KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₆ ≤ X₄ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 2 ≤ X₄+X₆ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₂+X₆ ∧ 1 ≤ X₁+X₆ ∧ X₅ ≤ 0 ∧ 1+X₅ ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₁+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location eval_Loopus2015_ex2_bb5_in

Found invariant X₆ ≤ X₄ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₄+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ X₁+X₆ ∧ X₅ ≤ 0 ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location eval_Loopus2015_ex2_bb4_in

Found invariant X₅ ≤ X₃ ∧ 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location eval_Loopus2015_ex2_bb3_in

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location eval_Loopus2015_ex2_bb1_in

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location eval_Loopus2015_ex2_1

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location eval_Loopus2015_ex2_0

Found invariant X₅ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location eval_Loopus2015_ex2_bb2_in

Problem after Preprocessing

Start: eval_Loopus2015_ex2_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef.0
Locations: eval_Loopus2015_ex2_0, eval_Loopus2015_ex2_1, eval_Loopus2015_ex2_bb0_in, eval_Loopus2015_ex2_bb1_in, eval_Loopus2015_ex2_bb2_in, eval_Loopus2015_ex2_bb3_in, eval_Loopus2015_ex2_bb4_in, eval_Loopus2015_ex2_bb5_in, eval_Loopus2015_ex2_bb6_in, eval_Loopus2015_ex2_start, eval_Loopus2015_ex2_stop
Transitions:
t₇: eval_Loopus2015_ex2_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_1(nondef.0, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₈: eval_Loopus2015_ex2_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_bb2_in(X₀, X₁, X₂, X₃, X₁, X₃, X₆) :|: 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₉: eval_Loopus2015_ex2_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_bb2_in(X₀, X₁, X₂, X₃, X₂, X₃, X₆) :|: X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₄: eval_Loopus2015_ex2_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
t₁: eval_Loopus2015_ex2_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₃ ≤ 0
t₂: eval_Loopus2015_ex2_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₁ ≤ 0
t₃: eval_Loopus2015_ex2_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₂ ≤ 0
t₅: eval_Loopus2015_ex2_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₁₀: eval_Loopus2015_ex2_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₁₁: eval_Loopus2015_ex2_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₄) :|: X₅ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₁₂: eval_Loopus2015_ex2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_bb2_in(X₀, X₁, X₂, X₃, 2+X₄, X₅-1, X₆) :|: 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₄
t₁₃: eval_Loopus2015_ex2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₆ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₁+X₅ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₁+X₆ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₄+X₆ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ 0 ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆
t₁₄: eval_Loopus2015_ex2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₁+X₅ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₁+X₆ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₄+X₆ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ 0 ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆
t₁₅: eval_Loopus2015_ex2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1) :|: 1 ≤ X₁+X₄ ∧ 1 ≤ X₁+X₆ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₂+X₆ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 1 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₄+X₆ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₅ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₅ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₅ ∧ X₅ ≤ 0
t₁₆: eval_Loopus2015_ex2_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₀: eval_Loopus2015_ex2_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

MPRF for transition t₁₀: eval_Loopus2015_ex2_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₁+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

2⋅X₃+2 {O(n)}

MPRF:

• eval_Loopus2015_ex2_bb2_in: [1+X₅]
• eval_Loopus2015_ex2_bb3_in: [X₅]

MPRF for transition t₁₂: eval_Loopus2015_ex2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_bb2_in(X₀, X₁, X₂, X₃, 2+X₄, X₅-1, X₆) :|: 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₄ of depth 1:

new bound:

2⋅X₃ {O(n)}

MPRF:

• eval_Loopus2015_ex2_bb2_in: [X₅]
• eval_Loopus2015_ex2_bb3_in: [X₅]

MPRF for transition t₁₃: eval_Loopus2015_ex2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₆ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₄ ∧ 0 ≤ X₁+X₅ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₁+X₆ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₂+X₅ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₄+X₆ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ 0 ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆ of depth 1:

new bound:

2⋅X₁+2⋅X₂+4⋅X₃+1 {O(n)}

MPRF:

• eval_Loopus2015_ex2_bb4_in: [1+X₆]
• eval_Loopus2015_ex2_bb5_in: [X₆]

MPRF for transition t₁₅: eval_Loopus2015_ex2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2015_ex2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1) :|: 1 ≤ X₁+X₄ ∧ 1 ≤ X₁+X₆ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₂+X₆ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 1 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₄+X₆ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₁+X₅ ∧ X₅ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₅ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ X₅ ≤ X₃ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 of depth 1:

new bound:

2⋅X₁+2⋅X₂+4⋅X₃ {O(n)}

MPRF:

• eval_Loopus2015_ex2_bb4_in: [X₆]
• eval_Loopus2015_ex2_bb5_in: [X₆]

All Bounds

Timebounds

Overall timebound:12⋅X₃+4⋅X₁+4⋅X₂+15 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 2⋅X₃+2 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 2⋅X₃ {O(n)}
t₁₃: 2⋅X₁+2⋅X₂+4⋅X₃+1 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: 2⋅X₁+2⋅X₂+4⋅X₃ {O(n)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 12⋅X₃+4⋅X₁+4⋅X₂+15 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 2⋅X₃+2 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 2⋅X₃ {O(n)}
t₁₃: 2⋅X₁+2⋅X₂+4⋅X₃+1 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: 2⋅X₁+2⋅X₂+4⋅X₃ {O(n)}
t₁₆: 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)}
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, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₁ {O(n)}
t₈, X₅: X₃ {O(n)}
t₈, X₆: X₆ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: X₂ {O(n)}
t₉, X₅: X₃ {O(n)}
t₉, X₆: X₆ {O(n)}
t₁₀, X₁: 2⋅X₁ {O(n)}
t₁₀, X₂: 2⋅X₂ {O(n)}
t₁₀, X₃: 2⋅X₃ {O(n)}
t₁₀, X₄: 4⋅X₃+X₁+X₂ {O(n)}
t₁₀, X₅: 2⋅X₃ {O(n)}
t₁₀, X₆: 2⋅X₆ {O(n)}
t₁₁, X₁: 4⋅X₁ {O(n)}
t₁₁, X₂: 4⋅X₂ {O(n)}
t₁₁, X₃: 4⋅X₃ {O(n)}
t₁₁, X₄: 2⋅X₁+2⋅X₂+4⋅X₃ {O(n)}
t₁₁, X₅: 0 {O(1)}
t₁₁, X₆: 2⋅X₁+2⋅X₂+4⋅X₃ {O(n)}
t₁₂, X₁: 2⋅X₁ {O(n)}
t₁₂, X₂: 2⋅X₂ {O(n)}
t₁₂, X₃: 2⋅X₃ {O(n)}
t₁₂, X₄: 4⋅X₃+X₁+X₂ {O(n)}
t₁₂, X₅: 2⋅X₃ {O(n)}
t₁₂, X₆: 2⋅X₆ {O(n)}
t₁₃, X₁: 4⋅X₁ {O(n)}
t₁₃, X₂: 4⋅X₂ {O(n)}
t₁₃, X₃: 4⋅X₃ {O(n)}
t₁₃, X₄: 2⋅X₁+2⋅X₂+4⋅X₃ {O(n)}
t₁₃, X₅: 0 {O(1)}
t₁₃, X₆: 2⋅X₁+2⋅X₂+4⋅X₃ {O(n)}
t₁₄, X₁: 8⋅X₁ {O(n)}
t₁₄, X₂: 8⋅X₂ {O(n)}
t₁₄, X₃: 8⋅X₃ {O(n)}
t₁₄, X₄: 4⋅X₁+4⋅X₂+8⋅X₃ {O(n)}
t₁₄, X₅: 0 {O(1)}
t₁₄, X₆: 0 {O(1)}
t₁₅, X₁: 4⋅X₁ {O(n)}
t₁₅, X₂: 4⋅X₂ {O(n)}
t₁₅, X₃: 4⋅X₃ {O(n)}
t₁₅, X₄: 2⋅X₁+2⋅X₂+4⋅X₃ {O(n)}
t₁₅, X₅: 0 {O(1)}
t₁₅, X₆: 2⋅X₁+2⋅X₂+4⋅X₃ {O(n)}
t₁₆, X₁: 11⋅X₁ {O(n)}
t₁₆, X₂: 11⋅X₂ {O(n)}
t₁₆, X₃: 11⋅X₃ {O(n)}
t₁₆, X₄: 3⋅X₄+4⋅X₁+4⋅X₂+8⋅X₃ {O(n)}
t₁₆, X₅: 3⋅X₅ {O(n)}
t₁₆, X₆: 3⋅X₆ {O(n)}