KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₀ ≤ X₅ for location eval_foo_bb5_in

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_0

Found invariant X₀ ≤ X₅ for location eval_foo_stop

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb3_in

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_3

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb2_in

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_1

Found invariant X₀ ≤ X₅ for location eval_foo_bb1_in

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_4

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb4_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef.0, nondef.1
Locations: eval_foo_0, eval_foo_1, eval_foo_3, eval_foo_4, eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_start, eval_foo_stop
Transitions:
t₇: eval_foo_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_1(X₀, X₁, nondef.0, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₀ ≤ X₅
t₈: eval_foo_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₂ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₀ ≤ X₅
t₉: eval_foo_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₀ ≤ X₅
t₁₀: eval_foo_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₀ ≤ X₅
t₁₃: eval_foo_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_4(X₀, X₁, X₂, X₃, nondef.1, X₅, X₆) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃
t₁₄: eval_foo_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb1_in(X₃, X₄, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb1_in(X₅, X₆, X₂, X₃, X₄, X₅, X₆)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₅
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0 ∧ X₀ ≤ X₅
t₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ ≤ 0 ∧ X₀ ≤ X₅
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₀ ≤ X₅
t₁₁: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_3(X₀, X₁, X₂, X₀-1, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₀ ≤ X₅
t₁₅: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb1_in(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₁₆: eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ X₅
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

MPRF for transition t₈: eval_foo_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₂ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_foo_0: [X₀]
• eval_foo_1: [X₀]
• eval_foo_3: [X₃]
• eval_foo_4: [X₃]
• eval_foo_bb1_in: [X₀]
• eval_foo_bb2_in: [X₀]
• eval_foo_bb3_in: [X₀-1]
• eval_foo_bb4_in: [X₀]

MPRF for transition t₉: eval_foo_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

MPRF for transition t₁₁: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_3(X₀, X₁, X₂, X₀-1, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

• eval_foo_0: [1+X₀]
• eval_foo_1: [1+X₀]
• eval_foo_3: [1+X₃]
• eval_foo_4: [X₀]
• eval_foo_bb1_in: [1+X₀]
• eval_foo_bb2_in: [1+X₀]
• eval_foo_bb3_in: [1+X₀]
• eval_foo_bb4_in: [1+X₀]

MPRF for transition t₁₃: eval_foo_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_4(X₀, X₁, X₂, X₃, nondef.1, X₅, X₆) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

• eval_foo_0: [1+X₀]
• eval_foo_1: [1+X₀]
• eval_foo_3: [2+X₃]
• eval_foo_4: [X₀]
• eval_foo_bb1_in: [1+X₀]
• eval_foo_bb2_in: [1+X₀]
• eval_foo_bb3_in: [1+X₀]
• eval_foo_bb4_in: [1+X₀]

MPRF for transition t₁₄: eval_foo_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb1_in(X₃, X₄, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_foo_0: [X₀]
• eval_foo_1: [X₀]
• eval_foo_3: [X₀]
• eval_foo_4: [1+X₃]
• eval_foo_bb1_in: [X₀]
• eval_foo_bb2_in: [X₀]
• eval_foo_bb3_in: [X₀]
• eval_foo_bb4_in: [X₀]

Cut unreachable locations [eval_foo_1] from the program graph

Found invariant X₀ ≤ X₅ for location eval_foo_bb5_in

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb1_in_v1

Found invariant X₀ ≤ X₅ for location eval_foo_stop

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_0_v1

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb3_in

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_1_v1

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb2_in_v2

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_0_v2

Found invariant X₀ ≤ X₅ for location eval_foo_bb1_in

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb2_in_v1

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb4_in_v1

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: inf {Infinity}
t₇: inf {Infinity}
t₈: X₅ {O(n)}
t₉: X₅ {O(n)}
t₁₀: inf {Infinity}
t₁₁: X₅+1 {O(n)}
t₁₃: X₅+1 {O(n)}
t₁₄: X₅ {O(n)}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: inf {Infinity}
t₇: inf {Infinity}
t₈: X₅ {O(n)}
t₉: X₅ {O(n)}
t₁₀: inf {Infinity}
t₁₁: X₅+1 {O(n)}
t₁₃: X₅+1 {O(n)}
t₁₄: X₅ {O(n)}
t₁₅: inf {Infinity}
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: 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, X₃: 2⋅X₅+X₃ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₃, X₀: 2⋅X₅ {O(n)}
t₃, X₃: 2⋅X₅+X₃ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₃, X₆: 2⋅X₆ {O(n)}
t₄, X₀: 3⋅X₅ {O(n)}
t₄, X₃: 2⋅X₃+4⋅X₅ {O(n)}
t₄, X₅: 3⋅X₅ {O(n)}
t₄, X₆: 3⋅X₆ {O(n)}
t₅, X₀: X₅ {O(n)}
t₅, X₃: 2⋅X₅+X₃ {O(n)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₆ {O(n)}
t₇, X₀: X₅ {O(n)}
t₇, X₃: 2⋅X₅+X₃ {O(n)}
t₇, X₅: X₅ {O(n)}
t₇, X₆: X₆ {O(n)}
t₈, X₀: X₅ {O(n)}
t₈, X₃: 2⋅X₅+X₃ {O(n)}
t₈, X₅: X₅ {O(n)}
t₈, X₆: X₆ {O(n)}
t₉, X₀: X₅ {O(n)}
t₉, X₃: 2⋅X₅+X₃ {O(n)}
t₉, X₅: X₅ {O(n)}
t₉, X₆: X₆ {O(n)}
t₁₀, X₀: X₅ {O(n)}
t₁₀, X₂: 0 {O(1)}
t₁₀, X₃: 2⋅X₅+X₃ {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₀, X₆: X₆ {O(n)}
t₁₁, X₀: X₅ {O(n)}
t₁₁, X₃: 2⋅X₅ {O(n)}
t₁₁, X₅: X₅ {O(n)}
t₁₁, X₆: X₆ {O(n)}
t₁₃, X₀: X₅ {O(n)}
t₁₃, X₃: 2⋅X₅ {O(n)}
t₁₃, X₅: X₅ {O(n)}
t₁₃, X₆: X₆ {O(n)}
t₁₄, X₀: X₅ {O(n)}
t₁₄, X₃: 2⋅X₅ {O(n)}
t₁₄, X₅: X₅ {O(n)}
t₁₄, X₆: X₆ {O(n)}
t₁₅, X₀: X₅ {O(n)}
t₁₅, X₂: 0 {O(1)}
t₁₅, X₃: 2⋅X₅+X₃ {O(n)}
t₁₅, X₅: X₅ {O(n)}
t₁₅, X₆: X₆ {O(n)}
t₁₆, X₀: 5⋅X₅ {O(n)}
t₁₆, X₃: 3⋅X₃+6⋅X₅ {O(n)}
t₁₆, X₅: 5⋅X₅ {O(n)}
t₁₆, X₆: 5⋅X₆ {O(n)}