KoAT2 Proof Output

Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₂, X₁, X₂) :|: 1 ≤ X₁
t₂: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₁ ≤ 0
t₃: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁
t₄: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 1+X₁ ≤ X₀
t₅: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₆: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb1_in(0, X₁, X₂) :|: 1+X₁ ≤ X₀
t₇: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb1_in(1+X₀, X₁, X₂) :|: X₀ ≤ X₁
t₈: eval_foo_bb3_in(X₀, X₁, X₂) → eval_foo_stop(X₀, X₁, X₂)
t₀: eval_foo_start(X₀, X₁, X₂) → eval_foo_bb0_in(X₀, X₁, X₂)

Preprocessing

Found invariant 1 ≤ X₁ for location eval_foo_bb2_in

Found invariant 1 ≤ X₁ for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₂, X₁, X₂) :|: 1 ≤ X₁
t₂: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₁ ≤ 0
t₃: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₁
t₄: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁
t₅: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₁
t₆: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb1_in(0, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁
t₇: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb1_in(1+X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 1 ≤ X₁
t₈: eval_foo_bb3_in(X₀, X₁, X₂) → eval_foo_stop(X₀, X₁, X₂)
t₀: eval_foo_start(X₀, X₁, X₂) → eval_foo_bb0_in(X₀, X₁, X₂)

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ for location eval_foo_bb1_in_v1

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location eval_foo_bb1_in_v3

Found invariant 4 ≤ X₂ ∧ 7 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 6 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location eval_foo_bb2_in_v5

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location eval_foo_bb1_in_v2

Found invariant 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location eval_foo_bb2_in_v4

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location eval_foo_bb2_in_v2

Found invariant 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location eval_foo_bb1_in_v4

Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ for location eval_foo_bb1_in

Found invariant X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_foo_bb2_in_v1

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location eval_foo_bb2_in_v3

Analysing control-flow refined program

MPRF for transition t₆₄: eval_foo_bb1_in_v4(X₀, X₁, X₂) → eval_foo_bb2_in_v5(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₁ ∧ 5 ≤ X₀+X₂ ∧ 5 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₂+2 {O(n)}

MPRF:

• eval_foo_bb1_in_v4: [X₂-X₀]
• eval_foo_bb2_in_v5: [X₂-1-X₀]

MPRF for transition t₆₅: eval_foo_bb2_in_v5(X₀, X₁, X₂) → eval_foo_bb1_in_v4(1+X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₂ ∧ 5 ≤ X₀+X₁ ∧ 6 ≤ X₀+X₂ ∧ 7 ≤ X₁+X₂ of depth 1:

new bound:

X₁+3 {O(n)}

MPRF:

• eval_foo_bb1_in_v4: [1+X₁-X₀]
• eval_foo_bb2_in_v5: [1+X₁-X₀]

MPRF for transition t₅₄: eval_foo_bb2_in_v2(X₀, X₁, X₂) → eval_foo_bb1_in_v1(1+X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF:

• eval_foo_bb1_in_v1: [1+X₁-X₀]
• eval_foo_bb2_in_v2: [1+X₁-X₀]

MPRF for transition t₅₆: eval_foo_bb1_in_v1(X₀, X₁, X₂) → eval_foo_bb2_in_v2(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ X₀ ≤ 1+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₁+X₂ {O(n)}

MPRF:

• eval_foo_bb1_in_v1: [1+X₁-X₀]
• eval_foo_bb2_in_v2: [X₁-X₀]

CFR: Improvement to new bound with the following program:

method: PartialEvaluation new bound:

O(n)

cfr-program:

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb1_in_v1, eval_foo_bb1_in_v2, eval_foo_bb1_in_v3, eval_foo_bb1_in_v4, eval_foo_bb2_in_v1, eval_foo_bb2_in_v2, eval_foo_bb2_in_v3, eval_foo_bb2_in_v4, eval_foo_bb2_in_v5, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₂, X₁, X₂) :|: 1 ≤ X₁
t₂: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₁ ≤ 0
t₅₂: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in_v1(X₀, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₅₃: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in_v2(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₅: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₅₁: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₅₆: eval_foo_bb1_in_v1(X₀, X₁, X₂) → eval_foo_bb2_in_v2(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ X₀ ≤ 1+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ X₁
t₅₅: eval_foo_bb1_in_v1(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ X₀ ≤ 1+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₁
t₅₈: eval_foo_bb1_in_v2(X₀, X₁, X₂) → eval_foo_bb2_in_v3(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁
t₆₁: eval_foo_bb1_in_v3(X₀, X₁, X₂) → eval_foo_bb2_in_v4(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁
t₆₀: eval_foo_bb1_in_v3(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀
t₆₄: eval_foo_bb1_in_v4(X₀, X₁, X₂) → eval_foo_bb2_in_v5(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₁ ∧ 5 ≤ X₀+X₂ ∧ 5 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁
t₆₃: eval_foo_bb1_in_v4(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ 0 ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₁ ∧ 5 ≤ X₀+X₂ ∧ 5 ≤ X₁+X₂ ∧ 0 ≤ X₀
t₅₇: eval_foo_bb2_in_v1(X₀, X₁, X₂) → eval_foo_bb1_in_v2(0, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₅₄: eval_foo_bb2_in_v2(X₀, X₁, X₂) → eval_foo_bb1_in_v1(1+X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀
t₅₉: eval_foo_bb2_in_v3(X₀, X₁, X₂) → eval_foo_bb1_in_v3(1+X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
t₆₂: eval_foo_bb2_in_v4(X₀, X₁, X₂) → eval_foo_bb1_in_v4(1+X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 5 ≤ X₁+X₂
t₆₅: eval_foo_bb2_in_v5(X₀, X₁, X₂) → eval_foo_bb1_in_v4(1+X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀ ∧ 2+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₂ ∧ 5 ≤ X₀+X₁ ∧ 6 ≤ X₀+X₂ ∧ 7 ≤ X₁+X₂
t₈: eval_foo_bb3_in(X₀, X₁, X₂) → eval_foo_stop(X₀, X₁, X₂)
t₀: eval_foo_start(X₀, X₁, X₂) → eval_foo_bb0_in(X₀, X₁, X₂)

All Bounds

Timebounds

Overall timebound:3⋅X₁+3⋅X₂+22 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: 1 {O(1)}
t₈: 1 {O(1)}
t₅₁: 1 {O(1)}
t₅₂: 1 {O(1)}
t₅₃: 1 {O(1)}
t₅₄: X₁+X₂+1 {O(n)}
t₅₅: 1 {O(1)}
t₅₆: X₁+X₂ {O(n)}
t₅₇: 1 {O(1)}
t₅₈: 1 {O(1)}
t₅₉: 1 {O(1)}
t₆₀: 1 {O(1)}
t₆₁: 1 {O(1)}
t₆₂: 1 {O(1)}
t₆₃: 1 {O(1)}
t₆₄: X₂+2 {O(n)}
t₆₅: X₁+3 {O(n)}

Costbounds

Overall costbound: 3⋅X₁+3⋅X₂+22 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: 1 {O(1)}
t₈: 1 {O(1)}
t₅₁: 1 {O(1)}
t₅₂: 1 {O(1)}
t₅₃: 1 {O(1)}
t₅₄: X₁+X₂+1 {O(n)}
t₅₅: 1 {O(1)}
t₅₆: X₁+X₂ {O(n)}
t₅₇: 1 {O(1)}
t₅₈: 1 {O(1)}
t₅₉: 1 {O(1)}
t₆₀: 1 {O(1)}
t₆₁: 1 {O(1)}
t₆₂: 1 {O(1)}
t₆₃: 1 {O(1)}
t₆₄: X₂+2 {O(n)}
t₆₅: X₁+3 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₅, X₀: X₂ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₈, X₀: 2⋅X₁+4⋅X₂+X₀+11 {O(n)}
t₈, X₁: 6⋅X₁+1 {O(n)}
t₈, X₂: 7⋅X₂ {O(n)}
t₅₁, X₀: X₂ {O(n)}
t₅₁, X₁: X₁ {O(n)}
t₅₁, X₂: X₂ {O(n)}
t₅₂, X₀: X₂ {O(n)}
t₅₂, X₁: X₁ {O(n)}
t₅₂, X₂: X₂ {O(n)}
t₅₃, X₀: X₂ {O(n)}
t₅₃, X₁: X₁ {O(n)}
t₅₃, X₂: X₂ {O(n)}
t₅₄, X₀: 2⋅X₂+X₁+2 {O(n)}
t₅₄, X₁: X₁ {O(n)}
t₅₄, X₂: X₂ {O(n)}
t₅₅, X₀: 2⋅X₂+X₁+2 {O(n)}
t₅₅, X₁: X₁ {O(n)}
t₅₅, X₂: X₂ {O(n)}
t₅₆, X₀: 2⋅X₂+X₁+2 {O(n)}
t₅₆, X₁: X₁ {O(n)}
t₅₆, X₂: X₂ {O(n)}
t₅₇, X₀: 0 {O(1)}
t₅₇, X₁: X₁ {O(n)}
t₅₇, X₂: X₂ {O(n)}
t₅₈, X₀: 0 {O(1)}
t₅₈, X₁: X₁ {O(n)}
t₅₈, X₂: X₂ {O(n)}
t₅₉, X₀: 1 {O(1)}
t₅₉, X₁: X₁ {O(n)}
t₅₉, X₂: X₂ {O(n)}
t₆₀, X₀: 1 {O(1)}
t₆₀, X₁: 1 {O(1)}
t₆₀, X₂: X₂ {O(n)}
t₆₁, X₀: 1 {O(1)}
t₆₁, X₁: X₁ {O(n)}
t₆₁, X₂: X₂ {O(n)}
t₆₂, X₀: 2 {O(1)}
t₆₂, X₁: X₁ {O(n)}
t₆₂, X₂: X₂ {O(n)}
t₆₃, X₀: X₁+8 {O(n)}
t₆₃, X₁: 2⋅X₁ {O(n)}
t₆₃, X₂: 2⋅X₂ {O(n)}
t₆₄, X₀: X₁+6 {O(n)}
t₆₄, X₁: X₁ {O(n)}
t₆₄, X₂: X₂ {O(n)}
t₆₅, X₀: X₁+6 {O(n)}
t₆₅, X₁: X₁ {O(n)}
t₆₅, X₂: X₂ {O(n)}