KoAT2 Proof Output

Initial Problem

Start: eval_ax_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: eval_ax_0, eval_ax_1, eval_ax_12, eval_ax_13, eval_ax_2, eval_ax_3, eval_ax_4, eval_ax_5, eval_ax_6, eval_ax_bb0_in, eval_ax_bb1_in, eval_ax_bb2_in, eval_ax_bb3_in, eval_ax_bb4_in, eval_ax_bb5_in, eval_ax_start, eval_ax_stop
Transitions:
t₂: eval_ax_0(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_1(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: eval_ax_1(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_2(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₄: eval_ax_12(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_13(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₅: eval_ax_13(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_bb1_in(X₂, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ 1+X₁ ∧ 2+X₂ ≤ X₅
t₁₆: eval_ax_13(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2+X₁ ≤ X₅
t₁₇: eval_ax_13(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ 1+X₂
t₄: eval_ax_2(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_3(X₀, X₁, X₂, X₃, X₄, X₅)
t₅: eval_ax_3(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_4(X₀, X₁, X₂, X₃, X₄, X₅)
t₆: eval_ax_4(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_5(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: eval_ax_5(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_6(X₀, X₁, X₂, X₃, X₄, X₅)
t₈: eval_ax_6(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_bb1_in(0, X₁, X₂, X₃, X₄, X₅)
t₁: eval_ax_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_0(X₀, X₁, X₂, X₃, X₄, X₅)
t₉: eval_ax_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_bb2_in(X₀, 0, X₂, X₃, X₄, X₅)
t₁₀: eval_ax_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2+X₁ ≤ X₅
t₁₁: eval_ax_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ 1+X₁
t₁₂: eval_ax_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_bb2_in(X₀, 1+X₁, X₂, X₃, X₄, X₅)
t₁₃: eval_ax_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_12(X₀, X₁, 1+X₀, X₃, X₄, X₅)
t₁₈: eval_ax_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_stop(X₀, X₁, X₂, X₃, X₄, X₅)
t₀: eval_ax_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ax_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Eliminate variables [X₃; X₄] that do not contribute to the problem

Found invariant X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 2+X₀ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_stop

Found invariant X₃ ≤ 1+X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb4_in

Found invariant X₃ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_12

Found invariant X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 2+X₀ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb5_in

Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb2_in

Found invariant 2 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb3_in

Found invariant X₃ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_13

Found invariant 0 ≤ X₀ for location eval_ax_bb1_in

Cut unsatisfiable transition [t₄₁: eval_ax_13→eval_ax_bb5_in]

Problem after Preprocessing

Start: eval_ax_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_ax_0, eval_ax_1, eval_ax_12, eval_ax_13, eval_ax_2, eval_ax_3, eval_ax_4, eval_ax_5, eval_ax_6, eval_ax_bb0_in, eval_ax_bb1_in, eval_ax_bb2_in, eval_ax_bb3_in, eval_ax_bb4_in, eval_ax_bb5_in, eval_ax_start, eval_ax_stop
Transitions:
t₃₇: eval_ax_0(X₀, X₁, X₂, X₃) → eval_ax_1(X₀, X₁, X₂, X₃)
t₃₈: eval_ax_1(X₀, X₁, X₂, X₃) → eval_ax_2(X₀, X₁, X₂, X₃)
t₃₉: eval_ax_12(X₀, X₁, X₂, X₃) → eval_ax_13(X₀, X₁, X₂, X₃) :|: X₂ ≤ 1+X₀ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₄₀: eval_ax_13(X₀, X₁, X₂, X₃) → eval_ax_bb1_in(X₂, X₁, X₂, X₃) :|: X₃ ≤ 1+X₁ ∧ 2+X₂ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₄₂: eval_ax_13(X₀, X₁, X₂, X₃) → eval_ax_bb5_in(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1+X₂ ∧ X₂ ≤ 1+X₀ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₄₃: eval_ax_2(X₀, X₁, X₂, X₃) → eval_ax_3(X₀, X₁, X₂, X₃)
t₄₄: eval_ax_3(X₀, X₁, X₂, X₃) → eval_ax_4(X₀, X₁, X₂, X₃)
t₄₅: eval_ax_4(X₀, X₁, X₂, X₃) → eval_ax_5(X₀, X₁, X₂, X₃)
t₄₆: eval_ax_5(X₀, X₁, X₂, X₃) → eval_ax_6(X₀, X₁, X₂, X₃)
t₄₇: eval_ax_6(X₀, X₁, X₂, X₃) → eval_ax_bb1_in(0, X₁, X₂, X₃)
t₄₈: eval_ax_bb0_in(X₀, X₁, X₂, X₃) → eval_ax_0(X₀, X₁, X₂, X₃)
t₄₉: eval_ax_bb1_in(X₀, X₁, X₂, X₃) → eval_ax_bb2_in(X₀, 0, X₂, X₃) :|: 0 ≤ X₀
t₅₀: eval_ax_bb2_in(X₀, X₁, X₂, X₃) → eval_ax_bb3_in(X₀, X₁, X₂, X₃) :|: 2+X₁ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₅₁: eval_ax_bb2_in(X₀, X₁, X₂, X₃) → eval_ax_bb4_in(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₅₂: eval_ax_bb3_in(X₀, X₁, X₂, X₃) → eval_ax_bb2_in(X₀, 1+X₁, X₂, X₃) :|: 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₅₃: eval_ax_bb4_in(X₀, X₁, X₂, X₃) → eval_ax_12(X₀, X₁, 1+X₀, X₃) :|: X₃ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₅₄: eval_ax_bb5_in(X₀, X₁, X₂, X₃) → eval_ax_stop(X₀, X₁, X₂, X₃) :|: X₃ ≤ 2+X₀ ∧ X₂ ≤ 1+X₀ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₅₅: eval_ax_start(X₀, X₁, X₂, X₃) → eval_ax_bb0_in(X₀, X₁, X₂, X₃)

MPRF for transition t₄₀: eval_ax_13(X₀, X₁, X₂, X₃) → eval_ax_bb1_in(X₂, X₁, X₂, X₃) :|: X₃ ≤ 1+X₁ ∧ 2+X₂ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₃+2 {O(n)}

MPRF:

• eval_ax_12: [X₃-1-X₂]
• eval_ax_13: [X₃-1-X₂]
• eval_ax_bb1_in: [X₃-2-X₀]
• eval_ax_bb2_in: [X₃-2-X₀]
• eval_ax_bb3_in: [X₃-2-X₀]
• eval_ax_bb4_in: [X₃-2-X₀]

knowledge_propagation leads to new time bound X₃+3 {O(n)} for transition t₄₉: eval_ax_bb1_in(X₀, X₁, X₂, X₃) → eval_ax_bb2_in(X₀, 0, X₂, X₃) :|: 0 ≤ X₀

MPRF for transition t₃₉: eval_ax_12(X₀, X₁, X₂, X₃) → eval_ax_13(X₀, X₁, X₂, X₃) :|: X₂ ≤ 1+X₀ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

2⋅X₃+6 {O(n)}

MPRF:

• eval_ax_12: [2]
• eval_ax_13: [1]
• eval_ax_bb1_in: [1]
• eval_ax_bb2_in: [2]
• eval_ax_bb3_in: [2]
• eval_ax_bb4_in: [2]

MPRF for transition t₅₀: eval_ax_bb2_in(X₀, X₁, X₂, X₃) → eval_ax_bb3_in(X₀, X₁, X₂, X₃) :|: 2+X₁ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₃⋅X₃+3⋅X₃ {O(n^2)}

MPRF:

• eval_ax_12: [X₃-X₁]
• eval_ax_13: [X₃-X₁]
• eval_ax_bb1_in: [X₃-X₁]
• eval_ax_bb2_in: [X₃-X₁]
• eval_ax_bb3_in: [X₃-1-X₁]
• eval_ax_bb4_in: [X₃-X₁]

MPRF for transition t₅₁: eval_ax_bb2_in(X₀, X₁, X₂, X₃) → eval_ax_bb4_in(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₃+3 {O(n)}

MPRF:

• eval_ax_12: [0]
• eval_ax_13: [0]
• eval_ax_bb1_in: [0]
• eval_ax_bb2_in: [1]
• eval_ax_bb3_in: [1]
• eval_ax_bb4_in: [0]

MPRF for transition t₅₂: eval_ax_bb3_in(X₀, X₁, X₂, X₃) → eval_ax_bb2_in(X₀, 1+X₁, X₂, X₃) :|: 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₃⋅X₃+4⋅X₃+3 {O(n^2)}

MPRF:

• eval_ax_12: [X₃-X₁]
• eval_ax_13: [X₃-X₁]
• eval_ax_bb1_in: [X₃-X₁]
• eval_ax_bb2_in: [1+X₃-X₁]
• eval_ax_bb3_in: [1+X₃-X₁]
• eval_ax_bb4_in: [X₃-X₁]

MPRF for transition t₅₃: eval_ax_bb4_in(X₀, X₁, X₂, X₃) → eval_ax_12(X₀, X₁, 1+X₀, X₃) :|: X₃ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₃+3 {O(n)}

MPRF:

• eval_ax_12: [0]
• eval_ax_13: [0]
• eval_ax_bb1_in: [2-2⋅X₀]
• eval_ax_bb2_in: [1]
• eval_ax_bb3_in: [1]
• eval_ax_bb4_in: [1]

Found invariant X₃ ≤ 1+X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb4_in

Found invariant X₃ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_12

Found invariant 2 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb3_in_v1

Found invariant 3 ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb3_in_v2

Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb2_in

Found invariant X₃ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_13

Found invariant 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_ax_bb2_in_v1

Found invariant 0 ≤ X₀ for location eval_ax_bb1_in

All Bounds

Timebounds

Overall timebound:2⋅X₃⋅X₃+13⋅X₃+31 {O(n^2)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: 2⋅X₃+6 {O(n)}
t₄₀: X₃+2 {O(n)}
t₄₂: 1 {O(1)}
t₄₃: 1 {O(1)}
t₄₄: 1 {O(1)}
t₄₅: 1 {O(1)}
t₄₆: 1 {O(1)}
t₄₇: 1 {O(1)}
t₄₈: 1 {O(1)}
t₄₉: X₃+3 {O(n)}
t₅₀: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₅₁: X₃+3 {O(n)}
t₅₂: X₃⋅X₃+4⋅X₃+3 {O(n^2)}
t₅₃: X₃+3 {O(n)}
t₅₄: 1 {O(1)}
t₅₅: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₃⋅X₃+13⋅X₃+31 {O(n^2)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: 2⋅X₃+6 {O(n)}
t₄₀: X₃+2 {O(n)}
t₄₂: 1 {O(1)}
t₄₃: 1 {O(1)}
t₄₄: 1 {O(1)}
t₄₅: 1 {O(1)}
t₄₆: 1 {O(1)}
t₄₇: 1 {O(1)}
t₄₈: 1 {O(1)}
t₄₉: X₃+3 {O(n)}
t₅₀: X₃⋅X₃+3⋅X₃ {O(n^2)}
t₅₁: X₃+3 {O(n)}
t₅₂: X₃⋅X₃+4⋅X₃+3 {O(n^2)}
t₅₃: X₃+3 {O(n)}
t₅₄: 1 {O(1)}
t₅₅: 1 {O(1)}

Sizebounds

t₃₇, X₀: X₀ {O(n)}
t₃₇, X₁: X₁ {O(n)}
t₃₇, X₂: X₂ {O(n)}
t₃₇, X₃: X₃ {O(n)}
t₃₈, X₀: X₀ {O(n)}
t₃₈, X₁: X₁ {O(n)}
t₃₈, X₂: X₂ {O(n)}
t₃₈, X₃: X₃ {O(n)}
t₃₉, X₀: X₃+2 {O(n)}
t₃₉, X₁: X₃⋅X₃+4⋅X₃+3 {O(n^2)}
t₃₉, X₂: X₃+3 {O(n)}
t₃₉, X₃: X₃ {O(n)}
t₄₀, X₀: X₃+2 {O(n)}
t₄₀, X₁: X₃⋅X₃+4⋅X₃+3 {O(n^2)}
t₄₀, X₂: X₃+3 {O(n)}
t₄₀, X₃: X₃ {O(n)}
t₄₂, X₀: X₃+2 {O(n)}
t₄₂, X₁: X₃⋅X₃+4⋅X₃+3 {O(n^2)}
t₄₂, X₂: X₃+3 {O(n)}
t₄₂, X₃: X₃ {O(n)}
t₄₃, X₀: X₀ {O(n)}
t₄₃, X₁: X₁ {O(n)}
t₄₃, X₂: X₂ {O(n)}
t₄₃, X₃: X₃ {O(n)}
t₄₄, X₀: X₀ {O(n)}
t₄₄, X₁: X₁ {O(n)}
t₄₄, X₂: X₂ {O(n)}
t₄₄, X₃: X₃ {O(n)}
t₄₅, X₀: X₀ {O(n)}
t₄₅, X₁: X₁ {O(n)}
t₄₅, X₂: X₂ {O(n)}
t₄₅, X₃: X₃ {O(n)}
t₄₆, X₀: X₀ {O(n)}
t₄₆, X₁: X₁ {O(n)}
t₄₆, X₂: X₂ {O(n)}
t₄₆, X₃: X₃ {O(n)}
t₄₇, X₀: 0 {O(1)}
t₄₇, X₁: X₁ {O(n)}
t₄₇, X₂: X₂ {O(n)}
t₄₇, X₃: X₃ {O(n)}
t₄₈, X₀: X₀ {O(n)}
t₄₈, X₁: X₁ {O(n)}
t₄₈, X₂: X₂ {O(n)}
t₄₈, X₃: X₃ {O(n)}
t₄₉, X₀: X₃+2 {O(n)}
t₄₉, X₁: 0 {O(1)}
t₄₉, X₂: X₂+X₃+3 {O(n)}
t₄₉, X₃: X₃ {O(n)}
t₅₀, X₀: X₃+2 {O(n)}
t₅₀, X₁: X₃⋅X₃+4⋅X₃+3 {O(n^2)}
t₅₀, X₂: X₂+X₃+3 {O(n)}
t₅₀, X₃: X₃ {O(n)}
t₅₁, X₀: X₃+2 {O(n)}
t₅₁, X₁: X₃⋅X₃+4⋅X₃+3 {O(n^2)}
t₅₁, X₂: 2⋅X₂+2⋅X₃+6 {O(n)}
t₅₁, X₃: X₃ {O(n)}
t₅₂, X₀: X₃+2 {O(n)}
t₅₂, X₁: X₃⋅X₃+4⋅X₃+3 {O(n^2)}
t₅₂, X₂: X₂+X₃+3 {O(n)}
t₅₂, X₃: X₃ {O(n)}
t₅₃, X₀: X₃+2 {O(n)}
t₅₃, X₁: X₃⋅X₃+4⋅X₃+3 {O(n^2)}
t₅₃, X₂: X₃+3 {O(n)}
t₅₃, X₃: X₃ {O(n)}
t₅₄, X₀: X₃+2 {O(n)}
t₅₄, X₁: X₃⋅X₃+4⋅X₃+3 {O(n^2)}
t₅₄, X₂: X₃+3 {O(n)}
t₅₄, X₃: X₃ {O(n)}
t₅₅, X₀: X₀ {O(n)}
t₅₅, X₁: X₁ {O(n)}
t₅₅, X₂: X₂ {O(n)}
t₅₅, X₃: X₃ {O(n)}