KoAT2 Proof Output

Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
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, X₇) → eval_foo_1(X₀, X₁, nondef.0, X₃, X₄, X₅, X₆, X₇)
t₈: eval_foo_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂ ≤ 41
t₉: eval_foo_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 42 ≤ X₂
t₁₂: eval_foo_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_4(X₀, X₁, X₂, X₃, nondef.1, X₅, X₆, X₇)
t₁₃: eval_foo_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb1_in(X₃, X₄, X₂, X₃, X₄, X₅, X₆, X₇)
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb1_in(X₆, X₇, X₂, X₃, X₄, X₅, X₆, X₇)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0
t₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ 0
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁₀: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_3(X₀, X₁, X₂, X₀-1, X₄, X₅, X₆, X₇)
t₁₄: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb1_in(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇)
t₁₅: eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)

Preprocessing

Eliminate variables [X₅] that do not contribute to the problem

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 ∧ X₂ ≤ 40+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ 41 ∧ X₂ ≤ 40+X₁ ∧ X₂ ≤ 40+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb3_in

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ X₂ ≤ 40+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₂ ≤ 41+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ X₂ ≤ 41 ∧ X₂ ≤ 40+X₁ ∧ X₂ ≤ 40+X₀ ∧ 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 ∧ 43 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 42 ≤ X₂ ∧ 43 ≤ X₁+X₂ ∧ 43 ≤ 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:
t₂₉: 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
t₃₀: eval_foo_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 41 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₀ ≤ X₅
t₃₁: eval_foo_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 42 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₀ ≤ X₅
t₃₂: eval_foo_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_4(X₀, X₁, X₂, X₃, nondef.1, X₅, X₆) :|: X₂ ≤ 41 ∧ X₂ ≤ 41+X₃ ∧ X₂ ≤ 40+X₀ ∧ X₂ ≤ 40+X₁ ∧ X₂ ≤ 40+X₅ ∧ 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
t₃₃: eval_foo_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb1_in(X₃, X₄, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 41 ∧ X₂ ≤ 41+X₃ ∧ X₂ ≤ 40+X₀ ∧ X₂ ≤ 40+X₁ ∧ X₂ ≤ 40+X₅ ∧ 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
t₃₄: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb1_in(X₅, X₆, X₂, X₃, X₄, X₅, X₆)
t₃₅: 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
t₃₆: 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
t₃₇: 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
t₃₈: 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
t₃₉: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_3(X₀, X₁, X₂, X₀-1, X₄, X₅, X₆) :|: X₂ ≤ 41 ∧ X₂ ≤ 40+X₀ ∧ X₂ ≤ 40+X₁ ∧ X₂ ≤ 40+X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₀ ≤ X₅
t₄₀: 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 ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ 42 ≤ X₂ ∧ 43 ≤ X₀+X₂ ∧ 43 ≤ X₁+X₂ ∧ 43 ≤ X₂+X₅ ∧ X₀ ≤ X₅
t₄₁: eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ X₅
t₄₂: eval_foo_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

MPRF for transition t₃₀: eval_foo_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 41 ∧ 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: [X₀-1]
• eval_foo_4: [X₀-1]
• eval_foo_bb1_in: [X₀]
• eval_foo_bb2_in: [X₀]
• eval_foo_bb3_in: [X₀-1]
• eval_foo_bb4_in: [X₀]

MPRF for transition t₃₂: eval_foo_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_4(X₀, X₁, X₂, X₃, nondef.1, X₅, X₆) :|: X₂ ≤ 41 ∧ X₂ ≤ 41+X₃ ∧ X₂ ≤ 40+X₀ ∧ X₂ ≤ 40+X₁ ∧ X₂ ≤ 40+X₅ ∧ 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: [1+X₃]
• eval_foo_4: [X₃]
• eval_foo_bb1_in: [X₀]
• eval_foo_bb2_in: [X₀]
• eval_foo_bb3_in: [X₀]
• eval_foo_bb4_in: [X₀]

MPRF for transition t₃₃: eval_foo_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb1_in(X₃, X₄, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ 41 ∧ X₂ ≤ 41+X₃ ∧ X₂ ≤ 40+X₀ ∧ X₂ ≤ 40+X₁ ∧ X₂ ≤ 40+X₅ ∧ 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: [1+X₃]
• 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]

MPRF for transition t₃₉: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_3(X₀, X₁, X₂, X₀-1, X₄, X₅, X₆) :|: X₂ ≤ 41 ∧ X₂ ≤ 40+X₀ ∧ X₂ ≤ 40+X₁ ∧ X₂ ≤ 40+X₅ ∧ 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]
• 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 ∧ 43 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 42 ≤ X₂ ∧ 42 ≤ X₁+X₂ ∧ 43 ≤ 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_1_v1

Found invariant 1 ≤ X₅ ∧ 43 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 42 ≤ X₂ ∧ 43 ≤ X₁+X₂ ∧ 43 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb2_in_v2

Found invariant 1 ≤ X₅ ∧ 43 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 42 ≤ X₂ ∧ 43 ≤ X₁+X₂ ∧ 43 ≤ 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 ∧ 43 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 42 ≤ X₂ ∧ 43 ≤ X₁+X₂ ∧ 43 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb4_in_v1

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₂₉: inf {Infinity}
t₃₀: X₅ {O(n)}
t₃₁: inf {Infinity}
t₃₂: X₅ {O(n)}
t₃₃: X₅ {O(n)}
t₃₄: 1 {O(1)}
t₃₅: inf {Infinity}
t₃₆: 1 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: inf {Infinity}
t₃₉: X₅ {O(n)}
t₄₀: inf {Infinity}
t₄₁: 1 {O(1)}
t₄₂: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₂₉: inf {Infinity}
t₃₀: X₅ {O(n)}
t₃₁: inf {Infinity}
t₃₂: X₅ {O(n)}
t₃₃: X₅ {O(n)}
t₃₄: 1 {O(1)}
t₃₅: inf {Infinity}
t₃₆: 1 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: inf {Infinity}
t₃₉: X₅ {O(n)}
t₄₀: inf {Infinity}
t₄₁: 1 {O(1)}
t₄₂: 1 {O(1)}

Sizebounds

t₂₉, X₀: X₅ {O(n)}
t₂₉, X₃: X₃+X₅ {O(n)}
t₂₉, X₅: X₅ {O(n)}
t₂₉, X₆: X₆ {O(n)}
t₃₀, X₀: X₅ {O(n)}
t₃₀, X₃: X₃+X₅ {O(n)}
t₃₀, X₅: X₅ {O(n)}
t₃₀, X₆: X₆ {O(n)}
t₃₁, X₀: X₅ {O(n)}
t₃₁, X₃: X₃+X₅ {O(n)}
t₃₁, X₅: X₅ {O(n)}
t₃₁, X₆: X₆ {O(n)}
t₃₂, X₀: X₅ {O(n)}
t₃₂, X₃: X₅ {O(n)}
t₃₂, X₅: X₅ {O(n)}
t₃₂, X₆: X₆ {O(n)}
t₃₃, X₀: X₅ {O(n)}
t₃₃, X₃: X₅ {O(n)}
t₃₃, X₅: X₅ {O(n)}
t₃₃, X₆: X₆ {O(n)}
t₃₄, X₀: X₅ {O(n)}
t₃₄, X₁: X₆ {O(n)}
t₃₄, X₂: X₂ {O(n)}
t₃₄, X₃: X₃ {O(n)}
t₃₄, X₄: X₄ {O(n)}
t₃₄, X₅: X₅ {O(n)}
t₃₄, X₆: X₆ {O(n)}
t₃₅, X₀: X₅ {O(n)}
t₃₅, X₃: X₃+X₅ {O(n)}
t₃₅, X₅: X₅ {O(n)}
t₃₅, X₆: X₆ {O(n)}
t₃₆, X₀: 2⋅X₅ {O(n)}
t₃₆, X₃: X₃+X₅ {O(n)}
t₃₆, X₅: 2⋅X₅ {O(n)}
t₃₆, X₆: 2⋅X₆ {O(n)}
t₃₇, X₀: 3⋅X₅ {O(n)}
t₃₇, X₃: 2⋅X₃+2⋅X₅ {O(n)}
t₃₇, X₅: 3⋅X₅ {O(n)}
t₃₇, X₆: 3⋅X₆ {O(n)}
t₃₈, X₀: X₅ {O(n)}
t₃₈, X₃: X₃+X₅ {O(n)}
t₃₈, X₅: X₅ {O(n)}
t₃₈, X₆: X₆ {O(n)}
t₃₉, X₀: X₅ {O(n)}
t₃₉, X₃: X₅ {O(n)}
t₃₉, X₅: X₅ {O(n)}
t₃₉, X₆: X₆ {O(n)}
t₄₀, X₀: X₅ {O(n)}
t₄₀, X₃: X₃+X₅ {O(n)}
t₄₀, X₅: X₅ {O(n)}
t₄₀, X₆: X₆ {O(n)}
t₄₁, X₀: 5⋅X₅ {O(n)}
t₄₁, X₃: 3⋅X₃+3⋅X₅ {O(n)}
t₄₁, X₅: 5⋅X₅ {O(n)}
t₄₁, X₆: 5⋅X₆ {O(n)}
t₄₂, X₀: X₀ {O(n)}
t₄₂, X₁: X₁ {O(n)}
t₄₂, X₂: X₂ {O(n)}
t₄₂, X₃: X₃ {O(n)}
t₄₂, X₄: X₄ {O(n)}
t₄₂, X₅: X₅ {O(n)}
t₄₂, X₆: X₆ {O(n)}