KoAT2 Proof Output

Initial Problem

Start: eval_non_linear16_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂
Temp_Vars: nondef.0, nondef.1
Locations: eval_non_linear16_3, eval_non_linear16_4, eval_non_linear16_7, eval_non_linear16_8, eval_non_linear16_bb0_in, eval_non_linear16_bb1_in, eval_non_linear16_bb2_in, eval_non_linear16_bb3_in, eval_non_linear16_bb4_in, eval_non_linear16_bb5_in, eval_non_linear16_bb6_in, eval_non_linear16_start, eval_non_linear16_stop
Transitions:
t₈: eval_non_linear16_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_4(X₀, X₁, X₂, X₃, nondef.0, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂)
t₉: eval_non_linear16_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb4_in(X₀, X₁, X₁₁, X₁₂, X₄, X₅, X₆, X₇, X₄, X₉, X₁₀, X₁₁, X₁₂)
t₁₅: eval_non_linear16_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, nondef.1, X₈, X₉, X₁₀, X₁₁, X₁₂)
t₁₆: eval_non_linear16_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb4_in(X₀, X₁, X₅, X₆, X₄, X₅, X₆, X₇, X₇, X₉, X₁₀, X₁₁, X₁₂)
t₁: eval_non_linear16_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb1_in(X₉, X₁₀, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂)
t₂: eval_non_linear16_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁
t₃: eval_non_linear16_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: X₀ ≤ X₁
t₄: eval_non_linear16_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: X₁ ≤ 0
t₅: eval_non_linear16_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb1_in(2⋅X₀, 3⋅X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂)
t₆: eval_non_linear16_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂)
t₁₀: eval_non_linear16_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₈
t₁₁: eval_non_linear16_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: X₂ ≤ 0
t₁₂: eval_non_linear16_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: X₈ ≤ 0
t₁₃: eval_non_linear16_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_7(X₀, X₁, X₂, X₃, X₄, X₂+X₃, X₃-X₈, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂)
t₁₇: eval_non_linear16_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂)
t₀: eval_non_linear16_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂)

Preprocessing

Found invariant X₉ ≤ X₀ ∧ 1 ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ 2+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₃ ∧ 1+X₆ ≤ X₁₂ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ X₁₂ ∧ 1 ≤ X₂ ∧ X₁₀ ≤ X₁ for location eval_non_linear16_8

Found invariant X₉ ≤ X₀ ∧ X₃ ≤ X₁₂ ∧ X₁₀ ≤ X₁ for location eval_non_linear16_bb4_in

Found invariant X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ for location eval_non_linear16_3

Found invariant X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ ∧ 1+X₁₀ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_non_linear16_bb2_in

Found invariant X₉ ≤ X₀ ∧ 1 ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ X₃ ≤ X₁₂ ∧ 1 ≤ X₂ ∧ X₁₀ ≤ X₁ for location eval_non_linear16_bb5_in

Found invariant X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ for location eval_non_linear16_bb3_in

Found invariant X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ for location eval_non_linear16_4

Found invariant X₉ ≤ X₀ ∧ 1 ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ 2+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₃ ∧ 1+X₆ ≤ X₁₂ ∧ 1+X₃ ≤ X₅ ∧ X₃ ≤ X₁₂ ∧ 1 ≤ X₂ ∧ X₁₀ ≤ X₁ for location eval_non_linear16_7

Found invariant X₉ ≤ X₀ ∧ X₃ ≤ X₁₂ ∧ X₁₀ ≤ X₁ for location eval_non_linear16_bb6_in

Found invariant X₉ ≤ X₀ ∧ X₃ ≤ X₁₂ ∧ X₁₀ ≤ X₁ for location eval_non_linear16_stop

Found invariant X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ for location eval_non_linear16_bb1_in

Problem after Preprocessing

Start: eval_non_linear16_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂
Temp_Vars: nondef.0, nondef.1
Locations: eval_non_linear16_3, eval_non_linear16_4, eval_non_linear16_7, eval_non_linear16_8, eval_non_linear16_bb0_in, eval_non_linear16_bb1_in, eval_non_linear16_bb2_in, eval_non_linear16_bb3_in, eval_non_linear16_bb4_in, eval_non_linear16_bb5_in, eval_non_linear16_bb6_in, eval_non_linear16_start, eval_non_linear16_stop
Transitions:
t₈: eval_non_linear16_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_4(X₀, X₁, X₂, X₃, nondef.0, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: X₉ ≤ X₀ ∧ X₁₀ ≤ X₁
t₉: eval_non_linear16_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb4_in(X₀, X₁, X₁₁, X₁₂, X₄, X₅, X₆, X₇, X₄, X₉, X₁₀, X₁₁, X₁₂) :|: X₉ ≤ X₀ ∧ X₁₀ ≤ X₁
t₁₅: eval_non_linear16_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, nondef.1, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: 1 ≤ X₂ ∧ 1+X₆ ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 1+X₆ ≤ X₁₂ ∧ 1 ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ 2+X₆ ≤ X₅ ∧ X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ ∧ X₃ ≤ X₁₂
t₁₆: eval_non_linear16_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb4_in(X₀, X₁, X₅, X₆, X₄, X₅, X₆, X₇, X₇, X₉, X₁₀, X₁₁, X₁₂) :|: 1 ≤ X₂ ∧ 1+X₆ ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 1+X₆ ≤ X₁₂ ∧ 1 ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ 2+X₆ ≤ X₅ ∧ X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ ∧ X₃ ≤ X₁₂
t₁: eval_non_linear16_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb1_in(X₉, X₁₀, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂)
t₂: eval_non_linear16_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₉ ≤ X₀ ∧ X₁₀ ≤ X₁
t₃: eval_non_linear16_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: X₀ ≤ X₁ ∧ X₉ ≤ X₀ ∧ X₁₀ ≤ X₁
t₄: eval_non_linear16_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: X₁ ≤ 0 ∧ X₉ ≤ X₀ ∧ X₁₀ ≤ X₁
t₅: eval_non_linear16_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb1_in(2⋅X₀, 3⋅X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: 1+X₁ ≤ X₀ ∧ 1+X₁₀ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₉ ≤ X₀ ∧ X₁₀ ≤ X₁
t₆: eval_non_linear16_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: X₉ ≤ X₀ ∧ X₁₀ ≤ X₁
t₁₀: eval_non_linear16_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₈ ∧ X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ ∧ X₃ ≤ X₁₂
t₁₁: eval_non_linear16_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: X₂ ≤ 0 ∧ X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ ∧ X₃ ≤ X₁₂
t₁₂: eval_non_linear16_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: X₈ ≤ 0 ∧ X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ ∧ X₃ ≤ X₁₂
t₁₃: eval_non_linear16_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_7(X₀, X₁, X₂, X₃, X₄, X₂+X₃, X₃-X₈, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ ∧ X₃ ≤ X₁₂
t₁₇: eval_non_linear16_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ ∧ X₃ ≤ X₁₂
t₀: eval_non_linear16_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂)

Found invariant X₉ ≤ X₀ ∧ X₃ ≤ X₁₂ ∧ X₁₀ ≤ X₁ for location eval_non_linear16_bb4_in

Found invariant X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ for location eval_non_linear16_3

Found invariant X₉ ≤ X₀ ∧ 1 ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ X₃ ≤ X₁₂ ∧ 1 ≤ X₂ ∧ X₁₀ ≤ X₁ for location eval_non_linear16_bb5_in

Found invariant X₉ ≤ X₀ ∧ 2 ≤ X₉ ∧ 3 ≤ X₉+X₁₀ ∧ 1+X₁₀ ≤ X₉ ∧ 3 ≤ X₁+X₉ ∧ 1+X₁ ≤ X₉ ∧ 4 ≤ X₀+X₉ ∧ X₀ ≤ X₉ ∧ X₁₀ ≤ X₁ ∧ 1+X₁₀ ≤ X₀ ∧ 1 ≤ X₁₀ ∧ 2 ≤ X₁+X₁₀ ∧ X₁ ≤ X₁₀ ∧ 3 ≤ X₀+X₁₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_non_linear16_bb2_in_v1

Found invariant 2+X₉ ≤ X₀ ∧ 2 ≤ X₉ ∧ 3 ≤ X₉+X₁₀ ∧ 1+X₁₀ ≤ X₉ ∧ 5 ≤ X₁+X₉ ∧ 6 ≤ X₀+X₉ ∧ 2+X₁₀ ≤ X₁ ∧ 3+X₁₀ ≤ X₀ ∧ 1 ≤ X₁₀ ∧ 4 ≤ X₁+X₁₀ ∧ 5 ≤ X₀+X₁₀ ∧ 1+X₁ ≤ X₀ ∧ 3 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location eval_non_linear16_bb2_in_v2

Found invariant X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ for location eval_non_linear16_bb3_in

Found invariant X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ for location eval_non_linear16_4

Found invariant 2+X₉ ≤ X₀ ∧ 2 ≤ X₉ ∧ 3 ≤ X₉+X₁₀ ∧ 1+X₁₀ ≤ X₉ ∧ 5 ≤ X₁+X₉ ∧ 6 ≤ X₀+X₉ ∧ 2+X₁₀ ≤ X₁ ∧ 3+X₁₀ ≤ X₀ ∧ 1 ≤ X₁₀ ∧ 4 ≤ X₁+X₁₀ ∧ 5 ≤ X₀+X₁₀ ∧ 3 ≤ X₁ ∧ 7 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location eval_non_linear16_bb1_in_v1

Found invariant X₉ ≤ X₀ ∧ X₃ ≤ X₁₂ ∧ X₁₀ ≤ X₁ for location eval_non_linear16_bb6_in

Found invariant X₉ ≤ X₀ ∧ X₃ ≤ X₁₂ ∧ X₁₀ ≤ X₁ for location eval_non_linear16_stop

Found invariant X₉ ≤ X₀ ∧ X₀ ≤ X₉ ∧ X₁₀ ≤ X₁ ∧ X₁ ≤ X₁₀ for location eval_non_linear16_bb1_in

MPRF for transition t₁₀: eval_non_linear16_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₈ ∧ X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ ∧ X₃ ≤ X₁₂ of depth 2:

new bound:

24⋅X₁₁+24⋅X₁₂+9 {O(n)}

MPRF:

• eval_non_linear16_7: [X₆+X₈; X₅]
• eval_non_linear16_8: [X₆+X₈; X₅]
• eval_non_linear16_bb4_in: [1+X₃; X₂]
• eval_non_linear16_bb5_in: [X₃; X₂+X₃]

MPRF for transition t₁₃: eval_non_linear16_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_7(X₀, X₁, X₂, X₃, X₄, X₂+X₃, X₃-X₈, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ ∧ X₃ ≤ X₁₂ of depth 2:

new bound:

24⋅X₁₁+24⋅X₁₂+9 {O(n)}

MPRF:

• eval_non_linear16_7: [X₃; X₅]
• eval_non_linear16_8: [X₃; X₅]
• eval_non_linear16_bb4_in: [1+X₃; X₂]
• eval_non_linear16_bb5_in: [1+X₃; X₂]

MPRF for transition t₁₅: eval_non_linear16_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, nondef.1, X₈, X₉, X₁₀, X₁₁, X₁₂) :|: 1 ≤ X₂ ∧ 1+X₆ ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 1+X₆ ≤ X₁₂ ∧ 1 ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ 2+X₆ ≤ X₅ ∧ X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ ∧ X₃ ≤ X₁₂ of depth 2:

new bound:

24⋅X₁₁+24⋅X₁₂+9 {O(n)}

MPRF:

• eval_non_linear16_7: [1+X₃; X₅-X₃]
• eval_non_linear16_8: [X₃; X₅]
• eval_non_linear16_bb4_in: [1+X₃; X₂]
• eval_non_linear16_bb5_in: [1+X₃; X₂]

MPRF for transition t₁₆: eval_non_linear16_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) → eval_non_linear16_bb4_in(X₀, X₁, X₅, X₆, X₄, X₅, X₆, X₇, X₇, X₉, X₁₀, X₁₁, X₁₂) :|: 1 ≤ X₂ ∧ 1+X₆ ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 1+X₆ ≤ X₁₂ ∧ 1 ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ 2+X₆ ≤ X₅ ∧ X₉ ≤ X₀ ∧ X₁₀ ≤ X₁ ∧ X₃ ≤ X₁₂ of depth 2:

new bound:

24⋅X₁₁+24⋅X₁₂+9 {O(n)}

MPRF:

• eval_non_linear16_7: [1+X₃; X₅-X₃]
• eval_non_linear16_8: [1+X₃; X₅-X₃]
• eval_non_linear16_bb4_in: [1+X₃; X₂]
• eval_non_linear16_bb5_in: [1+X₃; X₂]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: inf {Infinity}
t₆: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 24⋅X₁₁+24⋅X₁₂+9 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 24⋅X₁₁+24⋅X₁₂+9 {O(n)}
t₁₅: 24⋅X₁₁+24⋅X₁₂+9 {O(n)}
t₁₆: 24⋅X₁₁+24⋅X₁₂+9 {O(n)}
t₁₇: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: inf {Infinity}
t₆: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 24⋅X₁₁+24⋅X₁₂+9 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 24⋅X₁₁+24⋅X₁₂+9 {O(n)}
t₁₅: 24⋅X₁₁+24⋅X₁₂+9 {O(n)}
t₁₆: 24⋅X₁₁+24⋅X₁₂+9 {O(n)}
t₁₇: 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)}
t₀, X₉: X₉ {O(n)}
t₀, X₁₀: X₁₀ {O(n)}
t₀, X₁₁: X₁₁ {O(n)}
t₀, X₁₂: X₁₂ {O(n)}
t₁, X₀: X₉ {O(n)}
t₁, X₁: X₁₀ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₁, X₇: X₇ {O(n)}
t₁, X₈: X₈ {O(n)}
t₁, X₉: X₉ {O(n)}
t₁, X₁₀: X₁₀ {O(n)}
t₁, X₁₁: X₁₁ {O(n)}
t₁, X₁₂: X₁₂ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₂, X₇: X₇ {O(n)}
t₂, X₈: X₈ {O(n)}
t₂, X₉: X₉ {O(n)}
t₂, X₁₀: X₁₀ {O(n)}
t₂, X₁₁: X₁₁ {O(n)}
t₂, X₁₂: X₁₂ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₃, X₆: 2⋅X₆ {O(n)}
t₃, X₇: 2⋅X₇ {O(n)}
t₃, X₈: 2⋅X₈ {O(n)}
t₃, X₉: 2⋅X₉ {O(n)}
t₃, X₁₀: 2⋅X₁₀ {O(n)}
t₃, X₁₁: 2⋅X₁₁ {O(n)}
t₃, X₁₂: 2⋅X₁₂ {O(n)}
t₄, X₀: X₉ {O(n)}
t₄, X₁: X₁₀ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {O(n)}
t₄, X₇: X₇ {O(n)}
t₄, X₈: X₈ {O(n)}
t₄, X₉: X₉ {O(n)}
t₄, X₁₀: X₁₀ {O(n)}
t₄, X₁₁: X₁₁ {O(n)}
t₄, X₁₂: X₁₂ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₆ {O(n)}
t₅, X₇: X₇ {O(n)}
t₅, X₈: X₈ {O(n)}
t₅, X₉: X₉ {O(n)}
t₅, X₁₀: X₁₀ {O(n)}
t₅, X₁₁: X₁₁ {O(n)}
t₅, X₁₂: X₁₂ {O(n)}
t₆, X₂: 3⋅X₂ {O(n)}
t₆, X₃: 3⋅X₃ {O(n)}
t₆, X₄: 3⋅X₄ {O(n)}
t₆, X₅: 3⋅X₅ {O(n)}
t₆, X₆: 3⋅X₆ {O(n)}
t₆, X₇: 3⋅X₇ {O(n)}
t₆, X₈: 3⋅X₈ {O(n)}
t₆, X₉: 3⋅X₉ {O(n)}
t₆, X₁₀: 3⋅X₁₀ {O(n)}
t₆, X₁₁: 3⋅X₁₁ {O(n)}
t₆, X₁₂: 3⋅X₁₂ {O(n)}
t₈, X₂: 3⋅X₂ {O(n)}
t₈, X₃: 3⋅X₃ {O(n)}
t₈, X₅: 3⋅X₅ {O(n)}
t₈, X₆: 3⋅X₆ {O(n)}
t₈, X₇: 3⋅X₇ {O(n)}
t₈, X₈: 3⋅X₈ {O(n)}
t₈, X₉: 3⋅X₉ {O(n)}
t₈, X₁₀: 3⋅X₁₀ {O(n)}
t₈, X₁₁: 3⋅X₁₁ {O(n)}
t₈, X₁₂: 3⋅X₁₂ {O(n)}
t₉, X₂: 3⋅X₁₁ {O(n)}
t₉, X₃: 3⋅X₁₂ {O(n)}
t₉, X₅: 3⋅X₅ {O(n)}
t₉, X₆: 3⋅X₆ {O(n)}
t₉, X₇: 3⋅X₇ {O(n)}
t₉, X₉: 3⋅X₉ {O(n)}
t₉, X₁₀: 3⋅X₁₀ {O(n)}
t₉, X₁₁: 3⋅X₁₁ {O(n)}
t₉, X₁₂: 3⋅X₁₂ {O(n)}
t₁₀, X₉: 3⋅X₉ {O(n)}
t₁₀, X₁₀: 3⋅X₁₀ {O(n)}
t₁₀, X₁₁: 3⋅X₁₁ {O(n)}
t₁₀, X₁₂: 3⋅X₁₂ {O(n)}
t₁₁, X₉: 6⋅X₉ {O(n)}
t₁₁, X₁₀: 6⋅X₁₀ {O(n)}
t₁₁, X₁₁: 6⋅X₁₁ {O(n)}
t₁₁, X₁₂: 6⋅X₁₂ {O(n)}
t₁₂, X₉: 6⋅X₉ {O(n)}
t₁₂, X₁₀: 6⋅X₁₀ {O(n)}
t₁₂, X₁₁: 6⋅X₁₁ {O(n)}
t₁₂, X₁₂: 6⋅X₁₂ {O(n)}
t₁₃, X₉: 3⋅X₉ {O(n)}
t₁₃, X₁₀: 3⋅X₁₀ {O(n)}
t₁₃, X₁₁: 3⋅X₁₁ {O(n)}
t₁₃, X₁₂: 3⋅X₁₂ {O(n)}
t₁₅, X₉: 3⋅X₉ {O(n)}
t₁₅, X₁₀: 3⋅X₁₀ {O(n)}
t₁₅, X₁₁: 3⋅X₁₁ {O(n)}
t₁₅, X₁₂: 3⋅X₁₂ {O(n)}
t₁₆, X₉: 3⋅X₉ {O(n)}
t₁₆, X₁₀: 3⋅X₁₀ {O(n)}
t₁₆, X₁₁: 3⋅X₁₁ {O(n)}
t₁₆, X₁₂: 3⋅X₁₂ {O(n)}
t₁₇, X₉: 12⋅X₉ {O(n)}
t₁₇, X₁₀: 12⋅X₁₀ {O(n)}
t₁₇, X₁₁: 12⋅X₁₁ {O(n)}
t₁₇, X₁₂: 12⋅X₁₂ {O(n)}