KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₄+X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀ for location eval_exp_paper3_3

Found invariant 1 ≤ X₇ ∧ 1+X₄ ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀ for location eval_exp_paper3_6

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₀ for location eval_exp_paper3_0

Found invariant 1 ≤ X₇ ∧ 1+X₄ ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀ for location eval_exp_paper3_bb5_in

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₀ for location eval_exp_paper3_bb2_in

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₀ for location eval_exp_paper3_1

Found invariant 1 ≤ X₇ ∧ 1+X₄ ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀ for location eval_exp_paper3_7

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₅+X₇ ∧ 2 ≤ X₄+X₇ ∧ 2 ≤ X₂+X₇ ∧ 2 ≤ X₁+X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_exp_paper3_bb4_in

Found invariant X₀ ≤ X₇ for location eval_exp_paper3_bb1_in

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₀ for location eval_exp_paper3_bb6_in

Found invariant X₀ ≤ X₇ ∧ X₀ ≤ 0 for location eval_exp_paper3_stop

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₄+X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀ for location eval_exp_paper3_bb3_in

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₄+X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀ for location eval_exp_paper3_2

Found invariant X₀ ≤ X₇ ∧ X₀ ≤ 0 for location eval_exp_paper3_bb7_in

Problem after Preprocessing

Start: eval_exp_paper3_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars: nondef.0, nondef.1, nondef.2
Locations: eval_exp_paper3_0, eval_exp_paper3_1, eval_exp_paper3_2, eval_exp_paper3_3, eval_exp_paper3_6, eval_exp_paper3_7, eval_exp_paper3_bb0_in, eval_exp_paper3_bb1_in, eval_exp_paper3_bb2_in, eval_exp_paper3_bb3_in, eval_exp_paper3_bb4_in, eval_exp_paper3_bb5_in, eval_exp_paper3_bb6_in, eval_exp_paper3_bb7_in, eval_exp_paper3_start, eval_exp_paper3_stop
Transitions:
t₆: eval_exp_paper3_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_1(X₀, X₁, X₂, X₃, nondef.0, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇
t₇: eval_exp_paper3_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb3_in(X₀, X₁, X₁, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇
t₈: eval_exp_paper3_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₄ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇
t₁₁: eval_exp_paper3_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_3(X₀, X₁, X₂, X₃, X₄, nondef.1, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄+X₇ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁
t₁₂: eval_exp_paper3_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₂ ∧ 1 ≤ X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄+X₇ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁
t₁₃: eval_exp_paper3_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb6_in(X₀, X₁, X₂, X₂, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₅ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄+X₇ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁
t₁₄: eval_exp_paper3_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb6_in(X₀, X₁, X₂, X₂, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₂ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄+X₇ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁
t₁₈: eval_exp_paper3_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_7(X₀, X₁, X₂, X₃, X₄, X₅, nondef.2, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1+X₄ ≤ X₇ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₄ ≤ 0
t₁₉: eval_exp_paper3_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb6_in(X₀, X₁, X₂, 1+X₁, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₆ ∧ 1 ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1+X₄ ≤ X₇ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₄ ≤ 0
t₂₀: eval_exp_paper3_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb6_in(X₀, X₁, X₂, X₉, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₆ ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1+X₄ ≤ X₇ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₄ ≤ 0
t₁: eval_exp_paper3_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb1_in(X₇, X₈, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₂: eval_exp_paper3_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ X₀ ≤ X₇
t₃: eval_exp_paper3_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₀ ≤ 0 ∧ X₀ ≤ X₇
t₄: eval_exp_paper3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇
t₉: eval_exp_paper3_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄+X₇ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁
t₁₅: eval_exp_paper3_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb3_in(X₀, X₁, X₂-1, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₁+X₇ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₂+X₇ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₇ ∧ 2 ≤ X₅+X₇ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁
t₁₆: eval_exp_paper3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1+X₄ ≤ X₇ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₄ ≤ 0
t₂₁: eval_exp_paper3_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb1_in(X₀-1, X₃, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇
t₂₂: eval_exp_paper3_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₀ ≤ 0 ∧ X₀ ≤ X₇
t₀: eval_exp_paper3_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)

MPRF for transition t₂: eval_exp_paper3_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ X₀ ≤ X₇ of depth 1:

new bound:

X₇ {O(n)}

MPRF:

• eval_exp_paper3_0: [X₀-1]
• eval_exp_paper3_1: [X₀-1]
• eval_exp_paper3_2: [X₀-1]
• eval_exp_paper3_3: [X₀-1]
• eval_exp_paper3_6: [X₀-1]
• eval_exp_paper3_7: [X₀-1]
• eval_exp_paper3_bb1_in: [X₀]
• eval_exp_paper3_bb2_in: [X₀-1]
• eval_exp_paper3_bb3_in: [X₀-1]
• eval_exp_paper3_bb4_in: [X₀-1]
• eval_exp_paper3_bb5_in: [X₀-1]
• eval_exp_paper3_bb6_in: [X₀-1]

MPRF for transition t₄: eval_exp_paper3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ of depth 1:

new bound:

X₇ {O(n)}

MPRF:

• eval_exp_paper3_0: [X₀-1]
• eval_exp_paper3_1: [X₀-1]
• eval_exp_paper3_2: [X₀-1]
• eval_exp_paper3_3: [X₀-1]
• eval_exp_paper3_6: [X₀-1]
• eval_exp_paper3_7: [X₀-1]
• eval_exp_paper3_bb1_in: [X₀]
• eval_exp_paper3_bb2_in: [X₀]
• eval_exp_paper3_bb3_in: [X₀-1]
• eval_exp_paper3_bb4_in: [X₀-1]
• eval_exp_paper3_bb5_in: [X₀-1]
• eval_exp_paper3_bb6_in: [X₀-1]

MPRF for transition t₆: eval_exp_paper3_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_1(X₀, X₁, X₂, X₃, nondef.0, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ of depth 1:

new bound:

X₇ {O(n)}

MPRF:

• eval_exp_paper3_0: [X₀]
• eval_exp_paper3_1: [X₀-1]
• eval_exp_paper3_2: [X₀-1]
• eval_exp_paper3_3: [X₀-1]
• eval_exp_paper3_6: [X₀-1]
• eval_exp_paper3_7: [X₀-1]
• eval_exp_paper3_bb1_in: [X₀]
• eval_exp_paper3_bb2_in: [X₀]
• eval_exp_paper3_bb3_in: [X₀-1]
• eval_exp_paper3_bb4_in: [X₀-1]
• eval_exp_paper3_bb5_in: [X₀-1]
• eval_exp_paper3_bb6_in: [X₀-1]

MPRF for transition t₇: eval_exp_paper3_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb3_in(X₀, X₁, X₁, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ of depth 1:

new bound:

X₇ {O(n)}

MPRF:

• eval_exp_paper3_0: [X₀]
• eval_exp_paper3_1: [X₀]
• eval_exp_paper3_2: [X₀-1]
• eval_exp_paper3_3: [X₀-1]
• eval_exp_paper3_6: [X₀]
• eval_exp_paper3_7: [X₀]
• eval_exp_paper3_bb1_in: [X₀]
• eval_exp_paper3_bb2_in: [X₀]
• eval_exp_paper3_bb3_in: [X₀-1]
• eval_exp_paper3_bb4_in: [X₀-1]
• eval_exp_paper3_bb5_in: [X₀]
• eval_exp_paper3_bb6_in: [X₀-1]

MPRF for transition t₈: eval_exp_paper3_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₄ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ of depth 1:

new bound:

X₇ {O(n)}

MPRF:

• eval_exp_paper3_0: [X₀]
• eval_exp_paper3_1: [X₀]
• eval_exp_paper3_2: [X₀-1]
• eval_exp_paper3_3: [X₀-1]
• eval_exp_paper3_6: [X₀-1]
• eval_exp_paper3_7: [X₀-1]
• eval_exp_paper3_bb1_in: [X₀]
• eval_exp_paper3_bb2_in: [X₀]
• eval_exp_paper3_bb3_in: [X₀-1]
• eval_exp_paper3_bb4_in: [X₀-1]
• eval_exp_paper3_bb5_in: [X₀-1]
• eval_exp_paper3_bb6_in: [X₀-1]

MPRF for transition t₁₃: eval_exp_paper3_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb6_in(X₀, X₁, X₂, X₂, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₅ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄+X₇ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₇ {O(n)}

MPRF:

• eval_exp_paper3_0: [X₀]
• eval_exp_paper3_1: [X₀]
• eval_exp_paper3_2: [X₀]
• eval_exp_paper3_3: [X₀]
• eval_exp_paper3_6: [X₀]
• eval_exp_paper3_7: [X₀]
• eval_exp_paper3_bb1_in: [X₀]
• eval_exp_paper3_bb2_in: [X₀]
• eval_exp_paper3_bb3_in: [X₀]
• eval_exp_paper3_bb4_in: [X₀]
• eval_exp_paper3_bb5_in: [X₀]
• eval_exp_paper3_bb6_in: [X₀-1]

MPRF for transition t₁₄: eval_exp_paper3_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb6_in(X₀, X₁, X₂, X₂, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₂ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄+X₇ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₇+1 {O(n)}

MPRF:

• eval_exp_paper3_0: [1+X₀]
• eval_exp_paper3_1: [1+X₀]
• eval_exp_paper3_2: [1+X₀]
• eval_exp_paper3_3: [1+X₀]
• eval_exp_paper3_6: [X₀]
• eval_exp_paper3_7: [X₀]
• eval_exp_paper3_bb1_in: [1+X₀]
• eval_exp_paper3_bb2_in: [1+X₀]
• eval_exp_paper3_bb3_in: [1+X₀]
• eval_exp_paper3_bb4_in: [1+X₀]
• eval_exp_paper3_bb5_in: [X₀]
• eval_exp_paper3_bb6_in: [X₀]

MPRF for transition t₁₆: eval_exp_paper3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1+X₄ ≤ X₇ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₄ ≤ 0 of depth 1:

new bound:

X₇ {O(n)}

MPRF:

MPRF for transition t₁₈: eval_exp_paper3_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_7(X₀, X₁, X₂, X₃, X₄, X₅, nondef.2, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1+X₄ ≤ X₇ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₄ ≤ 0 of depth 1:

new bound:

X₇ {O(n)}

MPRF:

• eval_exp_paper3_0: [X₀]
• eval_exp_paper3_1: [X₀]
• eval_exp_paper3_2: [X₀-1]
• eval_exp_paper3_3: [X₀-1]
• eval_exp_paper3_6: [X₀]
• eval_exp_paper3_7: [X₀-1]
• eval_exp_paper3_bb1_in: [X₀]
• eval_exp_paper3_bb2_in: [X₀]
• eval_exp_paper3_bb3_in: [X₀-1]
• eval_exp_paper3_bb4_in: [X₀-1]
• eval_exp_paper3_bb5_in: [X₀]
• eval_exp_paper3_bb6_in: [X₀-1]

MPRF for transition t₁₉: eval_exp_paper3_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb6_in(X₀, X₁, X₂, 1+X₁, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₆ ∧ 1 ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1+X₄ ≤ X₇ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₄ ≤ 0 of depth 1:

new bound:

X₇ {O(n)}

MPRF:

MPRF for transition t₂₀: eval_exp_paper3_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb6_in(X₀, X₁, X₂, X₉, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₆ ≤ 0 ∧ 1 ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1+X₄ ≤ X₇ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₄ ≤ 0 of depth 1:

new bound:

X₇ {O(n)}

MPRF:

MPRF for transition t₂₁: eval_exp_paper3_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb1_in(X₀-1, X₃, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ of depth 1:

new bound:

X₇ {O(n)}

MPRF:

MPRF for transition t₁₂: eval_exp_paper3_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₂ ∧ 1 ≤ X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄+X₇ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₇⋅X₇+X₇⋅X₉+X₇+X₈+1 {O(n^2)}

MPRF:

• eval_exp_paper3_0: [1+X₀+X₁]
• eval_exp_paper3_1: [1+X₀+X₁]
• eval_exp_paper3_2: [X₀+X₂]
• eval_exp_paper3_3: [X₀+X₂]
• eval_exp_paper3_6: [1+X₀+X₁]
• eval_exp_paper3_7: [1+X₀+X₁]
• eval_exp_paper3_bb1_in: [1+X₀+X₁]
• eval_exp_paper3_bb2_in: [1+X₀+X₁]
• eval_exp_paper3_bb3_in: [X₀+X₂]
• eval_exp_paper3_bb4_in: [X₀+X₂-1]
• eval_exp_paper3_bb5_in: [1+X₀+X₁]
• eval_exp_paper3_bb6_in: [X₀+X₃]

MPRF for transition t₁₅: eval_exp_paper3_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_bb3_in(X₀, X₁, X₂-1, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₁+X₇ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₂+X₇ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₇ ∧ 2 ≤ X₅+X₇ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₇⋅X₇+X₇⋅X₉+X₇+X₈+1 {O(n^2)}

MPRF:

• eval_exp_paper3_0: [1+X₀+X₁]
• eval_exp_paper3_1: [1+X₀+X₁]
• eval_exp_paper3_2: [X₀+X₂]
• eval_exp_paper3_3: [X₀+X₂]
• eval_exp_paper3_6: [1+X₀+X₁]
• eval_exp_paper3_7: [1+X₀+X₁]
• eval_exp_paper3_bb1_in: [1+X₀+X₁]
• eval_exp_paper3_bb2_in: [1+X₀+X₁]
• eval_exp_paper3_bb3_in: [X₀+X₂]
• eval_exp_paper3_bb4_in: [X₀+X₂]
• eval_exp_paper3_bb5_in: [1+X₀+X₁]
• eval_exp_paper3_bb6_in: [X₀+X₃]

knowledge_propagation leads to new time bound X₇⋅X₇+X₇⋅X₉+2⋅X₇+X₈+1 {O(n^2)} for transition t₉: eval_exp_paper3_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄+X₇ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁

knowledge_propagation leads to new time bound X₇⋅X₇+X₇⋅X₉+2⋅X₇+X₈+1 {O(n^2)} for transition t₁₁: eval_exp_paper3_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_exp_paper3_3(X₀, X₁, X₂, X₃, X₄, nondef.1, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄+X₇ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁

Cut unreachable locations [eval_exp_paper3_3] from the program graph

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₀ for location eval_exp_paper3_bb2_in

Found invariant X₀ ≤ X₇ for location eval_exp_paper3_bb1_in

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₅+X₇ ∧ 2 ≤ X₄+X₇ ∧ 2 ≤ X₂+X₇ ∧ 3 ≤ X₁+X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₂+X₅ ∧ 3 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_exp_paper3_bb4_in_v2

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₄+X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ for location eval_exp_paper3_3_v1

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₄+X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ for location eval_exp_paper3_2_v1

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₄+X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ for location eval_exp_paper3_bb3_in

Found invariant 1 ≤ X₇ ∧ 1+X₄ ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀ for location eval_exp_paper3_6

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₀ for location eval_exp_paper3_0

Found invariant 1 ≤ X₇ ∧ 1+X₄ ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀ for location eval_exp_paper3_bb5_in

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₅+X₇ ∧ 2 ≤ X₄+X₇ ∧ 1 ≤ X₂+X₇ ∧ 2 ≤ X₁+X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_exp_paper3_2_v2

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₀ for location eval_exp_paper3_1

Found invariant 1 ≤ X₇ ∧ 1+X₄ ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀ for location eval_exp_paper3_7

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₀ for location eval_exp_paper3_bb6_in

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₄+X₇ ∧ 1 ≤ X₂+X₇ ∧ 2 ≤ X₁+X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_exp_paper3_3_v2

Found invariant X₀ ≤ X₇ ∧ X₀ ≤ 0 for location eval_exp_paper3_stop

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₅+X₇ ∧ 2 ≤ X₄+X₇ ∧ 2 ≤ X₂+X₇ ∧ 2 ≤ X₁+X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_exp_paper3_bb4_in_v1

Found invariant X₀ ≤ X₇ ∧ X₀ ≤ 0 for location eval_exp_paper3_bb7_in

All Bounds

Timebounds

Overall timebound:4⋅X₇⋅X₇+4⋅X₇⋅X₉+18⋅X₇+4⋅X₈+9 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₇ {O(n)}
t₃: 1 {O(1)}
t₄: X₇ {O(n)}
t₆: X₇ {O(n)}
t₇: X₇ {O(n)}
t₈: X₇ {O(n)}
t₉: X₇⋅X₇+X₇⋅X₉+2⋅X₇+X₈+1 {O(n^2)}
t₁₁: X₇⋅X₇+X₇⋅X₉+2⋅X₇+X₈+1 {O(n^2)}
t₁₂: X₇⋅X₇+X₇⋅X₉+X₇+X₈+1 {O(n^2)}
t₁₃: X₇ {O(n)}
t₁₄: X₇+1 {O(n)}
t₁₅: X₇⋅X₇+X₇⋅X₉+X₇+X₈+1 {O(n^2)}
t₁₆: X₇ {O(n)}
t₁₈: X₇ {O(n)}
t₁₉: X₇ {O(n)}
t₂₀: X₇ {O(n)}
t₂₁: X₇ {O(n)}
t₂₂: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₇⋅X₇+4⋅X₇⋅X₉+18⋅X₇+4⋅X₈+9 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₇ {O(n)}
t₃: 1 {O(1)}
t₄: X₇ {O(n)}
t₆: X₇ {O(n)}
t₇: X₇ {O(n)}
t₈: X₇ {O(n)}
t₉: X₇⋅X₇+X₇⋅X₉+2⋅X₇+X₈+1 {O(n^2)}
t₁₁: X₇⋅X₇+X₇⋅X₉+2⋅X₇+X₈+1 {O(n^2)}
t₁₂: X₇⋅X₇+X₇⋅X₉+X₇+X₈+1 {O(n^2)}
t₁₃: X₇ {O(n)}
t₁₄: X₇+1 {O(n)}
t₁₅: X₇⋅X₇+X₇⋅X₉+X₇+X₈+1 {O(n^2)}
t₁₆: X₇ {O(n)}
t₁₈: X₇ {O(n)}
t₁₉: X₇ {O(n)}
t₂₀: X₇ {O(n)}
t₂₁: X₇ {O(n)}
t₂₂: 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)}
t₀, X₇: X₇ {O(n)}
t₀, X₈: X₈ {O(n)}
t₀, X₉: X₉ {O(n)}
t₁, X₀: X₇ {O(n)}
t₁, X₁: X₈ {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)}
t₁, X₇: X₇ {O(n)}
t₁, X₈: X₈ {O(n)}
t₁, X₉: X₉ {O(n)}
t₂, X₀: X₇ {O(n)}
t₂, X₁: X₇+X₈+X₉ {O(n)}
t₂, X₂: 2⋅X₇+2⋅X₈+2⋅X₉+X₂ {O(n)}
t₂, X₃: 3⋅X₇+3⋅X₈+4⋅X₉+X₃ {O(n)}
t₂, X₇: X₇ {O(n)}
t₂, X₈: X₈ {O(n)}
t₂, X₉: X₉ {O(n)}
t₃, X₀: 2⋅X₇ {O(n)}
t₃, X₁: 2⋅X₈+X₇+X₉ {O(n)}
t₃, X₂: 2⋅X₂+2⋅X₇+2⋅X₈+2⋅X₉ {O(n)}
t₃, X₃: 3⋅X₇+3⋅X₈+4⋅X₉+X₃ {O(n)}
t₃, X₇: 2⋅X₇ {O(n)}
t₃, X₈: 2⋅X₈ {O(n)}
t₃, X₉: 2⋅X₉ {O(n)}
t₄, X₀: X₇ {O(n)}
t₄, X₁: X₇+X₈+X₉ {O(n)}
t₄, X₂: 2⋅X₇+2⋅X₈+2⋅X₉+X₂ {O(n)}
t₄, X₃: 3⋅X₇+3⋅X₈+4⋅X₉+X₃ {O(n)}
t₄, X₇: X₇ {O(n)}
t₄, X₈: X₈ {O(n)}
t₄, X₉: X₉ {O(n)}
t₆, X₀: X₇ {O(n)}
t₆, X₁: X₇+X₈+X₉ {O(n)}
t₆, X₂: 2⋅X₇+2⋅X₈+2⋅X₉+X₂ {O(n)}
t₆, X₃: 3⋅X₇+3⋅X₈+4⋅X₉+X₃ {O(n)}
t₆, X₇: X₇ {O(n)}
t₆, X₈: X₈ {O(n)}
t₆, X₉: X₉ {O(n)}
t₇, X₀: X₇ {O(n)}
t₇, X₁: X₇+X₈+X₉ {O(n)}
t₇, X₂: X₇+X₈+X₉ {O(n)}
t₇, X₃: 3⋅X₇+3⋅X₈+4⋅X₉+X₃ {O(n)}
t₇, X₇: X₇ {O(n)}
t₇, X₈: X₈ {O(n)}
t₇, X₉: X₉ {O(n)}
t₈, X₀: X₇ {O(n)}
t₈, X₁: X₇+X₈+X₉ {O(n)}
t₈, X₂: 2⋅X₇+2⋅X₈+2⋅X₉+X₂ {O(n)}
t₈, X₃: 3⋅X₇+3⋅X₈+4⋅X₉+X₃ {O(n)}
t₈, X₇: X₇ {O(n)}
t₈, X₈: X₈ {O(n)}
t₈, X₉: X₉ {O(n)}
t₉, X₀: X₇ {O(n)}
t₉, X₁: X₇+X₈+X₉ {O(n)}
t₉, X₂: X₇+X₈+X₉ {O(n)}
t₉, X₃: 3⋅X₇+3⋅X₈+4⋅X₉+X₃ {O(n)}
t₉, X₇: X₇ {O(n)}
t₉, X₈: X₈ {O(n)}
t₉, X₉: X₉ {O(n)}
t₁₁, X₀: X₇ {O(n)}
t₁₁, X₁: X₇+X₈+X₉ {O(n)}
t₁₁, X₂: X₇+X₈+X₉ {O(n)}
t₁₁, X₃: 3⋅X₇+3⋅X₈+4⋅X₉+X₃ {O(n)}
t₁₁, X₇: X₇ {O(n)}
t₁₁, X₈: X₈ {O(n)}
t₁₁, X₉: X₉ {O(n)}
t₁₂, X₀: X₇ {O(n)}
t₁₂, X₁: X₇+X₈+X₉ {O(n)}
t₁₂, X₂: X₇+X₈+X₉ {O(n)}
t₁₂, X₃: 3⋅X₇+3⋅X₈+4⋅X₉+X₃ {O(n)}
t₁₂, X₇: X₇ {O(n)}
t₁₂, X₈: X₈ {O(n)}
t₁₂, X₉: X₉ {O(n)}
t₁₃, X₀: X₇ {O(n)}
t₁₃, X₁: X₇+X₈+X₉ {O(n)}
t₁₃, X₂: X₇+X₈+X₉ {O(n)}
t₁₃, X₃: X₇+X₈+X₉ {O(n)}
t₁₃, X₇: X₇ {O(n)}
t₁₃, X₈: X₈ {O(n)}
t₁₃, X₉: X₉ {O(n)}
t₁₄, X₀: X₇ {O(n)}
t₁₄, X₁: X₇+X₈+X₉ {O(n)}
t₁₄, X₂: X₇+X₈+X₉ {O(n)}
t₁₄, X₃: X₇+X₈+X₉ {O(n)}
t₁₄, X₇: X₇ {O(n)}
t₁₄, X₈: X₈ {O(n)}
t₁₄, X₉: X₉ {O(n)}
t₁₅, X₀: X₇ {O(n)}
t₁₅, X₁: X₇+X₈+X₉ {O(n)}
t₁₅, X₂: X₇+X₈+X₉ {O(n)}
t₁₅, X₃: 3⋅X₇+3⋅X₈+4⋅X₉+X₃ {O(n)}
t₁₅, X₇: X₇ {O(n)}
t₁₅, X₈: X₈ {O(n)}
t₁₅, X₉: X₉ {O(n)}
t₁₆, X₀: X₇ {O(n)}
t₁₆, X₁: X₇+X₈+X₉ {O(n)}
t₁₆, X₂: 2⋅X₇+2⋅X₈+2⋅X₉+X₂ {O(n)}
t₁₆, X₃: 3⋅X₇+3⋅X₈+4⋅X₉+X₃ {O(n)}
t₁₆, X₇: X₇ {O(n)}
t₁₆, X₈: X₈ {O(n)}
t₁₆, X₉: X₉ {O(n)}
t₁₈, X₀: X₇ {O(n)}
t₁₈, X₁: X₇+X₈+X₉ {O(n)}
t₁₈, X₂: 2⋅X₇+2⋅X₈+2⋅X₉+X₂ {O(n)}
t₁₈, X₃: 3⋅X₇+3⋅X₈+4⋅X₉+X₃ {O(n)}
t₁₈, X₇: X₇ {O(n)}
t₁₈, X₈: X₈ {O(n)}
t₁₈, X₉: X₉ {O(n)}
t₁₉, X₀: X₇ {O(n)}
t₁₉, X₁: X₇+X₈+X₉ {O(n)}
t₁₉, X₂: 2⋅X₇+2⋅X₈+2⋅X₉+X₂ {O(n)}
t₁₉, X₃: X₇+X₈+X₉ {O(n)}
t₁₉, X₇: X₇ {O(n)}
t₁₉, X₈: X₈ {O(n)}
t₁₉, X₉: X₉ {O(n)}
t₂₀, X₀: X₇ {O(n)}
t₂₀, X₁: X₇+X₈+X₉ {O(n)}
t₂₀, X₂: 2⋅X₇+2⋅X₈+2⋅X₉+X₂ {O(n)}
t₂₀, X₃: X₉ {O(n)}
t₂₀, X₇: X₇ {O(n)}
t₂₀, X₈: X₈ {O(n)}
t₂₀, X₉: X₉ {O(n)}
t₂₁, X₀: X₇ {O(n)}
t₂₁, X₁: X₇+X₈+X₉ {O(n)}
t₂₁, X₂: 2⋅X₇+2⋅X₈+2⋅X₉+X₂ {O(n)}
t₂₁, X₃: 3⋅X₇+3⋅X₈+4⋅X₉ {O(n)}
t₂₁, X₇: X₇ {O(n)}
t₂₁, X₈: X₈ {O(n)}
t₂₁, X₉: X₉ {O(n)}
t₂₂, X₀: 2⋅X₇ {O(n)}
t₂₂, X₁: 2⋅X₈+X₇+X₉ {O(n)}
t₂₂, X₂: 2⋅X₂+2⋅X₇+2⋅X₈+2⋅X₉ {O(n)}
t₂₂, X₃: 3⋅X₇+3⋅X₈+4⋅X₉+X₃ {O(n)}
t₂₂, X₇: 2⋅X₇ {O(n)}
t₂₂, X₈: 2⋅X₈ {O(n)}
t₂₂, X₉: 2⋅X₉ {O(n)}