KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₇ ≤ X₃ ∧ 0 ≤ 1+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₆ ≤ X₇ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ X₃+X₇ ∧ 0 ≤ X₂+X₇ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₃ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ for location eval_serpent_bb6_in

Found invariant X₆ ≤ X₅ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₀ for location eval_serpent_bb3_in

Found invariant X₇ ≤ X₃ ∧ 0 ≤ 1+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₆ ≤ X₇ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₃ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₃ for location eval_serpent_11

Found invariant X₆ ≤ X₅ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ 1 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₃ for location eval_serpent_3

Found invariant X₆ ≤ X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₃ for location eval_serpent_8

Found invariant X₆ ≤ X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₃ for location eval_serpent_bb1_in

Found invariant X₆ ≤ X₅ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ 1 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₃ for location eval_serpent_2

Found invariant X₆ ≤ X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₃ for location eval_serpent_9

Found invariant X₆ ≤ X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₃ for location eval_serpent__critedge_in

Found invariant X₆ ≤ X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₃ for location eval_serpent_7

Found invariant X₆ ≤ X₅ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ 1 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₃ for location eval_serpent_bb2_in

Found invariant 0 ≤ 1+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₆ ≤ X₇ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₃ for location eval_serpent_bb4_in

Found invariant 0 ≤ 1+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₃ for location eval_serpent__critedge1_in

Problem after Preprocessing

Start: eval_serpent_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: nondef_0, nondef_1
Locations: eval_serpent_0, eval_serpent_1, eval_serpent_10, eval_serpent_11, eval_serpent_2, eval_serpent_3, eval_serpent_7, eval_serpent_8, eval_serpent_9, eval_serpent__critedge1_in, eval_serpent__critedge_in, eval_serpent_bb0_in, eval_serpent_bb1_in, eval_serpent_bb2_in, eval_serpent_bb3_in, eval_serpent_bb4_in, eval_serpent_bb5_in, eval_serpent_bb6_in, eval_serpent_bb7_in, eval_serpent_start, eval_serpent_stop
Transitions:
t₂: eval_serpent_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₄: eval_serpent_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₃, X₃, X₆, X₇) :|: 1 ≤ X₃
t₃: eval_serpent_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₃ ≤ 0
t₂₁: eval_serpent_10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_11(X₀, X₁, nondef_1, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇
t₂₃: eval_serpent_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₁, X₇, X₆, X₇) :|: X₂ ≤ 0 ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇
t₂₂: eval_serpent_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₂ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇
t₁₀: eval_serpent_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_3(nondef_0, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆
t₁₂: eval_serpent_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0 ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆
t₁₁: eval_serpent_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆
t₁₅: eval_serpent_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₅
t₁₆: eval_serpent_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₅
t₁₇: eval_serpent_9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₆) :|: 0 ≤ 2+X₅+X₆ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₅
t₅: eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₅, X₇) :|: 0 ≤ X₄ ∧ 0 ≤ 1+X₅ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅
t₆: eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₄ ≤ 0 ∧ 0 ≤ 1+X₅ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅
t₁₄: eval_serpent__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_7(X₀, X₄-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₅
t₁: eval_serpent_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₈: eval_serpent_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₆ ≤ 0 ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₅
t₇: eval_serpent_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₅
t₉: eval_serpent_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆
t₁₃: eval_serpent_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆
t₁₉: eval_serpent_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₁, X₇, X₆, X₇) :|: 1+X₃ ≤ X₇ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇
t₁₈: eval_serpent_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₇ ≤ X₃ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇
t₂₀: eval_serpent_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇
t₂₄: eval_serpent_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 1+X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ X₂+X₇ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇
t₂₅: eval_serpent_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₀: eval_serpent_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)

MPRF for transition t₅: eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₅, X₇) :|: 0 ≤ X₄ ∧ 0 ≤ 1+X₅ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ of depth 1:

new bound:

2⋅X₃+1 {O(n)}

MPRF:

• eval_serpent_10: [1+X₁+X₄]
• eval_serpent_11: [1+X₁+X₄]
• eval_serpent_2: [2⋅X₄]
• eval_serpent_3: [2⋅X₄]
• eval_serpent_7: [2+2⋅X₁]
• eval_serpent_8: [1+X₁+X₄]
• eval_serpent_9: [1+X₁+X₄]
• eval_serpent__critedge1_in: [1+2⋅X₄]
• eval_serpent__critedge_in: [2⋅X₄]
• eval_serpent_bb1_in: [2⋅X₄]
• eval_serpent_bb2_in: [2⋅X₄]
• eval_serpent_bb3_in: [2⋅X₄]
• eval_serpent_bb4_in: [1+X₁+X₄]
• eval_serpent_bb5_in: [1+X₁+X₄]
• eval_serpent_bb6_in: [1+X₁+X₄]

MPRF for transition t₈: eval_serpent_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₆ ≤ 0 ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₅ of depth 1:

new bound:

2⋅X₃+1 {O(n)}

MPRF:

• eval_serpent_10: [0]
• eval_serpent_11: [0]
• eval_serpent_2: [1]
• eval_serpent_3: [1]
• eval_serpent_7: [0]
• eval_serpent_8: [0]
• eval_serpent_9: [0]
• eval_serpent__critedge1_in: [0]
• eval_serpent__critedge_in: [0]
• eval_serpent_bb1_in: [1]
• eval_serpent_bb2_in: [1]
• eval_serpent_bb3_in: [1]
• eval_serpent_bb4_in: [0]
• eval_serpent_bb5_in: [0]
• eval_serpent_bb6_in: [0]

MPRF for transition t₁₂: eval_serpent_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0 ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆ of depth 1:

new bound:

2⋅X₃+1 {O(n)}

MPRF:

• eval_serpent_10: [-1]
• eval_serpent_11: [-1]
• eval_serpent_2: [1]
• eval_serpent_3: [1]
• eval_serpent_7: [-1]
• eval_serpent_8: [-1]
• eval_serpent_9: [-1]
• eval_serpent__critedge1_in: [-1]
• eval_serpent__critedge_in: [-1]
• eval_serpent_bb1_in: [1]
• eval_serpent_bb2_in: [1]
• eval_serpent_bb3_in: [1]
• eval_serpent_bb4_in: [-1]
• eval_serpent_bb5_in: [-1]
• eval_serpent_bb6_in: [-1]

MPRF for transition t₁₄: eval_serpent__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_7(X₀, X₄-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₅ of depth 1:

new bound:

2⋅X₃+1 {O(n)}

MPRF:

• eval_serpent_10: [0]
• eval_serpent_11: [0]
• eval_serpent_2: [1]
• eval_serpent_3: [1]
• eval_serpent_7: [0]
• eval_serpent_8: [0]
• eval_serpent_9: [0]
• eval_serpent__critedge1_in: [0]
• eval_serpent__critedge_in: [1]
• eval_serpent_bb1_in: [1]
• eval_serpent_bb2_in: [1]
• eval_serpent_bb3_in: [1]
• eval_serpent_bb4_in: [0]
• eval_serpent_bb5_in: [0]
• eval_serpent_bb6_in: [0]

MPRF for transition t₁₅: eval_serpent_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₅ of depth 1:

new bound:

2⋅X₃+1 {O(n)}

MPRF:

• eval_serpent_10: [0]
• eval_serpent_11: [0]
• eval_serpent_2: [1]
• eval_serpent_3: [1]
• eval_serpent_7: [1]
• eval_serpent_8: [0]
• eval_serpent_9: [0]
• eval_serpent__critedge1_in: [0]
• eval_serpent__critedge_in: [1]
• eval_serpent_bb1_in: [1]
• eval_serpent_bb2_in: [1]
• eval_serpent_bb3_in: [1]
• eval_serpent_bb4_in: [0]
• eval_serpent_bb5_in: [0]
• eval_serpent_bb6_in: [0]

MPRF for transition t₁₆: eval_serpent_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₅ of depth 1:

new bound:

2⋅X₃+1 {O(n)}

MPRF:

• eval_serpent_10: [0]
• eval_serpent_11: [0]
• eval_serpent_2: [1]
• eval_serpent_3: [1]
• eval_serpent_7: [1]
• eval_serpent_8: [1]
• eval_serpent_9: [0]
• eval_serpent__critedge1_in: [0]
• eval_serpent__critedge_in: [1]
• eval_serpent_bb1_in: [1]
• eval_serpent_bb2_in: [1]
• eval_serpent_bb3_in: [1]
• eval_serpent_bb4_in: [0]
• eval_serpent_bb5_in: [0]
• eval_serpent_bb6_in: [0]

MPRF for transition t₁₇: eval_serpent_9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₆) :|: 0 ≤ 2+X₅+X₆ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₅ of depth 1:

new bound:

2⋅X₃⋅X₃+X₃ {O(n^2)}

MPRF:

• eval_serpent_10: [X₃-1]
• eval_serpent_11: [X₃-1]
• eval_serpent_2: [X₃]
• eval_serpent_3: [X₃]
• eval_serpent_7: [X₃]
• eval_serpent_8: [X₃]
• eval_serpent_9: [X₃]
• eval_serpent__critedge1_in: [X₃-1]
• eval_serpent__critedge_in: [X₃]
• eval_serpent_bb1_in: [X₃]
• eval_serpent_bb2_in: [X₃]
• eval_serpent_bb3_in: [X₃]
• eval_serpent_bb4_in: [X₃-1]
• eval_serpent_bb5_in: [X₃-1]
• eval_serpent_bb6_in: [X₃-1]

MPRF for transition t₁₈: eval_serpent_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₇ ≤ X₃ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ of depth 1:

new bound:

2⋅X₃⋅X₃+5⋅X₃+2 {O(n^2)}

MPRF:

• eval_serpent_10: [1+X₃+X₆-X₇]
• eval_serpent_11: [1+X₃+X₆-X₇]
• eval_serpent_2: [2+X₃]
• eval_serpent_3: [2+X₃]
• eval_serpent_7: [2+X₃]
• eval_serpent_8: [2+X₃]
• eval_serpent_9: [2+X₃]
• eval_serpent__critedge1_in: [X₃+X₆-X₇]
• eval_serpent__critedge_in: [2+X₃]
• eval_serpent_bb1_in: [2+X₃]
• eval_serpent_bb2_in: [2+X₃]
• eval_serpent_bb3_in: [2+X₃]
• eval_serpent_bb4_in: [2+X₃+X₆-X₇]
• eval_serpent_bb5_in: [1+X₃+X₆-X₇]
• eval_serpent_bb6_in: [1+X₃+X₆-X₇]

MPRF for transition t₁₉: eval_serpent_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₁, X₇, X₆, X₇) :|: 1+X₃ ≤ X₇ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ of depth 1:

new bound:

2⋅X₃+1 {O(n)}

MPRF:

• eval_serpent_10: [1]
• eval_serpent_11: [1]
• eval_serpent_2: [1]
• eval_serpent_3: [1]
• eval_serpent_7: [1]
• eval_serpent_8: [1]
• eval_serpent_9: [1]
• eval_serpent__critedge1_in: [-1-2⋅X₅]
• eval_serpent__critedge_in: [1]
• eval_serpent_bb1_in: [1]
• eval_serpent_bb2_in: [1]
• eval_serpent_bb3_in: [1]
• eval_serpent_bb4_in: [1]
• eval_serpent_bb5_in: [1]
• eval_serpent_bb6_in: [1]

MPRF for transition t₂₀: eval_serpent_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ of depth 1:

new bound:

2⋅X₃⋅X₃+5⋅X₃+2 {O(n^2)}

MPRF:

• eval_serpent_10: [X₃-X₇]
• eval_serpent_11: [X₃-X₇]
• eval_serpent_2: [2+X₃]
• eval_serpent_3: [2+X₃]
• eval_serpent_7: [2+X₃]
• eval_serpent_8: [2+X₃]
• eval_serpent_9: [2+X₃]
• eval_serpent__critedge1_in: [X₃-X₇]
• eval_serpent__critedge_in: [2+X₃]
• eval_serpent_bb1_in: [2+X₃]
• eval_serpent_bb2_in: [2+X₃]
• eval_serpent_bb3_in: [2+X₃]
• eval_serpent_bb4_in: [1+X₃-X₇]
• eval_serpent_bb5_in: [1+X₃-X₇]
• eval_serpent_bb6_in: [X₃-X₇]

MPRF for transition t₂₁: eval_serpent_10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_11(X₀, X₁, nondef_1, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ of depth 1:

new bound:

4⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}

MPRF:

• eval_serpent_10: [1+2⋅X₃+X₆-X₇]
• eval_serpent_11: [2⋅X₃+X₆-X₇]
• eval_serpent_2: [1+2⋅X₃]
• eval_serpent_3: [1+2⋅X₃]
• eval_serpent_7: [1+2⋅X₃]
• eval_serpent_8: [1+2⋅X₃]
• eval_serpent_9: [1+2⋅X₃]
• eval_serpent__critedge1_in: [2⋅X₃+X₆-X₇]
• eval_serpent__critedge_in: [1+2⋅X₃]
• eval_serpent_bb1_in: [1+2⋅X₃]
• eval_serpent_bb2_in: [1+2⋅X₃]
• eval_serpent_bb3_in: [1+2⋅X₃]
• eval_serpent_bb4_in: [1+2⋅X₃+X₆-X₇]
• eval_serpent_bb5_in: [1+2⋅X₃+X₆-X₇]
• eval_serpent_bb6_in: [2⋅X₃+X₆-X₇]

MPRF for transition t₂₂: eval_serpent_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₂ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ of depth 1:

new bound:

2⋅X₃⋅X₃+5⋅X₃+2 {O(n^2)}

MPRF:

• eval_serpent_10: [1+X₃-X₇]
• eval_serpent_11: [1+X₃-X₇]
• eval_serpent_2: [2+X₃]
• eval_serpent_3: [2+X₃]
• eval_serpent_7: [2+X₃]
• eval_serpent_8: [2+X₃]
• eval_serpent_9: [2+X₃]
• eval_serpent__critedge1_in: [X₃-X₇]
• eval_serpent__critedge_in: [2+X₃]
• eval_serpent_bb1_in: [2+X₃]
• eval_serpent_bb2_in: [2+X₃]
• eval_serpent_bb3_in: [2+X₃]
• eval_serpent_bb4_in: [1+X₃-X₇]
• eval_serpent_bb5_in: [1+X₃-X₇]
• eval_serpent_bb6_in: [X₃-X₇]

MPRF for transition t₂₃: eval_serpent_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₁, X₇, X₆, X₇) :|: X₂ ≤ 0 ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ of depth 1:

new bound:

2⋅X₃+1 {O(n)}

MPRF:

• eval_serpent_10: [1]
• eval_serpent_11: [1]
• eval_serpent_2: [1]
• eval_serpent_3: [1]
• eval_serpent_7: [1]
• eval_serpent_8: [1]
• eval_serpent_9: [1]
• eval_serpent__critedge1_in: [0]
• eval_serpent__critedge_in: [1]
• eval_serpent_bb1_in: [1]
• eval_serpent_bb2_in: [1]
• eval_serpent_bb3_in: [1]
• eval_serpent_bb4_in: [1]
• eval_serpent_bb5_in: [1]
• eval_serpent_bb6_in: [1]

MPRF for transition t₂₄: eval_serpent_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 1+X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ X₂+X₇ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ of depth 1:

new bound:

2⋅X₃⋅X₃+5⋅X₃+2 {O(n^2)}

MPRF:

knowledge_propagation leads to new time bound 2⋅X₃+1 {O(n)} for transition t₁₇: eval_serpent_9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₆) :|: 0 ≤ 2+X₅+X₆ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₅

MPRF for transition t₇: eval_serpent_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₅ of depth 1:

new bound:

8⋅X₃⋅X₃⋅X₃+28⋅X₃⋅X₃+33⋅X₃+11 {O(n^3)}

MPRF:

• eval_serpent_10: [1+X₁-X₃-X₄]
• eval_serpent_11: [1+X₁-X₃-X₄]
• eval_serpent_2: [X₆]
• eval_serpent_3: [X₆]
• eval_serpent_7: [X₆]
• eval_serpent_8: [X₆]
• eval_serpent_9: [X₆]
• eval_serpent__critedge1_in: [1+X₅]
• eval_serpent__critedge_in: [X₆]
• eval_serpent_bb1_in: [1+X₆]
• eval_serpent_bb2_in: [X₆]
• eval_serpent_bb3_in: [X₆]
• eval_serpent_bb4_in: [-X₃]
• eval_serpent_bb5_in: [1+X₁-X₃-X₄]
• eval_serpent_bb6_in: [1+X₁-X₃-X₄]

MPRF for transition t₉: eval_serpent_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆ of depth 1:

new bound:

8⋅X₃⋅X₃⋅X₃+52⋅X₃⋅X₃+55⋅X₃+15 {O(n^3)}

MPRF:

• eval_serpent_10: [X₄+X₆-1-X₁]
• eval_serpent_11: [X₄+X₆-1-X₁]
• eval_serpent_2: [X₆]
• eval_serpent_3: [X₆]
• eval_serpent_7: [X₆]
• eval_serpent_8: [X₆]
• eval_serpent_9: [X₆]
• eval_serpent__critedge1_in: [1+2⋅X₄+X₅]
• eval_serpent__critedge_in: [X₆]
• eval_serpent_bb1_in: [1+X₆]
• eval_serpent_bb2_in: [1+X₆]
• eval_serpent_bb3_in: [X₆]
• eval_serpent_bb4_in: [X₆]
• eval_serpent_bb5_in: [X₆]
• eval_serpent_bb6_in: [X₄+X₆-1-X₁]

MPRF for transition t₁₀: eval_serpent_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_3(nondef_0, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆ of depth 1:

new bound:

8⋅X₃⋅X₃⋅X₃+52⋅X₃⋅X₃+55⋅X₃+15 {O(n^3)}

MPRF:

• eval_serpent_10: [X₄+X₆-1-X₁]
• eval_serpent_11: [X₄+X₆-1-X₁]
• eval_serpent_2: [1+X₆]
• eval_serpent_3: [X₆]
• eval_serpent_7: [X₆]
• eval_serpent_8: [X₆]
• eval_serpent_9: [X₆]
• eval_serpent__critedge1_in: [1+2⋅X₄+X₅]
• eval_serpent__critedge_in: [X₆]
• eval_serpent_bb1_in: [1+X₆]
• eval_serpent_bb2_in: [1+X₆]
• eval_serpent_bb3_in: [X₆]
• eval_serpent_bb4_in: [X₆]
• eval_serpent_bb5_in: [X₆]
• eval_serpent_bb6_in: [X₄+X₆-1-X₁]

MPRF for transition t₁₁: eval_serpent_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆ of depth 1:

new bound:

4⋅X₃⋅X₃⋅X₃⋅X₃+22⋅X₃⋅X₃⋅X₃+44⋅X₃⋅X₃+38⋅X₃+11 {O(n^4)}

MPRF:

• eval_serpent_10: [1+X₇]
• eval_serpent_11: [1+X₇]
• eval_serpent_2: [1+X₆]
• eval_serpent_3: [1+X₆]
• eval_serpent_7: [1+X₆]
• eval_serpent_8: [1+X₆]
• eval_serpent_9: [1+X₆]
• eval_serpent__critedge1_in: [1+X₅]
• eval_serpent__critedge_in: [1+X₆]
• eval_serpent_bb1_in: [1+X₆]
• eval_serpent_bb2_in: [1+X₆]
• eval_serpent_bb3_in: [X₆]
• eval_serpent_bb4_in: [1+X₇]
• eval_serpent_bb5_in: [1+X₇]
• eval_serpent_bb6_in: [1+X₇]

MPRF for transition t₁₃: eval_serpent_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆ of depth 1:

new bound:

4⋅X₃⋅X₃⋅X₃⋅X₃+40⋅X₃⋅X₃⋅X₃+93⋅X₃⋅X₃+66⋅X₃+15 {O(n^4)}

MPRF:

• eval_serpent_10: [X₄+X₇-X₁]
• eval_serpent_11: [X₄+X₇-X₁]
• eval_serpent_2: [1+X₆]
• eval_serpent_3: [1+X₆]
• eval_serpent_7: [1+X₆]
• eval_serpent_8: [1+X₆]
• eval_serpent_9: [X₄+X₆-X₁]
• eval_serpent__critedge1_in: [1+X₅]
• eval_serpent__critedge_in: [1+X₆]
• eval_serpent_bb1_in: [1+X₆]
• eval_serpent_bb2_in: [1+X₆]
• eval_serpent_bb3_in: [1+X₆]
• eval_serpent_bb4_in: [X₄+X₇-X₁]
• eval_serpent_bb5_in: [X₄+X₇-X₁]
• eval_serpent_bb6_in: [X₄+X₇-X₁]

knowledge_propagation leads to new time bound 8⋅X₃⋅X₃⋅X₃+52⋅X₃⋅X₃+55⋅X₃+15 {O(n^3)} for transition t₁₁: eval_serpent_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆

knowledge_propagation leads to new time bound 8⋅X₃⋅X₃⋅X₃+52⋅X₃⋅X₃+55⋅X₃+15 {O(n^3)} for transition t₁₃: eval_serpent_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆

Cut unreachable locations [eval_serpent_11; eval_serpent_3] from the program graph

Found invariant 1+X₆ ≤ X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₀+X₆ ∧ 0 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₀ for location eval_serpent_bb1_in_v1

Found invariant X₇ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₃ ∧ 0 ≤ 1+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₆ ≤ X₇ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ X₃+X₇ ∧ 0 ≤ X₂+X₇ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₃ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ for location eval_serpent_bb6_in_v1

Found invariant X₇ ≤ 1+X₃ ∧ 0 ≤ X₇ ∧ 0 ≤ 1+X₆+X₇ ∧ 1+X₆ ≤ X₇ ∧ 0 ≤ 1+X₅+X₇ ∧ 1 ≤ X₃+X₇ ∧ 1 ≤ X₂+X₇ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₃ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ for location eval_serpent_bb4_in_v1

Found invariant 1+X₆ ≤ X₅ ∧ 0 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₀ for location eval_serpent_bb3_in_v2

Found invariant X₆ ≤ X₅ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₄+X₆ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₀ for location eval_serpent_bb3_in_v1

Found invariant X₇ ≤ X₃ ∧ 0 ≤ X₇ ∧ 0 ≤ 1+X₆+X₇ ∧ 1+X₆ ≤ X₇ ∧ 0 ≤ 1+X₅+X₇ ∧ 1 ≤ X₃+X₇ ∧ 1 ≤ X₂+X₇ ∧ X₆ ≤ X₅ ∧ 1+X₆ ≤ X₃ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ for location eval_serpent_10_v2

Found invariant X₆ ≤ X₅ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₄+X₆ ∧ 1 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃ for location eval_serpent_2_v1

Found invariant 1+X₆ ≤ X₅ ∧ 0 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₀ for location eval_serpent_bb2_in_v2

Found invariant X₆ ≤ X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ 1+X₄+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃ for location eval_serpent_bb1_in

Found invariant X₆ ≤ X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₃ for location eval_serpent__critedge_in

Found invariant X₆ ≤ X₅ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₄+X₆ ∧ 1 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃ for location eval_serpent_bb2_in_v1

Found invariant X₇ ≤ X₆ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₃ ∧ 0 ≤ 1+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₆ ≤ X₇ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₃ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₃ for location eval_serpent_10_v1

Found invariant X₇ ≤ X₃ ∧ 0 ≤ X₇ ∧ 0 ≤ 1+X₆+X₇ ∧ 1+X₆ ≤ X₇ ∧ 0 ≤ 1+X₅+X₇ ∧ 1 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ 1+X₆ ≤ X₃ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₃ for location eval_serpent_11_v2

Found invariant 1+X₆ ≤ X₅ ∧ 0 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₀ for location eval_serpent_2_v2

Found invariant 1+X₆ ≤ X₅ ∧ 0 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₃ for location eval_serpent_3_v2

Found invariant X₇ ≤ X₆ ∧ X₇ ≤ X₅ ∧ 0 ≤ 1+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₆ ≤ X₇ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₃ for location eval_serpent_bb4_in

Found invariant X₆ ≤ X₅ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₄+X₆ ∧ 1 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃ for location eval_serpent_3_v1

Found invariant 0 ≤ 1+X₅ ∧ 0 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₃ for location eval_serpent__critedge1_in

Analysing control-flow refined program

knowledge_propagation leads to new time bound 2⋅X₃+1 {O(n)} for transition t₁₃₅: eval_serpent_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb2_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 1+X₄+X₅ ∧ 0 ≤ 1+X₄+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₄ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆

knowledge_propagation leads to new time bound 2⋅X₃+1 {O(n)} for transition t₁₃₆: eval_serpent_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₆ ≤ 0 ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 1+X₄+X₅ ∧ 0 ≤ 1+X₄+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₄ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆

knowledge_propagation leads to new time bound 2⋅X₃+1 {O(n)} for transition t₁₃₇: eval_serpent_bb2_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_2_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₄+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆

knowledge_propagation leads to new time bound 2⋅X₃+1 {O(n)} for transition t₁₃₈: eval_serpent_2_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_3_v1(nondef_0, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₄+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆

knowledge_propagation leads to new time bound 2⋅X₃+1 {O(n)} for transition t₁₃₉: eval_serpent_3_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb3_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₄+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆

knowledge_propagation leads to new time bound 2⋅X₃+1 {O(n)} for transition t₁₄₀: eval_serpent_3_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0 ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₄+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆

knowledge_propagation leads to new time bound 2⋅X₃+1 {O(n)} for transition t₁₄₁: eval_serpent_bb3_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb1_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₄+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆

knowledge_propagation leads to new time bound 2⋅X₃+1 {O(n)} for transition t₁₄₉: eval_serpent_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb5_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₇ ≤ X₃ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇

knowledge_propagation leads to new time bound 2⋅X₃+1 {O(n)} for transition t₁₅₀: eval_serpent_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₁, X₇, X₆, X₇) :|: 1+X₃ ≤ X₇ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇

knowledge_propagation leads to new time bound 2⋅X₃+1 {O(n)} for transition t₁₅₁: eval_serpent_bb5_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_10_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇

knowledge_propagation leads to new time bound 2⋅X₃+1 {O(n)} for transition t₁₅₂: eval_serpent_10_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_11_v1(X₀, X₁, nondef_1, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇

knowledge_propagation leads to new time bound 2⋅X₃+1 {O(n)} for transition t₁₅₃: eval_serpent_11_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb6_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₂ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇

knowledge_propagation leads to new time bound 2⋅X₃+1 {O(n)} for transition t₁₅₄: eval_serpent_11_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₁, X₇, X₆, X₇) :|: X₂ ≤ 0 ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇

knowledge_propagation leads to new time bound 2⋅X₃+1 {O(n)} for transition t₁₅₅: eval_serpent_bb6_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb4_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 1+X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ X₂+X₇ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇

MPRF for transition t₁₄₂: eval_serpent_bb1_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb2_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₆ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1+X₆ ≤ X₅ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ X₆ ≤ X₅ of depth 1:

new bound:

2⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}

MPRF:

• eval_serpent_10_v1: [X₇]
• eval_serpent_10_v2: [1+X₃]
• eval_serpent_11_v1: [X₇]
• eval_serpent_11_v2: [1+X₃]
• eval_serpent_2_v1: [X₆]
• eval_serpent_2_v2: [X₆]
• eval_serpent_3_v1: [X₅]
• eval_serpent_3_v2: [X₆]
• eval_serpent_7: [X₆]
• eval_serpent_8: [X₆]
• eval_serpent_9: [X₆]
• eval_serpent__critedge1_in: [X₅]
• eval_serpent__critedge_in: [X₆]
• eval_serpent_bb1_in: [X₆]
• eval_serpent_bb1_in_v1: [1+X₆]
• eval_serpent_bb2_in_v1: [X₅]
• eval_serpent_bb2_in_v2: [X₆]
• eval_serpent_bb3_in_v1: [2⋅X₆-X₅]
• eval_serpent_bb3_in_v2: [X₆]
• eval_serpent_bb4_in: [X₇]
• eval_serpent_bb4_in_v1: [1+X₃]
• eval_serpent_bb5_in_v1: [X₇]
• eval_serpent_bb5_in_v2: [1+X₃]
• eval_serpent_bb6_in_v1: [X₇]
• eval_serpent_bb6_in_v2: [1+X₃]

MPRF for transition t₁₄₃: eval_serpent_bb1_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₆ ≤ 0 ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₆ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1+X₆ ≤ X₅ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ X₆ ≤ X₅ of depth 1:

new bound:

94⋅X₃⋅X₃+78⋅X₃+17 {O(n^2)}

MPRF:

• eval_serpent_10_v1: [2+X₇]
• eval_serpent_10_v2: [2⋅X₃+5⋅X₄-5⋅X₁]
• eval_serpent_11_v1: [2+X₇]
• eval_serpent_11_v2: [1+2⋅X₃+4⋅X₄-4⋅X₁]
• eval_serpent_2_v1: [2+X₅]
• eval_serpent_2_v2: [2+X₅]
• eval_serpent_3_v1: [2+X₆]
• eval_serpent_3_v2: [2+X₅]
• eval_serpent_7: [2+X₆]
• eval_serpent_8: [2+X₆]
• eval_serpent_9: [2+X₆]
• eval_serpent__critedge1_in: [2+X₅]
• eval_serpent__critedge_in: [2+X₆]
• eval_serpent_bb1_in: [2+X₆]
• eval_serpent_bb1_in_v1: [2+X₅]
• eval_serpent_bb2_in_v1: [2+X₆]
• eval_serpent_bb2_in_v2: [2+X₅]
• eval_serpent_bb3_in_v1: [2+X₅]
• eval_serpent_bb3_in_v2: [2+X₅]
• eval_serpent_bb4_in: [2+X₇]
• eval_serpent_bb4_in_v1: [2⋅X₃+5⋅X₄-5⋅X₁]
• eval_serpent_bb5_in_v1: [2+X₇]
• eval_serpent_bb5_in_v2: [2⋅X₃+5⋅X₄-5⋅X₁]
• eval_serpent_bb6_in_v1: [2+X₇]
• eval_serpent_bb6_in_v2: [1+2⋅X₃+4⋅X₄-4⋅X₁]

MPRF for transition t₁₄₄: eval_serpent_bb2_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_2_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₅+X₆ ∧ 1+X₆ ≤ X₅ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆ of depth 1:

new bound:

20⋅X₃⋅X₃+17⋅X₃+3 {O(n^2)}

MPRF:

• eval_serpent_10_v1: [X₆]
• eval_serpent_10_v2: [X₃+X₄-X₁]
• eval_serpent_11_v1: [X₆]
• eval_serpent_11_v2: [X₃+X₄-X₁]
• eval_serpent_2_v1: [X₅]
• eval_serpent_2_v2: [X₆]
• eval_serpent_3_v1: [X₆]
• eval_serpent_3_v2: [X₆]
• eval_serpent_7: [X₆]
• eval_serpent_8: [X₆]
• eval_serpent_9: [X₆]
• eval_serpent__critedge1_in: [X₅]
• eval_serpent__critedge_in: [X₆]
• eval_serpent_bb1_in: [X₅]
• eval_serpent_bb1_in_v1: [1+X₆]
• eval_serpent_bb2_in_v1: [X₆]
• eval_serpent_bb2_in_v2: [1+X₆]
• eval_serpent_bb3_in_v1: [X₅]
• eval_serpent_bb3_in_v2: [X₆]
• eval_serpent_bb4_in: [X₆]
• eval_serpent_bb4_in_v1: [X₃+X₄-X₁]
• eval_serpent_bb5_in_v1: [X₆]
• eval_serpent_bb5_in_v2: [X₃+X₄-X₁]
• eval_serpent_bb6_in_v1: [3⋅X₇-2⋅X₆]
• eval_serpent_bb6_in_v2: [X₃+X₄-X₁]

MPRF for transition t₁₄₅: eval_serpent_2_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_3_v2(nondef_0, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₅+X₆ ∧ 1+X₆ ≤ X₅ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆ of depth 1:

new bound:

2⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}

MPRF:

• eval_serpent_10_v1: [X₇]
• eval_serpent_10_v2: [1+X₃]
• eval_serpent_11_v1: [X₇]
• eval_serpent_11_v2: [1+X₃]
• eval_serpent_2_v1: [X₆]
• eval_serpent_2_v2: [1+X₆]
• eval_serpent_3_v1: [X₅]
• eval_serpent_3_v2: [X₆]
• eval_serpent_7: [X₆]
• eval_serpent_8: [X₆]
• eval_serpent_9: [X₆]
• eval_serpent__critedge1_in: [X₅]
• eval_serpent__critedge_in: [X₆]
• eval_serpent_bb1_in: [X₆]
• eval_serpent_bb1_in_v1: [1+X₆]
• eval_serpent_bb2_in_v1: [X₆]
• eval_serpent_bb2_in_v2: [1+X₆]
• eval_serpent_bb3_in_v1: [X₆]
• eval_serpent_bb3_in_v2: [X₆]
• eval_serpent_bb4_in: [X₇]
• eval_serpent_bb4_in_v1: [1+X₃]
• eval_serpent_bb5_in_v1: [X₇]
• eval_serpent_bb5_in_v2: [1+X₃]
• eval_serpent_bb6_in_v1: [X₇]
• eval_serpent_bb6_in_v2: [1+X₃]

MPRF for transition t₁₄₆: eval_serpent_3_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb3_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₅+X₆ ∧ 1+X₆ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆ of depth 1:

new bound:

2⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}

MPRF:

• eval_serpent_10_v1: [X₇]
• eval_serpent_10_v2: [1+X₃]
• eval_serpent_11_v1: [X₇]
• eval_serpent_11_v2: [1+X₃]
• eval_serpent_2_v1: [X₅]
• eval_serpent_2_v2: [1+X₆]
• eval_serpent_3_v1: [X₆]
• eval_serpent_3_v2: [1+X₆]
• eval_serpent_7: [X₆]
• eval_serpent_8: [X₆]
• eval_serpent_9: [X₆]
• eval_serpent__critedge1_in: [X₅]
• eval_serpent__critedge_in: [X₆]
• eval_serpent_bb1_in: [X₆]
• eval_serpent_bb1_in_v1: [1+X₆]
• eval_serpent_bb2_in_v1: [X₅]
• eval_serpent_bb2_in_v2: [1+X₆]
• eval_serpent_bb3_in_v1: [X₅]
• eval_serpent_bb3_in_v2: [X₆]
• eval_serpent_bb4_in: [X₇]
• eval_serpent_bb4_in_v1: [1+X₃]
• eval_serpent_bb5_in_v1: [X₇]
• eval_serpent_bb5_in_v2: [1+X₃]
• eval_serpent_bb6_in_v1: [X₇]
• eval_serpent_bb6_in_v2: [1+X₃]

MPRF for transition t₁₄₇: eval_serpent_3_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0 ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₅+X₆ ∧ 1+X₆ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆ of depth 1:

new bound:

2⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}

MPRF:

• eval_serpent_10_v1: [X₆]
• eval_serpent_10_v2: [1+X₃]
• eval_serpent_11_v1: [X₆]
• eval_serpent_11_v2: [1+X₃]
• eval_serpent_2_v1: [X₅]
• eval_serpent_2_v2: [X₅]
• eval_serpent_3_v1: [X₅]
• eval_serpent_3_v2: [X₅]
• eval_serpent_7: [X₆]
• eval_serpent_8: [X₆]
• eval_serpent_9: [X₆]
• eval_serpent__critedge1_in: [X₅]
• eval_serpent__critedge_in: [X₆]
• eval_serpent_bb1_in: [X₆]
• eval_serpent_bb1_in_v1: [X₅]
• eval_serpent_bb2_in_v1: [X₆]
• eval_serpent_bb2_in_v2: [X₅]
• eval_serpent_bb3_in_v1: [X₆]
• eval_serpent_bb3_in_v2: [X₅]
• eval_serpent_bb4_in: [X₆]
• eval_serpent_bb4_in_v1: [1+X₃]
• eval_serpent_bb5_in_v1: [X₆]
• eval_serpent_bb5_in_v2: [1+X₃]
• eval_serpent_bb6_in_v1: [1+X₁+X₇-X₄]
• eval_serpent_bb6_in_v2: [1+X₃]

MPRF for transition t₁₄₈: eval_serpent_bb3_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb1_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₅+X₆ ∧ 1+X₆ ≤ X₅ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆ of depth 1:

new bound:

2⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}

MPRF:

• eval_serpent_10_v1: [X₆]
• eval_serpent_10_v2: [1+X₃]
• eval_serpent_11_v1: [X₆]
• eval_serpent_11_v2: [1+X₃]
• eval_serpent_2_v1: [X₆]
• eval_serpent_2_v2: [1+X₆]
• eval_serpent_3_v1: [X₅]
• eval_serpent_3_v2: [1+X₆]
• eval_serpent_7: [X₆]
• eval_serpent_8: [X₆]
• eval_serpent_9: [X₆]
• eval_serpent__critedge1_in: [X₅]
• eval_serpent__critedge_in: [X₆]
• eval_serpent_bb1_in: [X₆]
• eval_serpent_bb1_in_v1: [1+X₆]
• eval_serpent_bb2_in_v1: [X₆]
• eval_serpent_bb2_in_v2: [1+X₆]
• eval_serpent_bb3_in_v1: [X₆]
• eval_serpent_bb3_in_v2: [1+X₆]
• eval_serpent_bb4_in: [X₆]
• eval_serpent_bb4_in_v1: [1+X₃]
• eval_serpent_bb5_in_v1: [X₆]
• eval_serpent_bb5_in_v2: [1+X₃]
• eval_serpent_bb6_in_v1: [X₆]
• eval_serpent_bb6_in_v2: [1+X₃]

MPRF for transition t₁₅₆: eval_serpent_bb4_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb5_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₇ ≤ X₃ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ X₇ ≤ 1+X₃ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₇ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₆+X₇ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₇ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₆ ≤ X₇ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ ∧ 0 ≤ X₇ of depth 1:

new bound:

4⋅X₃⋅X₃+4⋅X₃+2 {O(n^2)}

MPRF:

• eval_serpent_10_v1: [1]
• eval_serpent_10_v2: [1+X₃-X₇]
• eval_serpent_11_v1: [1]
• eval_serpent_11_v2: [1+X₃-X₇]
• eval_serpent_2_v1: [1]
• eval_serpent_2_v2: [1]
• eval_serpent_3_v1: [1]
• eval_serpent_3_v2: [1]
• eval_serpent_7: [1]
• eval_serpent_8: [1]
• eval_serpent_9: [1]
• eval_serpent__critedge1_in: [1]
• eval_serpent__critedge_in: [1]
• eval_serpent_bb1_in: [1]
• eval_serpent_bb1_in_v1: [1]
• eval_serpent_bb2_in_v1: [1]
• eval_serpent_bb2_in_v2: [1]
• eval_serpent_bb3_in_v1: [1]
• eval_serpent_bb3_in_v2: [1]
• eval_serpent_bb4_in: [1]
• eval_serpent_bb4_in_v1: [2+X₃-X₇]
• eval_serpent_bb5_in_v1: [1]
• eval_serpent_bb5_in_v2: [1+X₃-X₇]
• eval_serpent_bb6_in_v1: [1+2⋅X₃]
• eval_serpent_bb6_in_v2: [1+X₃-X₇]

MPRF for transition t₁₅₇: eval_serpent_bb4_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₁, X₇, X₆, X₇) :|: 1+X₃ ≤ X₇ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ X₇ ≤ 1+X₃ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₇ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₆+X₇ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₇ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₆ ≤ X₇ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ ∧ 0 ≤ X₇ of depth 1:

new bound:

2⋅X₃+1 {O(n)}

MPRF:

• eval_serpent_10_v1: [1+X₁-X₄]
• eval_serpent_10_v2: [1]
• eval_serpent_11_v1: [1+X₁-X₄]
• eval_serpent_11_v2: [1]
• eval_serpent_2_v1: [0]
• eval_serpent_2_v2: [0]
• eval_serpent_3_v1: [0]
• eval_serpent_3_v2: [0]
• eval_serpent_7: [0]
• eval_serpent_8: [0]
• eval_serpent_9: [0]
• eval_serpent__critedge1_in: [0]
• eval_serpent__critedge_in: [0]
• eval_serpent_bb1_in: [0]
• eval_serpent_bb1_in_v1: [0]
• eval_serpent_bb2_in_v1: [0]
• eval_serpent_bb2_in_v2: [0]
• eval_serpent_bb3_in_v1: [0]
• eval_serpent_bb3_in_v2: [0]
• eval_serpent_bb4_in: [0]
• eval_serpent_bb4_in_v1: [1]
• eval_serpent_bb5_in_v1: [0]
• eval_serpent_bb5_in_v2: [1]
• eval_serpent_bb6_in_v1: [1+X₁-X₄]
• eval_serpent_bb6_in_v2: [1]

MPRF for transition t₁₅₈: eval_serpent_bb5_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_10_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₇ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₆+X₇ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₇ ∧ 1 ≤ X₃ ∧ 1+X₆ ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₆ ≤ X₇ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ ∧ 0 ≤ X₇ of depth 1:

new bound:

4⋅X₃⋅X₃+2⋅X₃ {O(n^2)}

MPRF:

• eval_serpent_10_v1: [0]
• eval_serpent_10_v2: [X₃-X₇]
• eval_serpent_11_v1: [0]
• eval_serpent_11_v2: [X₃-X₇]
• eval_serpent_2_v1: [0]
• eval_serpent_2_v2: [0]
• eval_serpent_3_v1: [0]
• eval_serpent_3_v2: [0]
• eval_serpent_7: [0]
• eval_serpent_8: [0]
• eval_serpent_9: [0]
• eval_serpent__critedge1_in: [0]
• eval_serpent__critedge_in: [0]
• eval_serpent_bb1_in: [X₅-X₆]
• eval_serpent_bb1_in_v1: [0]
• eval_serpent_bb2_in_v1: [0]
• eval_serpent_bb2_in_v2: [0]
• eval_serpent_bb3_in_v1: [0]
• eval_serpent_bb3_in_v2: [0]
• eval_serpent_bb4_in: [0]
• eval_serpent_bb4_in_v1: [1+X₃-X₇]
• eval_serpent_bb5_in_v1: [0]
• eval_serpent_bb5_in_v2: [1+X₃-X₇]
• eval_serpent_bb6_in_v1: [2⋅X₃]
• eval_serpent_bb6_in_v2: [X₃-X₇]

MPRF for transition t₁₅₉: eval_serpent_10_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_11_v2(X₀, X₁, nondef_1, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₇ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₆+X₇ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₇ ∧ 1 ≤ X₃ ∧ 1+X₆ ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₆ ≤ X₇ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ ∧ 0 ≤ X₇ of depth 1:

new bound:

4⋅X₃⋅X₃⋅X₃+20⋅X₃⋅X₃+17⋅X₃+5 {O(n^3)}

MPRF:

• eval_serpent_10_v1: [-1]
• eval_serpent_10_v2: [1+2⋅X₃+X₆-X₇]
• eval_serpent_11_v1: [2⋅X₄-3-2⋅X₁]
• eval_serpent_11_v2: [2⋅X₃+X₆-X₇]
• eval_serpent_2_v1: [-1]
• eval_serpent_2_v2: [-1]
• eval_serpent_3_v1: [-1]
• eval_serpent_3_v2: [-1]
• eval_serpent_7: [-1]
• eval_serpent_8: [-1]
• eval_serpent_9: [-1]
• eval_serpent__critedge1_in: [-1]
• eval_serpent__critedge_in: [-1]
• eval_serpent_bb1_in: [-1]
• eval_serpent_bb1_in_v1: [-1]
• eval_serpent_bb2_in_v1: [-1]
• eval_serpent_bb2_in_v2: [-1]
• eval_serpent_bb3_in_v1: [-1]
• eval_serpent_bb3_in_v2: [-1]
• eval_serpent_bb4_in: [-1]
• eval_serpent_bb4_in_v1: [1+2⋅X₃+X₆-X₇]
• eval_serpent_bb5_in_v1: [-1]
• eval_serpent_bb5_in_v2: [1+2⋅X₃+X₆-X₇]
• eval_serpent_bb6_in_v1: [3⋅X₃+X₆]
• eval_serpent_bb6_in_v2: [2⋅X₃+X₆-X₇]

MPRF for transition t₁₆₀: eval_serpent_11_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb6_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₂ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₇ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₆+X₇ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₆ ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₆ ≤ X₇ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ ∧ 0 ≤ X₇ of depth 1:

new bound:

8⋅X₃⋅X₃+6⋅X₃+1 {O(n^2)}

MPRF:

• eval_serpent_10_v1: [2⋅X₃-1]
• eval_serpent_10_v2: [3⋅X₃-X₇]
• eval_serpent_11_v1: [2⋅X₃-1]
• eval_serpent_11_v2: [3⋅X₃-X₇]
• eval_serpent_2_v1: [2⋅X₃-1]
• eval_serpent_2_v2: [2⋅X₃-1]
• eval_serpent_3_v1: [2⋅X₃-1]
• eval_serpent_3_v2: [2⋅X₃-1]
• eval_serpent_7: [2⋅X₃-1]
• eval_serpent_8: [2⋅X₃-1]
• eval_serpent_9: [2⋅X₃-1]
• eval_serpent__critedge1_in: [2⋅X₃-1]
• eval_serpent__critedge_in: [2⋅X₃-1]
• eval_serpent_bb1_in: [2⋅X₃+X₆-1-X₅]
• eval_serpent_bb1_in_v1: [2⋅X₃-1]
• eval_serpent_bb2_in_v1: [2⋅X₃-1]
• eval_serpent_bb2_in_v2: [2⋅X₃-1]
• eval_serpent_bb3_in_v1: [2⋅X₃-1]
• eval_serpent_bb3_in_v2: [2⋅X₃-1]
• eval_serpent_bb4_in: [2⋅X₃-1]
• eval_serpent_bb4_in_v1: [3⋅X₃-X₇]
• eval_serpent_bb5_in_v1: [2⋅X₃-1]
• eval_serpent_bb5_in_v2: [3⋅X₃-X₇]
• eval_serpent_bb6_in_v1: [4⋅X₃]
• eval_serpent_bb6_in_v2: [3⋅X₃-1-X₇]

MPRF for transition t₁₆₁: eval_serpent_11_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₁, X₇, X₆, X₇) :|: X₂ ≤ 0 ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₇ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₆+X₇ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₆ ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₆ ≤ X₇ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ ∧ 0 ≤ X₇ of depth 1:

new bound:

4⋅X₃+3 {O(n)}

MPRF:

• eval_serpent_10_v1: [1]
• eval_serpent_10_v2: [2]
• eval_serpent_11_v1: [1]
• eval_serpent_11_v2: [2]
• eval_serpent_2_v1: [1]
• eval_serpent_2_v2: [1]
• eval_serpent_3_v1: [1]
• eval_serpent_3_v2: [1]
• eval_serpent_7: [1]
• eval_serpent_8: [1]
• eval_serpent_9: [1]
• eval_serpent__critedge1_in: [1]
• eval_serpent__critedge_in: [1]
• eval_serpent_bb1_in: [1]
• eval_serpent_bb1_in_v1: [1]
• eval_serpent_bb2_in_v1: [1]
• eval_serpent_bb2_in_v2: [1]
• eval_serpent_bb3_in_v1: [1]
• eval_serpent_bb3_in_v2: [1]
• eval_serpent_bb4_in: [1]
• eval_serpent_bb4_in_v1: [2]
• eval_serpent_bb5_in_v1: [1]
• eval_serpent_bb5_in_v2: [2]
• eval_serpent_bb6_in_v1: [1]
• eval_serpent_bb6_in_v2: [2]

MPRF for transition t₁₆₂: eval_serpent_bb6_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb4_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 1+X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₇ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₆+X₇ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₇ ∧ 1 ≤ X₃ ∧ 1+X₆ ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₆ ≤ X₇ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ X₂+X₇ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ ∧ 0 ≤ X₇ of depth 1:

new bound:

8⋅X₃⋅X₃+6⋅X₃ {O(n^2)}

MPRF:

• eval_serpent_10_v1: [2⋅X₃]
• eval_serpent_10_v2: [1+3⋅X₃-X₇]
• eval_serpent_11_v1: [2⋅X₃]
• eval_serpent_11_v2: [1+3⋅X₃-X₇]
• eval_serpent_2_v1: [2⋅X₃]
• eval_serpent_2_v2: [2⋅X₃]
• eval_serpent_3_v1: [2⋅X₃]
• eval_serpent_3_v2: [2⋅X₃]
• eval_serpent_7: [2⋅X₃]
• eval_serpent_8: [2⋅X₃]
• eval_serpent_9: [2⋅X₃]
• eval_serpent__critedge1_in: [2⋅X₃]
• eval_serpent__critedge_in: [2⋅X₃]
• eval_serpent_bb1_in: [2⋅X₃]
• eval_serpent_bb1_in_v1: [2⋅X₃]
• eval_serpent_bb2_in_v1: [2⋅X₃]
• eval_serpent_bb2_in_v2: [2⋅X₃]
• eval_serpent_bb3_in_v1: [2⋅X₃]
• eval_serpent_bb3_in_v2: [2⋅X₃]
• eval_serpent_bb4_in: [2⋅X₃]
• eval_serpent_bb4_in_v1: [1+3⋅X₃-X₇]
• eval_serpent_bb5_in_v1: [2⋅X₃]
• eval_serpent_bb5_in_v2: [1+3⋅X₃-X₇]
• eval_serpent_bb6_in_v1: [4⋅X₃]
• eval_serpent_bb6_in_v2: [1+3⋅X₃-X₇]

knowledge_propagation leads to new time bound 4⋅X₃⋅X₃+2⋅X₃ {O(n^2)} for transition t₁₅₉: eval_serpent_10_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_11_v2(X₀, X₁, nondef_1, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₇ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₆+X₇ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₇ ∧ 1 ≤ X₃ ∧ 1+X₆ ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₆ ≤ X₇ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ ∧ 0 ≤ X₇

CFR: Improvement to new bound with the following program:

method: PartialEvaluation new bound:

O(n^2)

cfr-program:

Start: eval_serpent_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: nondef_0, nondef_1
Locations: eval_serpent_0, eval_serpent_1, eval_serpent_10_v1, eval_serpent_10_v2, eval_serpent_11_v1, eval_serpent_11_v2, eval_serpent_2_v1, eval_serpent_2_v2, eval_serpent_3_v1, eval_serpent_3_v2, eval_serpent_7, eval_serpent_8, eval_serpent_9, eval_serpent__critedge1_in, eval_serpent__critedge_in, eval_serpent_bb0_in, eval_serpent_bb1_in, eval_serpent_bb1_in_v1, eval_serpent_bb2_in_v1, eval_serpent_bb2_in_v2, eval_serpent_bb3_in_v1, eval_serpent_bb3_in_v2, eval_serpent_bb4_in, eval_serpent_bb4_in_v1, eval_serpent_bb5_in_v1, eval_serpent_bb5_in_v2, eval_serpent_bb6_in_v1, eval_serpent_bb6_in_v2, eval_serpent_bb7_in, eval_serpent_start, eval_serpent_stop
Transitions:
t₂: eval_serpent_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₄: eval_serpent_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₃, X₃, X₆, X₇) :|: 1 ≤ X₃
t₃: eval_serpent_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₃ ≤ 0
t₁₅₂: eval_serpent_10_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_11_v1(X₀, X₁, nondef_1, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁₅₉: eval_serpent_10_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_11_v2(X₀, X₁, nondef_1, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₇ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₆+X₇ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₇ ∧ 1 ≤ X₃ ∧ 1+X₆ ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₆ ≤ X₇ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ ∧ 0 ≤ X₇
t₁₅₄: eval_serpent_11_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₁, X₇, X₆, X₇) :|: X₂ ≤ 0 ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁₅₃: eval_serpent_11_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb6_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₂ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁₆₁: eval_serpent_11_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₁, X₇, X₆, X₇) :|: X₂ ≤ 0 ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₇ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₆+X₇ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₆ ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₆ ≤ X₇ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ ∧ 0 ≤ X₇
t₁₆₀: eval_serpent_11_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb6_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₂ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₇ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₆+X₇ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₆ ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₆ ≤ X₇ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ ∧ 0 ≤ X₇
t₁₃₈: eval_serpent_2_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_3_v1(nondef_0, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₄+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆
t₁₄₅: eval_serpent_2_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_3_v2(nondef_0, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₅+X₆ ∧ 1+X₆ ≤ X₅ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆
t₁₄₀: eval_serpent_3_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0 ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₄+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆
t₁₃₉: eval_serpent_3_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb3_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₄+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆
t₁₄₇: eval_serpent_3_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0 ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₅+X₆ ∧ 1+X₆ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆
t₁₄₆: eval_serpent_3_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb3_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₅+X₆ ∧ 1+X₆ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆
t₁₅: eval_serpent_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₅
t₁₆: eval_serpent_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₅
t₁₇: eval_serpent_9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₆) :|: 0 ≤ 2+X₅+X₆ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₅
t₅: eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₅, X₇) :|: 0 ≤ X₄ ∧ 0 ≤ 1+X₅ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅
t₆: eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₄ ≤ 0 ∧ 0 ≤ 1+X₅ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅
t₁₄: eval_serpent__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_7(X₀, X₄-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₅
t₁: eval_serpent_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₈: eval_serpent_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₆ ≤ 0 ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 1+X₄+X₅ ∧ 0 ≤ 1+X₄+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₄ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆
t₁₃₆: eval_serpent_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₆ ≤ 0 ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 1+X₄+X₅ ∧ 0 ≤ 1+X₄+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₄ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆
t₁₃₅: eval_serpent_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb2_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 1+X₄+X₅ ∧ 0 ≤ 1+X₄+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₄ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆
t₁₄₃: eval_serpent_bb1_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₆ ≤ 0 ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₆ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1+X₆ ≤ X₅ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ X₆ ≤ X₅
t₁₄₂: eval_serpent_bb1_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb2_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₆ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₆ ∧ 0 ≤ 1+X₆ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1+X₆ ≤ X₅ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ X₆ ≤ X₅
t₁₃₇: eval_serpent_bb2_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_2_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₄+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆
t₁₄₄: eval_serpent_bb2_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_2_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₅+X₆ ∧ 1+X₆ ≤ X₅ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆
t₁₄₁: eval_serpent_bb3_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb1_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₄+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆
t₁₄₈: eval_serpent_bb3_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb1_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₅ ∧ 1 ≤ X₅+X₆ ∧ 1+X₆ ≤ X₅ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆
t₁₉: eval_serpent_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₁, X₇, X₆, X₇) :|: 1+X₃ ≤ X₇ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁₅₀: eval_serpent_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₁, X₇, X₆, X₇) :|: 1+X₃ ≤ X₇ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁₄₉: eval_serpent_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb5_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₇ ≤ X₃ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁₅₇: eval_serpent_bb4_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent__critedge1_in(X₀, X₁, X₂, X₃, X₁, X₇, X₆, X₇) :|: 1+X₃ ≤ X₇ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ X₇ ≤ 1+X₃ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₇ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₆+X₇ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₇ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₆ ≤ X₇ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ ∧ 0 ≤ X₇
t₁₅₆: eval_serpent_bb4_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb5_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₇ ≤ X₃ ∧ 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ X₇ ≤ 1+X₃ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₇ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₆+X₇ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₇ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₆ ≤ X₇ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ ∧ 0 ≤ X₇
t₁₅₁: eval_serpent_bb5_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_10_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁₅₈: eval_serpent_bb5_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_10_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₇ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₆+X₇ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₇ ∧ 1 ≤ X₃ ∧ 1+X₆ ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₆ ≤ X₇ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ ∧ 0 ≤ X₇
t₁₅₅: eval_serpent_bb6_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb4_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 1+X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ X₂+X₇ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₇ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁₆₂: eval_serpent_bb6_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb4_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 1+X₇) :|: 0 ≤ 2+X₅+X₆ ∧ 0 ≤ 2+X₅+X₇ ∧ 0 ≤ 2+X₆+X₇ ∧ X₄ ≤ 1+X₁ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₅+X₇ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₆+X₇ ∧ 0 ≤ 1+X₇ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₇ ∧ 1 ≤ X₃ ∧ 1+X₆ ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₆ ≤ X₇ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ X₂+X₇ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ X₆ ≤ X₃ ∧ 0 ≤ X₃+X₇ ∧ X₇ ≤ X₃ ∧ X₆ ≤ X₅ ∧ X₆ ≤ X₇ ∧ 0 ≤ X₇
t₂₅: eval_serpent_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₀: eval_serpent_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_serpent_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)

All Bounds

Timebounds

Overall timebound:152⋅X₃⋅X₃+183⋅X₃+60 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 2⋅X₃+1 {O(n)}
t₆: 1 {O(1)}
t₈: 2⋅X₃+1 {O(n)}
t₁₄: 2⋅X₃+1 {O(n)}
t₁₅: 2⋅X₃+1 {O(n)}
t₁₆: 2⋅X₃+1 {O(n)}
t₁₇: 2⋅X₃+1 {O(n)}
t₁₉: 2⋅X₃+1 {O(n)}
t₂₅: 1 {O(1)}
t₁₃₅: 2⋅X₃+1 {O(n)}
t₁₃₆: 2⋅X₃+1 {O(n)}
t₁₃₇: 2⋅X₃+1 {O(n)}
t₁₃₈: 2⋅X₃+1 {O(n)}
t₁₃₉: 2⋅X₃+1 {O(n)}
t₁₄₀: 2⋅X₃+1 {O(n)}
t₁₄₁: 2⋅X₃+1 {O(n)}
t₁₄₂: 2⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}
t₁₄₃: 94⋅X₃⋅X₃+78⋅X₃+17 {O(n^2)}
t₁₄₄: 20⋅X₃⋅X₃+17⋅X₃+3 {O(n^2)}
t₁₄₅: 2⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}
t₁₄₆: 2⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}
t₁₄₇: 2⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}
t₁₄₈: 2⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}
t₁₄₉: 2⋅X₃+1 {O(n)}
t₁₅₀: 2⋅X₃+1 {O(n)}
t₁₅₁: 2⋅X₃+1 {O(n)}
t₁₅₂: 2⋅X₃+1 {O(n)}
t₁₅₃: 2⋅X₃+1 {O(n)}
t₁₅₄: 2⋅X₃+1 {O(n)}
t₁₅₅: 2⋅X₃+1 {O(n)}
t₁₅₆: 4⋅X₃⋅X₃+4⋅X₃+2 {O(n^2)}
t₁₅₇: 2⋅X₃+1 {O(n)}
t₁₅₈: 4⋅X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₅₉: 4⋅X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₆₀: 8⋅X₃⋅X₃+6⋅X₃+1 {O(n^2)}
t₁₆₁: 4⋅X₃+3 {O(n)}
t₁₆₂: 8⋅X₃⋅X₃+6⋅X₃ {O(n^2)}

Costbounds

Overall costbound: 152⋅X₃⋅X₃+183⋅X₃+60 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 2⋅X₃+1 {O(n)}
t₆: 1 {O(1)}
t₈: 2⋅X₃+1 {O(n)}
t₁₄: 2⋅X₃+1 {O(n)}
t₁₅: 2⋅X₃+1 {O(n)}
t₁₆: 2⋅X₃+1 {O(n)}
t₁₇: 2⋅X₃+1 {O(n)}
t₁₉: 2⋅X₃+1 {O(n)}
t₂₅: 1 {O(1)}
t₁₃₅: 2⋅X₃+1 {O(n)}
t₁₃₆: 2⋅X₃+1 {O(n)}
t₁₃₇: 2⋅X₃+1 {O(n)}
t₁₃₈: 2⋅X₃+1 {O(n)}
t₁₃₉: 2⋅X₃+1 {O(n)}
t₁₄₀: 2⋅X₃+1 {O(n)}
t₁₄₁: 2⋅X₃+1 {O(n)}
t₁₄₂: 2⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}
t₁₄₃: 94⋅X₃⋅X₃+78⋅X₃+17 {O(n^2)}
t₁₄₄: 20⋅X₃⋅X₃+17⋅X₃+3 {O(n^2)}
t₁₄₅: 2⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}
t₁₄₆: 2⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}
t₁₄₇: 2⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}
t₁₄₈: 2⋅X₃⋅X₃+4⋅X₃+1 {O(n^2)}
t₁₄₉: 2⋅X₃+1 {O(n)}
t₁₅₀: 2⋅X₃+1 {O(n)}
t₁₅₁: 2⋅X₃+1 {O(n)}
t₁₅₂: 2⋅X₃+1 {O(n)}
t₁₅₃: 2⋅X₃+1 {O(n)}
t₁₅₄: 2⋅X₃+1 {O(n)}
t₁₅₅: 2⋅X₃+1 {O(n)}
t₁₅₆: 4⋅X₃⋅X₃+4⋅X₃+2 {O(n^2)}
t₁₅₇: 2⋅X₃+1 {O(n)}
t₁₅₈: 4⋅X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₅₉: 4⋅X₃⋅X₃+2⋅X₃ {O(n^2)}
t₁₆₀: 8⋅X₃⋅X₃+6⋅X₃+1 {O(n^2)}
t₁₆₁: 4⋅X₃+3 {O(n)}
t₁₆₂: 8⋅X₃⋅X₃+6⋅X₃ {O(n^2)}

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: X₃ {O(n)}
t₄, X₅: X₃ {O(n)}
t₄, X₆: X₆ {O(n)}
t₄, X₇: X₇ {O(n)}
t₅, X₁: 9⋅X₃+X₁+3 {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: 3⋅X₃+1 {O(n)}
t₅, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₅, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₅, X₇: 6⋅X₃⋅X₃+18⋅X₃+X₇+12 {O(n^2)}
t₆, X₁: 9⋅X₃+3 {O(n)}
t₆, X₃: 2⋅X₃ {O(n)}
t₆, X₄: 6⋅X₃+2 {O(n)}
t₆, X₅: 4⋅X₃⋅X₃+12⋅X₃+8 {O(n^2)}
t₆, X₆: 6⋅X₃⋅X₃+18⋅X₃+12 {O(n^2)}
t₆, X₇: 6⋅X₃⋅X₃+18⋅X₃+12 {O(n^2)}
t₈, X₁: 9⋅X₃+X₁+3 {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: 3⋅X₃+1 {O(n)}
t₈, X₅: 1 {O(1)}
t₈, X₆: 1 {O(1)}
t₈, X₇: 6⋅X₃⋅X₃+18⋅X₃+X₇+12 {O(n^2)}
t₁₄, X₁: 3⋅X₃+1 {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: 6⋅X₃+2 {O(n)}
t₁₄, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₄, X₇: 18⋅X₃⋅X₃+3⋅X₇+54⋅X₃+36 {O(n^2)}
t₁₅, X₁: 3⋅X₃+1 {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: 6⋅X₃+2 {O(n)}
t₁₅, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₅, X₇: 18⋅X₃⋅X₃+3⋅X₇+54⋅X₃+36 {O(n^2)}
t₁₆, X₁: 3⋅X₃+1 {O(n)}
t₁₆, X₃: X₃ {O(n)}
t₁₆, X₄: 6⋅X₃+2 {O(n)}
t₁₆, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₆, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₆, X₇: 18⋅X₃⋅X₃+3⋅X₇+54⋅X₃+36 {O(n^2)}
t₁₇, X₁: 3⋅X₃+1 {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: 6⋅X₃+2 {O(n)}
t₁₇, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₇, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₇, X₇: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₉, X₁: 6⋅X₃+2 {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₁₉, X₄: 3⋅X₃+1 {O(n)}
t₁₉, X₅: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₉, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₉, X₇: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₂₅, X₁: 9⋅X₃+X₁+3 {O(n)}
t₂₅, X₃: 3⋅X₃ {O(n)}
t₂₅, X₄: 6⋅X₃+X₄+2 {O(n)}
t₂₅, X₅: 4⋅X₃⋅X₃+12⋅X₃+X₅+8 {O(n^2)}
t₂₅, X₆: 6⋅X₃⋅X₃+18⋅X₃+X₆+12 {O(n^2)}
t₂₅, X₇: 6⋅X₃⋅X₃+18⋅X₃+X₇+12 {O(n^2)}
t₁₃₅, X₁: 9⋅X₃+X₁+3 {O(n)}
t₁₃₅, X₃: X₃ {O(n)}
t₁₃₅, X₄: 3⋅X₃+1 {O(n)}
t₁₃₅, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₃₅, X₆: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₃₅, X₇: 6⋅X₃⋅X₃+18⋅X₃+X₇+12 {O(n^2)}
t₁₃₆, X₁: 9⋅X₃+X₁+3 {O(n)}
t₁₃₆, X₃: X₃ {O(n)}
t₁₃₆, X₄: 3⋅X₃+1 {O(n)}
t₁₃₆, X₅: 1 {O(1)}
t₁₃₆, X₆: 1 {O(1)}
t₁₃₆, X₇: 6⋅X₃⋅X₃+18⋅X₃+X₇+12 {O(n^2)}
t₁₃₇, X₁: 9⋅X₃+X₁+3 {O(n)}
t₁₃₇, X₃: X₃ {O(n)}
t₁₃₇, X₄: 3⋅X₃+1 {O(n)}
t₁₃₇, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₃₇, X₆: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₃₇, X₇: 6⋅X₃⋅X₃+18⋅X₃+X₇+12 {O(n^2)}
t₁₃₈, X₁: 9⋅X₃+X₁+3 {O(n)}
t₁₃₈, X₃: X₃ {O(n)}
t₁₃₈, X₄: 3⋅X₃+1 {O(n)}
t₁₃₈, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₃₈, X₆: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₃₈, X₇: 6⋅X₃⋅X₃+18⋅X₃+X₇+12 {O(n^2)}
t₁₃₉, X₁: 9⋅X₃+X₁+3 {O(n)}
t₁₃₉, X₃: X₃ {O(n)}
t₁₃₉, X₄: 3⋅X₃+1 {O(n)}
t₁₃₉, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₃₉, X₆: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₃₉, X₇: 6⋅X₃⋅X₃+18⋅X₃+X₇+12 {O(n^2)}
t₁₄₀, X₁: 9⋅X₃+X₁+3 {O(n)}
t₁₄₀, X₃: X₃ {O(n)}
t₁₄₀, X₄: 3⋅X₃+1 {O(n)}
t₁₄₀, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₀, X₆: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₀, X₇: 6⋅X₃⋅X₃+18⋅X₃+X₇+12 {O(n^2)}
t₁₄₁, X₁: 9⋅X₃+X₁+3 {O(n)}
t₁₄₁, X₃: X₃ {O(n)}
t₁₄₁, X₄: 3⋅X₃+1 {O(n)}
t₁₄₁, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₁, X₆: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₁, X₇: 6⋅X₃⋅X₃+18⋅X₃+X₇+12 {O(n^2)}
t₁₄₂, X₁: 9⋅X₃+X₁+3 {O(n)}
t₁₄₂, X₃: X₃ {O(n)}
t₁₄₂, X₄: 3⋅X₃+1 {O(n)}
t₁₄₂, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₂, X₆: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₂, X₇: 6⋅X₃⋅X₃+18⋅X₃+X₇+12 {O(n^2)}
t₁₄₃, X₁: 18⋅X₃+2⋅X₁+6 {O(n)}
t₁₄₃, X₃: X₃ {O(n)}
t₁₄₃, X₄: 3⋅X₃+1 {O(n)}
t₁₄₃, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₃, X₆: 1 {O(1)}
t₁₄₃, X₇: 12⋅X₃⋅X₃+2⋅X₇+36⋅X₃+24 {O(n^2)}
t₁₄₄, X₁: 9⋅X₃+X₁+3 {O(n)}
t₁₄₄, X₃: X₃ {O(n)}
t₁₄₄, X₄: 3⋅X₃+1 {O(n)}
t₁₄₄, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₄, X₆: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₄, X₇: 6⋅X₃⋅X₃+18⋅X₃+X₇+12 {O(n^2)}
t₁₄₅, X₁: 9⋅X₃+X₁+3 {O(n)}
t₁₄₅, X₃: X₃ {O(n)}
t₁₄₅, X₄: 3⋅X₃+1 {O(n)}
t₁₄₅, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₅, X₆: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₅, X₇: 6⋅X₃⋅X₃+18⋅X₃+X₇+12 {O(n^2)}
t₁₄₆, X₁: 9⋅X₃+X₁+3 {O(n)}
t₁₄₆, X₃: X₃ {O(n)}
t₁₄₆, X₄: 3⋅X₃+1 {O(n)}
t₁₄₆, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₆, X₆: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₆, X₇: 6⋅X₃⋅X₃+18⋅X₃+X₇+12 {O(n^2)}
t₁₄₇, X₁: 9⋅X₃+X₁+3 {O(n)}
t₁₄₇, X₃: X₃ {O(n)}
t₁₄₇, X₄: 3⋅X₃+1 {O(n)}
t₁₄₇, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₇, X₆: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₇, X₇: 6⋅X₃⋅X₃+18⋅X₃+X₇+12 {O(n^2)}
t₁₄₈, X₁: 9⋅X₃+X₁+3 {O(n)}
t₁₄₈, X₃: X₃ {O(n)}
t₁₄₈, X₄: 3⋅X₃+1 {O(n)}
t₁₄₈, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₈, X₆: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₈, X₇: 6⋅X₃⋅X₃+18⋅X₃+X₇+12 {O(n^2)}
t₁₄₉, X₁: 3⋅X₃+1 {O(n)}
t₁₄₉, X₃: X₃ {O(n)}
t₁₄₉, X₄: 6⋅X₃+2 {O(n)}
t₁₄₉, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₄₉, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₄₉, X₇: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₀, X₁: 3⋅X₃+1 {O(n)}
t₁₅₀, X₃: X₃ {O(n)}
t₁₅₀, X₄: 3⋅X₃+1 {O(n)}
t₁₅₀, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₀, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₅₀, X₇: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₅₁, X₁: 3⋅X₃+1 {O(n)}
t₁₅₁, X₃: X₃ {O(n)}
t₁₅₁, X₄: 6⋅X₃+2 {O(n)}
t₁₅₁, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₁, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₅₁, X₇: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₂, X₁: 3⋅X₃+1 {O(n)}
t₁₅₂, X₃: X₃ {O(n)}
t₁₅₂, X₄: 6⋅X₃+2 {O(n)}
t₁₅₂, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₂, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₅₂, X₇: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₃, X₁: 3⋅X₃+1 {O(n)}
t₁₅₃, X₃: X₃ {O(n)}
t₁₅₃, X₄: 6⋅X₃+2 {O(n)}
t₁₅₃, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₃, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₅₃, X₇: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₄, X₁: 3⋅X₃+1 {O(n)}
t₁₅₄, X₃: X₃ {O(n)}
t₁₅₄, X₄: 3⋅X₃+1 {O(n)}
t₁₅₄, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₄, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₅₄, X₇: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₅, X₁: 3⋅X₃+1 {O(n)}
t₁₅₅, X₃: X₃ {O(n)}
t₁₅₅, X₄: 6⋅X₃+2 {O(n)}
t₁₅₅, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₅, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₅₅, X₇: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₆, X₁: 3⋅X₃+1 {O(n)}
t₁₅₆, X₃: X₃ {O(n)}
t₁₅₆, X₄: 6⋅X₃+2 {O(n)}
t₁₅₆, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₆, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₅₆, X₇: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₇, X₁: 6⋅X₃+2 {O(n)}
t₁₅₇, X₃: X₃ {O(n)}
t₁₅₇, X₄: 3⋅X₃+1 {O(n)}
t₁₅₇, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₇, X₆: 4⋅X₃⋅X₃+12⋅X₃+8 {O(n^2)}
t₁₅₇, X₇: 16⋅X₃⋅X₃+18⋅X₃+14 {O(n^2)}
t₁₅₈, X₁: 3⋅X₃+1 {O(n)}
t₁₅₈, X₃: X₃ {O(n)}
t₁₅₈, X₄: 6⋅X₃+2 {O(n)}
t₁₅₈, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₈, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₅₈, X₇: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₉, X₁: 3⋅X₃+1 {O(n)}
t₁₅₉, X₃: X₃ {O(n)}
t₁₅₉, X₄: 6⋅X₃+2 {O(n)}
t₁₅₉, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₅₉, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₅₉, X₇: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₆₀, X₁: 3⋅X₃+1 {O(n)}
t₁₆₀, X₃: X₃ {O(n)}
t₁₆₀, X₄: 6⋅X₃+2 {O(n)}
t₁₆₀, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₆₀, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₆₀, X₇: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₆₁, X₁: 3⋅X₃+1 {O(n)}
t₁₆₁, X₃: X₃ {O(n)}
t₁₆₁, X₄: 3⋅X₃+1 {O(n)}
t₁₆₁, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₆₁, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₆₁, X₇: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₆₂, X₁: 3⋅X₃+1 {O(n)}
t₁₆₂, X₃: X₃ {O(n)}
t₁₆₂, X₄: 6⋅X₃+2 {O(n)}
t₁₆₂, X₅: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}
t₁₆₂, X₆: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₆₂, X₇: 8⋅X₃⋅X₃+9⋅X₃+7 {O(n^2)}