KoAT2 Proof Output

Initial Problem

Start: eval_p3_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: nondef_0, nondef_1, nondef_2
Locations: eval_p3_0, eval_p3_1, eval_p3_15, eval_p3_16, eval_p3_2, eval_p3_3, eval_p3_4, eval_p3_5, eval_p3_6, eval_p3_7, eval_p3_bb0_in, eval_p3_bb1_in, eval_p3_bb2_in, eval_p3_bb3_in, eval_p3_bb4_in, eval_p3_bb5_in, eval_p3_bb6_in, eval_p3_bb7_in, eval_p3_start, eval_p3_stop
Transitions:
t₂: eval_p3_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₃: eval_p3_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₂₀: eval_p3_15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₂₁: eval_p3_16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb3_in(X₀, X₁, X₄, X₃, X₄, X₅, X₆, X₇)
t₄: eval_p3_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₅: eval_p3_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₆: eval_p3_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₇: eval_p3_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₈: eval_p3_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₉: eval_p3_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb1_in(X₅, X₆, X₂, X₃, X₄, X₅, X₆, X₇)
t₁: eval_p3_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁₀: eval_p3_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀
t₁₁: eval_p3_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0
t₁₂: eval_p3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb3_in(X₀, X₁, X₁, X₃, X₄, X₅, X₆, X₇) :|: 1+nondef_0 ≤ 0
t₁₃: eval_p3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb3_in(X₀, X₁, X₁, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ nondef_0
t₁₄: eval_p3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ nondef_0 ∧ nondef_0 ≤ 0
t₁₅: eval_p3_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+nondef_1 ≤ 0 ∧ 1 ≤ X₂
t₁₆: eval_p3_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ nondef_1 ∧ 1 ≤ X₂
t₁₇: eval_p3_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb6_in(X₀, X₁, X₂, X₂, X₄, X₅, X₆, X₇) :|: 0 ≤ nondef_1 ∧ nondef_1 ≤ 0
t₁₈: eval_p3_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb6_in(X₀, X₁, X₂, X₂, X₄, X₅, X₆, X₇) :|: X₂ ≤ 0
t₁₉: eval_p3_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_15(X₀, X₁, X₂, X₃, X₂-1, X₅, X₆, X₇)
t₂₂: eval_p3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb6_in(X₀, X₁, X₂, 1+X₁, X₄, X₅, X₆, X₇) :|: 1+nondef_2 ≤ 0
t₂₃: eval_p3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb6_in(X₀, X₁, X₂, 1+X₁, X₄, X₅, X₆, X₇) :|: 1 ≤ nondef_2
t₂₄: eval_p3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb6_in(X₀, X₁, X₂, X₇, X₄, X₅, X₆, X₇) :|: 0 ≤ nondef_2 ∧ nondef_2 ≤ 0
t₂₅: eval_p3_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb1_in(X₀-1, X₃, X₂, X₃, X₄, X₅, X₆, X₇)
t₂₆: eval_p3_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₀: eval_p3_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)

Preprocessing

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_p3_16

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀ for location eval_p3_bb3_in

Found invariant X₀ ≤ X₅ for location eval_p3_bb1_in

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location eval_p3_stop

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_p3_bb2_in

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location eval_p3_bb7_in

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_p3_bb5_in

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_p3_bb6_in

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_p3_bb4_in

Problem after Preprocessing

Start: eval_p3_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: nondef_0, nondef_1, nondef_2
Locations: eval_p3_0, eval_p3_1, eval_p3_15, eval_p3_16, eval_p3_2, eval_p3_3, eval_p3_4, eval_p3_5, eval_p3_6, eval_p3_7, eval_p3_bb0_in, eval_p3_bb1_in, eval_p3_bb2_in, eval_p3_bb3_in, eval_p3_bb4_in, eval_p3_bb5_in, eval_p3_bb6_in, eval_p3_bb7_in, eval_p3_start, eval_p3_stop
Transitions:
t₂: eval_p3_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₃: eval_p3_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₂₀: eval_p3_15(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₂+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₄
t₂₁: eval_p3_16(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb3_in(X₀, X₁, X₄, X₃, X₄, X₅, X₆, X₇) :|: X₂ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₄ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₂+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₄
t₄: eval_p3_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₅: eval_p3_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₆: eval_p3_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₇: eval_p3_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₈: eval_p3_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₉: eval_p3_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb1_in(X₅, X₆, X₂, X₃, X₄, X₅, X₆, X₇)
t₁: eval_p3_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁₀: eval_p3_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ X₀ ≤ X₅
t₁₁: eval_p3_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0 ∧ X₀ ≤ X₅
t₁₂: eval_p3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb3_in(X₀, X₁, X₁, X₃, X₄, X₅, X₆, X₇) :|: 1+nondef_0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₁₃: eval_p3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb3_in(X₀, X₁, X₁, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ nondef_0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₁₄: eval_p3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ nondef_0 ∧ nondef_0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₁₅: eval_p3_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+nondef_1 ≤ 0 ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁
t₁₆: eval_p3_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ nondef_1 ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁
t₁₇: eval_p3_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb6_in(X₀, X₁, X₂, X₂, X₄, X₅, X₆, X₇) :|: 0 ≤ nondef_1 ∧ nondef_1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁
t₁₈: eval_p3_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb6_in(X₀, X₁, X₂, X₂, X₄, X₅, X₆, X₇) :|: X₂ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁
t₁₉: eval_p3_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_15(X₀, X₁, X₂, X₃, X₂-1, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₂+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁
t₂₂: eval_p3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb6_in(X₀, X₁, X₂, 1+X₁, X₄, X₅, X₆, X₇) :|: 1+nondef_2 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₂₃: eval_p3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb6_in(X₀, X₁, X₂, 1+X₁, X₄, X₅, X₆, X₇) :|: 1 ≤ nondef_2 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₂₄: eval_p3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb6_in(X₀, X₁, X₂, X₇, X₄, X₅, X₆, X₇) :|: 0 ≤ nondef_2 ∧ nondef_2 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₂₅: eval_p3_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb1_in(X₀-1, X₃, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₂₆: eval_p3_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0 ∧ X₀ ≤ X₅
t₀: eval_p3_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)

MPRF for transition t₁₀: eval_p3_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_p3_15: [X₀-1]
• eval_p3_16: [X₀-1]
• eval_p3_bb1_in: [X₀]
• eval_p3_bb2_in: [X₀-1]
• eval_p3_bb3_in: [X₀-1]
• eval_p3_bb4_in: [X₀-1]
• eval_p3_bb5_in: [X₀-1]
• eval_p3_bb6_in: [X₀-1]

MPRF for transition t₁₂: eval_p3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb3_in(X₀, X₁, X₁, X₃, X₄, X₅, X₆, X₇) :|: 1+nondef_0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_p3_15: [X₀-1]
• eval_p3_16: [X₀-1]
• eval_p3_bb1_in: [X₀]
• eval_p3_bb2_in: [X₀]
• eval_p3_bb3_in: [X₀-1]
• eval_p3_bb4_in: [X₀-1]
• eval_p3_bb5_in: [X₀]
• eval_p3_bb6_in: [X₀-1]

MPRF for transition t₁₃: eval_p3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb3_in(X₀, X₁, X₁, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ nondef_0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

MPRF for transition t₁₄: eval_p3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ nondef_0 ∧ nondef_0 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_p3_15: [X₀-1]
• eval_p3_16: [X₀-1]
• eval_p3_bb1_in: [X₀]
• eval_p3_bb2_in: [X₀]
• eval_p3_bb3_in: [X₀-1]
• eval_p3_bb4_in: [X₀-1]
• eval_p3_bb5_in: [X₀-1]
• eval_p3_bb6_in: [X₀-1]

MPRF for transition t₁₇: eval_p3_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb6_in(X₀, X₁, X₂, X₂, X₄, X₅, X₆, X₇) :|: 0 ≤ nondef_1 ∧ nondef_1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_p3_15: [X₀+X₂-1-X₄]
• eval_p3_16: [X₀+X₂-1-X₄]
• eval_p3_bb1_in: [X₀]
• eval_p3_bb2_in: [X₀]
• eval_p3_bb3_in: [X₀]
• eval_p3_bb4_in: [X₀]
• eval_p3_bb5_in: [X₀]
• eval_p3_bb6_in: [X₀-1]

MPRF for transition t₁₈: eval_p3_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb6_in(X₀, X₁, X₂, X₂, X₄, X₅, X₆, X₇) :|: X₂ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_p3_15: [X₀]
• eval_p3_16: [X₀]
• eval_p3_bb1_in: [X₀]
• eval_p3_bb2_in: [X₀]
• eval_p3_bb3_in: [X₀]
• eval_p3_bb4_in: [X₀]
• eval_p3_bb5_in: [X₀]
• eval_p3_bb6_in: [X₀-1]

MPRF for transition t₂₂: eval_p3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb6_in(X₀, X₁, X₂, 1+X₁, X₄, X₅, X₆, X₇) :|: 1+nondef_2 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

MPRF for transition t₂₃: eval_p3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb6_in(X₀, X₁, X₂, 1+X₁, X₄, X₅, X₆, X₇) :|: 1 ≤ nondef_2 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

MPRF for transition t₂₄: eval_p3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_p3_bb6_in(X₀, X₁, X₂, X₇, X₄, X₅, X₆, X₇) :|: 0 ≤ nondef_2 ∧ nondef_2 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

new bound:

X₅⋅X₅+X₅⋅X₇+2⋅X₅+X₆ {O(n^2)}

MPRF:

• eval_p3_15: [X₀+X₄]
• eval_p3_16: [X₀+X₂-1]
• eval_p3_bb1_in: [X₀+X₁]
• eval_p3_bb2_in: [X₀+X₁]
• eval_p3_bb3_in: [X₀+X₂-1]
• eval_p3_bb4_in: [X₀+X₂-1]
• eval_p3_bb5_in: [X₀+X₁]
• eval_p3_bb6_in: [X₀+X₃-1]

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ for location eval_p3_bb3_in

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_p3_bb3_in_v1

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1 ≤ X₁+X₄ ∧ X₁ ≤ 1+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_p3_16_v1

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_p3_bb4_in_v1

Found invariant X₀ ≤ X₅ for location eval_p3_bb1_in

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₂+X₅ ∧ 3 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 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_p3_bb4_in_v2

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location eval_p3_stop

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₂+X₅ ∧ 3 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_p3_16_v2

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_p3_bb2_in

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location eval_p3_bb7_in

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_p3_bb5_in

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_p3_bb6_in

All Bounds

Timebounds

Overall timebound:5⋅X₅⋅X₇+6⋅X₅⋅X₅+22⋅X₅+5⋅X₆+13 {O(n^2)}
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: X₅ {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₅ {O(n)}
t₁₃: X₅ {O(n)}
t₁₄: X₅ {O(n)}
t₁₅: X₅⋅X₅+X₅⋅X₇+2⋅X₅+X₆ {O(n^2)}
t₁₆: X₅⋅X₅+X₅⋅X₇+2⋅X₅+X₆ {O(n^2)}
t₁₇: X₅ {O(n)}
t₁₈: X₅ {O(n)}
t₁₉: X₅⋅X₅+X₅⋅X₇+3⋅X₅+X₆+1 {O(n^2)}
t₂₀: 2⋅X₅⋅X₅+X₅⋅X₇+3⋅X₅+X₆ {O(n^2)}
t₂₁: X₅⋅X₅+X₅⋅X₇+2⋅X₅+X₆ {O(n^2)}
t₂₂: X₅ {O(n)}
t₂₃: X₅ {O(n)}
t₂₄: X₅ {O(n)}
t₂₅: X₅ {O(n)}
t₂₆: 1 {O(1)}

Costbounds

Overall costbound: 5⋅X₅⋅X₇+6⋅X₅⋅X₅+22⋅X₅+5⋅X₆+13 {O(n^2)}
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: X₅ {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₅ {O(n)}
t₁₃: X₅ {O(n)}
t₁₄: X₅ {O(n)}
t₁₅: X₅⋅X₅+X₅⋅X₇+2⋅X₅+X₆ {O(n^2)}
t₁₆: X₅⋅X₅+X₅⋅X₇+2⋅X₅+X₆ {O(n^2)}
t₁₇: X₅ {O(n)}
t₁₈: X₅ {O(n)}
t₁₉: X₅⋅X₅+X₅⋅X₇+3⋅X₅+X₆+1 {O(n^2)}
t₂₀: 2⋅X₅⋅X₅+X₅⋅X₇+3⋅X₅+X₆ {O(n^2)}
t₂₁: X₅⋅X₅+X₅⋅X₇+2⋅X₅+X₆ {O(n^2)}
t₂₂: X₅ {O(n)}
t₂₃: X₅ {O(n)}
t₂₄: X₅ {O(n)}
t₂₅: X₅ {O(n)}
t₂₆: 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: X₅ {O(n)}
t₈, X₆: X₆ {O(n)}
t₈, X₇: X₇ {O(n)}
t₉, X₀: X₅ {O(n)}
t₉, X₁: X₆ {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)}
t₁₀, X₀: X₅ {O(n)}
t₁₀, X₁: 2⋅X₅+X₆+X₇ {O(n)}
t₁₀, X₂: 12⋅X₅+6⋅X₆+6⋅X₇+X₂ {O(n)}
t₁₀, X₃: 4⋅X₆+5⋅X₇+8⋅X₅+X₃ {O(n)}
t₁₀, X₄: 2⋅X₆+2⋅X₇+4⋅X₅+X₄ {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₀, X₆: X₆ {O(n)}
t₁₀, X₇: X₇ {O(n)}
t₁₁, X₀: 2⋅X₅ {O(n)}
t₁₁, X₁: 2⋅X₅+2⋅X₆+X₇ {O(n)}
t₁₁, X₂: 12⋅X₅+2⋅X₂+6⋅X₆+6⋅X₇ {O(n)}
t₁₁, X₃: 4⋅X₆+5⋅X₇+8⋅X₅+X₃ {O(n)}
t₁₁, X₄: 2⋅X₄+2⋅X₆+2⋅X₇+4⋅X₅ {O(n)}
t₁₁, X₅: 2⋅X₅ {O(n)}
t₁₁, X₆: 2⋅X₆ {O(n)}
t₁₁, X₇: 2⋅X₇ {O(n)}
t₁₂, X₀: X₅ {O(n)}
t₁₂, X₁: 2⋅X₅+X₆+X₇ {O(n)}
t₁₂, X₂: 2⋅X₅+X₆+X₇ {O(n)}
t₁₂, X₃: 4⋅X₆+5⋅X₇+8⋅X₅+X₃ {O(n)}
t₁₂, X₄: 2⋅X₆+2⋅X₇+4⋅X₅+X₄ {O(n)}
t₁₂, X₅: X₅ {O(n)}
t₁₂, X₆: X₆ {O(n)}
t₁₂, X₇: X₇ {O(n)}
t₁₃, X₀: X₅ {O(n)}
t₁₃, X₁: 2⋅X₅+X₆+X₇ {O(n)}
t₁₃, X₂: 2⋅X₅+X₆+X₇ {O(n)}
t₁₃, X₃: 4⋅X₆+5⋅X₇+8⋅X₅+X₃ {O(n)}
t₁₃, X₄: 2⋅X₆+2⋅X₇+4⋅X₅+X₄ {O(n)}
t₁₃, X₅: X₅ {O(n)}
t₁₃, X₆: X₆ {O(n)}
t₁₃, X₇: X₇ {O(n)}
t₁₄, X₀: X₅ {O(n)}
t₁₄, X₁: 2⋅X₅+X₆+X₇ {O(n)}
t₁₄, X₂: 12⋅X₅+6⋅X₆+6⋅X₇+X₂ {O(n)}
t₁₄, X₃: 4⋅X₆+5⋅X₇+8⋅X₅+X₃ {O(n)}
t₁₄, X₄: 2⋅X₆+2⋅X₇+4⋅X₅+X₄ {O(n)}
t₁₄, X₅: X₅ {O(n)}
t₁₄, X₆: X₆ {O(n)}
t₁₄, X₇: X₇ {O(n)}
t₁₅, X₀: X₅ {O(n)}
t₁₅, X₁: 2⋅X₆+2⋅X₇+4⋅X₅ {O(n)}
t₁₅, X₂: 2⋅X₅+X₆+X₇ {O(n)}
t₁₅, X₃: 10⋅X₇+16⋅X₅+2⋅X₃+8⋅X₆ {O(n)}
t₁₅, X₄: 12⋅X₅+2⋅X₄+6⋅X₆+6⋅X₇ {O(n)}
t₁₅, X₅: X₅ {O(n)}
t₁₅, X₆: X₆ {O(n)}
t₁₅, X₇: X₇ {O(n)}
t₁₆, X₀: X₅ {O(n)}
t₁₆, X₁: 2⋅X₆+2⋅X₇+4⋅X₅ {O(n)}
t₁₆, X₂: 2⋅X₅+X₆+X₇ {O(n)}
t₁₆, X₃: 10⋅X₇+16⋅X₅+2⋅X₃+8⋅X₆ {O(n)}
t₁₆, X₄: 12⋅X₅+2⋅X₄+6⋅X₆+6⋅X₇ {O(n)}
t₁₆, X₅: X₅ {O(n)}
t₁₆, X₆: X₆ {O(n)}
t₁₆, X₇: X₇ {O(n)}
t₁₇, X₀: X₅ {O(n)}
t₁₇, X₁: 4⋅X₆+4⋅X₇+8⋅X₅ {O(n)}
t₁₇, X₂: 3⋅X₆+3⋅X₇+6⋅X₅ {O(n)}
t₁₇, X₃: 2⋅X₅+X₆+X₇ {O(n)}
t₁₇, X₄: 2⋅X₆+2⋅X₇+4⋅X₅+X₄ {O(n)}
t₁₇, X₅: X₅ {O(n)}
t₁₇, X₆: X₆ {O(n)}
t₁₇, X₇: X₇ {O(n)}
t₁₈, X₀: X₅ {O(n)}
t₁₈, X₁: 4⋅X₆+4⋅X₇+8⋅X₅ {O(n)}
t₁₈, X₂: 3⋅X₆+3⋅X₇+6⋅X₅ {O(n)}
t₁₈, X₃: 2⋅X₅+X₆+X₇ {O(n)}
t₁₈, X₄: 2⋅X₆+2⋅X₇+4⋅X₅+X₄ {O(n)}
t₁₈, X₅: X₅ {O(n)}
t₁₈, X₆: X₆ {O(n)}
t₁₈, X₇: X₇ {O(n)}
t₁₉, X₀: X₅ {O(n)}
t₁₉, X₁: 2⋅X₆+2⋅X₇+4⋅X₅ {O(n)}
t₁₉, X₂: 2⋅X₅+X₆+X₇ {O(n)}
t₁₉, X₃: 10⋅X₇+16⋅X₅+2⋅X₃+8⋅X₆ {O(n)}
t₁₉, X₄: 2⋅X₆+2⋅X₇+4⋅X₅ {O(n)}
t₁₉, X₅: X₅ {O(n)}
t₁₉, X₆: X₆ {O(n)}
t₁₉, X₇: X₇ {O(n)}
t₂₀, X₀: X₅ {O(n)}
t₂₀, X₁: 2⋅X₆+2⋅X₇+4⋅X₅ {O(n)}
t₂₀, X₂: 2⋅X₅+X₆+X₇ {O(n)}
t₂₀, X₃: 10⋅X₇+16⋅X₅+2⋅X₃+8⋅X₆ {O(n)}
t₂₀, X₄: 2⋅X₆+2⋅X₇+4⋅X₅ {O(n)}
t₂₀, X₅: X₅ {O(n)}
t₂₀, X₆: X₆ {O(n)}
t₂₀, X₇: X₇ {O(n)}
t₂₁, X₀: X₅ {O(n)}
t₂₁, X₁: 2⋅X₆+2⋅X₇+4⋅X₅ {O(n)}
t₂₁, X₂: 2⋅X₅+X₆+X₇ {O(n)}
t₂₁, X₃: 10⋅X₇+16⋅X₅+2⋅X₃+8⋅X₆ {O(n)}
t₂₁, X₄: 2⋅X₆+2⋅X₇+4⋅X₅ {O(n)}
t₂₁, X₅: X₅ {O(n)}
t₂₁, X₆: X₆ {O(n)}
t₂₁, X₇: X₇ {O(n)}
t₂₂, X₀: X₅ {O(n)}
t₂₂, X₁: 2⋅X₅+X₆+X₇ {O(n)}
t₂₂, X₂: 12⋅X₅+6⋅X₆+6⋅X₇+X₂ {O(n)}
t₂₂, X₃: 2⋅X₅+X₆+X₇ {O(n)}
t₂₂, X₄: 2⋅X₆+2⋅X₇+4⋅X₅+X₄ {O(n)}
t₂₂, X₅: X₅ {O(n)}
t₂₂, X₆: X₆ {O(n)}
t₂₂, X₇: X₇ {O(n)}
t₂₃, X₀: X₅ {O(n)}
t₂₃, X₁: 2⋅X₅+X₆+X₇ {O(n)}
t₂₃, X₂: 12⋅X₅+6⋅X₆+6⋅X₇+X₂ {O(n)}
t₂₃, X₃: 2⋅X₅+X₆+X₇ {O(n)}
t₂₃, X₄: 2⋅X₆+2⋅X₇+4⋅X₅+X₄ {O(n)}
t₂₃, X₅: X₅ {O(n)}
t₂₃, X₆: X₆ {O(n)}
t₂₃, X₇: X₇ {O(n)}
t₂₄, X₀: X₅ {O(n)}
t₂₄, X₁: 2⋅X₅+X₆+X₇ {O(n)}
t₂₄, X₂: 12⋅X₅+6⋅X₆+6⋅X₇+X₂ {O(n)}
t₂₄, X₃: X₇ {O(n)}
t₂₄, X₄: 2⋅X₆+2⋅X₇+4⋅X₅+X₄ {O(n)}
t₂₄, X₅: X₅ {O(n)}
t₂₄, X₆: X₆ {O(n)}
t₂₄, X₇: X₇ {O(n)}
t₂₅, X₀: X₅ {O(n)}
t₂₅, X₁: 2⋅X₅+X₆+X₇ {O(n)}
t₂₅, X₂: 12⋅X₅+6⋅X₆+6⋅X₇+X₂ {O(n)}
t₂₅, X₃: 4⋅X₆+5⋅X₇+8⋅X₅ {O(n)}
t₂₅, X₄: 2⋅X₆+2⋅X₇+4⋅X₅+X₄ {O(n)}
t₂₅, X₅: X₅ {O(n)}
t₂₅, X₆: X₆ {O(n)}
t₂₅, X₇: X₇ {O(n)}
t₂₆, X₀: 2⋅X₅ {O(n)}
t₂₆, X₁: 2⋅X₅+2⋅X₆+X₇ {O(n)}
t₂₆, X₂: 12⋅X₅+2⋅X₂+6⋅X₆+6⋅X₇ {O(n)}
t₂₆, X₃: 4⋅X₆+5⋅X₇+8⋅X₅+X₃ {O(n)}
t₂₆, X₄: 2⋅X₄+2⋅X₆+2⋅X₇+4⋅X₅ {O(n)}
t₂₆, X₅: 2⋅X₅ {O(n)}
t₂₆, X₆: 2⋅X₆ {O(n)}
t₂₆, X₇: 2⋅X₇ {O(n)}