KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₃ ≤ 1 for location eval_rank2_stop

Found invariant 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 2 ≤ X₃ for location eval_rank2_.critedge_in

Found invariant 2 ≤ X₇ ∧ 3 ≤ X₄+X₇ ∧ 1+X₄ ≤ X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 2 ≤ X₃ for location eval_rank2_5

Found invariant 1+X₈ ≤ X₇ ∧ 1 ≤ X₈ ∧ 3 ≤ X₇+X₈ ∧ 2 ≤ X₅+X₈ ∧ X₅ ≤ X₈ ∧ 2 ≤ X₄+X₈ ∧ X₄ ≤ X₈ ∧ 3 ≤ X₃+X₈ ∧ X₃ ≤ 1+X₈ ∧ 2 ≤ X₁+X₈ ∧ 2 ≤ X₇ ∧ 3 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 3 ≤ X₄+X₇ ∧ 1+X₄ ≤ X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 3 ≤ X₁+X₇ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ X₃ ≤ 1+X₅ ∧ 2 ≤ X₁+X₅ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₁ for location eval_rank2_.critedge1_in

Found invariant 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 2 ≤ X₃ for location eval_rank2_bb3_in

Found invariant 1+X₈ ≤ X₇ ∧ 4 ≤ X₈ ∧ 9 ≤ X₇+X₈ ∧ 5 ≤ X₅+X₈ ∧ 3+X₅ ≤ X₈ ∧ 5 ≤ X₄+X₈ ∧ 3+X₄ ≤ X₈ ∧ 6 ≤ X₃+X₈ ∧ 2+X₃ ≤ X₈ ∧ 5 ≤ X₁+X₈ ∧ 5 ≤ X₇ ∧ 6 ≤ X₅+X₇ ∧ 4+X₅ ≤ X₇ ∧ 6 ≤ X₄+X₇ ∧ 4+X₄ ≤ X₇ ∧ 7 ≤ X₃+X₇ ∧ 3+X₃ ≤ X₇ ∧ 6 ≤ X₁+X₇ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ X₃ ≤ 1+X₅ ∧ 2 ≤ X₁+X₅ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₁ for location eval_rank2_bb7_in

Found invariant 2 ≤ X₃ for location eval_rank2_bb2_in

Found invariant 1+X₈ ≤ X₇ ∧ 4 ≤ X₈ ∧ 9 ≤ X₇+X₈ ∧ 5 ≤ X₅+X₈ ∧ 3+X₅ ≤ X₈ ∧ 5 ≤ X₄+X₈ ∧ 3+X₄ ≤ X₈ ∧ 6 ≤ X₃+X₈ ∧ 2+X₃ ≤ X₈ ∧ 5 ≤ X₁+X₈ ∧ 5 ≤ X₀+X₈ ∧ 5 ≤ X₇ ∧ 6 ≤ X₅+X₇ ∧ 4+X₅ ≤ X₇ ∧ 6 ≤ X₄+X₇ ∧ 4+X₄ ≤ X₇ ∧ 7 ≤ X₃+X₇ ∧ 3+X₃ ≤ X₇ ∧ 6 ≤ X₁+X₇ ∧ 6 ≤ X₀+X₇ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ X₃ ≤ 1+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_rank2_bb8_in

Found invariant 2 ≤ X₇ ∧ 3 ≤ X₄+X₇ ∧ 1+X₄ ≤ X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 3 ≤ X₁+X₇ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₁ for location eval_rank2_bb5_in

Found invariant 2 ≤ X₇ ∧ 3 ≤ X₄+X₇ ∧ 1+X₄ ≤ X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 2 ≤ X₃ for location eval_rank2_6

Found invariant X₃ ≤ 1 for location eval_rank2_bb9_in

Found invariant 2 ≤ X₇ ∧ 3 ≤ X₄+X₇ ∧ 1+X₄ ≤ X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 2 ≤ X₃ for location eval_rank2_bb4_in

Problem after Preprocessing

Start: eval_rank2_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars: nondef.0, nondef.1
Locations: eval_rank2_.critedge1_in, eval_rank2_.critedge_in, eval_rank2_11, eval_rank2_12, eval_rank2_5, eval_rank2_6, 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_bb7_in, eval_rank2_bb8_in, eval_rank2_bb9_in, eval_rank2_start, eval_rank2_stop
Transitions:
t₂₁: eval_rank2_.critedge1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₅, X₅, X₆, X₈-1, X₈) :|: X₃ ≤ 1+X₄ ∧ X₃ ≤ 1+X₅ ∧ X₃ ≤ 1+X₈ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₇ ∧ 1 ≤ X₅ ∧ 1+X₅ ≤ X₇ ∧ 1+X₈ ≤ X₇ ∧ 1 ≤ X₈ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₁+X₈ ∧ 2 ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₇ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₁+X₇ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₃+X₈ ∧ 3 ≤ X₄+X₇ ∧ 3 ≤ X₅+X₇ ∧ 3 ≤ X₇+X₈ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₈ ∧ X₅ ≤ X₈
t₂₂: eval_rank2_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb1_in(X₀, X₁, X₂, X₄-1, X₄, X₅, 1+X₇-X₄, X₇, X₈) :|: X₃ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₃+X₄
t₁₇: eval_rank2_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_12(nondef.1, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃ ≤ 1+X₄ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1+X₈ ≤ X₇ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₃ ∧ 2+X₃ ≤ X₈ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₃+X₅ ∧ 3+X₃ ≤ X₇ ∧ 3+X₄ ≤ X₈ ∧ 3+X₅ ≤ X₈ ∧ 4+X₄ ≤ X₇ ∧ 4+X₅ ≤ X₇ ∧ 4 ≤ X₈ ∧ 5 ≤ X₁+X₈ ∧ 5 ≤ X₄+X₈ ∧ 5 ≤ X₅+X₈ ∧ 5 ≤ X₇ ∧ 6 ≤ X₁+X₇ ∧ 6 ≤ X₃+X₈ ∧ 6 ≤ X₄+X₇ ∧ 6 ≤ X₅+X₇ ∧ 7 ≤ X₃+X₇ ∧ 9 ≤ X₇+X₈ ∧ X₄ ≤ X₅
t₁₉: eval_rank2_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_.critedge1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₀ ≤ 0 ∧ X₃ ≤ 1+X₄ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1+X₈ ≤ X₇ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₃ ∧ 2+X₃ ≤ X₈ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₃+X₅ ∧ 3+X₃ ≤ X₇ ∧ 3+X₄ ≤ X₈ ∧ 3+X₅ ≤ X₈ ∧ 4+X₄ ≤ X₇ ∧ 4+X₅ ≤ X₇ ∧ 4 ≤ X₈ ∧ 5 ≤ X₁+X₈ ∧ 5 ≤ X₄+X₈ ∧ 5 ≤ X₅+X₈ ∧ 5 ≤ X₇ ∧ 6 ≤ X₁+X₇ ∧ 6 ≤ X₃+X₈ ∧ 6 ≤ X₄+X₇ ∧ 6 ≤ X₅+X₇ ∧ 7 ≤ X₃+X₇ ∧ 9 ≤ X₇+X₈ ∧ X₄ ≤ X₅
t₁₈: eval_rank2_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1 ≤ X₀ ∧ X₃ ≤ 1+X₄ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1+X₈ ≤ X₇ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₃ ∧ 2+X₃ ≤ X₈ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₃+X₅ ∧ 3+X₃ ≤ X₇ ∧ 3+X₄ ≤ X₈ ∧ 3+X₅ ≤ X₈ ∧ 4+X₄ ≤ X₇ ∧ 4+X₅ ≤ X₇ ∧ 4 ≤ X₈ ∧ 5 ≤ X₁+X₈ ∧ 5 ≤ X₄+X₈ ∧ 5 ≤ X₅+X₈ ∧ 5 ≤ X₇ ∧ 6 ≤ X₁+X₇ ∧ 6 ≤ X₃+X₈ ∧ 6 ≤ X₄+X₇ ∧ 6 ≤ X₅+X₇ ∧ 7 ≤ X₃+X₇ ∧ 9 ≤ X₇+X₈ ∧ X₄ ≤ X₅
t₉: eval_rank2_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_6(X₀, nondef.0, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₇ ∧ 2 ≤ X₃ ∧ 2 ≤ X₇ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₄+X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇
t₁₁: eval_rank2_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₁ ≤ 0 ∧ X₃ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₇ ∧ 2 ≤ X₃ ∧ 2 ≤ X₇ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₄+X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇
t₁₀: eval_rank2_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1 ≤ X₁ ∧ X₃ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₇ ∧ 2 ≤ X₃ ∧ 2 ≤ X₇ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₄+X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇
t₁: eval_rank2_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb1_in(X₀, X₁, X₂, X₂, X₄, X₅, X₂, X₇, X₈)
t₂: eval_rank2_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 2 ≤ X₃
t₃: eval_rank2_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb9_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃ ≤ 1
t₄: eval_rank2_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₃-1, X₅, X₆, X₃+X₆-1, X₈) :|: 2 ≤ X₃
t₆: eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₇ ≤ X₄ ∧ X₃ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₃+X₄
t₅: eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₄ ≤ X₇ ∧ X₃ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₃+X₄
t₇: eval_rank2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₇ ∧ 2 ≤ X₃ ∧ 2 ≤ X₇ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₄+X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇
t₁₂: eval_rank2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb6_in(X₀, X₁, X₂, X₃, X₄, X₄, X₆, X₇, X₇-1) :|: X₃ ≤ 1+X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₇ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₃ ∧ 2 ≤ X₇ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₁+X₇ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₄+X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇
t₁₄: eval_rank2_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_.critedge1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₈ ≤ 2+X₅ ∧ X₃ ≤ 1+X₄ ∧ X₃ ≤ 1+X₅ ∧ X₃ ≤ 1+X₈ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₇ ∧ 1 ≤ X₅ ∧ 1+X₅ ≤ X₇ ∧ 1+X₈ ≤ X₇ ∧ 1 ≤ X₈ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₁+X₈ ∧ 2 ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₇ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₁+X₇ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₃+X₈ ∧ 3 ≤ X₄+X₇ ∧ 3 ≤ X₅+X₇ ∧ 3 ≤ X₇+X₈ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₈ ∧ X₅ ≤ X₈
t₁₃: eval_rank2_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 3+X₅ ≤ X₈ ∧ X₃ ≤ 1+X₄ ∧ X₃ ≤ 1+X₅ ∧ X₃ ≤ 1+X₈ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₇ ∧ 1 ≤ X₅ ∧ 1+X₅ ≤ X₇ ∧ 1+X₈ ≤ X₇ ∧ 1 ≤ X₈ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₁+X₈ ∧ 2 ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₇ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₁+X₇ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₃+X₈ ∧ 3 ≤ X₄+X₇ ∧ 3 ≤ X₅+X₇ ∧ 3 ≤ X₇+X₈ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₈ ∧ X₅ ≤ X₈
t₁₅: eval_rank2_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃ ≤ 1+X₄ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1+X₈ ≤ X₇ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₃ ∧ 2+X₃ ≤ X₈ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₃+X₅ ∧ 3+X₃ ≤ X₇ ∧ 3+X₄ ≤ X₈ ∧ 3+X₅ ≤ X₈ ∧ 4+X₄ ≤ X₇ ∧ 4+X₅ ≤ X₇ ∧ 4 ≤ X₈ ∧ 5 ≤ X₁+X₈ ∧ 5 ≤ X₄+X₈ ∧ 5 ≤ X₅+X₈ ∧ 5 ≤ X₇ ∧ 6 ≤ X₁+X₇ ∧ 6 ≤ X₃+X₈ ∧ 6 ≤ X₄+X₇ ∧ 6 ≤ X₅+X₇ ∧ 7 ≤ X₃+X₇ ∧ 9 ≤ X₇+X₈ ∧ X₄ ≤ X₅
t₂₀: eval_rank2_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb6_in(X₀, X₁, X₂, X₃, X₄, 1+X₅, X₆, X₇, X₈-2) :|: X₃ ≤ 1+X₄ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1+X₈ ≤ X₇ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₃ ∧ 2+X₃ ≤ X₈ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₃+X₅ ∧ 3+X₃ ≤ X₇ ∧ 3+X₄ ≤ X₈ ∧ 3+X₅ ≤ X₈ ∧ 4+X₄ ≤ X₇ ∧ 4+X₅ ≤ X₇ ∧ 4 ≤ X₈ ∧ 5 ≤ X₀+X₈ ∧ 5 ≤ X₁+X₈ ∧ 5 ≤ X₄+X₈ ∧ 5 ≤ X₅+X₈ ∧ 5 ≤ X₇ ∧ 6 ≤ X₀+X₇ ∧ 6 ≤ X₁+X₇ ∧ 6 ≤ X₃+X₈ ∧ 6 ≤ X₄+X₇ ∧ 6 ≤ X₅+X₇ ∧ 7 ≤ X₃+X₇ ∧ 9 ≤ X₇+X₈ ∧ X₄ ≤ X₅
t₂₃: eval_rank2_bb9_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃ ≤ 1
t₀: eval_rank2_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)

MPRF for transition t₅: eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₄ ≤ X₇ ∧ X₃ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₃+X₄ of depth 1:

new bound:

2⋅X₂+2 {O(n)}

MPRF:

• eval_rank2_.critedge1_in: [X₇-3]
• eval_rank2_.critedge_in: [X₇-2]
• eval_rank2_11: [X₇-3]
• eval_rank2_12: [X₇-3]
• eval_rank2_5: [X₇-2]
• eval_rank2_6: [X₇-2]
• eval_rank2_bb1_in: [X₃+X₆-2]
• eval_rank2_bb2_in: [X₃+X₆-2]
• eval_rank2_bb3_in: [X₇-1]
• eval_rank2_bb4_in: [X₇-2]
• eval_rank2_bb5_in: [X₇-2]
• eval_rank2_bb6_in: [X₇-3]
• eval_rank2_bb7_in: [X₇-3]
• eval_rank2_bb8_in: [X₇-3]

MPRF for transition t₇: eval_rank2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₇ ∧ 2 ≤ X₃ ∧ 2 ≤ X₇ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₄+X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ of depth 1:

new bound:

2⋅X₂ {O(n)}

MPRF:

• eval_rank2_.critedge1_in: [1+X₈]
• eval_rank2_.critedge_in: [X₇]
• eval_rank2_11: [X₇]
• eval_rank2_12: [X₇]
• eval_rank2_5: [X₇]
• eval_rank2_6: [X₇]
• eval_rank2_bb1_in: [X₃+X₆]
• eval_rank2_bb2_in: [X₃+X₆]
• eval_rank2_bb3_in: [1+X₇]
• eval_rank2_bb4_in: [1+X₇]
• eval_rank2_bb5_in: [X₇]
• eval_rank2_bb6_in: [X₇]
• eval_rank2_bb7_in: [X₇]
• eval_rank2_bb8_in: [X₇]

MPRF for transition t₉: eval_rank2_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_6(X₀, nondef.0, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₇ ∧ 2 ≤ X₃ ∧ 2 ≤ X₇ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₄+X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ of depth 1:

new bound:

2⋅X₂ {O(n)}

MPRF:

• eval_rank2_.critedge1_in: [X₈]
• eval_rank2_.critedge_in: [X₇]
• eval_rank2_11: [X₈]
• eval_rank2_12: [X₈]
• eval_rank2_5: [1+X₇]
• eval_rank2_6: [X₇]
• eval_rank2_bb1_in: [X₃+X₆]
• eval_rank2_bb2_in: [X₃+X₆]
• eval_rank2_bb3_in: [1+X₇]
• eval_rank2_bb4_in: [1+X₇]
• eval_rank2_bb5_in: [X₇]
• eval_rank2_bb6_in: [1+X₈]
• eval_rank2_bb7_in: [X₈]
• eval_rank2_bb8_in: [X₈-1]

MPRF for transition t₁₀: eval_rank2_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1 ≤ X₁ ∧ X₃ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₇ ∧ 2 ≤ X₃ ∧ 2 ≤ X₇ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₄+X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ of depth 1:

new bound:

2⋅X₂ {O(n)}

MPRF:

• eval_rank2_.critedge1_in: [X₈]
• eval_rank2_.critedge_in: [X₇]
• eval_rank2_11: [X₈]
• eval_rank2_12: [X₈]
• eval_rank2_5: [1+X₇]
• eval_rank2_6: [1+X₇]
• eval_rank2_bb1_in: [X₃+X₆]
• eval_rank2_bb2_in: [X₃+X₆]
• eval_rank2_bb3_in: [1+X₇]
• eval_rank2_bb4_in: [1+X₇]
• eval_rank2_bb5_in: [X₇-1]
• eval_rank2_bb6_in: [X₈]
• eval_rank2_bb7_in: [X₈]
• eval_rank2_bb8_in: [X₈-2]

MPRF for transition t₁₁: eval_rank2_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₁ ≤ 0 ∧ X₃ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₇ ∧ 2 ≤ X₃ ∧ 2 ≤ X₇ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₄+X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ of depth 1:

new bound:

2⋅X₂ {O(n)}

MPRF:

• eval_rank2_.critedge1_in: [X₈]
• eval_rank2_.critedge_in: [X₇]
• eval_rank2_11: [X₇]
• eval_rank2_12: [X₇]
• eval_rank2_5: [1+X₇]
• eval_rank2_6: [1+X₇]
• eval_rank2_bb1_in: [X₃+X₆]
• eval_rank2_bb2_in: [X₃+X₆]
• eval_rank2_bb3_in: [1+X₇]
• eval_rank2_bb4_in: [1+X₇]
• eval_rank2_bb5_in: [X₇]
• eval_rank2_bb6_in: [X₇]
• eval_rank2_bb7_in: [X₇]
• eval_rank2_bb8_in: [X₇]

MPRF for transition t₁₂: eval_rank2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb6_in(X₀, X₁, X₂, X₃, X₄, X₄, X₆, X₇, X₇-1) :|: X₃ ≤ 1+X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₇ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₃ ∧ 2 ≤ X₇ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₁+X₇ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₄+X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ of depth 1:

new bound:

4⋅X₂+1 {O(n)}

MPRF:

• eval_rank2_.critedge1_in: [2⋅X₇]
• eval_rank2_.critedge_in: [2⋅X₇]
• eval_rank2_11: [2⋅X₇]
• eval_rank2_12: [2⋅X₇]
• eval_rank2_5: [1+2⋅X₇]
• eval_rank2_6: [1+2⋅X₇]
• eval_rank2_bb1_in: [2⋅X₃+2⋅X₆-1]
• eval_rank2_bb2_in: [2⋅X₃+2⋅X₆-1]
• eval_rank2_bb3_in: [1+2⋅X₇]
• eval_rank2_bb4_in: [1+2⋅X₇]
• eval_rank2_bb5_in: [1+2⋅X₇]
• eval_rank2_bb6_in: [2⋅X₇]
• eval_rank2_bb7_in: [2⋅X₇]
• eval_rank2_bb8_in: [2⋅X₇]

MPRF for transition t₁₃: eval_rank2_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 3+X₅ ≤ X₈ ∧ X₃ ≤ 1+X₄ ∧ X₃ ≤ 1+X₅ ∧ X₃ ≤ 1+X₈ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₇ ∧ 1 ≤ X₅ ∧ 1+X₅ ≤ X₇ ∧ 1+X₈ ≤ X₇ ∧ 1 ≤ X₈ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₁+X₈ ∧ 2 ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₇ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₁+X₇ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₃+X₈ ∧ 3 ≤ X₄+X₇ ∧ 3 ≤ X₅+X₇ ∧ 3 ≤ X₇+X₈ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₈ ∧ X₅ ≤ X₈ of depth 1:

new bound:

3⋅X₂ {O(n)}

MPRF:

• eval_rank2_.critedge1_in: [2⋅X₈-1-X₅]
• eval_rank2_.critedge_in: [1+2⋅X₇-X₄]
• eval_rank2_11: [2⋅X₇-3-X₅]
• eval_rank2_12: [2⋅X₇-3-X₅]
• eval_rank2_5: [1+2⋅X₇-X₄]
• eval_rank2_6: [1+2⋅X₇-X₄]
• eval_rank2_bb1_in: [X₃+2⋅X₆]
• eval_rank2_bb2_in: [X₃+2⋅X₆]
• eval_rank2_bb3_in: [1+2⋅X₇-X₄]
• eval_rank2_bb4_in: [1+2⋅X₇-X₄]
• eval_rank2_bb5_in: [1+2⋅X₇-X₄]
• eval_rank2_bb6_in: [2⋅X₇-2-X₅]
• eval_rank2_bb7_in: [2⋅X₇-3-X₅]
• eval_rank2_bb8_in: [2⋅X₇-3-X₅]

MPRF for transition t₁₄: eval_rank2_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_.critedge1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₈ ≤ 2+X₅ ∧ X₃ ≤ 1+X₄ ∧ X₃ ≤ 1+X₅ ∧ X₃ ≤ 1+X₈ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₇ ∧ 1 ≤ X₅ ∧ 1+X₅ ≤ X₇ ∧ 1+X₈ ≤ X₇ ∧ 1 ≤ X₈ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₁+X₈ ∧ 2 ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₇ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₁+X₇ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₃+X₈ ∧ 3 ≤ X₄+X₇ ∧ 3 ≤ X₅+X₇ ∧ 3 ≤ X₇+X₈ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₈ ∧ X₅ ≤ X₈ of depth 1:

new bound:

2⋅X₂+1 {O(n)}

MPRF:

• eval_rank2_.critedge1_in: [X₈-1]
• eval_rank2_.critedge_in: [X₇]
• eval_rank2_11: [X₈]
• eval_rank2_12: [X₈]
• eval_rank2_5: [X₇]
• eval_rank2_6: [X₇]
• eval_rank2_bb1_in: [X₃+X₆-1]
• eval_rank2_bb2_in: [X₃+X₆-1]
• eval_rank2_bb3_in: [X₇]
• eval_rank2_bb4_in: [X₇]
• eval_rank2_bb5_in: [X₇-1]
• eval_rank2_bb6_in: [X₈]
• eval_rank2_bb7_in: [X₈]
• eval_rank2_bb8_in: [X₈]

MPRF for transition t₁₅: eval_rank2_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃ ≤ 1+X₄ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1+X₈ ≤ X₇ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₃ ∧ 2+X₃ ≤ X₈ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₃+X₅ ∧ 3+X₃ ≤ X₇ ∧ 3+X₄ ≤ X₈ ∧ 3+X₅ ≤ X₈ ∧ 4+X₄ ≤ X₇ ∧ 4+X₅ ≤ X₇ ∧ 4 ≤ X₈ ∧ 5 ≤ X₁+X₈ ∧ 5 ≤ X₄+X₈ ∧ 5 ≤ X₅+X₈ ∧ 5 ≤ X₇ ∧ 6 ≤ X₁+X₇ ∧ 6 ≤ X₃+X₈ ∧ 6 ≤ X₄+X₇ ∧ 6 ≤ X₅+X₇ ∧ 7 ≤ X₃+X₇ ∧ 9 ≤ X₇+X₈ ∧ X₄ ≤ X₅ of depth 1:

new bound:

3⋅X₂ {O(n)}

MPRF:

• eval_rank2_.critedge1_in: [2⋅X₈-X₅]
• eval_rank2_.critedge_in: [1+2⋅X₇-X₄]
• eval_rank2_11: [2+2⋅X₈-X₅]
• eval_rank2_12: [2+2⋅X₈-X₅]
• eval_rank2_5: [1+2⋅X₇-X₄]
• eval_rank2_6: [1+2⋅X₇-X₄]
• eval_rank2_bb1_in: [X₃+2⋅X₆]
• eval_rank2_bb2_in: [X₃+2⋅X₆]
• eval_rank2_bb3_in: [1+2⋅X₇-X₄]
• eval_rank2_bb4_in: [1+2⋅X₇-X₄]
• eval_rank2_bb5_in: [1+2⋅X₇-X₄]
• eval_rank2_bb6_in: [3+2⋅X₈-X₅]
• eval_rank2_bb7_in: [3+2⋅X₈-X₅]
• eval_rank2_bb8_in: [2+2⋅X₈-X₅]

MPRF for transition t₁₇: eval_rank2_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_12(nondef.1, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃ ≤ 1+X₄ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1+X₈ ≤ X₇ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₃ ∧ 2+X₃ ≤ X₈ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₃+X₅ ∧ 3+X₃ ≤ X₇ ∧ 3+X₄ ≤ X₈ ∧ 3+X₅ ≤ X₈ ∧ 4+X₄ ≤ X₇ ∧ 4+X₅ ≤ X₇ ∧ 4 ≤ X₈ ∧ 5 ≤ X₁+X₈ ∧ 5 ≤ X₄+X₈ ∧ 5 ≤ X₅+X₈ ∧ 5 ≤ X₇ ∧ 6 ≤ X₁+X₇ ∧ 6 ≤ X₃+X₈ ∧ 6 ≤ X₄+X₇ ∧ 6 ≤ X₅+X₇ ∧ 7 ≤ X₃+X₇ ∧ 9 ≤ X₇+X₈ ∧ X₄ ≤ X₅ of depth 1:

new bound:

2⋅X₂+5 {O(n)}

MPRF:

• eval_rank2_.critedge1_in: [X₈-4]
• eval_rank2_.critedge_in: [X₇-4]
• eval_rank2_11: [X₈-3]
• eval_rank2_12: [X₈-4]
• eval_rank2_5: [X₇-4]
• eval_rank2_6: [X₇-4]
• eval_rank2_bb1_in: [X₃+X₆-5]
• eval_rank2_bb2_in: [X₃+X₆-5]
• eval_rank2_bb3_in: [X₇-4]
• eval_rank2_bb4_in: [X₇-4]
• eval_rank2_bb5_in: [X₇-4]
• eval_rank2_bb6_in: [X₈-3]
• eval_rank2_bb7_in: [X₈-3]
• eval_rank2_bb8_in: [X₈-5]

MPRF for transition t₁₈: eval_rank2_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1 ≤ X₀ ∧ X₃ ≤ 1+X₄ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1+X₈ ≤ X₇ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₃ ∧ 2+X₃ ≤ X₈ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₃+X₅ ∧ 3+X₃ ≤ X₇ ∧ 3+X₄ ≤ X₈ ∧ 3+X₅ ≤ X₈ ∧ 4+X₄ ≤ X₇ ∧ 4+X₅ ≤ X₇ ∧ 4 ≤ X₈ ∧ 5 ≤ X₁+X₈ ∧ 5 ≤ X₄+X₈ ∧ 5 ≤ X₅+X₈ ∧ 5 ≤ X₇ ∧ 6 ≤ X₁+X₇ ∧ 6 ≤ X₃+X₈ ∧ 6 ≤ X₄+X₇ ∧ 6 ≤ X₅+X₇ ∧ 7 ≤ X₃+X₇ ∧ 9 ≤ X₇+X₈ ∧ X₄ ≤ X₅ of depth 1:

new bound:

2⋅X₂ {O(n)}

MPRF:

• eval_rank2_.critedge1_in: [1+X₈]
• eval_rank2_.critedge_in: [X₇]
• eval_rank2_11: [1+X₈]
• eval_rank2_12: [1+X₈]
• eval_rank2_5: [X₇]
• eval_rank2_6: [X₇]
• eval_rank2_bb1_in: [X₃+X₆]
• eval_rank2_bb2_in: [X₃+X₆-1]
• eval_rank2_bb3_in: [X₇]
• eval_rank2_bb4_in: [X₇]
• eval_rank2_bb5_in: [X₇]
• eval_rank2_bb6_in: [1+X₈]
• eval_rank2_bb7_in: [1+X₈]
• eval_rank2_bb8_in: [X₈]

MPRF for transition t₁₉: eval_rank2_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_.critedge1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₀ ≤ 0 ∧ X₃ ≤ 1+X₄ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1+X₈ ≤ X₇ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₃ ∧ 2+X₃ ≤ X₈ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₃+X₅ ∧ 3+X₃ ≤ X₇ ∧ 3+X₄ ≤ X₈ ∧ 3+X₅ ≤ X₈ ∧ 4+X₄ ≤ X₇ ∧ 4+X₅ ≤ X₇ ∧ 4 ≤ X₈ ∧ 5 ≤ X₁+X₈ ∧ 5 ≤ X₄+X₈ ∧ 5 ≤ X₅+X₈ ∧ 5 ≤ X₇ ∧ 6 ≤ X₁+X₇ ∧ 6 ≤ X₃+X₈ ∧ 6 ≤ X₄+X₇ ∧ 6 ≤ X₅+X₇ ∧ 7 ≤ X₃+X₇ ∧ 9 ≤ X₇+X₈ ∧ X₄ ≤ X₅ of depth 1:

new bound:

2⋅X₂ {O(n)}

MPRF:

• eval_rank2_.critedge1_in: [X₈]
• eval_rank2_.critedge_in: [X₇]
• eval_rank2_11: [1+X₈]
• eval_rank2_12: [1+X₈]
• eval_rank2_5: [1+X₇]
• eval_rank2_6: [1+X₇]
• eval_rank2_bb1_in: [X₃+X₆]
• eval_rank2_bb2_in: [X₃+X₆]
• eval_rank2_bb3_in: [1+X₇]
• eval_rank2_bb4_in: [1+X₇]
• eval_rank2_bb5_in: [X₇]
• eval_rank2_bb6_in: [1+X₈]
• eval_rank2_bb7_in: [1+X₈]
• eval_rank2_bb8_in: [1+X₈]

MPRF for transition t₂₀: eval_rank2_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb6_in(X₀, X₁, X₂, X₃, X₄, 1+X₅, X₆, X₇, X₈-2) :|: X₃ ≤ 1+X₄ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1+X₈ ≤ X₇ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₃ ∧ 2+X₃ ≤ X₈ ∧ 2 ≤ X₄+X₅ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₃+X₅ ∧ 3+X₃ ≤ X₇ ∧ 3+X₄ ≤ X₈ ∧ 3+X₅ ≤ X₈ ∧ 4+X₄ ≤ X₇ ∧ 4+X₅ ≤ X₇ ∧ 4 ≤ X₈ ∧ 5 ≤ X₀+X₈ ∧ 5 ≤ X₁+X₈ ∧ 5 ≤ X₄+X₈ ∧ 5 ≤ X₅+X₈ ∧ 5 ≤ X₇ ∧ 6 ≤ X₀+X₇ ∧ 6 ≤ X₁+X₇ ∧ 6 ≤ X₃+X₈ ∧ 6 ≤ X₄+X₇ ∧ 6 ≤ X₅+X₇ ∧ 7 ≤ X₃+X₇ ∧ 9 ≤ X₇+X₈ ∧ X₄ ≤ X₅ of depth 1:

new bound:

2⋅X₂+3 {O(n)}

MPRF:

• eval_rank2_.critedge1_in: [X₈-3]
• eval_rank2_.critedge_in: [X₇-3]
• eval_rank2_11: [X₈-3]
• eval_rank2_12: [X₈-3]
• eval_rank2_5: [X₇-3]
• eval_rank2_6: [X₇-3]
• eval_rank2_bb1_in: [X₃+X₆-3]
• eval_rank2_bb2_in: [X₃+X₆-4]
• eval_rank2_bb3_in: [X₇-3]
• eval_rank2_bb4_in: [X₇-3]
• eval_rank2_bb5_in: [X₇-3]
• eval_rank2_bb6_in: [X₈-2]
• eval_rank2_bb7_in: [X₈-2]
• eval_rank2_bb8_in: [X₈-3]

MPRF for transition t₂₁: eval_rank2_.critedge1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₅, X₅, X₆, X₈-1, X₈) :|: X₃ ≤ 1+X₄ ∧ X₃ ≤ 1+X₅ ∧ X₃ ≤ 1+X₈ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 1+X₄ ≤ X₇ ∧ 1 ≤ X₅ ∧ 1+X₅ ≤ X₇ ∧ 1+X₈ ≤ X₇ ∧ 1 ≤ X₈ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₁+X₈ ∧ 2 ≤ X₃ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₇ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₁+X₇ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₃+X₈ ∧ 3 ≤ X₄+X₇ ∧ 3 ≤ X₅+X₇ ∧ 3 ≤ X₇+X₈ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ X₄ ≤ X₅ ∧ X₄ ≤ X₈ ∧ X₅ ≤ X₈ of depth 1:

new bound:

2⋅X₂ {O(n)}

MPRF:

• eval_rank2_.critedge1_in: [X₈]
• eval_rank2_.critedge_in: [X₇]
• eval_rank2_11: [X₈]
• eval_rank2_12: [X₈]
• eval_rank2_5: [X₇]
• eval_rank2_6: [X₇]
• eval_rank2_bb1_in: [X₃+X₆]
• eval_rank2_bb2_in: [X₃+X₆]
• eval_rank2_bb3_in: [X₇]
• eval_rank2_bb4_in: [X₇]
• eval_rank2_bb5_in: [X₇-1]
• eval_rank2_bb6_in: [X₈]
• eval_rank2_bb7_in: [X₈]
• eval_rank2_bb8_in: [X₈]

MPRF for transition t₂: eval_rank2_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 2 ≤ X₃ of depth 1:

new bound:

6⋅X₂⋅X₂+11⋅X₂+1 {O(n^2)}

MPRF:

• eval_rank2_.critedge1_in: [-1]
• eval_rank2_.critedge_in: [X₄-2]
• eval_rank2_11: [-1]
• eval_rank2_12: [-1]
• eval_rank2_5: [X₄-2]
• eval_rank2_6: [X₄-2]
• eval_rank2_bb1_in: [X₃-1]
• eval_rank2_bb2_in: [X₃-2]
• eval_rank2_bb3_in: [X₄-2]
• eval_rank2_bb4_in: [X₄-2]
• eval_rank2_bb5_in: [X₄-2]
• eval_rank2_bb6_in: [-1]
• eval_rank2_bb7_in: [-1]
• eval_rank2_bb8_in: [-1]

MPRF for transition t₄: eval_rank2_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₃-1, X₅, X₆, X₃+X₆-1, X₈) :|: 2 ≤ X₃ of depth 1:

new bound:

6⋅X₂⋅X₂+9⋅X₂ {O(n^2)}

MPRF:

• eval_rank2_.critedge1_in: [X₅+X₈-X₇]
• eval_rank2_.critedge_in: [X₄-1]
• eval_rank2_11: [X₅+X₈-X₇]
• eval_rank2_12: [X₅+X₈-X₇]
• eval_rank2_5: [X₄-1]
• eval_rank2_6: [X₄-1]
• eval_rank2_bb1_in: [X₃]
• eval_rank2_bb2_in: [X₃-1]
• eval_rank2_bb3_in: [X₄-1]
• eval_rank2_bb4_in: [X₄-1]
• eval_rank2_bb5_in: [X₄-1]
• eval_rank2_bb6_in: [X₅+X₈-X₇]
• eval_rank2_bb7_in: [X₅+X₈-X₇]
• eval_rank2_bb8_in: [X₅+X₈-1-X₇]

MPRF for transition t₆: eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₇ ≤ X₄ ∧ X₃ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₃+X₄ of depth 1:

new bound:

6⋅X₂⋅X₂+11⋅X₂+2 {O(n^2)}

MPRF:

• eval_rank2_.critedge1_in: [X₅+X₈-X₇]
• eval_rank2_.critedge_in: [1+X₄]
• eval_rank2_11: [X₅+X₈-X₇]
• eval_rank2_12: [X₅+X₈-X₇]
• eval_rank2_5: [1+X₄]
• eval_rank2_6: [1+X₄]
• eval_rank2_bb1_in: [2+X₃]
• eval_rank2_bb2_in: [1+X₃]
• eval_rank2_bb3_in: [2+X₄]
• eval_rank2_bb4_in: [1+X₄]
• eval_rank2_bb5_in: [X₄]
• eval_rank2_bb6_in: [X₅+X₈-X₇]
• eval_rank2_bb7_in: [X₅+X₈-X₇]
• eval_rank2_bb8_in: [X₅+X₈-1-X₇]

MPRF for transition t₂₂: eval_rank2_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_rank2_bb1_in(X₀, X₁, X₂, X₄-1, X₄, X₅, 1+X₇-X₄, X₇, X₈) :|: X₃ ≤ 1+X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₃+X₄ of depth 1:

new bound:

6⋅X₂⋅X₂+9⋅X₂+1 {O(n^2)}

MPRF:

• eval_rank2_.critedge1_in: [2⋅X₅+X₈-X₄-X₇]
• eval_rank2_.critedge_in: [1+X₄]
• eval_rank2_11: [2⋅X₅+X₈-X₄-X₇]
• eval_rank2_12: [2⋅X₅+X₈-X₄-X₇]
• eval_rank2_5: [1+X₄]
• eval_rank2_6: [1+X₄]
• eval_rank2_bb1_in: [1+X₃]
• eval_rank2_bb2_in: [1+X₃]
• eval_rank2_bb3_in: [1+X₄]
• eval_rank2_bb4_in: [1+X₄]
• eval_rank2_bb5_in: [X₄]
• eval_rank2_bb6_in: [2⋅X₅+X₈-X₄-X₇]
• eval_rank2_bb7_in: [2⋅X₅+X₈-X₄-X₇]
• eval_rank2_bb8_in: [2⋅X₅+X₈-X₄-X₇]

Found invariant X₃ ≤ 1 for location eval_rank2_stop

Found invariant 2 ≤ X₇ ∧ 3 ≤ X₄+X₇ ∧ 1+X₄ ≤ X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 2+X₁ ≤ X₇ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 1+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ X₁ ≤ 0 for location eval_rank2_.critedge_in

Found invariant 2 ≤ X₇ ∧ 3 ≤ X₄+X₇ ∧ 1+X₄ ≤ X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 2 ≤ X₃ for location eval_rank2_5

Found invariant X₇ ≤ X₄ ∧ X₇ ≤ 1+X₃ ∧ 2+X₆ ≤ X₇ ∧ X₆ ≤ 1 ∧ 2+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₃ ∧ X₄ ≤ 1+X₃ ∧ 3 ≤ X₄ ∧ 5 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 2 ≤ X₃ for location eval_rank2_bb2_in_v2

Found invariant 1+X₆ ≤ X₇ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 2 ≤ X₃ for location eval_rank2_bb3_in_v1

Found invariant 2 ≤ X₇ ∧ 4 ≤ X₆+X₇ ∧ X₆ ≤ X₇ ∧ 3 ≤ X₄+X₇ ∧ 1+X₄ ≤ X₇ ∧ 2 ≤ X₃+X₇ ∧ 2+X₃ ≤ X₇ ∧ 2+X₁ ≤ X₇ ∧ 3 ≤ X₄+X₆ ∧ 2 ≤ X₃+X₆ ∧ X₄ ≤ 1+X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₁ ≤ 0 for location eval_rank2_bb1_in_v1

Found invariant X₈ ≤ 1+X₇ ∧ 1 ≤ X₈ ∧ 1 ≤ X₇+X₈ ∧ 1+X₇ ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ X₅ ≤ X₈ ∧ 2 ≤ X₄+X₈ ∧ X₄ ≤ X₈ ∧ 3 ≤ X₃+X₈ ∧ X₃ ≤ 1+X₈ ∧ 2 ≤ X₁+X₈ ∧ 0 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ X₅ ≤ 1+X₇ ∧ 1 ≤ X₄+X₇ ∧ X₄ ≤ 1+X₇ ∧ 2 ≤ X₃+X₇ ∧ X₃ ≤ 2+X₇ ∧ 1 ≤ X₁+X₇ ∧ X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ X₃ ≤ 1+X₅ ∧ 2 ≤ X₁+X₅ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₁ for location eval_rank2_bb3_in

Found invariant X₈ ≤ 1+X₇ ∧ X₈ ≤ 1+X₅ ∧ X₈ ≤ 1+X₄ ∧ 1 ≤ X₈ ∧ 1 ≤ X₇+X₈ ∧ 1+X₇ ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ X₅ ≤ X₈ ∧ 2 ≤ X₄+X₈ ∧ X₄ ≤ X₈ ∧ 3 ≤ X₃+X₈ ∧ X₃ ≤ 1+X₈ ∧ 2 ≤ X₁+X₈ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₄ ∧ 0 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ X₅ ≤ 1+X₇ ∧ 1 ≤ X₄+X₇ ∧ X₄ ≤ 1+X₇ ∧ 2 ≤ X₃+X₇ ∧ X₃ ≤ 2+X₇ ∧ 1 ≤ X₁+X₇ ∧ X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ X₃ ≤ 1+X₅ ∧ 2 ≤ X₁+X₅ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₁ for location eval_rank2_.critedge_in_v2

Found invariant X₇ ≤ X₄ ∧ 1+X₇ ≤ X₃ ∧ 1+X₆ ≤ X₇ ∧ 1+X₆ ≤ X₄ ∧ 2+X₆ ≤ X₃ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 2 ≤ X₃ for location eval_rank2_.critedge_in_v1

Found invariant X₇ ≤ X₄ ∧ X₇ ≤ 1+X₃ ∧ X₆ ≤ X₇ ∧ X₆ ≤ X₄ ∧ X₆ ≤ 1+X₃ ∧ X₄ ≤ 1+X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 0 ≤ X₃ for location eval_rank2_bb1_in_v2

Found invariant 2 ≤ X₇ ∧ 3 ≤ X₄+X₇ ∧ 1+X₄ ≤ X₇ ∧ 4 ≤ X₃+X₇ ∧ X₃ ≤ X₇ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 2 ≤ X₃ for location eval_rank2_6

Found invariant X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ X₃ ≤ X₆ ∧ X₂ ≤ X₆ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location eval_rank2_bb1_in

Found invariant X₃ ≤ 1 for location eval_rank2_bb9_in

Found invariant 4 ≤ X₇ ∧ 4 ≤ X₆+X₇ ∧ 2+X₆ ≤ X₇ ∧ 7 ≤ X₄+X₇ ∧ 1+X₄ ≤ X₇ ∧ 6 ≤ X₃+X₇ ∧ 2+X₃ ≤ X₇ ∧ 4+X₁ ≤ X₇ ∧ 3 ≤ X₄+X₆ ∧ 2 ≤ X₃+X₆ ∧ X₄ ≤ 1+X₃ ∧ 3 ≤ X₄ ∧ 5 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3+X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ X₁ ≤ 0 for location eval_rank2_bb2_in_v1

Found invariant X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ 2 ≤ X₆ ∧ 4 ≤ X₃+X₆ ∧ X₃ ≤ X₆ ∧ 4 ≤ X₂+X₆ ∧ X₂ ≤ X₆ ∧ X₃ ≤ X₂ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₂ for location eval_rank2_bb2_in_v3

All Bounds

Timebounds

Overall timebound:24⋅X₂⋅X₂+72⋅X₂+20 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 6⋅X₂⋅X₂+11⋅X₂+1 {O(n^2)}
t₃: 1 {O(1)}
t₄: 6⋅X₂⋅X₂+9⋅X₂ {O(n^2)}
t₅: 2⋅X₂+2 {O(n)}
t₆: 6⋅X₂⋅X₂+11⋅X₂+2 {O(n^2)}
t₇: 2⋅X₂ {O(n)}
t₉: 2⋅X₂ {O(n)}
t₁₀: 2⋅X₂ {O(n)}
t₁₁: 2⋅X₂ {O(n)}
t₁₂: 4⋅X₂+1 {O(n)}
t₁₃: 3⋅X₂ {O(n)}
t₁₄: 2⋅X₂+1 {O(n)}
t₁₅: 3⋅X₂ {O(n)}
t₁₇: 2⋅X₂+5 {O(n)}
t₁₈: 2⋅X₂ {O(n)}
t₁₉: 2⋅X₂ {O(n)}
t₂₀: 2⋅X₂+3 {O(n)}
t₂₁: 2⋅X₂ {O(n)}
t₂₂: 6⋅X₂⋅X₂+9⋅X₂+1 {O(n^2)}
t₂₃: 1 {O(1)}

Costbounds

Overall costbound: 24⋅X₂⋅X₂+72⋅X₂+20 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 6⋅X₂⋅X₂+11⋅X₂+1 {O(n^2)}
t₃: 1 {O(1)}
t₄: 6⋅X₂⋅X₂+9⋅X₂ {O(n^2)}
t₅: 2⋅X₂+2 {O(n)}
t₆: 6⋅X₂⋅X₂+11⋅X₂+2 {O(n^2)}
t₇: 2⋅X₂ {O(n)}
t₉: 2⋅X₂ {O(n)}
t₁₀: 2⋅X₂ {O(n)}
t₁₁: 2⋅X₂ {O(n)}
t₁₂: 4⋅X₂+1 {O(n)}
t₁₃: 3⋅X₂ {O(n)}
t₁₄: 2⋅X₂+1 {O(n)}
t₁₅: 3⋅X₂ {O(n)}
t₁₇: 2⋅X₂+5 {O(n)}
t₁₈: 2⋅X₂ {O(n)}
t₁₉: 2⋅X₂ {O(n)}
t₂₀: 2⋅X₂+3 {O(n)}
t₂₁: 2⋅X₂ {O(n)}
t₂₂: 6⋅X₂⋅X₂+9⋅X₂+1 {O(n^2)}
t₂₃: 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: X₂ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₂ {O(n)}
t₁, X₇: X₇ {O(n)}
t₁, X₈: X₈ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: 3⋅X₂+3 {O(n)}
t₂, X₄: 6⋅X₂+X₄+6 {O(n)}
t₂, X₅: 6⋅X₂+X₅+6 {O(n)}
t₂, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₂, X₇: 108⋅X₂⋅X₂⋅X₂+270⋅X₂⋅X₂+194⋅X₂+X₇+30 {O(n^3)}
t₂, X₈: 162⋅X₂⋅X₂⋅X₂+405⋅X₂⋅X₂+291⋅X₂+X₈+45 {O(n^3)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 4⋅X₂+3 {O(n)}
t₃, X₄: 6⋅X₂+X₄+6 {O(n)}
t₃, X₅: 2⋅X₅+6⋅X₂+6 {O(n)}
t₃, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+98⋅X₂+15 {O(n^3)}
t₃, X₇: 108⋅X₂⋅X₂⋅X₂+270⋅X₂⋅X₂+194⋅X₂+X₇+30 {O(n^3)}
t₃, X₈: 162⋅X₂⋅X₂⋅X₂+405⋅X₂⋅X₂+2⋅X₈+291⋅X₂+45 {O(n^3)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: 3⋅X₂+3 {O(n)}
t₄, X₄: 3⋅X₂+3 {O(n)}
t₄, X₅: 6⋅X₂+X₅+6 {O(n)}
t₄, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₄, X₇: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₄, X₈: 162⋅X₂⋅X₂⋅X₂+405⋅X₂⋅X₂+291⋅X₂+X₈+45 {O(n^3)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: 3⋅X₂+3 {O(n)}
t₅, X₄: 3⋅X₂+3 {O(n)}
t₅, X₅: 6⋅X₂+X₅+6 {O(n)}
t₅, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₅, X₇: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₅, X₈: 162⋅X₂⋅X₂⋅X₂+405⋅X₂⋅X₂+291⋅X₂+X₈+45 {O(n^3)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: 6⋅X₂+6 {O(n)}
t₆, X₄: 3⋅X₂+3 {O(n)}
t₆, X₅: 6⋅X₂+X₅+6 {O(n)}
t₆, X₆: 108⋅X₂⋅X₂⋅X₂+270⋅X₂⋅X₂+194⋅X₂+30 {O(n^3)}
t₆, X₇: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₆, X₈: 162⋅X₂⋅X₂⋅X₂+405⋅X₂⋅X₂+291⋅X₂+X₈+45 {O(n^3)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: 3⋅X₂+3 {O(n)}
t₇, X₄: 3⋅X₂+3 {O(n)}
t₇, X₅: 6⋅X₂+X₅+6 {O(n)}
t₇, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₇, X₇: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₇, X₈: 162⋅X₂⋅X₂⋅X₂+405⋅X₂⋅X₂+291⋅X₂+X₈+45 {O(n^3)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: 3⋅X₂+3 {O(n)}
t₉, X₄: 3⋅X₂+3 {O(n)}
t₉, X₅: 6⋅X₂+X₅+6 {O(n)}
t₉, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₉, X₇: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₉, X₈: 162⋅X₂⋅X₂⋅X₂+405⋅X₂⋅X₂+291⋅X₂+X₈+45 {O(n^3)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: 3⋅X₂+3 {O(n)}
t₁₀, X₄: 3⋅X₂+3 {O(n)}
t₁₀, X₅: 6⋅X₂+X₅+6 {O(n)}
t₁₀, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₀, X₇: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₀, X₈: 162⋅X₂⋅X₂⋅X₂+405⋅X₂⋅X₂+291⋅X₂+X₈+45 {O(n^3)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: 3⋅X₂+3 {O(n)}
t₁₁, X₄: 3⋅X₂+3 {O(n)}
t₁₁, X₅: 6⋅X₂+X₅+6 {O(n)}
t₁₁, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₁, X₇: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₁, X₈: 162⋅X₂⋅X₂⋅X₂+405⋅X₂⋅X₂+291⋅X₂+X₈+45 {O(n^3)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: 3⋅X₂+3 {O(n)}
t₁₂, X₄: 3⋅X₂+3 {O(n)}
t₁₂, X₅: 3⋅X₂+3 {O(n)}
t₁₂, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₂, X₇: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₂, X₈: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: 3⋅X₂+3 {O(n)}
t₁₃, X₄: 3⋅X₂+3 {O(n)}
t₁₃, X₅: 3⋅X₂+3 {O(n)}
t₁₃, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₃, X₇: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₃, X₈: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: 3⋅X₂+3 {O(n)}
t₁₄, X₄: 6⋅X₂+6 {O(n)}
t₁₄, X₅: 3⋅X₂+3 {O(n)}
t₁₄, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₄, X₇: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₄, X₈: 108⋅X₂⋅X₂⋅X₂+270⋅X₂⋅X₂+194⋅X₂+30 {O(n^3)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: 3⋅X₂+3 {O(n)}
t₁₅, X₄: 3⋅X₂+3 {O(n)}
t₁₅, X₅: 3⋅X₂+3 {O(n)}
t₁₅, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₅, X₇: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₅, X₈: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: 3⋅X₂+3 {O(n)}
t₁₇, X₄: 3⋅X₂+3 {O(n)}
t₁₇, X₅: 3⋅X₂+3 {O(n)}
t₁₇, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₇, X₇: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₇, X₈: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: 3⋅X₂+3 {O(n)}
t₁₈, X₄: 3⋅X₂+3 {O(n)}
t₁₈, X₅: 3⋅X₂+3 {O(n)}
t₁₈, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₈, X₇: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₈, X₈: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: 3⋅X₂+3 {O(n)}
t₁₉, X₄: 3⋅X₂+3 {O(n)}
t₁₉, X₅: 3⋅X₂+3 {O(n)}
t₁₉, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₉, X₇: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₁₉, X₈: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: 3⋅X₂+3 {O(n)}
t₂₀, X₄: 3⋅X₂+3 {O(n)}
t₂₀, X₅: 3⋅X₂+3 {O(n)}
t₂₀, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₂₀, X₇: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₂₀, X₈: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₃: 3⋅X₂+3 {O(n)}
t₂₁, X₄: 3⋅X₂+3 {O(n)}
t₂₁, X₅: 6⋅X₂+6 {O(n)}
t₂₁, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₂₁, X₇: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₂₁, X₈: 162⋅X₂⋅X₂⋅X₂+405⋅X₂⋅X₂+291⋅X₂+45 {O(n^3)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: 3⋅X₂+3 {O(n)}
t₂₂, X₄: 6⋅X₂+6 {O(n)}
t₂₂, X₅: 6⋅X₂+X₅+6 {O(n)}
t₂₂, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+97⋅X₂+15 {O(n^3)}
t₂₂, X₇: 108⋅X₂⋅X₂⋅X₂+270⋅X₂⋅X₂+194⋅X₂+30 {O(n^3)}
t₂₂, X₈: 162⋅X₂⋅X₂⋅X₂+405⋅X₂⋅X₂+291⋅X₂+X₈+45 {O(n^3)}
t₂₃, X₂: 2⋅X₂ {O(n)}
t₂₃, X₃: 4⋅X₂+3 {O(n)}
t₂₃, X₄: 6⋅X₂+X₄+6 {O(n)}
t₂₃, X₅: 2⋅X₅+6⋅X₂+6 {O(n)}
t₂₃, X₆: 54⋅X₂⋅X₂⋅X₂+135⋅X₂⋅X₂+98⋅X₂+15 {O(n^3)}
t₂₃, X₇: 108⋅X₂⋅X₂⋅X₂+270⋅X₂⋅X₂+194⋅X₂+X₇+30 {O(n^3)}
t₂₃, X₈: 162⋅X₂⋅X₂⋅X₂+405⋅X₂⋅X₂+2⋅X₈+291⋅X₂+45 {O(n^3)}