KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₀ ≤ X₅ for location eval_t13_bb1_in

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ for location eval_t13_bb3_in

Found invariant 1 ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_t13_bb5_in

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_t13_bb2_in

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location eval_t13_stop

Found invariant 1 ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀ for location eval_t13_bb4_in

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ for location eval_t13_1

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location eval_t13_bb6_in

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ for location eval_t13_2

Problem after Preprocessing

Start: eval_t13_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef.0
Locations: eval_t13_1, eval_t13_2, eval_t13_bb0_in, eval_t13_bb1_in, eval_t13_bb2_in, eval_t13_bb3_in, eval_t13_bb4_in, eval_t13_bb5_in, eval_t13_bb6_in, eval_t13_start, eval_t13_stop
Transitions:
t₆: eval_t13_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_2(X₀, X₁, X₂, X₃, nondef.0, X₅, X₆) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃
t₇: eval_t13_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₄ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃
t₈: eval_t13_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_bb4_in(X₀, X₁, X₁, X₃, X₄, X₅, X₆) :|: X₄ ≤ 0 ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃
t₁: eval_t13_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_bb1_in(X₅, X₆, X₂, X₃, X₄, X₅, X₆)
t₂: eval_t13_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ X₀ ≤ X₅
t₃: eval_t13_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0 ∧ X₀ ≤ X₅
t₄: eval_t13_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_1(X₀, X₁, X₂, X₀-1, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₉: eval_t13_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_bb1_in(X₃, 1+X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₄+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃
t₁₁: eval_t13_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_bb1_in(X₃, X₂, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 0 ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 0
t₁₀: eval_t13_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₂ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 0
t₁₂: eval_t13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_bb4_in(X₀, X₁, X₂-1, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₂+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 0
t₁₃: eval_t13_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0 ∧ X₀ ≤ X₅
t₀: eval_t13_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

MPRF for transition t₂: eval_t13_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_t13_1: [X₃]
• eval_t13_2: [X₃]
• eval_t13_bb1_in: [X₀]
• eval_t13_bb2_in: [X₀-1]
• eval_t13_bb3_in: [X₃]
• eval_t13_bb4_in: [X₃]
• eval_t13_bb5_in: [X₃]

MPRF for transition t₄: eval_t13_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_1(X₀, X₁, X₂, X₀-1, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_t13_1: [X₀-1]
• eval_t13_2: [X₀-1]
• eval_t13_bb1_in: [X₀]
• eval_t13_bb2_in: [X₀]
• eval_t13_bb3_in: [X₀-1]
• eval_t13_bb4_in: [X₀-1]
• eval_t13_bb5_in: [X₀-1]

MPRF for transition t₆: eval_t13_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_2(X₀, X₁, X₂, X₃, nondef.0, X₅, X₆) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_t13_1: [1+X₃]
• eval_t13_2: [X₃]
• eval_t13_bb1_in: [X₀]
• eval_t13_bb2_in: [X₀]
• eval_t13_bb3_in: [X₃]
• eval_t13_bb4_in: [X₀-1]
• eval_t13_bb5_in: [X₀-1]

MPRF for transition t₇: eval_t13_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₄ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_t13_1: [X₀]
• eval_t13_2: [1+X₃]
• eval_t13_bb1_in: [X₀]
• eval_t13_bb2_in: [X₀]
• eval_t13_bb3_in: [X₃]
• eval_t13_bb4_in: [X₃]
• eval_t13_bb5_in: [X₃]

MPRF for transition t₈: eval_t13_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_bb4_in(X₀, X₁, X₁, X₃, X₄, X₅, X₆) :|: X₄ ≤ 0 ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_t13_1: [X₀]
• eval_t13_2: [1+X₃]
• eval_t13_bb1_in: [X₀]
• eval_t13_bb2_in: [X₀]
• eval_t13_bb3_in: [X₀]
• eval_t13_bb4_in: [X₃]
• eval_t13_bb5_in: [X₃]

MPRF for transition t₉: eval_t13_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_bb1_in(X₃, 1+X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₄+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_t13_1: [1+X₃]
• eval_t13_2: [1+X₃]
• eval_t13_bb1_in: [X₀]
• eval_t13_bb2_in: [X₀]
• eval_t13_bb3_in: [1+X₃]
• eval_t13_bb4_in: [X₃]
• eval_t13_bb5_in: [X₃]

MPRF for transition t₁₀: eval_t13_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₂ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 0 of depth 1:

new bound:

X₅+X₆ {O(n)}

MPRF:

• eval_t13_1: [1+X₁+X₃]
• eval_t13_2: [1+X₁+X₃]
• eval_t13_bb1_in: [X₀+X₁]
• eval_t13_bb2_in: [X₀+X₁]
• eval_t13_bb3_in: [1+X₁+X₃]
• eval_t13_bb4_in: [X₀+X₂]
• eval_t13_bb5_in: [X₀+X₂-1]

MPRF for transition t₁₁: eval_t13_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_bb1_in(X₃, X₂, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 0 ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 0 of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_t13_1: [X₀]
• eval_t13_2: [X₀]
• eval_t13_bb1_in: [X₀]
• eval_t13_bb2_in: [X₀]
• eval_t13_bb3_in: [X₀]
• eval_t13_bb4_in: [1+X₃]
• eval_t13_bb5_in: [1+X₃]

MPRF for transition t₁₂: eval_t13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_t13_bb4_in(X₀, X₁, X₂-1, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₂+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₃ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 0 of depth 1:

new bound:

X₅+X₆+1 {O(n)}

MPRF:

• eval_t13_1: [X₁+X₃]
• eval_t13_2: [X₁+X₃]
• eval_t13_bb1_in: [X₀+X₁-1]
• eval_t13_bb2_in: [X₀+X₁-1]
• eval_t13_bb3_in: [X₁+X₃]
• eval_t13_bb4_in: [X₂+X₃]
• eval_t13_bb5_in: [X₂+X₃]

All Bounds

Timebounds

Overall timebound:2⋅X₆+9⋅X₅+5 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₅ {O(n)}
t₃: 1 {O(1)}
t₄: X₅ {O(n)}
t₆: X₅ {O(n)}
t₇: X₅ {O(n)}
t₈: X₅ {O(n)}
t₉: X₅ {O(n)}
t₁₀: X₅+X₆ {O(n)}
t₁₁: X₅ {O(n)}
t₁₂: X₅+X₆+1 {O(n)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₆+9⋅X₅+5 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₅ {O(n)}
t₃: 1 {O(1)}
t₄: X₅ {O(n)}
t₆: X₅ {O(n)}
t₇: X₅ {O(n)}
t₈: X₅ {O(n)}
t₉: X₅ {O(n)}
t₁₀: X₅+X₆ {O(n)}
t₁₁: X₅ {O(n)}
t₁₂: X₅+X₆+1 {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)}
t₁, X₀: X₅ {O(n)}
t₁, X₁: X₆ {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: X₅ {O(n)}
t₂, X₁: X₅+X₆ {O(n)}
t₂, X₂: 2⋅X₅+2⋅X₆+X₂ {O(n)}
t₂, X₃: 3⋅X₅+X₃ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₃, X₀: 3⋅X₅ {O(n)}
t₃, X₁: 2⋅X₅+3⋅X₆ {O(n)}
t₃, X₂: 2⋅X₂+4⋅X₅+4⋅X₆ {O(n)}
t₃, X₃: 3⋅X₅+X₃ {O(n)}
t₃, X₅: 3⋅X₅ {O(n)}
t₃, X₆: 3⋅X₆ {O(n)}
t₄, X₀: X₅ {O(n)}
t₄, X₁: X₅+X₆ {O(n)}
t₄, X₂: 2⋅X₅+2⋅X₆+X₂ {O(n)}
t₄, X₃: X₅ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {O(n)}
t₆, X₀: X₅ {O(n)}
t₆, X₁: X₅+X₆ {O(n)}
t₆, X₂: 2⋅X₅+2⋅X₆+X₂ {O(n)}
t₆, X₃: X₅ {O(n)}
t₆, X₅: X₅ {O(n)}
t₆, X₆: X₆ {O(n)}
t₇, X₀: X₅ {O(n)}
t₇, X₁: X₅+X₆ {O(n)}
t₇, X₂: 2⋅X₅+2⋅X₆+X₂ {O(n)}
t₇, X₃: X₅ {O(n)}
t₇, X₅: X₅ {O(n)}
t₇, X₆: X₆ {O(n)}
t₈, X₀: X₅ {O(n)}
t₈, X₁: X₅+X₆ {O(n)}
t₈, X₂: X₅+X₆ {O(n)}
t₈, X₃: X₅ {O(n)}
t₈, X₅: X₅ {O(n)}
t₈, X₆: X₆ {O(n)}
t₉, X₀: X₅ {O(n)}
t₉, X₁: X₅+X₆ {O(n)}
t₉, X₂: 2⋅X₅+2⋅X₆+X₂ {O(n)}
t₉, X₃: X₅ {O(n)}
t₉, X₅: X₅ {O(n)}
t₉, X₆: X₆ {O(n)}
t₁₀, X₀: X₅ {O(n)}
t₁₀, X₁: X₅+X₆ {O(n)}
t₁₀, X₂: X₅+X₆ {O(n)}
t₁₀, X₃: X₅ {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₀, X₆: X₆ {O(n)}
t₁₁, X₀: X₅ {O(n)}
t₁₁, X₁: X₅+X₆ {O(n)}
t₁₁, X₂: 2⋅X₅+2⋅X₆ {O(n)}
t₁₁, X₃: 2⋅X₅ {O(n)}
t₁₁, X₅: X₅ {O(n)}
t₁₁, X₆: X₆ {O(n)}
t₁₂, X₀: X₅ {O(n)}
t₁₂, X₁: X₅+X₆ {O(n)}
t₁₂, X₂: X₅+X₆ {O(n)}
t₁₂, X₃: X₅ {O(n)}
t₁₂, X₅: X₅ {O(n)}
t₁₂, X₆: X₆ {O(n)}
t₁₃, X₀: 3⋅X₅ {O(n)}
t₁₃, X₁: 2⋅X₅+3⋅X₆ {O(n)}
t₁₃, X₂: 2⋅X₂+4⋅X₅+4⋅X₆ {O(n)}
t₁₃, X₃: 3⋅X₅+X₃ {O(n)}
t₁₃, X₅: 3⋅X₅ {O(n)}
t₁₃, X₆: 3⋅X₆ {O(n)}