound:

X₁⋅X₃+X₁⋅X₄+X₂⋅X₃+X₂⋅X₄+2⋅X₃+2⋅X₄+X₁+X₂+2 {O(n^2)}

MPRF:

• eval_abc_11: [X₄-X₆]
• eval_abc_12: [X₄-X₆]
• eval_abc_bb1_in: [1+X₄-X₃]
• eval_abc_bb2_in: [1+X₄-X₆]
• eval_abc_bb3_in: [X₄-X₆]
• eval_abc_bb4_in: [X₄-X₆]

MPRF for transition t₁₄: eval_abc_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆) :|: X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₃ ≤ X₄ ∧ X₃ ≤ X₆ ∧ X₆ ≤ X₄ of depth 1:

new bound:

X₁⋅X₃+X₁⋅X₄+X₂⋅X₃+X₂⋅X₄+2⋅X₃+2⋅X₄+X₁+X₂+2 {O(n^2)}

MPRF:

• eval_abc_11: [X₄-X₆]
• eval_abc_12: [X₄-X₆]
• eval_abc_bb1_in: [1+X₄-X₃]
• eval_abc_bb2_in: [1+X₄-X₆]
• eval_abc_bb3_in: [1+X₄-X₆]
• eval_abc_bb4_in: [X₄-X₆]

Found invariant X₆ ≤ 1+X₄ ∧ 1+X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂ for location eval_abc_bb2_in_v1

Found invariant 1+X₄ ≤ X₆ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ for location eval_abc_bb4_in

Found invariant X₁ ≤ X₅ for location eval_abc_bb1_in

Found invariant 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅ for location eval_abc_bb5_in

Found invariant X₆ ≤ X₃ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ for location eval_abc_bb2_in

Found invariant X₆ ≤ X₄ ∧ X₆ ≤ X₃ ∧ X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₁ ≤ X₂ for location eval_abc_bb3_in_v1

Found invariant X₆ ≤ X₄ ∧ 1+X₃ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₂ for location eval_abc_bb3_in_v2

Found invariant 1+X₂ ≤ X₅ ∧ X₁ ≤ X₅ for location eval_abc_stop

All Bounds

Timebounds

Overall timebound:2⋅X₁⋅X₃+2⋅X₁⋅X₄+2⋅X₂⋅X₃+2⋅X₂⋅X₄+4⋅X₃+4⋅X₄+7⋅X₁+7⋅X₂+21 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: X₁+X₂+1 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₁⋅X₃+X₁⋅X₄+X₂⋅X₃+X₂⋅X₄+2⋅X₃+2⋅X₄+X₁+X₂+2 {O(n^2)}
t₁₃: X₁+X₂+1 {O(n)}
t₁₄: X₁⋅X₃+X₁⋅X₄+X₂⋅X₃+X₂⋅X₄+2⋅X₃+2⋅X₄+X₁+X₂+2 {O(n^2)}
t₁₅: X₁+X₂+1 {O(n)}
t₁₆: X₁+X₂+1 {O(n)}
t₁₇: X₁+X₂+1 {O(n)}
t₁₈: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₁⋅X₃+2⋅X₁⋅X₄+2⋅X₂⋅X₃+2⋅X₂⋅X₄+4⋅X₃+4⋅X₄+7⋅X₁+7⋅X₂+21 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: X₁+X₂+1 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₁⋅X₃+X₁⋅X₄+X₂⋅X₃+X₂⋅X₄+2⋅X₃+2⋅X₄+X₁+X₂+2 {O(n^2)}
t₁₃: X₁+X₂+1 {O(n)}
t₁₄: X₁⋅X₃+X₁⋅X₄+X₂⋅X₃+X₂⋅X₄+2⋅X₃+2⋅X₄+X₁+X₂+2 {O(n^2)}
t₁₅: X₁+X₂+1 {O(n)}
t₁₆: X₁+X₂+1 {O(n)}
t₁₇: X₁+X₂+1 {O(n)}
t₁₈: 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: X₀ {O(n)}
t₁, X₁: X₁ {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: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {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, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {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, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₆, X₆: X₆ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₅ {O(n)}
t₇, X₆: X₆ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₈, X₆: X₆ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: X₁ {O(n)}
t₉, X₆: X₆ {O(n)}
t₁₀, X₀: 2⋅X₁+X₀+X₂+1 {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₀, X₆: 2⋅X₃ {O(n)}
t₁₁, X₀: 2⋅X₁+X₀+X₂+1 {O(n)}
t₁₁, X₁: 2⋅X₁ {O(n)}
t₁₁, X₂: 2⋅X₂ {O(n)}
t₁₁, X₃: 2⋅X₃ {O(n)}
t₁₁, X₄: 2⋅X₄ {O(n)}
t₁₁, X₅: 3⋅X₁+X₂+1 {O(n)}
t₁₁, X₆: X₁⋅X₃+X₁⋅X₄+X₂⋅X₃+X₂⋅X₄+2⋅X₄+6⋅X₃+X₁+X₂+X₆+2 {O(n^2)}
t₁₂, X₀: 2⋅X₁+X₀+X₂+1 {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₂, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₂, X₆: X₁⋅X₃+X₁⋅X₄+X₂⋅X₃+X₂⋅X₄+2⋅X₄+4⋅X₃+X₁+X₂+2 {O(n^2)}
t₁₃, X₀: 2⋅X₀+2⋅X₂+4⋅X₁+2 {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₃, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₃, X₆: X₁⋅X₃+X₁⋅X₄+X₂⋅X₃+X₂⋅X₄+2⋅X₄+6⋅X₃+X₁+X₂+2 {O(n^2)}
t₁₄, X₀: 2⋅X₁+X₀+X₂+1 {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₄, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₄, X₆: X₁⋅X₃+X₁⋅X₄+X₂⋅X₃+X₂⋅X₄+2⋅X₄+4⋅X₃+X₁+X₂+2 {O(n^2)}
t₁₅, X₀: 2⋅X₁+X₂+1 {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₅, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₅, X₆: X₁⋅X₃+X₁⋅X₄+X₂⋅X₃+X₂⋅X₄+2⋅X₄+6⋅X₃+X₁+X₂+2 {O(n^2)}
t₁₆, X₀: 2⋅X₁+X₂+1 {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₆, X₂: X₂ {O(n)}
t₁₆, X₃: X₃ {O(n)}
t₁₆, X₄: X₄ {O(n)}
t₁₆, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₆, X₆: X₁⋅X₃+X₁⋅X₄+X₂⋅X₃+X₂⋅X₄+2⋅X₄+6⋅X₃+X₁+X₂+2 {O(n^2)}
t₁₇, X₀: 2⋅X₁+X₂+1 {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: X₄ {O(n)}
t₁₇, X₅: 2⋅X₁+X₂+1 {O(n)}
t₁₇, X₆: X₁⋅X₃+X₁⋅X₄+X₂⋅X₃+X₂⋅X₄+2⋅X₄+6⋅X₃+X₁+X₂+2 {O(n^2)}
t₁₈, X₀: 2⋅X₁+X₀+X₂+1 {O(n)}
t₁₈, X₁: 2⋅X₁ {O(n)}
t₁₈, X₂: 2⋅X₂ {O(n)}
t₁₈, X₃: 2⋅X₃ {O(n)}
t₁₈, X₄: 2⋅X₄ {O(n)}
t₁₈, X₅: 3⋅X₁+X₂+1 {O(n)}
t₁₈, X₆: X₁⋅X₃+X₁⋅X₄+X₂⋅X₃+X₂⋅X₄+2⋅X₄+6⋅X₃+X₁+X₂+X₆+2 {O(n^2)}