KoAT2 Proof Output

Initial Problem

Start: eval_abc_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars:
Locations: eval_abc_0, eval_abc_1, eval_abc_16, eval_abc_17, eval_abc_19, eval_abc_2, eval_abc_20, eval_abc_3, eval_abc_4, eval_abc_5, eval_abc_6, eval_abc_7, eval_abc_8, eval_abc_bb0_in, eval_abc_bb1_in, eval_abc_bb2_in, eval_abc_bb3_in, eval_abc_bb4_in, eval_abc_bb5_in, eval_abc_bb6_in, eval_abc_bb7_in, eval_abc_bb8_in, eval_abc_start, eval_abc_stop
Transitions:
t₂: eval_abc_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₃: eval_abc_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂₀: eval_abc_16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂₁: eval_abc_17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₀, X₈)
t₂₃: eval_abc_19(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_20(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₄: eval_abc_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂₄: eval_abc_20(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₁, X₇, X₈)
t₅: eval_abc_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₆: eval_abc_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₇: eval_abc_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₈: eval_abc_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₉: eval_abc_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₀: eval_abc_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₂, X₇, X₈)
t₁: eval_abc_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₁: eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₄, X₈) :|: X₆ ≤ X₃
t₁₂: eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₃ ≤ X₆
t₁₃: eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₇ ≤ X₅
t₁₄: eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₅ ≤ X₇
t₁₅: eval_abc_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₆-X₇)
t₁₆: eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₈ ≤ X₆+X₇
t₁₇: eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₆+X₇ ≤ X₈
t₁₈: eval_abc_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, 1+X₈)
t₁₉: eval_abc_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_16(1+X₇, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂₂: eval_abc_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_19(X₀, 1+X₆, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂₅: eval_abc_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₀: eval_abc_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)

Preprocessing

Found invariant 1+X₅ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ 1+X₆ ≤ X₁ ∧ X₂ ≤ X₆ ∧ X₁ ≤ 1+X₆ ∧ X₂ ≤ X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ for location eval_abc_19

Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location eval_abc_bb4_in

Found invariant X₂ ≤ X₆ for location eval_abc_bb1_in

Found invariant X₇ ≤ X₅ ∧ 1+X₇ ≤ X₀ ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ for location eval_abc_17

Found invariant 1+X₅ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ 1+X₆ ≤ X₁ ∧ X₂ ≤ X₆ ∧ X₁ ≤ 1+X₆ ∧ X₂ ≤ X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₂ ≤ X₁ for location eval_abc_20

Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location eval_abc_bb6_in

Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location eval_abc_bb5_in

Found invariant X₇ ≤ X₅ ∧ 1+X₇ ≤ X₀ ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ for location eval_abc_16

Found invariant X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₃ for location eval_abc_bb2_in

Found invariant 1+X₅ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₃ for location eval_abc_bb7_in

Found invariant 1+X₃ ≤ X₆ ∧ X₂ ≤ X₆ for location eval_abc_bb8_in

Found invariant 1+X₃ ≤ X₆ ∧ X₂ ≤ X₆ for location eval_abc_stop

Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location eval_abc_bb3_in

Problem after Preprocessing

Start: eval_abc_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars:
Locations: eval_abc_0, eval_abc_1, eval_abc_16, eval_abc_17, eval_abc_19, eval_abc_2, eval_abc_20, eval_abc_3, eval_abc_4, eval_abc_5, eval_abc_6, eval_abc_7, eval_abc_8, eval_abc_bb0_in, eval_abc_bb1_in, eval_abc_bb2_in, eval_abc_bb3_in, eval_abc_bb4_in, eval_abc_bb5_in, eval_abc_bb6_in, eval_abc_bb7_in, eval_abc_bb8_in, eval_abc_start, eval_abc_stop
Transitions:
t₂: eval_abc_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₃: eval_abc_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂₀: eval_abc_16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₀ ≤ 1+X₅ ∧ X₀ ≤ 1+X₇ ∧ 1+X₄ ≤ X₀ ∧ 1+X₇ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅
t₂₁: eval_abc_17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₀, X₈) :|: X₀ ≤ 1+X₅ ∧ X₀ ≤ 1+X₇ ∧ 1+X₄ ≤ X₀ ∧ 1+X₇ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅
t₂₃: eval_abc_19(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_20(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₁ ≤ 1+X₃ ∧ X₁ ≤ 1+X₆ ∧ 1+X₂ ≤ X₁ ∧ 1+X₆ ≤ X₁ ∧ 1+X₅ ≤ X₇ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇
t₄: eval_abc_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂₄: eval_abc_20(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₁, X₇, X₈) :|: X₁ ≤ 1+X₃ ∧ X₁ ≤ 1+X₆ ∧ 1+X₂ ≤ X₁ ∧ 1+X₆ ≤ X₁ ∧ 1+X₅ ≤ X₇ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇
t₅: eval_abc_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₆: eval_abc_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₇: eval_abc_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₈: eval_abc_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₉: eval_abc_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₀: eval_abc_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₂, X₇, X₈)
t₁: eval_abc_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₁: eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₄, X₈) :|: X₆ ≤ X₃ ∧ X₂ ≤ X₆
t₁₂: eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₃ ≤ X₆ ∧ X₂ ≤ X₆
t₁₃: eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₇ ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇
t₁₄: eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₅ ≤ X₇ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇
t₁₅: eval_abc_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₆-X₇) :|: X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅
t₁₆: eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₈ ≤ X₆+X₇ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅
t₁₇: eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₆+X₇ ≤ X₈ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅
t₁₈: eval_abc_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, 1+X₈) :|: X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅
t₁₉: eval_abc_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_16(1+X₇, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅
t₂₂: eval_abc_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_19(X₀, 1+X₆, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₅ ≤ X₇ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇
t₂₅: eval_abc_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₃ ≤ X₆ ∧ X₂ ≤ X₆
t₀: eval_abc_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)

MPRF for transition t₁₁: eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₄, X₈) :|: X₆ ≤ X₃ ∧ X₂ ≤ X₆ of depth 1:

new bound:

X₂+X₃+1 {O(n)}

MPRF:

• eval_abc_16: [X₃-X₆]
• eval_abc_17: [X₃-X₆]
• eval_abc_19: [1+X₃-X₁]
• eval_abc_20: [1+X₃-X₁]
• eval_abc_bb1_in: [1+X₃-X₆]
• eval_abc_bb2_in: [X₃-X₆]
• eval_abc_bb3_in: [X₃-X₆]
• eval_abc_bb4_in: [X₃-X₆]
• eval_abc_bb5_in: [X₃-X₆]
• eval_abc_bb6_in: [X₃-X₆]
• eval_abc_bb7_in: [X₃-X₆]

MPRF for transition t₁₄: eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₅ ≤ X₇ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇ of depth 1:

new bound:

X₂+X₃+1 {O(n)}

MPRF:

• eval_abc_16: [1+X₃-X₆]
• eval_abc_17: [1+X₃-X₆]
• eval_abc_19: [1+X₃-X₁]
• eval_abc_20: [1+X₃-X₁]
• eval_abc_bb1_in: [1+X₃-X₆]
• eval_abc_bb2_in: [1+X₃-X₆]
• eval_abc_bb3_in: [1+X₃-X₆]
• eval_abc_bb4_in: [1+X₃-X₆]
• eval_abc_bb5_in: [1+X₃-X₆]
• eval_abc_bb6_in: [1+X₃-X₆]
• eval_abc_bb7_in: [X₃-X₆]

MPRF for transition t₂₂: eval_abc_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_19(X₀, 1+X₆, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₅ ≤ X₇ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇ of depth 1:

new bound:

X₂+X₃+1 {O(n)}

MPRF:

MPRF for transition t₂₃: eval_abc_19(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_20(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₁ ≤ 1+X₃ ∧ X₁ ≤ 1+X₆ ∧ 1+X₂ ≤ X₁ ∧ 1+X₆ ≤ X₁ ∧ 1+X₅ ≤ X₇ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇ of depth 1:

new bound:

X₂+X₃+1 {O(n)}

MPRF:

• eval_abc_16: [1+X₃-X₆]
• eval_abc_17: [1+X₃-X₆]
• eval_abc_19: [1+X₃-X₆]
• eval_abc_20: [X₃-X₆]
• eval_abc_bb1_in: [1+X₃-X₆]
• eval_abc_bb2_in: [1+X₃-X₆]
• eval_abc_bb3_in: [1+X₃-X₆]
• eval_abc_bb4_in: [1+X₃-X₆]
• eval_abc_bb5_in: [1+X₃-X₆]
• eval_abc_bb6_in: [1+X₃-X₆]
• eval_abc_bb7_in: [1+X₃-X₆]

MPRF for transition t₂₄: eval_abc_20(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₁, X₇, X₈) :|: X₁ ≤ 1+X₃ ∧ X₁ ≤ 1+X₆ ∧ 1+X₂ ≤ X₁ ∧ 1+X₆ ≤ X₁ ∧ 1+X₅ ≤ X₇ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇ of depth 1:

new bound:

X₂+X₃+1 {O(n)}

MPRF:

• eval_abc_16: [1+X₃-X₆]
• eval_abc_17: [1+X₃-X₆]
• eval_abc_19: [1+X₃-X₆]
• eval_abc_20: [1+X₃-X₆]
• eval_abc_bb1_in: [1+X₃-X₆]
• eval_abc_bb2_in: [1+X₃-X₆]
• eval_abc_bb3_in: [1+X₃-X₆]
• eval_abc_bb4_in: [1+X₃-X₆]
• eval_abc_bb5_in: [1+X₃-X₆]
• eval_abc_bb6_in: [1+X₃-X₆]
• eval_abc_bb7_in: [1+X₃-X₆]

MPRF for transition t₁₃: eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₇ ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₇ of depth 1:

new bound:

X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}

MPRF:

• eval_abc_16: [X₅-X₇]
• eval_abc_17: [1+X₅-X₀]
• eval_abc_19: [X₅-X₇]
• eval_abc_20: [X₅-X₇]
• eval_abc_bb1_in: [1+X₅-X₄]
• eval_abc_bb2_in: [1+X₅-X₇]
• eval_abc_bb3_in: [X₅-X₇]
• eval_abc_bb4_in: [X₅-X₇]
• eval_abc_bb5_in: [X₅-X₇]
• eval_abc_bb6_in: [X₅-X₇]
• eval_abc_bb7_in: [X₅-X₇]

MPRF for transition t₁₅: eval_abc_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₆-X₇) :|: X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ of depth 1:

new bound:

2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₄+4⋅X₅+X₂+X₃+2 {O(n^2)}

MPRF:

• eval_abc_16: [1+2⋅X₅-X₀-X₄]
• eval_abc_17: [1+2⋅X₅-X₀-X₄]
• eval_abc_19: [2⋅X₅-X₄-X₇]
• eval_abc_20: [2⋅X₅-X₄-X₇]
• eval_abc_bb1_in: [1+2⋅X₅-2⋅X₄]
• eval_abc_bb2_in: [1+2⋅X₅-X₄-X₇]
• eval_abc_bb3_in: [1+2⋅X₅-X₄-X₇]
• eval_abc_bb4_in: [2⋅X₅-X₄-X₇]
• eval_abc_bb5_in: [2⋅X₅-X₄-X₇]
• eval_abc_bb6_in: [2⋅X₅-X₄-X₇]
• eval_abc_bb7_in: [2⋅X₅-X₄-X₇]

MPRF for transition t₁₇: eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₆+X₇ ≤ X₈ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ of depth 1:

new bound:

X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}

MPRF:

• eval_abc_16: [X₅-X₇]
• eval_abc_17: [X₅-X₇]
• eval_abc_19: [X₅-X₇]
• eval_abc_20: [X₅-X₇]
• eval_abc_bb1_in: [1+X₅-X₄]
• eval_abc_bb2_in: [1+X₅-X₇]
• eval_abc_bb3_in: [1+X₅-X₇]
• eval_abc_bb4_in: [1+X₅-X₇]
• eval_abc_bb5_in: [1+X₅-X₇]
• eval_abc_bb6_in: [X₅-X₇]
• eval_abc_bb7_in: [X₅-X₇]

MPRF for transition t₁₉: eval_abc_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_16(1+X₇, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ of depth 1:

new bound:

2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₄+4⋅X₅+X₂+X₃+2 {O(n^2)}

MPRF:

• eval_abc_16: [1+2⋅X₅-X₀-X₄]
• eval_abc_17: [1+2⋅X₅-X₀-X₄]
• eval_abc_19: [2⋅X₅-X₄-X₇]
• eval_abc_20: [2⋅X₅-X₄-X₇]
• eval_abc_bb1_in: [1+2⋅X₅-2⋅X₄]
• eval_abc_bb2_in: [1+2⋅X₅-X₄-X₇]
• eval_abc_bb3_in: [1+2⋅X₅-X₄-X₇]
• eval_abc_bb4_in: [1+2⋅X₅-X₄-X₇]
• eval_abc_bb5_in: [1+2⋅X₅-X₄-X₇]
• eval_abc_bb6_in: [1+2⋅X₅-X₄-X₇]
• eval_abc_bb7_in: [2⋅X₅-X₄-X₇]

MPRF for transition t₂₀: eval_abc_16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₀ ≤ 1+X₅ ∧ X₀ ≤ 1+X₇ ∧ 1+X₄ ≤ X₀ ∧ 1+X₇ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ of depth 1:

new bound:

X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}

MPRF:

• eval_abc_16: [1+X₅-X₇]
• eval_abc_17: [X₅-X₇]
• eval_abc_19: [X₅-X₇]
• eval_abc_20: [X₅-X₇]
• eval_abc_bb1_in: [1+X₅-X₄]
• eval_abc_bb2_in: [1+X₅-X₇]
• eval_abc_bb3_in: [1+X₅-X₇]
• eval_abc_bb4_in: [1+X₅-X₇]
• eval_abc_bb5_in: [1+X₅-X₇]
• eval_abc_bb6_in: [1+X₅-X₇]
• eval_abc_bb7_in: [X₅-X₇]

MPRF for transition t₂₁: eval_abc_17(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₀, X₈) :|: X₀ ≤ 1+X₅ ∧ X₀ ≤ 1+X₇ ∧ 1+X₄ ≤ X₀ ∧ 1+X₇ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ of depth 1:

new bound:

X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}

MPRF:

• eval_abc_16: [1+X₅-X₇]
• eval_abc_17: [1+X₅-X₇]
• eval_abc_19: [X₅-X₇]
• eval_abc_20: [X₅-X₇]
• eval_abc_bb1_in: [1+X₅-X₄]
• eval_abc_bb2_in: [1+X₅-X₇]
• eval_abc_bb3_in: [1+X₅-X₇]
• eval_abc_bb4_in: [1+X₅-X₇]
• eval_abc_bb5_in: [1+X₅-X₇]
• eval_abc_bb6_in: [1+X₅-X₇]
• eval_abc_bb7_in: [X₅-X₇]

MPRF for transition t₁₆: eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₈ ≤ X₆+X₇ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ of depth 1:

new bound:

2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₅+3⋅X₃⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+X₂⋅X₄+X₃⋅X₄+2⋅X₄+8⋅X₅+X₂+X₃+3 {O(n^3)}

MPRF:

• eval_abc_16: [X₅+X₆-X₈]
• eval_abc_17: [X₅+X₆-X₈]
• eval_abc_19: [1+2⋅X₅]
• eval_abc_20: [1+2⋅X₅]
• eval_abc_bb1_in: [1+2⋅X₅]
• eval_abc_bb2_in: [1+2⋅X₅]
• eval_abc_bb3_in: [1+2⋅X₅]
• eval_abc_bb4_in: [1+X₅+X₆-X₈]
• eval_abc_bb5_in: [X₅+X₆-X₈]
• eval_abc_bb6_in: [X₅+X₆-X₈]
• eval_abc_bb7_in: [1+2⋅X₅]

TWN: t₁₈: eval_abc_bb5_in→eval_abc_bb4_in

cycle: [t₁₈: eval_abc_bb5_in→eval_abc_bb4_in; t₁₆: eval_abc_bb4_in→eval_abc_bb5_in]
original loop: (X₈ ≤ X₆+X₇ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅,(X₂,X₃,X₄,X₅,X₆,X₇,X₈) -> (X₂,X₃,X₄,X₅,X₆,X₇,1+X₈))
transformed loop: (X₈ ≤ X₆+X₇ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅,(X₂,X₃,X₄,X₅,X₆,X₇,X₈) -> (X₂,X₃,X₄,X₅,X₆,X₇,1+X₈))
loop: (X₈ ≤ X₆+X₇ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅,(X₂,X₃,X₄,X₅,X₆,X₇,X₈) -> (X₂,X₃,X₄,X₅,X₆,X₇,1+X₈))
order: [X₈; X₇; X₆; X₅; X₄; X₃; X₂]
closed-form:

X₈: X₈ + [[n != 0]]⋅n^1
X₇: X₇
X₆: X₆
X₅: X₅
X₄: X₄
X₃: X₃
X₂: X₂

Termination: true
Formula:

0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₈ ≤ X₆+X₇ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅ ∧ X₈ ≤ X₆+X₇ ∧ X₆+X₇ ≤ X₈
∨ 1 ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅

Stabilization-Threshold for: X₈ ≤ X₆+X₇

alphas_abs: 1+X₆+X₇+X₈
M: 0
N: 1
Bound: 2⋅X₆+2⋅X₇+2⋅X₈+4 {O(n)}

TWN - Lifting for [16: eval_abc_bb4_in->eval_abc_bb5_in; 18: eval_abc_bb5_in->eval_abc_bb4_in] of 2⋅X₆+2⋅X₇+2⋅X₈+6 {O(n)}

relevant size-bounds w.r.t. t₁₅: eval_abc_bb3_in→eval_abc_bb4_in:
X₆: 2⋅X₂+X₃+1 {O(n)}
X₇: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+6⋅X₄+X₂+X₃+2 {O(n^2)}
X₈: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+2⋅X₃+3⋅X₂+4⋅X₅+6⋅X₄+3 {O(n^2)}
Runtime-bound of t₁₅: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₄+4⋅X₅+X₂+X₃+2 {O(n^2)}
Results in: 16⋅X₂⋅X₂⋅X₄⋅X₄+16⋅X₂⋅X₂⋅X₅⋅X₅+16⋅X₃⋅X₃⋅X₄⋅X₄+16⋅X₃⋅X₃⋅X₅⋅X₅+32⋅X₂⋅X₂⋅X₄⋅X₅+32⋅X₂⋅X₃⋅X₄⋅X₄+32⋅X₂⋅X₃⋅X₅⋅X₅+32⋅X₃⋅X₃⋅X₄⋅X₅+64⋅X₂⋅X₃⋅X₄⋅X₅+144⋅X₂⋅X₄⋅X₅+144⋅X₃⋅X₄⋅X₅+24⋅X₃⋅X₃⋅X₄+24⋅X₃⋅X₃⋅X₅+32⋅X₂⋅X₂⋅X₄+32⋅X₂⋅X₂⋅X₅+56⋅X₂⋅X₃⋅X₄+56⋅X₂⋅X₃⋅X₅+64⋅X₂⋅X₅⋅X₅+64⋅X₃⋅X₅⋅X₅+80⋅X₂⋅X₄⋅X₄+80⋅X₃⋅X₄⋅X₄+100⋅X₃⋅X₅+108⋅X₃⋅X₄+116⋅X₂⋅X₅+12⋅X₂⋅X₂+124⋅X₂⋅X₄+160⋅X₄⋅X₅+20⋅X₂⋅X₃+64⋅X₅⋅X₅+8⋅X₃⋅X₃+96⋅X₄⋅X₄+104⋅X₅+120⋅X₄+34⋅X₃+42⋅X₂+36 {O(n^4)}

knowledge_propagation leads to new time bound 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₅+3⋅X₃⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+X₂⋅X₄+X₃⋅X₄+2⋅X₄+8⋅X₅+X₂+X₃+3 {O(n^3)} for transition t₁₈: eval_abc_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_abc_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, 1+X₈) :|: X₂ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₅

Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location eval_abc_bb5_in_v1

Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location eval_abc_bb4_in_v2

Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location eval_abc_bb4_in_v1

Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location eval_abc_bb6_in_v2

Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location eval_abc_bb6_in_v1

Found invariant X₇ ≤ X₄ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₃ for location eval_abc_bb2_in

Found invariant X₇ ≤ X₅ ∧ X₇ ≤ X₀ ∧ 1+X₄ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ for location eval_abc_bb3_in_v2

Found invariant X₇ ≤ X₅ ∧ 1+X₇ ≤ X₀ ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ for location eval_abc_16_v1

Found invariant 1+X₃ ≤ X₆ ∧ X₂ ≤ X₆ for location eval_abc_stop

Found invariant X₇ ≤ 1+X₅ ∧ X₇ ≤ X₀ ∧ 1+X₄ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ for location eval_abc_bb2_in_v1

Found invariant 1+X₆ ≤ X₈ ∧ 1+X₂ ≤ X₈ ∧ 1+X₇ ≤ 0 ∧ X₇ ≤ X₅ ∧ 2+X₄+X₇ ≤ 0 ∧ 1+X₇ ≤ X₀ ∧ 1+X₀+X₇ ≤ 0 ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1+X₀+X₄ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₀ ≤ 0 for location eval_abc_17_v2

Found invariant X₂ ≤ X₆ for location eval_abc_bb1_in

Found invariant X₇ ≤ X₅ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location eval_abc_bb5_in_v2

Found invariant X₇ ≤ X₅ ∧ 1+X₇ ≤ X₀ ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ for location eval_abc_17_v1

Found invariant 1+X₆ ≤ X₈ ∧ 1+X₂ ≤ X₈ ∧ X₇ ≤ 0 ∧ X₇ ≤ 1+X₅ ∧ 1+X₄+X₇ ≤ 0 ∧ X₇ ≤ X₀ ∧ X₀+X₇ ≤ 0 ∧ 1+X₄ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1+X₀+X₄ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₀ ≤ 0 for location eval_abc_bb2_in_v2

Found invariant X₇ ≤ X₅ ∧ X₇ ≤ X₄ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₂ ≤ X₃ for location eval_abc_bb3_in_v1

Found invariant 1+X₆ ≤ X₈ ∧ 1+X₂ ≤ X₈ ∧ X₇ ≤ X₅ ∧ 1+X₇ ≤ X₀ ∧ X₄ ≤ X₇ ∧ X₀ ≤ 1+X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₀ ≤ 1+X₅ ∧ 1+X₄ ≤ X₀ ∧ X₂ ≤ X₃ for location eval_abc_16_v2

Found invariant 1+X₅ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₂ ≤ X₃ for location eval_abc_bb7_in

Found invariant 1+X₃ ≤ X₆ ∧ X₂ ≤ X₆ for location eval_abc_bb8_in

Found invariant 1+X₆ ≤ X₈ ∧ 1+X₂ ≤ X₈ ∧ X₇ ≤ 0 ∧ X₇ ≤ X₅ ∧ 1+X₄+X₇ ≤ 0 ∧ X₇ ≤ X₀ ∧ X₀+X₇ ≤ 0 ∧ 1+X₄ ≤ X₇ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₃ ∧ X₂ ≤ X₆ ∧ 1+X₄ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1+X₀+X₄ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₀ ≤ 0 for location eval_abc_bb3_in_v3

All Bounds

Timebounds

Overall timebound:4⋅X₂⋅X₄⋅X₅+4⋅X₂⋅X₅⋅X₅+4⋅X₃⋅X₄⋅X₅+4⋅X₃⋅X₅⋅X₅+10⋅X₂⋅X₄+10⋅X₃⋅X₄+14⋅X₂⋅X₅+14⋅X₃⋅X₅+8⋅X₄⋅X₅+8⋅X₅⋅X₅+13⋅X₂+13⋅X₃+20⋅X₄+32⋅X₅+36 {O(n^3)}
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: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: X₂+X₃+1 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₁₄: X₂+X₃+1 {O(n)}
t₁₅: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₄+4⋅X₅+X₂+X₃+2 {O(n^2)}
t₁₆: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₅+3⋅X₃⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+X₂⋅X₄+X₃⋅X₄+2⋅X₄+8⋅X₅+X₂+X₃+3 {O(n^3)}
t₁₇: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₁₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₅+3⋅X₃⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+X₂⋅X₄+X₃⋅X₄+2⋅X₄+8⋅X₅+X₂+X₃+3 {O(n^3)}
t₁₉: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₄+4⋅X₅+X₂+X₃+2 {O(n^2)}
t₂₀: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₂₁: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₂₂: X₂+X₃+1 {O(n)}
t₂₃: X₂+X₃+1 {O(n)}
t₂₄: X₂+X₃+1 {O(n)}
t₂₅: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₂⋅X₄⋅X₅+4⋅X₂⋅X₅⋅X₅+4⋅X₃⋅X₄⋅X₅+4⋅X₃⋅X₅⋅X₅+10⋅X₂⋅X₄+10⋅X₃⋅X₄+14⋅X₂⋅X₅+14⋅X₃⋅X₅+8⋅X₄⋅X₅+8⋅X₅⋅X₅+13⋅X₂+13⋅X₃+20⋅X₄+32⋅X₅+36 {O(n^3)}
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: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: X₂+X₃+1 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₁₄: X₂+X₃+1 {O(n)}
t₁₅: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₄+4⋅X₅+X₂+X₃+2 {O(n^2)}
t₁₆: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₅+3⋅X₃⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+X₂⋅X₄+X₃⋅X₄+2⋅X₄+8⋅X₅+X₂+X₃+3 {O(n^3)}
t₁₇: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₁₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₅+3⋅X₃⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+X₂⋅X₄+X₃⋅X₄+2⋅X₄+8⋅X₅+X₂+X₃+3 {O(n^3)}
t₁₉: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₄+4⋅X₅+X₂+X₃+2 {O(n^2)}
t₂₀: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₂₁: X₂⋅X₄+X₂⋅X₅+X₃⋅X₄+X₃⋅X₅+2⋅X₄+2⋅X₅+X₂+X₃+2 {O(n^2)}
t₂₂: X₂+X₃+1 {O(n)}
t₂₃: X₂+X₃+1 {O(n)}
t₂₄: X₂+X₃+1 {O(n)}
t₂₅: 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)}
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)}
t₁, X₈: X₈ {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)}
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)}
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)}
t₄, X₈: X₈ {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)}
t₅, X₈: X₈ {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)}
t₆, X₈: X₈ {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)}
t₇, X₈: X₈ {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: X₅ {O(n)}
t₈, X₆: X₆ {O(n)}
t₈, X₇: X₇ {O(n)}
t₈, X₈: X₈ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: X₅ {O(n)}
t₉, X₆: X₆ {O(n)}
t₉, X₇: X₇ {O(n)}
t₉, X₈: X₈ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₀, X₆: X₂ {O(n)}
t₁₀, X₇: X₇ {O(n)}
t₁₀, X₈: X₈ {O(n)}
t₁₁, X₀: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+6⋅X₄+X₀+X₂+X₃+2 {O(n^2)}
t₁₁, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₁₁, X₅: X₅ {O(n)}
t₁₁, X₆: 2⋅X₂+X₃+1 {O(n)}
t₁₁, X₇: 2⋅X₄ {O(n)}
t₁₁, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₄+5⋅X₃⋅X₄+7⋅X₂⋅X₅+7⋅X₃⋅X₅+14⋅X₄+16⋅X₅+5⋅X₃+7⋅X₂+X₈+9 {O(n^3)}
t₁₂, X₀: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+2⋅X₀+4⋅X₅+6⋅X₄+X₂+X₃+2 {O(n^2)}
t₁₂, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₁₂, X₂: 2⋅X₂ {O(n)}
t₁₂, X₃: 2⋅X₃ {O(n)}
t₁₂, X₄: 2⋅X₄ {O(n)}
t₁₂, X₅: 2⋅X₅ {O(n)}
t₁₂, X₆: 3⋅X₂+X₃+1 {O(n)}
t₁₂, X₇: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+8⋅X₄+X₂+X₃+X₇+2 {O(n^2)}
t₁₂, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₄+5⋅X₃⋅X₄+7⋅X₂⋅X₅+7⋅X₃⋅X₅+14⋅X₄+16⋅X₅+2⋅X₈+5⋅X₃+7⋅X₂+9 {O(n^3)}
t₁₃, X₀: 4⋅X₂⋅X₄+4⋅X₂⋅X₅+4⋅X₃⋅X₄+4⋅X₃⋅X₅+12⋅X₄+2⋅X₂+2⋅X₃+8⋅X₅+X₀+4 {O(n^2)}
t₁₃, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₃, X₅: X₅ {O(n)}
t₁₃, X₆: 2⋅X₂+X₃+1 {O(n)}
t₁₃, X₇: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+6⋅X₄+X₂+X₃+2 {O(n^2)}
t₁₃, X₈: 4⋅X₂⋅X₄⋅X₅+4⋅X₂⋅X₅⋅X₅+4⋅X₃⋅X₄⋅X₅+4⋅X₃⋅X₅⋅X₅+10⋅X₂⋅X₄+10⋅X₃⋅X₄+14⋅X₂⋅X₅+14⋅X₃⋅X₅+8⋅X₄⋅X₅+8⋅X₅⋅X₅+10⋅X₃+14⋅X₂+28⋅X₄+32⋅X₅+X₈+18 {O(n^3)}
t₁₄, X₀: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+6⋅X₄+X₀+X₂+X₃+2 {O(n^2)}
t₁₄, X₁: 2⋅X₁+2⋅X₃+4⋅X₂+2 {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₄, X₅: X₅ {O(n)}
t₁₄, X₆: 2⋅X₂+X₃+1 {O(n)}
t₁₄, X₇: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+8⋅X₄+X₂+X₃+2 {O(n^2)}
t₁₄, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₄+5⋅X₃⋅X₄+7⋅X₂⋅X₅+7⋅X₃⋅X₅+14⋅X₄+16⋅X₅+5⋅X₃+7⋅X₂+X₈+9 {O(n^3)}
t₁₅, X₀: 4⋅X₂⋅X₄+4⋅X₂⋅X₅+4⋅X₃⋅X₄+4⋅X₃⋅X₅+12⋅X₄+2⋅X₂+2⋅X₃+8⋅X₅+X₀+4 {O(n^2)}
t₁₅, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₅, X₅: X₅ {O(n)}
t₁₅, X₆: 2⋅X₂+X₃+1 {O(n)}
t₁₅, X₇: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+6⋅X₄+X₂+X₃+2 {O(n^2)}
t₁₅, X₈: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+2⋅X₃+3⋅X₂+4⋅X₅+6⋅X₄+3 {O(n^2)}
t₁₆, X₀: 4⋅X₂⋅X₄+4⋅X₂⋅X₅+4⋅X₃⋅X₄+4⋅X₃⋅X₅+12⋅X₄+2⋅X₂+2⋅X₃+8⋅X₅+X₀+4 {O(n^2)}
t₁₆, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₁₆, X₂: X₂ {O(n)}
t₁₆, X₃: X₃ {O(n)}
t₁₆, X₄: X₄ {O(n)}
t₁₆, X₅: X₅ {O(n)}
t₁₆, X₆: 2⋅X₂+X₃+1 {O(n)}
t₁₆, X₇: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+6⋅X₄+X₂+X₃+2 {O(n^2)}
t₁₆, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₄+3⋅X₃⋅X₄+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₅+5⋅X₃⋅X₅+12⋅X₅+3⋅X₃+4⋅X₂+8⋅X₄+6 {O(n^3)}
t₁₇, X₀: 8⋅X₂⋅X₄+8⋅X₂⋅X₅+8⋅X₃⋅X₄+8⋅X₃⋅X₅+16⋅X₅+2⋅X₀+24⋅X₄+4⋅X₂+4⋅X₃+8 {O(n^2)}
t₁₇, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: X₄ {O(n)}
t₁₇, X₅: X₅ {O(n)}
t₁₇, X₆: 2⋅X₂+X₃+1 {O(n)}
t₁₇, X₇: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+6⋅X₄+X₂+X₃+2 {O(n^2)}
t₁₇, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₄+5⋅X₃⋅X₄+7⋅X₂⋅X₅+7⋅X₃⋅X₅+14⋅X₄+16⋅X₅+5⋅X₃+7⋅X₂+9 {O(n^3)}
t₁₈, X₀: 4⋅X₂⋅X₄+4⋅X₂⋅X₅+4⋅X₃⋅X₄+4⋅X₃⋅X₅+12⋅X₄+2⋅X₂+2⋅X₃+8⋅X₅+X₀+4 {O(n^2)}
t₁₈, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₈, X₅: X₅ {O(n)}
t₁₈, X₆: 2⋅X₂+X₃+1 {O(n)}
t₁₈, X₇: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+6⋅X₄+X₂+X₃+2 {O(n^2)}
t₁₈, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+3⋅X₂⋅X₄+3⋅X₃⋅X₄+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₅+5⋅X₃⋅X₅+12⋅X₅+3⋅X₃+4⋅X₂+8⋅X₄+6 {O(n^3)}
t₁₉, X₀: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+6⋅X₄+X₂+X₃+2 {O(n^2)}
t₁₉, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₁₉, X₅: X₅ {O(n)}
t₁₉, X₆: 2⋅X₂+X₃+1 {O(n)}
t₁₉, X₇: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+6⋅X₄+X₂+X₃+2 {O(n^2)}
t₁₉, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₄+5⋅X₃⋅X₄+7⋅X₂⋅X₅+7⋅X₃⋅X₅+14⋅X₄+16⋅X₅+5⋅X₃+7⋅X₂+9 {O(n^3)}
t₂₀, X₀: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+6⋅X₄+X₂+X₃+2 {O(n^2)}
t₂₀, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₀, X₄: X₄ {O(n)}
t₂₀, X₅: X₅ {O(n)}
t₂₀, X₆: 2⋅X₂+X₃+1 {O(n)}
t₂₀, X₇: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+6⋅X₄+X₂+X₃+2 {O(n^2)}
t₂₀, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₄+5⋅X₃⋅X₄+7⋅X₂⋅X₅+7⋅X₃⋅X₅+14⋅X₄+16⋅X₅+5⋅X₃+7⋅X₂+9 {O(n^3)}
t₂₁, X₀: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+6⋅X₄+X₂+X₃+2 {O(n^2)}
t₂₁, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₁, X₄: X₄ {O(n)}
t₂₁, X₅: X₅ {O(n)}
t₂₁, X₆: 2⋅X₂+X₃+1 {O(n)}
t₂₁, X₇: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+6⋅X₄+X₂+X₃+2 {O(n^2)}
t₂₁, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₄+5⋅X₃⋅X₄+7⋅X₂⋅X₅+7⋅X₃⋅X₅+14⋅X₄+16⋅X₅+5⋅X₃+7⋅X₂+9 {O(n^3)}
t₂₂, X₀: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+6⋅X₄+X₀+X₂+X₃+2 {O(n^2)}
t₂₂, X₁: 2⋅X₂+X₃+1 {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₂, X₅: X₅ {O(n)}
t₂₂, X₆: 2⋅X₂+X₃+1 {O(n)}
t₂₂, X₇: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+8⋅X₄+X₂+X₃+2 {O(n^2)}
t₂₂, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₄+5⋅X₃⋅X₄+7⋅X₂⋅X₅+7⋅X₃⋅X₅+14⋅X₄+16⋅X₅+5⋅X₃+7⋅X₂+X₈+9 {O(n^3)}
t₂₃, X₀: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+6⋅X₄+X₀+X₂+X₃+2 {O(n^2)}
t₂₃, X₁: 2⋅X₂+X₃+1 {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₃, X₅: X₅ {O(n)}
t₂₃, X₆: 2⋅X₂+X₃+1 {O(n)}
t₂₃, X₇: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+8⋅X₄+X₂+X₃+2 {O(n^2)}
t₂₃, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₄+5⋅X₃⋅X₄+7⋅X₂⋅X₅+7⋅X₃⋅X₅+14⋅X₄+16⋅X₅+5⋅X₃+7⋅X₂+X₈+9 {O(n^3)}
t₂₄, X₀: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+6⋅X₄+X₀+X₂+X₃+2 {O(n^2)}
t₂₄, X₁: 2⋅X₂+X₃+1 {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₄, X₄: X₄ {O(n)}
t₂₄, X₅: X₅ {O(n)}
t₂₄, X₆: 2⋅X₂+X₃+1 {O(n)}
t₂₄, X₇: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+8⋅X₄+X₂+X₃+2 {O(n^2)}
t₂₄, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₄+5⋅X₃⋅X₄+7⋅X₂⋅X₅+7⋅X₃⋅X₅+14⋅X₄+16⋅X₅+5⋅X₃+7⋅X₂+X₈+9 {O(n^3)}
t₂₅, X₀: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+2⋅X₀+4⋅X₅+6⋅X₄+X₂+X₃+2 {O(n^2)}
t₂₅, X₁: 2⋅X₂+X₁+X₃+1 {O(n)}
t₂₅, X₂: 2⋅X₂ {O(n)}
t₂₅, X₃: 2⋅X₃ {O(n)}
t₂₅, X₄: 2⋅X₄ {O(n)}
t₂₅, X₅: 2⋅X₅ {O(n)}
t₂₅, X₆: 3⋅X₂+X₃+1 {O(n)}
t₂₅, X₇: 2⋅X₂⋅X₄+2⋅X₂⋅X₅+2⋅X₃⋅X₄+2⋅X₃⋅X₅+4⋅X₅+8⋅X₄+X₂+X₃+X₇+2 {O(n^2)}
t₂₅, X₈: 2⋅X₂⋅X₄⋅X₅+2⋅X₂⋅X₅⋅X₅+2⋅X₃⋅X₄⋅X₅+2⋅X₃⋅X₅⋅X₅+4⋅X₄⋅X₅+4⋅X₅⋅X₅+5⋅X₂⋅X₄+5⋅X₃⋅X₄+7⋅X₂⋅X₅+7⋅X₃⋅X₅+14⋅X₄+16⋅X₅+2⋅X₈+5⋅X₃+7⋅X₂+9 {O(n^3)}