KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₅+X₁₅ ∧ 2 ≤ X₅+X₁₁ ∧ 2 ≤ X₀+X₅ ∧ X₄ ≤ X₁₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₀ for location eval_size10_bb3_in

Found invariant X₉ ≤ X₆ ∧ 1 ≤ X₈+X₉ ∧ 1 ≤ X₉+X₁₀ ∧ 1 ≤ X₆+X₈ ∧ X₁₀ ≤ X₈ ∧ 1 ≤ X₆+X₁₀ ∧ X₅ ≤ 0 ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₁₅ ∧ 1+X₅ ≤ X₁₁ ∧ 1+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅+X₁₅ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ X₁₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₀ for location eval_size10_bb5_in

Found invariant X₉ ≤ X₆ ∧ X₁₀ ≤ X₈ ∧ X₅ ≤ 0 ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₁₅ ∧ 1+X₅ ≤ X₁₁ ∧ 1+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅+X₁₅ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ X₁₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₀ for location eval_size10_bb4_in

Found invariant X₄ ≤ X₁₅ ∧ 0 ≤ X₄ ∧ 1 ≤ X₄+X₁₅ ∧ 1 ≤ X₄+X₁₁ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₀ for location eval_size10_bb1_in

Found invariant X₉ ≤ X₆ ∧ X₉+X₁₀ ≤ 0 ∧ X₁₀ ≤ X₈ ∧ X₅ ≤ 0 ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₁₅ ∧ 1+X₅ ≤ X₁₁ ∧ 1+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅+X₁₅ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ X₁₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₀ for location eval_size10_bb6_in

Found invariant X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅+X₁₅ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ X₁₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₀ for location eval_size10_bb2_in

Problem after Preprocessing

Start: eval_size10_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅
Temp_Vars:
Locations: eval_size10_bb0_in, eval_size10_bb1_in, eval_size10_bb2_in, eval_size10_bb3_in, eval_size10_bb4_in, eval_size10_bb5_in, eval_size10_bb6_in, eval_size10_bb7_in, eval_size10_start, eval_size10_stop
Transitions:
t₁: eval_size10_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb1_in(X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: 1 ≤ X₁₁ ∧ 1 ≤ X₁₅
t₂: eval_size10_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: X₁₁ ≤ 0
t₃: eval_size10_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: X₁₅ ≤ 0
t₄: eval_size10_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb2_in(X₀, X₁, X₂, X₃, X₄, X₀, X₁, X₂, X₃, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: 1 ≤ X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₄+X₁₁ ∧ 1 ≤ X₄+X₁₅ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₀+X₁₁ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ 0 ≤ X₄ ∧ X₄ ≤ X₁₅
t₅: eval_size10_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: X₄ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₄+X₁₁ ∧ 1 ≤ X₄+X₁₅ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₀+X₁₁ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ 0 ≤ X₄ ∧ X₄ ≤ X₁₅
t₆: eval_size10_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: 1 ≤ X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₅+X₁₅ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₁₁ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ X₅ ≤ X₀ ∧ X₄ ≤ X₁₅ ∧ 0 ≤ X₅
t₇: eval_size10_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₆, X₈, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: X₅ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₅+X₁₅ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₁₁ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ X₅ ≤ X₀ ∧ X₄ ≤ X₁₅ ∧ 0 ≤ X₅
t₈: eval_size10_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅-1, 3⋅X₆+2⋅X₇, -5⋅X₆-3⋅X₇, 1+(X₅)²+X₈-2⋅X₅, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₀+X₁₁ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₅+X₁₁ ∧ 2 ≤ X₅+X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ X₅ ≤ X₀ ∧ X₄ ≤ X₁₅
t₉: eval_size10_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: 1 ≤ X₉+X₁₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₅+X₁₅ ∧ 1+X₅ ≤ X₁₁ ∧ 1+X₅ ≤ X₁₅ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₁₁ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ X₄ ≤ X₁₅ ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ X₉ ≤ X₆ ∧ X₁₀ ≤ X₈
t₁₀: eval_size10_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: X₉+X₁₀ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₅+X₁₅ ∧ 1+X₅ ≤ X₁₁ ∧ 1+X₅ ≤ X₁₅ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₁₁ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ X₄ ≤ X₁₅ ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ X₉ ≤ X₆ ∧ X₁₀ ≤ X₈
t₁₁: eval_size10_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉-1, X₁₀-1, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₅+X₁₅ ∧ 1+X₅ ≤ X₁₁ ∧ 1+X₅ ≤ X₁₅ ∧ 1 ≤ X₆+X₈ ∧ 1 ≤ X₆+X₁₀ ∧ 1 ≤ X₈+X₉ ∧ 1 ≤ X₉+X₁₀ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₁₁ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ X₄ ≤ X₁₅ ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ X₉ ≤ X₆ ∧ X₁₀ ≤ X₈
t₁₂: eval_size10_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb1_in(X₄, 2⋅X₄, 3⋅X₄, X₄, X₄-1, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₅+X₁₅ ∧ 1+X₅ ≤ X₁₁ ∧ 1+X₅ ≤ X₁₅ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₁₁ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ X₄ ≤ X₁₅ ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ X₉ ≤ X₆ ∧ X₁₀ ≤ X₈ ∧ X₉+X₁₀ ≤ 0
t₁₃: eval_size10_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅)
t₀: eval_size10_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅)

MPRF for transition t₄: eval_size10_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb2_in(X₀, X₁, X₂, X₃, X₄, X₀, X₁, X₂, X₃, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: 1 ≤ X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₄+X₁₁ ∧ 1 ≤ X₄+X₁₅ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₀+X₁₁ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ 0 ≤ X₄ ∧ X₄ ≤ X₁₅ of depth 1:

new bound:

2⋅X₁₅ {O(n)}

MPRF:

• eval_size10_bb1_in: [X₄+X₁₅]
• eval_size10_bb2_in: [X₄+X₁₅-1]
• eval_size10_bb3_in: [X₄+X₁₅-1]
• eval_size10_bb4_in: [X₄+X₁₅-1]
• eval_size10_bb5_in: [X₄+X₁₅-1]
• eval_size10_bb6_in: [X₄+X₁₅-1]

MPRF for transition t₇: eval_size10_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₆, X₈, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: X₅ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₅+X₁₅ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₁₁ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ X₅ ≤ X₀ ∧ X₄ ≤ X₁₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₁₅ {O(n)}

MPRF:

• eval_size10_bb1_in: [X₄]
• eval_size10_bb2_in: [X₄]
• eval_size10_bb3_in: [X₄]
• eval_size10_bb4_in: [X₄-1]
• eval_size10_bb5_in: [X₄-1]
• eval_size10_bb6_in: [X₄-1]

MPRF for transition t₁₀: eval_size10_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: X₉+X₁₀ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₅+X₁₅ ∧ 1+X₅ ≤ X₁₁ ∧ 1+X₅ ≤ X₁₅ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₁₁ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ X₄ ≤ X₁₅ ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ X₉ ≤ X₆ ∧ X₁₀ ≤ X₈ of depth 1:

new bound:

X₁₅ {O(n)}

MPRF:

• eval_size10_bb1_in: [X₄]
• eval_size10_bb2_in: [X₄]
• eval_size10_bb3_in: [X₄]
• eval_size10_bb4_in: [X₄]
• eval_size10_bb5_in: [X₄]
• eval_size10_bb6_in: [X₄-1]

MPRF for transition t₁₂: eval_size10_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb1_in(X₄, 2⋅X₄, 3⋅X₄, X₄, X₄-1, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₅+X₁₅ ∧ 1+X₅ ≤ X₁₁ ∧ 1+X₅ ≤ X₁₅ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₁₁ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ X₄ ≤ X₁₅ ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ X₉ ≤ X₆ ∧ X₁₀ ≤ X₈ ∧ X₉+X₁₀ ≤ 0 of depth 1:

new bound:

X₁₅ {O(n)}

MPRF:

• eval_size10_bb1_in: [X₄]
• eval_size10_bb2_in: [X₄]
• eval_size10_bb3_in: [X₄]
• eval_size10_bb4_in: [X₄]
• eval_size10_bb5_in: [X₄]
• eval_size10_bb6_in: [X₄]

MPRF for transition t₆: eval_size10_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: 1 ≤ X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₅+X₁₅ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₁₁ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ X₅ ≤ X₀ ∧ X₄ ≤ X₁₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₁₅⋅X₁₅+X₁₁+X₁₅+1 {O(n^2)}

MPRF:

• eval_size10_bb1_in: [1+X₀]
• eval_size10_bb2_in: [1+X₅]
• eval_size10_bb3_in: [X₅]
• eval_size10_bb4_in: [0]
• eval_size10_bb5_in: [0]
• eval_size10_bb6_in: [0]

MPRF for transition t₈: eval_size10_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅-1, 3⋅X₆+2⋅X₇, -5⋅X₆-3⋅X₇, Temp_Int₉₃₀₁+Temp_Int₉₃₀₂+X₈-2⋅X₅, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: 1 ≤ Temp_Int₉₃₀₂ ∧ X₅ ≤ Temp_Int₉₃₀₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₀+X₁₁ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₅+X₁₁ ∧ 2 ≤ X₅+X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ X₅ ≤ X₀ ∧ X₄ ≤ X₁₅ of depth 1:

new bound:

X₁₅⋅X₁₅+X₁₁ {O(n^2)}

MPRF:

• eval_size10_bb1_in: [X₀]
• eval_size10_bb2_in: [X₅]
• eval_size10_bb3_in: [X₅]
• eval_size10_bb4_in: [X₅]
• eval_size10_bb5_in: [X₅]
• eval_size10_bb6_in: [0]

MPRF for transition t₉: eval_size10_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: 1 ≤ X₉+X₁₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₅+X₁₅ ∧ 1+X₅ ≤ X₁₁ ∧ 1+X₅ ≤ X₁₅ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₁₁ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ X₄ ≤ X₁₅ ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ X₉ ≤ X₆ ∧ X₁₀ ≤ X₈ of depth 1:

new bound:

3⋅X₁₁⋅X₁₁⋅X₁₁⋅X₁₅+3⋅X₁₅⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁⋅X₁₅+10⋅X₁₅⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅⋅X₁₅+11⋅X₁₁⋅X₁₅+2⋅X₁₃⋅X₁₅+26⋅X₁₅⋅X₁₅+4⋅X₁₂⋅X₁₅+X₁₄⋅X₁₅+4⋅X₁₅+X₁₀+X₉ {O(n^4)}

MPRF:

• eval_size10_bb1_in: [X₉+X₁₀]
• eval_size10_bb2_in: [X₉+X₁₀]
• eval_size10_bb3_in: [X₉+X₁₀]
• eval_size10_bb4_in: [X₆+X₁₀]
• eval_size10_bb5_in: [X₆+X₁₀-1]
• eval_size10_bb6_in: [X₆+X₁₀]

MPRF for transition t₁₁: eval_size10_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) → eval_size10_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉-1, X₁₀-1, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₅+X₁₅ ∧ 1+X₅ ≤ X₁₁ ∧ 1+X₅ ≤ X₁₅ ∧ 1 ≤ X₆+X₈ ∧ 1 ≤ X₆+X₁₀ ∧ 1 ≤ X₈+X₉ ∧ 1 ≤ X₉+X₁₀ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₁₁ ∧ 2 ≤ X₀+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ X₄ ≤ X₁₅ ∧ 0 ≤ X₅ ∧ X₅ ≤ 0 ∧ X₉ ≤ X₆ ∧ X₁₀ ≤ X₈ of depth 1:

new bound:

MPRF:

• eval_size10_bb1_in: [X₉+X₁₀]
• eval_size10_bb2_in: [X₉+X₁₀]
• eval_size10_bb3_in: [X₉+X₁₀]
• eval_size10_bb4_in: [X₈+X₉]
• eval_size10_bb5_in: [X₈+X₉]
• eval_size10_bb6_in: [X₈+X₉]

Cut unsatisfiable transition [t₇: eval_size10_bb2_in→eval_size10_bb4_in; t₇₂: eval_size10_bb2_in→eval_size10_bb4_in]

Found invariant 1+X₉ ≤ X₆ ∧ 0 ≤ X₈+X₉ ∧ 0 ≤ 1+X₉+X₁₀ ∧ 1 ≤ X₆+X₈ ∧ 1+X₁₀ ≤ X₈ ∧ 0 ≤ X₆+X₁₀ ∧ X₅ ≤ 0 ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₁₅ ∧ 1+X₅ ≤ X₁₁ ∧ 1+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅+X₁₅ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ X₁₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₀ for location eval_size10_bb4_in_v1

Found invariant X₉ ≤ X₆ ∧ X₆ ≤ X₉ ∧ X₈ ≤ X₁₀ ∧ X₁₀ ≤ X₈ ∧ X₅ ≤ 0 ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₁₅ ∧ 1+X₅ ≤ X₁₁ ∧ 1+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅+X₁₅ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ X₁₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₀ for location eval_size10_bb4_in

Found invariant 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₅+X₁₅ ∧ 2 ≤ X₅+X₁₁ ∧ 3 ≤ X₀+X₅ ∧ X₄ ≤ X₁₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 3 ≤ X₀+X₄ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ 3 ≤ X₀+X₁₅ ∧ 1 ≤ X₁₁ ∧ 3 ≤ X₀+X₁₁ ∧ 2 ≤ X₀ for location eval_size10_bb3_in_v2

Found invariant 1+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅+X₁₅ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ X₁₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₀ for location eval_size10_bb2_in_v1

Found invariant X₈ ≤ X₃ ∧ X₃ ≤ X₈ ∧ X₇ ≤ X₂ ∧ X₂ ≤ X₇ ∧ X₆ ≤ X₁ ∧ X₁ ≤ X₆ ∧ X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₅+X₁₅ ∧ 2 ≤ X₅+X₁₁ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₁₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₀ for location eval_size10_bb2_in

Found invariant X₉ ≤ X₆ ∧ 1 ≤ X₈+X₉ ∧ X₆ ≤ X₉ ∧ 1 ≤ X₉+X₁₀ ∧ X₈ ≤ X₁₀ ∧ 1 ≤ X₆+X₈ ∧ X₁₀ ≤ X₈ ∧ 1 ≤ X₆+X₁₀ ∧ X₅ ≤ 0 ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₁₅ ∧ 1+X₅ ≤ X₁₁ ∧ 1+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅+X₁₅ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ X₁₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₀ for location eval_size10_bb5_in_v1

Found invariant 1+X₉ ≤ X₆ ∧ 2 ≤ X₈+X₉ ∧ 1 ≤ X₉+X₁₀ ∧ 3 ≤ X₆+X₈ ∧ 1+X₁₀ ≤ X₈ ∧ 2 ≤ X₆+X₁₀ ∧ X₅ ≤ 0 ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₁₅ ∧ 1+X₅ ≤ X₁₁ ∧ 1+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅+X₁₅ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ X₁₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₄+X₁₅ ∧ 2 ≤ X₄+X₁₁ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁₅ ∧ 2 ≤ X₁₁+X₁₅ ∧ 2 ≤ X₀+X₁₅ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₀+X₁₁ ∧ 1 ≤ X₀ for location eval_size10_bb5_in_v2

All Bounds

Timebounds

Overall timebound:18⋅X₁₁⋅X₁₁⋅X₁₅⋅X₁₅+18⋅X₁₁⋅X₁₅⋅X₁₅⋅X₁₅+6⋅X₁₁⋅X₁₁⋅X₁₁⋅X₁₅+6⋅X₁₅⋅X₁₅⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₁⋅X₁₅+20⋅X₁₅⋅X₁₅⋅X₁₅+40⋅X₁₁⋅X₁₅⋅X₁₅+2⋅X₁₄⋅X₁₅+22⋅X₁₁⋅X₁₅+4⋅X₁₃⋅X₁₅+54⋅X₁₅⋅X₁₅+8⋅X₁₂⋅X₁₅+14⋅X₁₅+2⋅X₁₀+2⋅X₁₁+2⋅X₉+7 {O(n^4)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 2⋅X₁₅ {O(n)}
t₅: 1 {O(1)}
t₆: X₁₅⋅X₁₅+X₁₁+X₁₅+1 {O(n^2)}
t₇: X₁₅ {O(n)}
t₈: X₁₅⋅X₁₅+X₁₁ {O(n^2)}
t₉: 3⋅X₁₁⋅X₁₁⋅X₁₁⋅X₁₅+3⋅X₁₅⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁⋅X₁₅+10⋅X₁₅⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅⋅X₁₅+11⋅X₁₁⋅X₁₅+2⋅X₁₃⋅X₁₅+26⋅X₁₅⋅X₁₅+4⋅X₁₂⋅X₁₅+X₁₄⋅X₁₅+4⋅X₁₅+X₁₀+X₉ {O(n^4)}
t₁₀: X₁₅ {O(n)}
t₁₁: 3⋅X₁₁⋅X₁₁⋅X₁₁⋅X₁₅+3⋅X₁₅⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁⋅X₁₅+10⋅X₁₅⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅⋅X₁₅+11⋅X₁₁⋅X₁₅+2⋅X₁₃⋅X₁₅+26⋅X₁₅⋅X₁₅+4⋅X₁₂⋅X₁₅+X₁₄⋅X₁₅+4⋅X₁₅+X₁₀+X₉ {O(n^4)}
t₁₂: X₁₅ {O(n)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 18⋅X₁₁⋅X₁₁⋅X₁₅⋅X₁₅+18⋅X₁₁⋅X₁₅⋅X₁₅⋅X₁₅+6⋅X₁₁⋅X₁₁⋅X₁₁⋅X₁₅+6⋅X₁₅⋅X₁₅⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₁⋅X₁₅+20⋅X₁₅⋅X₁₅⋅X₁₅+40⋅X₁₁⋅X₁₅⋅X₁₅+2⋅X₁₄⋅X₁₅+22⋅X₁₁⋅X₁₅+4⋅X₁₃⋅X₁₅+54⋅X₁₅⋅X₁₅+8⋅X₁₂⋅X₁₅+14⋅X₁₅+2⋅X₁₀+2⋅X₁₁+2⋅X₉+7 {O(n^4)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 2⋅X₁₅ {O(n)}
t₅: 1 {O(1)}
t₆: X₁₅⋅X₁₅+X₁₁+X₁₅+1 {O(n^2)}
t₇: X₁₅ {O(n)}
t₈: X₁₅⋅X₁₅+X₁₁ {O(n^2)}
t₉: 3⋅X₁₁⋅X₁₁⋅X₁₁⋅X₁₅+3⋅X₁₅⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁⋅X₁₅+10⋅X₁₅⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅⋅X₁₅+11⋅X₁₁⋅X₁₅+2⋅X₁₃⋅X₁₅+26⋅X₁₅⋅X₁₅+4⋅X₁₂⋅X₁₅+X₁₄⋅X₁₅+4⋅X₁₅+X₁₀+X₉ {O(n^4)}
t₁₀: X₁₅ {O(n)}
t₁₁: 3⋅X₁₁⋅X₁₁⋅X₁₁⋅X₁₅+3⋅X₁₅⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁⋅X₁₅+10⋅X₁₅⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅⋅X₁₅+11⋅X₁₁⋅X₁₅+2⋅X₁₃⋅X₁₅+26⋅X₁₅⋅X₁₅+4⋅X₁₂⋅X₁₅+X₁₄⋅X₁₅+4⋅X₁₅+X₁₀+X₉ {O(n^4)}
t₁₂: X₁₅ {O(n)}
t₁₃: 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)}
t₀, X₁₀: X₁₀ {O(n)}
t₀, X₁₁: X₁₁ {O(n)}
t₀, X₁₂: X₁₂ {O(n)}
t₀, X₁₃: X₁₃ {O(n)}
t₀, X₁₄: X₁₄ {O(n)}
t₀, X₁₅: X₁₅ {O(n)}
t₁, X₀: X₁₁ {O(n)}
t₁, X₁: X₁₂ {O(n)}
t₁, X₂: X₁₃ {O(n)}
t₁, X₃: X₁₄ {O(n)}
t₁, X₄: X₁₅ {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)}
t₁, X₁₀: X₁₀ {O(n)}
t₁, X₁₁: X₁₁ {O(n)}
t₁, X₁₂: X₁₂ {O(n)}
t₁, X₁₃: X₁₃ {O(n)}
t₁, X₁₄: X₁₄ {O(n)}
t₁, X₁₅: X₁₅ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₂, X₇: X₇ {O(n)}
t₂, X₈: X₈ {O(n)}
t₂, X₉: X₉ {O(n)}
t₂, X₁₀: X₁₀ {O(n)}
t₂, X₁₁: X₁₁ {O(n)}
t₂, X₁₂: X₁₂ {O(n)}
t₂, X₁₃: X₁₃ {O(n)}
t₂, X₁₄: X₁₄ {O(n)}
t₂, X₁₅: X₁₅ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₃, X₅: X₅ {O(n)}
t₃, X₆: X₆ {O(n)}
t₃, X₇: X₇ {O(n)}
t₃, X₈: X₈ {O(n)}
t₃, X₉: X₉ {O(n)}
t₃, X₁₀: X₁₀ {O(n)}
t₃, X₁₁: X₁₁ {O(n)}
t₃, X₁₂: X₁₂ {O(n)}
t₃, X₁₃: X₁₃ {O(n)}
t₃, X₁₄: X₁₄ {O(n)}
t₃, X₁₅: X₁₅ {O(n)}
t₄, X₀: X₁₁+X₁₅ {O(n)}
t₄, X₁: 2⋅X₁₅+X₁₂ {O(n)}
t₄, X₂: 3⋅X₁₅+X₁₃ {O(n)}
t₄, X₃: X₁₄+X₁₅ {O(n)}
t₄, X₄: X₁₅ {O(n)}
t₄, X₅: X₁₁+X₁₅ {O(n)}
t₄, X₆: 2⋅X₁₅+X₁₂ {O(n)}
t₄, X₇: 3⋅X₁₅+X₁₃ {O(n)}
t₄, X₈: X₁₄+X₁₅ {O(n)}
t₄, X₉: 3⋅X₁₁⋅X₁₁⋅X₁₁+3⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁+10⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅+11⋅X₁₁+12⋅X₁₂+54⋅X₁₅+6⋅X₁₃+X₁₄+X₉+5 {O(n^3)}
t₄, X₁₀: 27⋅X₁₁⋅X₁₁⋅X₁₅+27⋅X₁₁⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₁+9⋅X₁₅⋅X₁₅⋅X₁₅+30⋅X₁₁⋅X₁₁+30⋅X₁₅⋅X₁₅+60⋅X₁₁⋅X₁₅+2⋅X₁₃+3⋅X₁₄+33⋅X₁₁+4⋅X₁₂+50⋅X₁₅+X₁₀+13 {O(n^3)}
t₄, X₁₁: X₁₁ {O(n)}
t₄, X₁₂: X₁₂ {O(n)}
t₄, X₁₃: X₁₃ {O(n)}
t₄, X₁₄: X₁₄ {O(n)}
t₄, X₁₅: X₁₅ {O(n)}
t₅, X₀: X₁₅ {O(n)}
t₅, X₁: 2⋅X₁₅ {O(n)}
t₅, X₂: 3⋅X₁₅ {O(n)}
t₅, X₃: X₁₅ {O(n)}
t₅, X₄: 0 {O(1)}
t₅, X₅: 0 {O(1)}
t₅, X₆: 28⋅X₁₅+4⋅X₁₃+8⋅X₁₂ {O(n)}
t₅, X₇: 12⋅X₁₂+48⋅X₁₅+8⋅X₁₃ {O(n)}
t₅, X₈: 18⋅X₁₁⋅X₁₁⋅X₁₅+18⋅X₁₁⋅X₁₅⋅X₁₅+6⋅X₁₁⋅X₁₁⋅X₁₁+6⋅X₁₅⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₁+20⋅X₁₅⋅X₁₅+40⋅X₁₁⋅X₁₅+2⋅X₁₄+22⋅X₁₁+24⋅X₁₅+8 {O(n^3)}
t₅, X₉: 3⋅X₁₁⋅X₁₁⋅X₁₁+3⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁+10⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅+11⋅X₁₁+12⋅X₁₂+54⋅X₁₅+6⋅X₁₃+X₁₄+5 {O(n^3)}
t₅, X₁₀: 27⋅X₁₁⋅X₁₁⋅X₁₅+27⋅X₁₁⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₁+9⋅X₁₅⋅X₁₅⋅X₁₅+30⋅X₁₁⋅X₁₁+30⋅X₁₅⋅X₁₅+60⋅X₁₁⋅X₁₅+2⋅X₁₃+3⋅X₁₄+33⋅X₁₁+4⋅X₁₂+50⋅X₁₅+13 {O(n^3)}
t₅, X₁₁: X₁₁ {O(n)}
t₅, X₁₂: X₁₂ {O(n)}
t₅, X₁₃: X₁₃ {O(n)}
t₅, X₁₄: X₁₄ {O(n)}
t₅, X₁₅: X₁₅ {O(n)}
t₆, X₀: X₁₁+X₁₅ {O(n)}
t₆, X₁: 2⋅X₁₅+X₁₂ {O(n)}
t₆, X₂: 3⋅X₁₅+X₁₃ {O(n)}
t₆, X₃: X₁₄+X₁₅ {O(n)}
t₆, X₄: X₁₅ {O(n)}
t₆, X₅: X₁₁+X₁₅ {O(n)}
t₆, X₆: 14⋅X₁₅+2⋅X₁₃+4⋅X₁₂ {O(n)}
t₆, X₇: 24⋅X₁₅+4⋅X₁₃+6⋅X₁₂ {O(n)}
t₆, X₈: 3⋅X₁₁⋅X₁₁⋅X₁₁+3⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅+16⋅X₁₁⋅X₁₁+16⋅X₁₅⋅X₁₅+32⋅X₁₁⋅X₁₅+28⋅X₁₁+29⋅X₁₅+X₁₄+16 {O(n^3)}
t₆, X₉: 3⋅X₁₁⋅X₁₁⋅X₁₁+3⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁+10⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅+11⋅X₁₁+12⋅X₁₂+54⋅X₁₅+6⋅X₁₃+X₁₄+X₉+5 {O(n^3)}
t₆, X₁₀: 27⋅X₁₁⋅X₁₁⋅X₁₅+27⋅X₁₁⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₁+9⋅X₁₅⋅X₁₅⋅X₁₅+30⋅X₁₁⋅X₁₁+30⋅X₁₅⋅X₁₅+60⋅X₁₁⋅X₁₅+2⋅X₁₃+3⋅X₁₄+33⋅X₁₁+4⋅X₁₂+50⋅X₁₅+X₁₀+13 {O(n^3)}
t₆, X₁₁: X₁₁ {O(n)}
t₆, X₁₂: X₁₂ {O(n)}
t₆, X₁₃: X₁₃ {O(n)}
t₆, X₁₄: X₁₄ {O(n)}
t₆, X₁₅: X₁₅ {O(n)}
t₇, X₀: X₁₁+X₁₅ {O(n)}
t₇, X₁: 2⋅X₁₅+X₁₂ {O(n)}
t₇, X₂: 3⋅X₁₅+X₁₃ {O(n)}
t₇, X₃: X₁₄+X₁₅ {O(n)}
t₇, X₄: X₁₅ {O(n)}
t₇, X₅: 0 {O(1)}
t₇, X₆: 14⋅X₁₅+2⋅X₁₃+4⋅X₁₂ {O(n)}
t₇, X₇: 24⋅X₁₅+4⋅X₁₃+6⋅X₁₂ {O(n)}
t₇, X₈: 3⋅X₁₁⋅X₁₁⋅X₁₁+3⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁+10⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅+11⋅X₁₁+12⋅X₁₅+X₁₄+4 {O(n^3)}
t₇, X₉: 14⋅X₁₅+2⋅X₁₃+4⋅X₁₂ {O(n)}
t₇, X₁₀: 3⋅X₁₁⋅X₁₁⋅X₁₁+3⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁+10⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅+11⋅X₁₁+12⋅X₁₅+X₁₄+4 {O(n^3)}
t₇, X₁₁: X₁₁ {O(n)}
t₇, X₁₂: X₁₂ {O(n)}
t₇, X₁₃: X₁₃ {O(n)}
t₇, X₁₄: X₁₄ {O(n)}
t₇, X₁₅: X₁₅ {O(n)}
t₈, X₀: X₁₁+X₁₅ {O(n)}
t₈, X₁: 2⋅X₁₅+X₁₂ {O(n)}
t₈, X₂: 3⋅X₁₅+X₁₃ {O(n)}
t₈, X₃: X₁₄+X₁₅ {O(n)}
t₈, X₄: X₁₅ {O(n)}
t₈, X₅: X₁₁+X₁₅ {O(n)}
t₈, X₆: 14⋅X₁₅+2⋅X₁₃+4⋅X₁₂ {O(n)}
t₈, X₇: 24⋅X₁₅+4⋅X₁₃+6⋅X₁₂ {O(n)}
t₈, X₈: 3⋅X₁₁⋅X₁₁⋅X₁₁+3⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁+10⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅+11⋅X₁₁+12⋅X₁₅+X₁₄+4 {O(n^3)}
t₈, X₉: 3⋅X₁₁⋅X₁₁⋅X₁₁+3⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁+10⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅+11⋅X₁₁+12⋅X₁₂+54⋅X₁₅+6⋅X₁₃+X₁₄+X₉+5 {O(n^3)}
t₈, X₁₀: 27⋅X₁₁⋅X₁₁⋅X₁₅+27⋅X₁₁⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₁+9⋅X₁₅⋅X₁₅⋅X₁₅+30⋅X₁₁⋅X₁₁+30⋅X₁₅⋅X₁₅+60⋅X₁₁⋅X₁₅+2⋅X₁₃+3⋅X₁₄+33⋅X₁₁+4⋅X₁₂+50⋅X₁₅+X₁₀+13 {O(n^3)}
t₈, X₁₁: X₁₁ {O(n)}
t₈, X₁₂: X₁₂ {O(n)}
t₈, X₁₃: X₁₃ {O(n)}
t₈, X₁₄: X₁₄ {O(n)}
t₈, X₁₅: X₁₅ {O(n)}
t₉, X₀: X₁₁+X₁₅ {O(n)}
t₉, X₁: 2⋅X₁₅+X₁₂ {O(n)}
t₉, X₂: 3⋅X₁₅+X₁₃ {O(n)}
t₉, X₃: X₁₄+X₁₅ {O(n)}
t₉, X₄: X₁₅ {O(n)}
t₉, X₅: 0 {O(1)}
t₉, X₆: 14⋅X₁₅+2⋅X₁₃+4⋅X₁₂ {O(n)}
t₉, X₇: 24⋅X₁₅+4⋅X₁₃+6⋅X₁₂ {O(n)}
t₉, X₈: 3⋅X₁₁⋅X₁₁⋅X₁₁+3⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁+10⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅+11⋅X₁₁+12⋅X₁₅+X₁₄+4 {O(n^3)}
t₉, X₉: 3⋅X₁₁⋅X₁₁⋅X₁₁+3⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁+10⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅+11⋅X₁₁+4⋅X₁₃+40⋅X₁₅+8⋅X₁₂+X₁₄+5 {O(n^3)}
t₉, X₁₀: 18⋅X₁₁⋅X₁₁⋅X₁₅+18⋅X₁₁⋅X₁₅⋅X₁₅+6⋅X₁₁⋅X₁₁⋅X₁₁+6⋅X₁₅⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₁+20⋅X₁₅⋅X₁₅+40⋅X₁₁⋅X₁₅+2⋅X₁₃+2⋅X₁₄+22⋅X₁₁+38⋅X₁₅+4⋅X₁₂+9 {O(n^3)}
t₉, X₁₁: X₁₁ {O(n)}
t₉, X₁₂: X₁₂ {O(n)}
t₉, X₁₃: X₁₃ {O(n)}
t₉, X₁₄: X₁₄ {O(n)}
t₉, X₁₅: X₁₅ {O(n)}
t₁₀, X₀: 2⋅X₁₁+2⋅X₁₅ {O(n)}
t₁₀, X₁: 2⋅X₁₂+4⋅X₁₅ {O(n)}
t₁₀, X₂: 2⋅X₁₃+6⋅X₁₅ {O(n)}
t₁₀, X₃: 2⋅X₁₄+2⋅X₁₅ {O(n)}
t₁₀, X₄: X₁₅ {O(n)}
t₁₀, X₅: 0 {O(1)}
t₁₀, X₆: 28⋅X₁₅+4⋅X₁₃+8⋅X₁₂ {O(n)}
t₁₀, X₇: 12⋅X₁₂+48⋅X₁₅+8⋅X₁₃ {O(n)}
t₁₀, X₈: 18⋅X₁₁⋅X₁₁⋅X₁₅+18⋅X₁₁⋅X₁₅⋅X₁₅+6⋅X₁₁⋅X₁₁⋅X₁₁+6⋅X₁₅⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₁+20⋅X₁₅⋅X₁₅+40⋅X₁₁⋅X₁₅+2⋅X₁₄+22⋅X₁₁+24⋅X₁₅+8 {O(n^3)}
t₁₀, X₉: 3⋅X₁₁⋅X₁₁⋅X₁₁+3⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁+10⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅+11⋅X₁₁+12⋅X₁₂+54⋅X₁₅+6⋅X₁₃+X₁₄+5 {O(n^3)}
t₁₀, X₁₀: 27⋅X₁₁⋅X₁₁⋅X₁₅+27⋅X₁₁⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₁+9⋅X₁₅⋅X₁₅⋅X₁₅+30⋅X₁₁⋅X₁₁+30⋅X₁₅⋅X₁₅+60⋅X₁₁⋅X₁₅+2⋅X₁₃+3⋅X₁₄+33⋅X₁₁+4⋅X₁₂+50⋅X₁₅+13 {O(n^3)}
t₁₀, X₁₁: X₁₁ {O(n)}
t₁₀, X₁₂: X₁₂ {O(n)}
t₁₀, X₁₃: X₁₃ {O(n)}
t₁₀, X₁₄: X₁₄ {O(n)}
t₁₀, X₁₅: X₁₅ {O(n)}
t₁₁, X₀: X₁₁+X₁₅ {O(n)}
t₁₁, X₁: 2⋅X₁₅+X₁₂ {O(n)}
t₁₁, X₂: 3⋅X₁₅+X₁₃ {O(n)}
t₁₁, X₃: X₁₄+X₁₅ {O(n)}
t₁₁, X₄: X₁₅ {O(n)}
t₁₁, X₅: 0 {O(1)}
t₁₁, X₆: 14⋅X₁₅+2⋅X₁₃+4⋅X₁₂ {O(n)}
t₁₁, X₇: 24⋅X₁₅+4⋅X₁₃+6⋅X₁₂ {O(n)}
t₁₁, X₈: 3⋅X₁₁⋅X₁₁⋅X₁₁+3⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁+10⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅+11⋅X₁₁+12⋅X₁₅+X₁₄+4 {O(n^3)}
t₁₁, X₉: 3⋅X₁₁⋅X₁₁⋅X₁₁+3⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁+10⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅+11⋅X₁₁+4⋅X₁₃+40⋅X₁₅+8⋅X₁₂+X₁₄+5 {O(n^3)}
t₁₁, X₁₀: 18⋅X₁₁⋅X₁₁⋅X₁₅+18⋅X₁₁⋅X₁₅⋅X₁₅+6⋅X₁₁⋅X₁₁⋅X₁₁+6⋅X₁₅⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₁+20⋅X₁₅⋅X₁₅+40⋅X₁₁⋅X₁₅+2⋅X₁₃+2⋅X₁₄+22⋅X₁₁+38⋅X₁₅+4⋅X₁₂+9 {O(n^3)}
t₁₁, X₁₁: X₁₁ {O(n)}
t₁₁, X₁₂: X₁₂ {O(n)}
t₁₁, X₁₃: X₁₃ {O(n)}
t₁₁, X₁₄: X₁₄ {O(n)}
t₁₁, X₁₅: X₁₅ {O(n)}
t₁₂, X₀: X₁₅ {O(n)}
t₁₂, X₁: 2⋅X₁₅ {O(n)}
t₁₂, X₂: 3⋅X₁₅ {O(n)}
t₁₂, X₃: X₁₅ {O(n)}
t₁₂, X₄: X₁₅ {O(n)}
t₁₂, X₅: 0 {O(1)}
t₁₂, X₆: 28⋅X₁₅+4⋅X₁₃+8⋅X₁₂ {O(n)}
t₁₂, X₇: 12⋅X₁₂+48⋅X₁₅+8⋅X₁₃ {O(n)}
t₁₂, X₈: 18⋅X₁₁⋅X₁₁⋅X₁₅+18⋅X₁₁⋅X₁₅⋅X₁₅+6⋅X₁₁⋅X₁₁⋅X₁₁+6⋅X₁₅⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₁+20⋅X₁₅⋅X₁₅+40⋅X₁₁⋅X₁₅+2⋅X₁₄+22⋅X₁₁+24⋅X₁₅+8 {O(n^3)}
t₁₂, X₉: 3⋅X₁₁⋅X₁₁⋅X₁₁+3⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁+10⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅+11⋅X₁₁+12⋅X₁₂+54⋅X₁₅+6⋅X₁₃+X₁₄+5 {O(n^3)}
t₁₂, X₁₀: 27⋅X₁₁⋅X₁₁⋅X₁₅+27⋅X₁₁⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₁+9⋅X₁₅⋅X₁₅⋅X₁₅+30⋅X₁₁⋅X₁₁+30⋅X₁₅⋅X₁₅+60⋅X₁₁⋅X₁₅+2⋅X₁₃+3⋅X₁₄+33⋅X₁₁+4⋅X₁₂+50⋅X₁₅+13 {O(n^3)}
t₁₂, X₁₁: X₁₁ {O(n)}
t₁₂, X₁₂: X₁₂ {O(n)}
t₁₂, X₁₃: X₁₃ {O(n)}
t₁₂, X₁₄: X₁₄ {O(n)}
t₁₂, X₁₅: X₁₅ {O(n)}
t₁₃, X₀: 2⋅X₀+X₁₅ {O(n)}
t₁₃, X₁: 2⋅X₁+2⋅X₁₅ {O(n)}
t₁₃, X₂: 2⋅X₂+3⋅X₁₅ {O(n)}
t₁₃, X₃: 2⋅X₃+X₁₅ {O(n)}
t₁₃, X₄: 2⋅X₄ {O(n)}
t₁₃, X₅: 2⋅X₅ {O(n)}
t₁₃, X₆: 2⋅X₆+28⋅X₁₅+4⋅X₁₃+8⋅X₁₂ {O(n)}
t₁₃, X₇: 12⋅X₁₂+2⋅X₇+48⋅X₁₅+8⋅X₁₃ {O(n)}
t₁₃, X₈: 18⋅X₁₁⋅X₁₁⋅X₁₅+18⋅X₁₁⋅X₁₅⋅X₁₅+6⋅X₁₁⋅X₁₁⋅X₁₁+6⋅X₁₅⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₁+20⋅X₁₅⋅X₁₅+40⋅X₁₁⋅X₁₅+2⋅X₁₄+2⋅X₈+22⋅X₁₁+24⋅X₁₅+8 {O(n^3)}
t₁₃, X₉: 3⋅X₁₁⋅X₁₁⋅X₁₁+3⋅X₁₅⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₅+9⋅X₁₁⋅X₁₅⋅X₁₅+10⋅X₁₁⋅X₁₁+10⋅X₁₅⋅X₁₅+20⋅X₁₁⋅X₁₅+11⋅X₁₁+12⋅X₁₂+2⋅X₉+54⋅X₁₅+6⋅X₁₃+X₁₄+5 {O(n^3)}
t₁₃, X₁₀: 27⋅X₁₁⋅X₁₁⋅X₁₅+27⋅X₁₁⋅X₁₅⋅X₁₅+9⋅X₁₁⋅X₁₁⋅X₁₁+9⋅X₁₅⋅X₁₅⋅X₁₅+30⋅X₁₁⋅X₁₁+30⋅X₁₅⋅X₁₅+60⋅X₁₁⋅X₁₅+2⋅X₁₀+2⋅X₁₃+3⋅X₁₄+33⋅X₁₁+4⋅X₁₂+50⋅X₁₅+13 {O(n^3)}
t₁₃, X₁₁: 3⋅X₁₁ {O(n)}
t₁₃, X₁₂: 3⋅X₁₂ {O(n)}
t₁₃, X₁₃: 3⋅X₁₃ {O(n)}
t₁₃, X₁₄: 3⋅X₁₄ {O(n)}
t₁₃, X₁₅: 3⋅X₁₅ {O(n)}