KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₅ ≤ 1 ∧ X₅ ≤ X₄ for location eval_rank2_stop

Found invariant X₅ ≤ X₄ ∧ X₅ ≤ 2+X₂ ∧ X₅ ≤ 1+X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2+X₂ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀ for location eval_rank2_15

Found invariant X₅ ≤ X₄ ∧ X₅ ≤ 1+X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₀ for location eval_rank2_bb3_in

Found invariant 1 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ X₅ ≤ 1+X₇ ∧ 3 ≤ X₄+X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 1+X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₀ for location eval_rank2_10

Found invariant X₅ ≤ X₄ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ 2 ≤ X₄ for location eval_rank2_bb2_in

Found invariant X₅ ≤ X₄ ∧ X₅ ≤ 1+X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₀ for location eval_rank2__critedge_in

Found invariant 1 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ X₅ ≤ 1+X₇ ∧ 3 ≤ X₄+X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 1+X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₀ for location eval_rank2_11

Found invariant X₃ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 2+X₂ ∧ X₅ ≤ 1+X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2+X₂ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀ for location eval_rank2_17

Found invariant 1 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ X₅ ≤ 1+X₇ ∧ 3 ≤ X₄+X₇ ∧ 2 ≤ X₁+X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 1+X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_rank2_bb5_in

Found invariant X₅ ≤ 1 ∧ X₅ ≤ X₄ for location eval_rank2_bb6_in

Found invariant X₅ ≤ X₄ for location eval_rank2_bb1_in

Found invariant 1 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ X₅ ≤ 1+X₇ ∧ 3 ≤ X₄+X₇ ∧ 2 ≤ X₀+X₇ ∧ X₀ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 1+X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₀ for location eval_rank2_bb4_in

Problem after Preprocessing

Start: eval_rank2_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: nondef_0
Locations: eval_rank2_0, eval_rank2_1, eval_rank2_10, eval_rank2_11, eval_rank2_15, eval_rank2_16, eval_rank2_17, eval_rank2_18, eval_rank2_2, eval_rank2_3, eval_rank2_4, eval_rank2_5, eval_rank2_6, eval_rank2__critedge_in, eval_rank2_bb0_in, eval_rank2_bb1_in, eval_rank2_bb2_in, eval_rank2_bb3_in, eval_rank2_bb4_in, eval_rank2_bb5_in, eval_rank2_bb6_in, eval_rank2_start, eval_rank2_stop
Transitions:
t₂: eval_rank2_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₃: eval_rank2_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁₅: eval_rank2_10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_11(X₀, nondef_0, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ ≤ 1+X₀ ∧ X₅ ≤ 1+X₇ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 3 ≤ X₄+X₇ ∧ 3 ≤ X₅+X₇ ∧ 4 ≤ X₄+X₅ ∧ X₀ ≤ X₇ ∧ X₅ ≤ X₄
t₁₇: eval_rank2_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ 0 ∧ X₅ ≤ 1+X₀ ∧ X₅ ≤ 1+X₇ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 3 ≤ X₄+X₇ ∧ 3 ≤ X₅+X₇ ∧ 4 ≤ X₄+X₅ ∧ X₀ ≤ X₇ ∧ X₅ ≤ X₄
t₁₆: eval_rank2_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₁ ∧ X₅ ≤ 1+X₀ ∧ X₅ ≤ 1+X₇ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 3 ≤ X₄+X₇ ∧ 3 ≤ X₅+X₇ ∧ 4 ≤ X₄+X₅ ∧ X₀ ≤ X₇ ∧ X₅ ≤ X₄
t₂₀: eval_rank2_15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ ≤ 2+X₂ ∧ X₅ ≤ 1+X₀ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₄ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 4 ≤ X₄+X₅ ∧ 0 ≤ X₂ ∧ X₅ ≤ X₄
t₂₁: eval_rank2_16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_17(X₀, X₁, X₂, X₇-X₂, X₄, X₅, X₆, X₇) :|: X₅ ≤ 2+X₂ ∧ X₅ ≤ 1+X₀ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₄ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 4 ≤ X₄+X₅ ∧ 0 ≤ X₂ ∧ X₅ ≤ X₄
t₂₂: eval_rank2_17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_18(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ ≤ 2+X₂ ∧ X₅ ≤ 1+X₀ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₄ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 4 ≤ X₄+X₅ ∧ 0 ≤ X₂ ∧ X₃ ≤ X₇ ∧ X₅ ≤ X₄
t₂₃: eval_rank2_18(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_bb1_in(X₀, X₁, X₂, X₃, X₄, X₂, X₃, X₇) :|: X₅ ≤ 2+X₂ ∧ X₅ ≤ 1+X₀ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₄ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 4 ≤ X₄+X₅ ∧ 0 ≤ X₂ ∧ X₃ ≤ X₇ ∧ X₅ ≤ X₄
t₄: eval_rank2_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₅: eval_rank2_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₆: eval_rank2_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₇: eval_rank2_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₈: eval_rank2_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_bb1_in(X₀, X₁, X₂, X₃, X₄, X₄, X₄, X₇)
t₁₉: eval_rank2__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_15(X₀, X₁, X₀-1, X₃, X₄, X₅, X₆, X₇) :|: X₅ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 4 ≤ X₄+X₅ ∧ X₅ ≤ X₄
t₁: eval_rank2_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₉: eval_rank2_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 2 ≤ X₅ ∧ X₅ ≤ X₄
t₁₀: eval_rank2_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ ≤ 1 ∧ X₅ ≤ X₄
t₁₁: eval_rank2_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_bb3_in(X₅-1, X₁, X₂, X₃, X₄, X₅, X₆, X₅+X₆-1) :|: 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ X₅ ≤ X₄
t₁₃: eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₇ ≤ X₀ ∧ X₅ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 4 ≤ X₄+X₅ ∧ X₅ ≤ X₄
t₁₂: eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ X₇ ∧ X₅ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 4 ≤ X₄+X₅ ∧ X₅ ≤ X₄
t₁₄: eval_rank2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ ≤ 1+X₀ ∧ X₅ ≤ 1+X₇ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 3 ≤ X₄+X₇ ∧ 3 ≤ X₅+X₇ ∧ 4 ≤ X₄+X₅ ∧ X₀ ≤ X₇ ∧ X₅ ≤ X₄
t₁₈: eval_rank2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇-1) :|: X₅ ≤ 1+X₀ ∧ X₅ ≤ 1+X₇ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₁+X₇ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₄+X₇ ∧ 3 ≤ X₅+X₇ ∧ 4 ≤ X₄+X₅ ∧ X₀ ≤ X₇ ∧ X₅ ≤ X₄
t₂₄: eval_rank2_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ ≤ 1 ∧ X₅ ≤ X₄
t₀: eval_rank2_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)

MPRF for transition t₉: eval_rank2_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 2 ≤ X₅ ∧ X₅ ≤ X₄ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

• eval_rank2_10: [X₅-2]
• eval_rank2_11: [X₅-2]
• eval_rank2_15: [X₅-2]
• eval_rank2_16: [X₅-2]
• eval_rank2_17: [X₅-2]
• eval_rank2_18: [X₂]
• eval_rank2__critedge_in: [X₅-2]
• eval_rank2_bb1_in: [X₅-1]
• eval_rank2_bb2_in: [X₅-2]
• eval_rank2_bb3_in: [X₅-2]
• eval_rank2_bb4_in: [X₅-2]
• eval_rank2_bb5_in: [X₅-2]

MPRF for transition t₁₁: eval_rank2_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_bb3_in(X₅-1, X₁, X₂, X₃, X₄, X₅, X₆, X₅+X₆-1) :|: 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ X₅ ≤ X₄ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

• eval_rank2_10: [X₅-2]
• eval_rank2_11: [X₅-2]
• eval_rank2_15: [X₂]
• eval_rank2_16: [X₂-1]
• eval_rank2_17: [X₅-3]
• eval_rank2_18: [X₀-2]
• eval_rank2__critedge_in: [X₀-1]
• eval_rank2_bb1_in: [X₅-1]
• eval_rank2_bb2_in: [X₅-1]
• eval_rank2_bb3_in: [X₀-1]
• eval_rank2_bb4_in: [X₅-2]
• eval_rank2_bb5_in: [X₀-1]

MPRF for transition t₁₂: eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ X₇ ∧ X₅ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 4 ≤ X₄+X₅ ∧ X₅ ≤ X₄ of depth 1:

new bound:

2⋅X₄+1 {O(n)}

MPRF:

• eval_rank2_10: [X₇-1]
• eval_rank2_11: [X₇-1]
• eval_rank2_15: [X₇-1]
• eval_rank2_16: [X₇-1]
• eval_rank2_17: [X₂+X₃-1]
• eval_rank2_18: [X₂+X₃-1]
• eval_rank2__critedge_in: [X₇-1]
• eval_rank2_bb1_in: [X₅+X₆-1]
• eval_rank2_bb2_in: [X₅+X₆-1]
• eval_rank2_bb3_in: [X₇]
• eval_rank2_bb4_in: [X₇-1]
• eval_rank2_bb5_in: [X₇-1]

MPRF for transition t₁₃: eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₇ ≤ X₀ ∧ X₅ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 4 ≤ X₄+X₅ ∧ X₅ ≤ X₄ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_rank2_10: [X₀]
• eval_rank2_11: [X₅-1]
• eval_rank2_15: [X₀-1]
• eval_rank2_16: [X₀-1]
• eval_rank2_17: [X₀-1]
• eval_rank2_18: [X₂]
• eval_rank2__critedge_in: [X₀-1]
• eval_rank2_bb1_in: [X₅]
• eval_rank2_bb2_in: [X₅-1]
• eval_rank2_bb3_in: [X₀]
• eval_rank2_bb4_in: [X₀]
• eval_rank2_bb5_in: [X₅-1]

MPRF for transition t₁₄: eval_rank2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ ≤ 1+X₀ ∧ X₅ ≤ 1+X₇ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 3 ≤ X₄+X₇ ∧ 3 ≤ X₅+X₇ ∧ 4 ≤ X₄+X₅ ∧ X₀ ≤ X₇ ∧ X₅ ≤ X₄ of depth 1:

new bound:

3⋅X₄ {O(n)}

MPRF:

• eval_rank2_10: [X₀+X₇]
• eval_rank2_11: [X₀+X₇]
• eval_rank2_15: [X₅+X₇-1]
• eval_rank2_16: [X₅+X₇-1]
• eval_rank2_17: [X₂+X₃+X₅-1]
• eval_rank2_18: [X₂+X₃+X₅-1]
• eval_rank2__critedge_in: [X₀+X₇]
• eval_rank2_bb1_in: [2⋅X₅+X₆]
• eval_rank2_bb2_in: [2⋅X₅+X₆]
• eval_rank2_bb3_in: [1+X₀+X₇]
• eval_rank2_bb4_in: [1+X₀+X₇]
• eval_rank2_bb5_in: [X₀+X₇]

MPRF for transition t₁₅: eval_rank2_10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_11(X₀, nondef_0, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ ≤ 1+X₀ ∧ X₅ ≤ 1+X₇ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 3 ≤ X₄+X₇ ∧ 3 ≤ X₅+X₇ ∧ 4 ≤ X₄+X₅ ∧ X₀ ≤ X₇ ∧ X₅ ≤ X₄ of depth 1:

new bound:

2⋅X₄+1 {O(n)}

MPRF:

• eval_rank2_10: [X₇]
• eval_rank2_11: [X₇-1]
• eval_rank2_15: [X₇-1]
• eval_rank2_16: [X₇-1]
• eval_rank2_17: [X₂+X₃-1]
• eval_rank2_18: [X₂+X₃-1]
• eval_rank2__critedge_in: [X₇-1]
• eval_rank2_bb1_in: [X₅+X₆-1]
• eval_rank2_bb2_in: [X₅+X₆-1]
• eval_rank2_bb3_in: [X₇]
• eval_rank2_bb4_in: [X₇]
• eval_rank2_bb5_in: [X₇-1]

MPRF for transition t₁₆: eval_rank2_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₁ ∧ X₅ ≤ 1+X₀ ∧ X₅ ≤ 1+X₇ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 3 ≤ X₄+X₇ ∧ 3 ≤ X₅+X₇ ∧ 4 ≤ X₄+X₅ ∧ X₀ ≤ X₇ ∧ X₅ ≤ X₄ of depth 1:

new bound:

2⋅X₄+1 {O(n)}

MPRF:

• eval_rank2_10: [2⋅X₅+X₇-2⋅X₀]
• eval_rank2_11: [2+X₇]
• eval_rank2_15: [1+X₇]
• eval_rank2_16: [1+X₇]
• eval_rank2_17: [X₃+X₅-1]
• eval_rank2_18: [1+X₂+X₃]
• eval_rank2__critedge_in: [1+X₇]
• eval_rank2_bb1_in: [1+X₅+X₆]
• eval_rank2_bb2_in: [1+X₅+X₆]
• eval_rank2_bb3_in: [2+X₇]
• eval_rank2_bb4_in: [2+X₇]
• eval_rank2_bb5_in: [1+X₇]

MPRF for transition t₁₇: eval_rank2_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ 0 ∧ X₅ ≤ 1+X₀ ∧ X₅ ≤ 1+X₇ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 3 ≤ X₄+X₇ ∧ 3 ≤ X₅+X₇ ∧ 4 ≤ X₄+X₅ ∧ X₀ ≤ X₇ ∧ X₅ ≤ X₄ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

• eval_rank2_10: [1+2⋅X₀-X₅]
• eval_rank2_11: [X₀]
• eval_rank2_15: [X₂]
• eval_rank2_16: [X₅-2]
• eval_rank2_17: [X₀-1]
• eval_rank2_18: [X₂]
• eval_rank2__critedge_in: [X₀-1]
• eval_rank2_bb1_in: [X₅-1]
• eval_rank2_bb2_in: [X₅-1]
• eval_rank2_bb3_in: [X₅-1]
• eval_rank2_bb4_in: [X₅-1]
• eval_rank2_bb5_in: [2⋅X₅-2-X₀]

MPRF for transition t₁₈: eval_rank2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇-1) :|: X₅ ≤ 1+X₀ ∧ X₅ ≤ 1+X₇ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₇ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₇ ∧ 2 ≤ X₁+X₇ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₄+X₇ ∧ 3 ≤ X₅+X₇ ∧ 4 ≤ X₄+X₅ ∧ X₀ ≤ X₇ ∧ X₅ ≤ X₄ of depth 1:

new bound:

2⋅X₄+1 {O(n)}

MPRF:

• eval_rank2_10: [X₇]
• eval_rank2_11: [X₇]
• eval_rank2_15: [X₇]
• eval_rank2_16: [X₇]
• eval_rank2_17: [X₂+X₃]
• eval_rank2_18: [X₂+X₃]
• eval_rank2__critedge_in: [X₇]
• eval_rank2_bb1_in: [X₅+X₆-1]
• eval_rank2_bb2_in: [X₅+X₆-1]
• eval_rank2_bb3_in: [X₇]
• eval_rank2_bb4_in: [X₇]
• eval_rank2_bb5_in: [X₇]

MPRF for transition t₁₉: eval_rank2__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_15(X₀, X₁, X₀-1, X₃, X₄, X₅, X₆, X₇) :|: X₅ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 4 ≤ X₄+X₅ ∧ X₅ ≤ X₄ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

• eval_rank2_10: [X₀]
• eval_rank2_11: [X₀]
• eval_rank2_15: [X₀-1]
• eval_rank2_16: [X₂]
• eval_rank2_17: [X₂-1]
• eval_rank2_18: [X₂-1]
• eval_rank2__critedge_in: [X₀]
• eval_rank2_bb1_in: [X₅-1]
• eval_rank2_bb2_in: [X₅-1]
• eval_rank2_bb3_in: [X₀]
• eval_rank2_bb4_in: [X₀]
• eval_rank2_bb5_in: [X₀]

MPRF for transition t₂₀: eval_rank2_15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ ≤ 2+X₂ ∧ X₅ ≤ 1+X₀ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₄ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 4 ≤ X₄+X₅ ∧ 0 ≤ X₂ ∧ X₅ ≤ X₄ of depth 1:

new bound:

X₄+2 {O(n)}

MPRF:

• eval_rank2_10: [1+X₅]
• eval_rank2_11: [1+X₅]
• eval_rank2_15: [1+X₅]
• eval_rank2_16: [1+X₀]
• eval_rank2_17: [X₅]
• eval_rank2_18: [X₅]
• eval_rank2__critedge_in: [1+X₅]
• eval_rank2_bb1_in: [2+X₅]
• eval_rank2_bb2_in: [2+X₅]
• eval_rank2_bb3_in: [1+X₅]
• eval_rank2_bb4_in: [1+X₅]
• eval_rank2_bb5_in: [2+X₀]

MPRF for transition t₂₁: eval_rank2_16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_17(X₀, X₁, X₂, X₇-X₂, X₄, X₅, X₆, X₇) :|: X₅ ≤ 2+X₂ ∧ X₅ ≤ 1+X₀ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₄ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 4 ≤ X₄+X₅ ∧ 0 ≤ X₂ ∧ X₅ ≤ X₄ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

• eval_rank2_10: [2+X₀]
• eval_rank2_11: [2+X₀]
• eval_rank2_15: [4⋅X₀-2⋅X₂-X₅]
• eval_rank2_16: [X₅]
• eval_rank2_17: [X₅-1]
• eval_rank2_18: [1+X₂]
• eval_rank2__critedge_in: [2+X₀]
• eval_rank2_bb1_in: [1+X₅]
• eval_rank2_bb2_in: [1+X₅]
• eval_rank2_bb3_in: [2+X₀]
• eval_rank2_bb4_in: [2+X₀]
• eval_rank2_bb5_in: [2+X₀]

MPRF for transition t₂₂: eval_rank2_17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_18(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₅ ≤ 2+X₂ ∧ X₅ ≤ 1+X₀ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₄ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 4 ≤ X₄+X₅ ∧ 0 ≤ X₂ ∧ X₃ ≤ X₇ ∧ X₅ ≤ X₄ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_rank2_10: [1+X₀]
• eval_rank2_11: [X₅]
• eval_rank2_15: [1+X₂]
• eval_rank2_16: [1+X₂]
• eval_rank2_17: [X₅-1]
• eval_rank2_18: [X₅-2]
• eval_rank2__critedge_in: [1+X₀]
• eval_rank2_bb1_in: [X₅]
• eval_rank2_bb2_in: [X₅]
• eval_rank2_bb3_in: [1+X₀]
• eval_rank2_bb4_in: [1+X₀]
• eval_rank2_bb5_in: [X₅]

MPRF for transition t₂₃: eval_rank2_18(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank2_bb1_in(X₀, X₁, X₂, X₃, X₄, X₂, X₃, X₇) :|: X₅ ≤ 2+X₂ ∧ X₅ ≤ 1+X₀ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₅ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₄ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₀+X₅ ∧ 4 ≤ X₄+X₅ ∧ 0 ≤ X₂ ∧ X₃ ≤ X₇ ∧ X₅ ≤ X₄ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_rank2_10: [X₀]
• eval_rank2_11: [X₀]
• eval_rank2_15: [X₅-1]
• eval_rank2_16: [X₀]
• eval_rank2_17: [X₀]
• eval_rank2_18: [1+X₂]
• eval_rank2__critedge_in: [X₅-1]
• eval_rank2_bb1_in: [X₅]
• eval_rank2_bb2_in: [X₅]
• eval_rank2_bb3_in: [X₅-1]
• eval_rank2_bb4_in: [X₅-1]
• eval_rank2_bb5_in: [X₀]

All Bounds

Timebounds

Overall timebound:20⋅X₄+22 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₄+1 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₄+1 {O(n)}
t₁₂: 2⋅X₄+1 {O(n)}
t₁₃: X₄ {O(n)}
t₁₄: 3⋅X₄ {O(n)}
t₁₅: 2⋅X₄+1 {O(n)}
t₁₆: 2⋅X₄+1 {O(n)}
t₁₇: X₄+1 {O(n)}
t₁₈: 2⋅X₄+1 {O(n)}
t₁₉: X₄+1 {O(n)}
t₂₀: X₄+2 {O(n)}
t₂₁: X₄+1 {O(n)}
t₂₂: X₄ {O(n)}
t₂₃: X₄ {O(n)}
t₂₄: 1 {O(1)}

Costbounds

Overall costbound: 20⋅X₄+22 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₄+1 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₄+1 {O(n)}
t₁₂: 2⋅X₄+1 {O(n)}
t₁₃: X₄ {O(n)}
t₁₄: 3⋅X₄ {O(n)}
t₁₅: 2⋅X₄+1 {O(n)}
t₁₆: 2⋅X₄+1 {O(n)}
t₁₇: X₄+1 {O(n)}
t₁₈: 2⋅X₄+1 {O(n)}
t₁₉: X₄+1 {O(n)}
t₂₀: X₄+2 {O(n)}
t₂₁: X₄+1 {O(n)}
t₂₂: X₄ {O(n)}
t₂₃: X₄ {O(n)}
t₂₄: 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)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {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)}
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)}
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)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {O(n)}
t₄, X₇: X₇ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₆ {O(n)}
t₅, X₇: X₇ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₆, X₆: X₆ {O(n)}
t₆, X₇: X₇ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₅ {O(n)}
t₇, X₆: X₆ {O(n)}
t₇, X₇: X₇ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₄ {O(n)}
t₈, X₆: X₄ {O(n)}
t₈, X₇: X₇ {O(n)}
t₉, X₀: 2⋅X₄+X₀ {O(n)}
t₉, X₂: X₂+X₄ {O(n)}
t₉, X₃: 2⋅X₄⋅X₄+5⋅X₄+X₃ {O(n^2)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: X₄ {O(n)}
t₉, X₆: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₉, X₇: 2⋅X₄⋅X₄+5⋅X₄+X₇ {O(n^2)}
t₁₀, X₀: 2⋅X₄+X₀ {O(n)}
t₁₀, X₂: X₂+X₄ {O(n)}
t₁₀, X₃: 2⋅X₄⋅X₄+5⋅X₄+X₃ {O(n^2)}
t₁₀, X₄: 2⋅X₄ {O(n)}
t₁₀, X₅: 2⋅X₄ {O(n)}
t₁₀, X₆: 2⋅X₄⋅X₄+6⋅X₄ {O(n^2)}
t₁₀, X₇: 2⋅X₄⋅X₄+5⋅X₄+X₇ {O(n^2)}
t₁₁, X₀: X₄ {O(n)}
t₁₁, X₂: X₂+X₄ {O(n)}
t₁₁, X₃: 2⋅X₄⋅X₄+5⋅X₄+X₃ {O(n^2)}
t₁₁, X₄: X₄ {O(n)}
t₁₁, X₅: X₄ {O(n)}
t₁₁, X₆: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₁₁, X₇: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₁₂, X₀: X₄ {O(n)}
t₁₂, X₂: X₂+X₄ {O(n)}
t₁₂, X₃: 2⋅X₄⋅X₄+5⋅X₄+X₃ {O(n^2)}
t₁₂, X₄: X₄ {O(n)}
t₁₂, X₅: X₄ {O(n)}
t₁₂, X₆: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₁₂, X₇: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₁₃, X₀: X₄ {O(n)}
t₁₃, X₂: 2⋅X₂+2⋅X₄ {O(n)}
t₁₃, X₃: 4⋅X₄⋅X₄+10⋅X₄+2⋅X₃ {O(n^2)}
t₁₃, X₄: X₄ {O(n)}
t₁₃, X₅: 2⋅X₄ {O(n)}
t₁₃, X₆: 4⋅X₄⋅X₄+10⋅X₄ {O(n^2)}
t₁₃, X₇: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₁₄, X₀: X₄ {O(n)}
t₁₄, X₂: X₂+X₄ {O(n)}
t₁₄, X₃: 2⋅X₄⋅X₄+5⋅X₄+X₃ {O(n^2)}
t₁₄, X₄: X₄ {O(n)}
t₁₄, X₅: X₄ {O(n)}
t₁₄, X₆: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₁₄, X₇: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₁₅, X₀: X₄ {O(n)}
t₁₅, X₂: X₂+X₄ {O(n)}
t₁₅, X₃: 2⋅X₄⋅X₄+5⋅X₄+X₃ {O(n^2)}
t₁₅, X₄: X₄ {O(n)}
t₁₅, X₅: X₄ {O(n)}
t₁₅, X₆: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₁₅, X₇: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₁₆, X₀: X₄ {O(n)}
t₁₆, X₂: X₂+X₄ {O(n)}
t₁₆, X₃: 2⋅X₄⋅X₄+5⋅X₄+X₃ {O(n^2)}
t₁₆, X₄: X₄ {O(n)}
t₁₆, X₅: X₄ {O(n)}
t₁₆, X₆: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₁₆, X₇: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₁₇, X₀: X₄ {O(n)}
t₁₇, X₂: X₂+X₄ {O(n)}
t₁₇, X₃: 2⋅X₄⋅X₄+5⋅X₄+X₃ {O(n^2)}
t₁₇, X₄: X₄ {O(n)}
t₁₇, X₅: X₄ {O(n)}
t₁₇, X₆: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₁₇, X₇: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₁₈, X₀: X₄ {O(n)}
t₁₈, X₂: X₂+X₄ {O(n)}
t₁₈, X₃: 2⋅X₄⋅X₄+5⋅X₄+X₃ {O(n^2)}
t₁₈, X₄: X₄ {O(n)}
t₁₈, X₅: X₄ {O(n)}
t₁₈, X₆: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₁₈, X₇: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₁₉, X₀: 2⋅X₄ {O(n)}
t₁₉, X₂: X₄ {O(n)}
t₁₉, X₃: 6⋅X₄⋅X₄+15⋅X₄+3⋅X₃ {O(n^2)}
t₁₉, X₄: X₄ {O(n)}
t₁₉, X₅: 3⋅X₄ {O(n)}
t₁₉, X₆: 6⋅X₄⋅X₄+15⋅X₄ {O(n^2)}
t₁₉, X₇: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₂₀, X₀: 2⋅X₄ {O(n)}
t₂₀, X₂: X₄ {O(n)}
t₂₀, X₃: 6⋅X₄⋅X₄+15⋅X₄+3⋅X₃ {O(n^2)}
t₂₀, X₄: X₄ {O(n)}
t₂₀, X₅: 3⋅X₄ {O(n)}
t₂₀, X₆: 6⋅X₄⋅X₄+15⋅X₄ {O(n^2)}
t₂₀, X₇: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₂₁, X₀: 2⋅X₄ {O(n)}
t₂₁, X₂: X₄ {O(n)}
t₂₁, X₃: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₂₁, X₄: X₄ {O(n)}
t₂₁, X₅: 3⋅X₄ {O(n)}
t₂₁, X₆: 6⋅X₄⋅X₄+15⋅X₄ {O(n^2)}
t₂₁, X₇: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₂₂, X₀: 2⋅X₄ {O(n)}
t₂₂, X₂: X₄ {O(n)}
t₂₂, X₃: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₂₂, X₄: X₄ {O(n)}
t₂₂, X₅: 3⋅X₄ {O(n)}
t₂₂, X₆: 6⋅X₄⋅X₄+15⋅X₄ {O(n^2)}
t₂₂, X₇: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₂₃, X₀: 2⋅X₄ {O(n)}
t₂₃, X₂: X₄ {O(n)}
t₂₃, X₃: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₂₃, X₄: X₄ {O(n)}
t₂₃, X₅: X₄ {O(n)}
t₂₃, X₆: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₂₃, X₇: 2⋅X₄⋅X₄+5⋅X₄ {O(n^2)}
t₂₄, X₀: 2⋅X₄+X₀ {O(n)}
t₂₄, X₂: X₂+X₄ {O(n)}
t₂₄, X₃: 2⋅X₄⋅X₄+5⋅X₄+X₃ {O(n^2)}
t₂₄, X₄: 2⋅X₄ {O(n)}
t₂₄, X₅: 2⋅X₄ {O(n)}
t₂₄, X₆: 2⋅X₄⋅X₄+6⋅X₄ {O(n^2)}
t₂₄, X₇: 2⋅X₄⋅X₄+5⋅X₄+X₇ {O(n^2)}