KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_abc_bb2_in

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 1+X₃ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_abc_10

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_abc_bb4_in

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 1+X₃ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_abc_9

Found invariant 1 ≤ X₂ for location eval_abc_bb1_in

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₂ for location eval_abc_stop

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_abc_bb3_in

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₂ for location eval_abc_bb5_in

Problem after Preprocessing

Start: eval_abc_start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: eval_abc_0, eval_abc_1, eval_abc_10, eval_abc_2, eval_abc_3, eval_abc_4, eval_abc_5, eval_abc_9, 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) → eval_abc_1(X₀, X₁, X₂, X₃, X₄)
t₃: eval_abc_1(X₀, X₁, X₂, X₃, X₄) → eval_abc_2(X₀, X₁, X₂, X₃, X₄)
t₁₅: eval_abc_10(X₀, X₁, X₂, X₃, X₄) → eval_abc_bb1_in(X₀, X₁, X₀, X₃, X₄) :|: X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₄ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₄ ∧ X₂ ≤ X₄
t₄: eval_abc_2(X₀, X₁, X₂, X₃, X₄) → eval_abc_3(X₀, X₁, X₂, X₃, X₄)
t₅: eval_abc_3(X₀, X₁, X₂, X₃, X₄) → eval_abc_4(X₀, X₁, X₂, X₃, X₄)
t₆: eval_abc_4(X₀, X₁, X₂, X₃, X₄) → eval_abc_5(X₀, X₁, X₂, X₃, X₄)
t₇: eval_abc_5(X₀, X₁, X₂, X₃, X₄) → eval_abc_bb1_in(X₀, X₁, 1, X₃, X₄)
t₁₄: eval_abc_9(X₀, X₁, X₂, X₃, X₄) → eval_abc_10(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₄ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₄ ∧ X₂ ≤ X₄
t₁: eval_abc_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_abc_0(X₀, X₁, X₂, X₃, X₄)
t₈: eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_abc_bb2_in(X₀, 1, X₂, X₃, X₄) :|: X₂ ≤ X₄ ∧ 1 ≤ X₂
t₉: eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_abc_bb5_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ 1 ≤ X₂
t₁₀: eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_abc_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄
t₁₁: eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄
t₁₂: eval_abc_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_abc_bb2_in(X₀, 1+X₁, X₂, X₃, X₄) :|: 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₄
t₁₃: eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_abc_9(1+X₂, X₁, X₂, X₃, X₄) :|: 1 ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄
t₁₆: eval_abc_bb5_in(X₀, X₁, X₂, X₃, X₄) → eval_abc_stop(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₂ ∧ 1+X₄ ≤ X₂
t₀: eval_abc_start(X₀, X₁, X₂, X₃, X₄) → eval_abc_bb0_in(X₀, X₁, X₂, X₃, X₄)

MPRF for transition t₈: eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_abc_bb2_in(X₀, 1, X₂, X₃, X₄) :|: X₂ ≤ X₄ ∧ 1 ≤ X₂ of depth 1:

new bound:

X₄+2 {O(n)}

MPRF:

• eval_abc_10: [X₄-X₂]
• eval_abc_9: [X₄-X₂]
• eval_abc_bb1_in: [1+X₄-X₂]
• eval_abc_bb2_in: [X₄-X₂]
• eval_abc_bb3_in: [X₄-X₂]
• eval_abc_bb4_in: [X₄-X₂]

MPRF for transition t₁₁: eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ of depth 1:

new bound:

X₄+2 {O(n)}

MPRF:

• eval_abc_10: [X₄-X₂]
• eval_abc_9: [X₄-X₂]
• eval_abc_bb1_in: [1+X₄-X₂]
• eval_abc_bb2_in: [1+X₄-X₂]
• eval_abc_bb3_in: [1+X₄-X₂]
• eval_abc_bb4_in: [X₄-X₂]

MPRF for transition t₁₃: eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_abc_9(1+X₂, X₁, X₂, X₃, X₄) :|: 1 ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ of depth 1:

new bound:

X₄+2 {O(n)}

MPRF:

• eval_abc_10: [X₄-X₂]
• eval_abc_9: [1+X₄-X₀]
• eval_abc_bb1_in: [1+X₄-X₂]
• eval_abc_bb2_in: [1+X₄-X₂]
• eval_abc_bb3_in: [1+X₄-X₂]
• eval_abc_bb4_in: [1+X₄-X₂]

MPRF for transition t₁₄: eval_abc_9(X₀, X₁, X₂, X₃, X₄) → eval_abc_10(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₄ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₄ ∧ X₂ ≤ X₄ of depth 1:

new bound:

X₄+2 {O(n)}

MPRF:

• eval_abc_10: [1+X₄-X₀]
• eval_abc_9: [2+X₄-X₀]
• eval_abc_bb1_in: [1+X₄-X₂]
• eval_abc_bb2_in: [1+X₄-X₂]
• eval_abc_bb3_in: [1+X₄-X₂]
• eval_abc_bb4_in: [1+X₄-X₂]

MPRF for transition t₁₅: eval_abc_10(X₀, X₁, X₂, X₃, X₄) → eval_abc_bb1_in(X₀, X₁, X₀, X₃, X₄) :|: X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₄ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₄ ∧ X₂ ≤ X₄ of depth 1:

new bound:

X₄+2 {O(n)}

MPRF:

• eval_abc_10: [2+X₄-X₀]
• eval_abc_9: [2+X₄-X₀]
• eval_abc_bb1_in: [1+X₄-X₂]
• eval_abc_bb2_in: [1+X₄-X₂]
• eval_abc_bb3_in: [1+X₄-X₂]
• eval_abc_bb4_in: [1+X₄-X₂]

MPRF for transition t₁₀: eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_abc_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ of depth 1:

new bound:

X₃⋅X₄+3⋅X₃ {O(n^2)}

MPRF:

• eval_abc_10: [X₃-X₁]
• eval_abc_9: [X₃-X₁]
• eval_abc_bb1_in: [X₃]
• eval_abc_bb2_in: [1+X₃-X₁]
• eval_abc_bb3_in: [X₃-X₁]
• eval_abc_bb4_in: [X₃-X₁]

MPRF for transition t₁₂: eval_abc_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_abc_bb2_in(X₀, 1+X₁, X₂, X₃, X₄) :|: 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₄ of depth 1:

new bound:

X₃⋅X₄+3⋅X₃ {O(n^2)}

MPRF:

• eval_abc_10: [X₃-X₁]
• eval_abc_9: [X₃-X₁]
• eval_abc_bb1_in: [X₃]
• eval_abc_bb2_in: [1+X₃-X₁]
• eval_abc_bb3_in: [1+X₃-X₁]
• eval_abc_bb4_in: [X₃-X₁]

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location eval_abc_bb2_in_v1

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_abc_bb4_in

Found invariant 1 ≤ X₂ for location eval_abc_bb1_in

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₂ for location eval_abc_bb5_in

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ for location eval_abc_bb2_in

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ for location eval_abc_bb3_in_v1

Found invariant 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location eval_abc_bb3_in_v2

Found invariant 1+X₄ ≤ X₂ ∧ 1 ≤ X₂ for location eval_abc_stop

All Bounds

Timebounds

Overall timebound:2⋅X₃⋅X₄+5⋅X₄+6⋅X₃+20 {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: X₄+2 {O(n)}
t₉: 1 {O(1)}
t₁₀: X₃⋅X₄+3⋅X₃ {O(n^2)}
t₁₁: X₄+2 {O(n)}
t₁₂: X₃⋅X₄+3⋅X₃ {O(n^2)}
t₁₃: X₄+2 {O(n)}
t₁₄: X₄+2 {O(n)}
t₁₅: X₄+2 {O(n)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₃⋅X₄+5⋅X₄+6⋅X₃+20 {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: X₄+2 {O(n)}
t₉: 1 {O(1)}
t₁₀: X₃⋅X₄+3⋅X₃ {O(n^2)}
t₁₁: X₄+2 {O(n)}
t₁₂: X₃⋅X₄+3⋅X₃ {O(n^2)}
t₁₃: X₄+2 {O(n)}
t₁₄: X₄+2 {O(n)}
t₁₅: X₄+2 {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)}
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)}
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)}
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)}
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)}
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)}
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)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: 1 {O(1)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₈, X₀: X₀+X₄+3 {O(n)}
t₈, X₁: 1 {O(1)}
t₈, X₂: X₄+3 {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₉, X₀: X₀+X₄+3 {O(n)}
t₉, X₁: X₃⋅X₄+3⋅X₃+X₁+2 {O(n^2)}
t₉, X₂: X₄+4 {O(n)}
t₉, X₃: 2⋅X₃ {O(n)}
t₉, X₄: 2⋅X₄ {O(n)}
t₁₀, X₀: X₀+X₄+3 {O(n)}
t₁₀, X₁: X₃⋅X₄+3⋅X₃+1 {O(n^2)}
t₁₀, X₂: X₄+3 {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₁, X₀: 2⋅X₀+2⋅X₄+6 {O(n)}
t₁₁, X₁: X₃⋅X₄+3⋅X₃+2 {O(n^2)}
t₁₁, X₂: X₄+3 {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₁₂, X₀: X₀+X₄+3 {O(n)}
t₁₂, X₁: X₃⋅X₄+3⋅X₃+1 {O(n^2)}
t₁₂, X₂: X₄+3 {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₃, X₀: X₄+3 {O(n)}
t₁₃, X₁: X₃⋅X₄+3⋅X₃+2 {O(n^2)}
t₁₃, X₂: X₄+3 {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₄, X₀: X₄+3 {O(n)}
t₁₄, X₁: X₃⋅X₄+3⋅X₃+2 {O(n^2)}
t₁₄, X₂: X₄+3 {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₅, X₀: X₄+3 {O(n)}
t₁₅, X₁: X₃⋅X₄+3⋅X₃+2 {O(n^2)}
t₁₅, X₂: X₄+3 {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₆, X₀: X₀+X₄+3 {O(n)}
t₁₆, X₁: X₃⋅X₄+3⋅X₃+X₁+2 {O(n^2)}
t₁₆, X₂: X₄+4 {O(n)}
t₁₆, X₃: 2⋅X₃ {O(n)}
t₁₆, X₄: 2⋅X₄ {O(n)}