KoAT2 Proof Output

Initial Problem

Start: eval_non_linear09_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃
Temp_Vars:
Locations: eval_non_linear09_1, eval_non_linear09_2, eval_non_linear09_bb0_in, eval_non_linear09_bb1_in, eval_non_linear09_bb2_in, eval_non_linear09_bb3_in, eval_non_linear09_bb4_in, eval_non_linear09_bb5_in, eval_non_linear09_bb6_in, eval_non_linear09_bb7_in, eval_non_linear09_start, eval_non_linear09_stop
Transitions:
t₆: eval_non_linear09_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → eval_non_linear09_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃)
t₇: eval_non_linear09_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → eval_non_linear09_bb3_in(X₀, X₄, 2, X₄, X₄, X₄, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃)
t₁: eval_non_linear09_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → eval_non_linear09_bb1_in(X₈, X₁, X₂, X₃, X₁₃, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃)
t₂: eval_non_linear09_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → eval_non_linear09_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: 1 ≤ X₄
t₃: eval_non_linear09_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → eval_non_linear09_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₀, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: X₄ ≤ 0
t₄: eval_non_linear09_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → eval_non_linear09_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₄-1, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃)
t₁₀: eval_non_linear09_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → eval_non_linear09_bb1_in(X₅, X₁, X₂, X₃, X₇, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: 32+X₃ ≤ (X₂)²
t₁₁: eval_non_linear09_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → eval_non_linear09_bb1_in(X₅, X₁, X₂, X₃, X₇, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: 0 ≤ X₂ ∧ X₂ ≤ 0
t₈: eval_non_linear09_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → eval_non_linear09_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: (X₂)² ≤ 31+X₃ ∧ 1+X₂ ≤ 0
t₉: eval_non_linear09_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → eval_non_linear09_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: (X₂)² ≤ 31+X₃ ∧ 1 ≤ X₂
t₁₂: eval_non_linear09_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → eval_non_linear09_bb3_in(X₀, -3⋅X₁-5⋅X₅, -2⋅X₂, 4+3⋅X₃, X₄, 2⋅X₁+3⋅X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃)
t₁₃: eval_non_linear09_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → eval_non_linear09_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: 1 ≤ X₆
t₁₄: eval_non_linear09_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → eval_non_linear09_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: X₆ ≤ 0
t₁₅: eval_non_linear09_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → eval_non_linear09_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃)
t₁₆: eval_non_linear09_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → eval_non_linear09_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃)
t₀: eval_non_linear09_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → eval_non_linear09_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃)

Preprocessing

Eliminate variables [X₉; X₁₀; X₁₁; X₁₂] that do not contribute to the problem

Found invariant 1 ≤ X₉ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₉ ∧ 2 ≤ X₃+X₉ ∧ 1+X₇ ≤ X₄ ∧ 1+X₇ ≤ X₃ ∧ 0 ≤ X₇ ∧ 1 ≤ X₄+X₇ ∧ X₄ ≤ 1+X₇ ∧ 1 ≤ X₃+X₇ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₃ for location eval_non_linear09_bb3_in

Found invariant X₄ ≤ X₉ ∧ X₆ ≤ X₀ ∧ X₄ ≤ 0 for location eval_non_linear09_bb5_in

Found invariant X₄ ≤ X₉ ∧ X₆ ≤ 0 ∧ X₄+X₆ ≤ 0 ∧ X₆ ≤ X₀ ∧ X₄ ≤ 0 for location eval_non_linear09_stop

Found invariant X₄ ≤ X₉ for location eval_non_linear09_bb1_in

Found invariant 1 ≤ X₉ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₉ ∧ 1+X₇ ≤ X₄ ∧ 0 ≤ X₇ ∧ 1 ≤ X₄+X₇ ∧ X₄ ≤ 1+X₇ ∧ 1 ≤ X₄ for location eval_non_linear09_2

Found invariant X₄ ≤ X₉ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₆ ∧ 1+X₄ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀ for location eval_non_linear09_bb6_in

Found invariant X₄ ≤ X₉ ∧ X₆ ≤ 0 ∧ X₄+X₆ ≤ 0 ∧ X₆ ≤ X₀ ∧ X₄ ≤ 0 for location eval_non_linear09_bb7_in

Found invariant 1 ≤ X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₉ ∧ 1 ≤ X₄ for location eval_non_linear09_bb2_in

Found invariant 1 ≤ X₉ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₉ ∧ 1+X₇ ≤ X₄ ∧ 0 ≤ X₇ ∧ 1 ≤ X₄+X₇ ∧ X₄ ≤ 1+X₇ ∧ 1 ≤ X₄ for location eval_non_linear09_1

Problem after Preprocessing

Start: eval_non_linear09_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars:
Locations: eval_non_linear09_1, eval_non_linear09_2, eval_non_linear09_bb0_in, eval_non_linear09_bb1_in, eval_non_linear09_bb2_in, eval_non_linear09_bb3_in, eval_non_linear09_bb4_in, eval_non_linear09_bb5_in, eval_non_linear09_bb6_in, eval_non_linear09_bb7_in, eval_non_linear09_start, eval_non_linear09_stop
Transitions:
t₃₂: eval_non_linear09_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₄ ≤ 1+X₇ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₇ ∧ 1+X₇ ≤ X₄ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 1 ≤ X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₉ ∧ 0 ≤ X₇
t₃₃: eval_non_linear09_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_bb3_in(X₀, X₄, 2, X₄, X₄, X₄, X₆, X₇, X₈, X₉) :|: X₄ ≤ 1+X₇ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₇ ∧ 1+X₇ ≤ X₄ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 1 ≤ X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₉ ∧ 0 ≤ X₇
t₃₄: eval_non_linear09_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_bb1_in(X₈, X₁, X₂, X₃, X₉, X₅, X₆, X₇, X₈, X₉)
t₃₅: eval_non_linear09_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₄ ∧ X₄ ≤ X₉
t₃₆: eval_non_linear09_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₀, X₇, X₈, X₉) :|: X₄ ≤ 0 ∧ X₄ ≤ X₉
t₃₇: eval_non_linear09_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₄-1, X₈, X₉) :|: 1 ≤ X₄ ∧ 1 ≤ X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₉
t₃₈: eval_non_linear09_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_bb1_in(X₅, X₁, X₂, X₃, X₇, X₅, X₆, X₇, X₈, X₉) :|: 32+X₃ ≤ (X₂)² ∧ X₄ ≤ 1+X₇ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₇ ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₇ ∧ 1+X₇ ≤ X₄ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 1 ≤ X₉ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₉ ∧ 0 ≤ X₇
t₃₉: eval_non_linear09_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_bb1_in(X₅, X₁, X₂, X₃, X₇, X₅, X₆, X₇, X₈, X₉) :|: 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₄ ≤ 1+X₇ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₇ ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₇ ∧ 1+X₇ ≤ X₄ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 1 ≤ X₉ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₉ ∧ 0 ≤ X₇
t₄₀: eval_non_linear09_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: (X₂)² ≤ 31+X₃ ∧ 1+X₂ ≤ 0 ∧ X₄ ≤ 1+X₇ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₇ ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₇ ∧ 1+X₇ ≤ X₄ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 1 ≤ X₉ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₉ ∧ 0 ≤ X₇
t₄₁: eval_non_linear09_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: (X₂)² ≤ 31+X₃ ∧ 1 ≤ X₂ ∧ X₄ ≤ 1+X₇ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₇ ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₇ ∧ 1+X₇ ≤ X₄ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 1 ≤ X₉ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₉ ∧ 0 ≤ X₇
t₄₂: eval_non_linear09_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_bb3_in(X₀, -3⋅X₁-5⋅X₅, -2⋅X₂, 4+3⋅X₃, X₄, 2⋅X₁+3⋅X₅, X₆, X₇, X₈, X₉) :|: X₄ ≤ 1+X₇ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₇ ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₇ ∧ 1+X₇ ≤ X₄ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 1 ≤ X₉ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₉ ∧ 0 ≤ X₇
t₄₃: eval_non_linear09_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₆ ∧ X₆ ≤ X₀ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₉
t₄₄: eval_non_linear09_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₆ ≤ 0 ∧ X₆ ≤ X₀ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₉
t₄₅: eval_non_linear09_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1, X₇, X₈, X₉) :|: 1 ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₆ ≤ X₀ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₉
t₄₆: eval_non_linear09_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₆ ≤ X₀ ∧ X₄ ≤ 0 ∧ X₄+X₆ ≤ 0 ∧ X₄ ≤ X₉ ∧ X₆ ≤ 0
t₄₇: eval_non_linear09_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)

MPRF for transition t₃₂: eval_non_linear09_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₄ ≤ 1+X₇ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₇ ∧ 1+X₇ ≤ X₄ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 1 ≤ X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₉ ∧ 0 ≤ X₇ of depth 1:

new bound:

X₉ {O(n)}

MPRF:

• eval_non_linear09_1: [1+X₇]
• eval_non_linear09_2: [1+2⋅X₇-X₄]
• eval_non_linear09_bb1_in: [X₄]
• eval_non_linear09_bb2_in: [X₄]
• eval_non_linear09_bb3_in: [X₇]
• eval_non_linear09_bb4_in: [X₄-1]

MPRF for transition t₃₃: eval_non_linear09_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_bb3_in(X₀, X₄, 2, X₄, X₄, X₄, X₆, X₇, X₈, X₉) :|: X₄ ≤ 1+X₇ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₇ ∧ 1+X₇ ≤ X₄ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 1 ≤ X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₉ ∧ 0 ≤ X₇ of depth 1:

new bound:

X₉ {O(n)}

MPRF:

• eval_non_linear09_1: [1+X₇]
• eval_non_linear09_2: [1+X₇]
• eval_non_linear09_bb1_in: [X₄]
• eval_non_linear09_bb2_in: [X₄]
• eval_non_linear09_bb3_in: [X₇]
• eval_non_linear09_bb4_in: [X₇]

MPRF for transition t₃₅: eval_non_linear09_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₄ ∧ X₄ ≤ X₉ of depth 1:

new bound:

X₉ {O(n)}

MPRF:

• eval_non_linear09_1: [X₄-1]
• eval_non_linear09_2: [X₄-1]
• eval_non_linear09_bb1_in: [X₄]
• eval_non_linear09_bb2_in: [X₄-1]
• eval_non_linear09_bb3_in: [X₇]
• eval_non_linear09_bb4_in: [X₇]

MPRF for transition t₃₇: eval_non_linear09_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₄-1, X₈, X₉) :|: 1 ≤ X₄ ∧ 1 ≤ X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₉ of depth 1:

new bound:

X₉ {O(n)}

MPRF:

• eval_non_linear09_1: [X₇]
• eval_non_linear09_2: [X₇]
• eval_non_linear09_bb1_in: [X₄]
• eval_non_linear09_bb2_in: [X₄]
• eval_non_linear09_bb3_in: [X₄-1]
• eval_non_linear09_bb4_in: [X₄-1]

MPRF for transition t₃₈: eval_non_linear09_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_bb1_in(X₅, X₁, X₂, X₃, X₇, X₅, X₆, X₇, X₈, X₉) :|: 32+X₃ ≤ (X₂)² ∧ X₄ ≤ 1+X₇ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₇ ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₇ ∧ 1+X₇ ≤ X₄ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 1 ≤ X₉ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₉ ∧ 0 ≤ X₇ of depth 1:

new bound:

X₉ {O(n)}

MPRF:

• eval_non_linear09_1: [X₄]
• eval_non_linear09_2: [X₄]
• eval_non_linear09_bb1_in: [X₄]
• eval_non_linear09_bb2_in: [X₄]
• eval_non_linear09_bb3_in: [1+X₇]
• eval_non_linear09_bb4_in: [1+X₇]

MPRF for transition t₃₉: eval_non_linear09_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_non_linear09_bb1_in(X₅, X₁, X₂, X₃, X₇, X₅, X₆, X₇, X₈, X₉) :|: 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₄ ≤ 1+X₇ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₇ ∧ 1+X₇ ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₇ ∧ 1+X₇ ≤ X₄ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 1 ≤ X₉ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₉ ∧ 0 ≤ X₇ of depth 1:

new bound:

X₉ {O(n)}

MPRF:

Cut unsatisfiable transition [t₃₈: eval_non_linear09_bb3_in→eval_non_linear09_bb1_in; t₃₉: eval_non_linear09_bb3_in→eval_non_linear09_bb1_in; t₈₄: eval_non_linear09_bb3_in→eval_non_linear09_bb4_in_v2; t₈₅: eval_non_linear09_bb3_in→eval_non_linear09_bb1_in; t₈₆: eval_non_linear09_bb3_in→eval_non_linear09_bb1_in]

Found invariant 1 ≤ X₉ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 2 ≤ X₅+X₉ ∧ X₅ ≤ X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₉ ∧ 2 ≤ X₃+X₉ ∧ X₃ ≤ X₉ ∧ 3 ≤ X₂+X₉ ∧ X₂ ≤ 1+X₉ ∧ 2 ≤ X₁+X₉ ∧ X₁ ≤ X₉ ∧ 1+X₇ ≤ X₅ ∧ 1+X₇ ≤ X₄ ∧ 1+X₇ ≤ X₃ ∧ 1+X₇ ≤ X₁ ∧ 0 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ X₅ ≤ 1+X₇ ∧ 1 ≤ X₄+X₇ ∧ X₄ ≤ 1+X₇ ∧ 1 ≤ X₃+X₇ ∧ X₃ ≤ 1+X₇ ∧ 2 ≤ X₂+X₇ ∧ X₂ ≤ 2+X₇ ∧ 1 ≤ X₁+X₇ ∧ X₁ ≤ 1+X₇ ∧ X₅ ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₅ ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ X₂ ≤ 1+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 2 ∧ X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_non_linear09_bb3_in

Found invariant 1 ≤ X₉ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₉ ∧ 26 ≤ X₃+X₉ ∧ 9 ≤ X₂+X₉ ∧ 1+X₇ ≤ X₄ ∧ 25+X₇ ≤ X₃ ∧ 0 ≤ X₇ ∧ 1 ≤ X₄+X₇ ∧ X₄ ≤ 1+X₇ ∧ 25 ≤ X₃+X₇ ∧ 8 ≤ X₂+X₇ ∧ 24+X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 26 ≤ X₃+X₄ ∧ 9 ≤ X₂+X₄ ∧ 25 ≤ X₃ ∧ 33 ≤ X₂+X₃ ∧ 8 ≤ X₂ for location eval_non_linear09_bb3_in_v1

Found invariant X₄ ≤ X₉ ∧ X₆ ≤ X₀ ∧ X₄ ≤ 0 for location eval_non_linear09_bb5_in

Found invariant X₄ ≤ X₉ ∧ X₆ ≤ 0 ∧ X₄+X₆ ≤ 0 ∧ X₆ ≤ X₀ ∧ X₄ ≤ 0 for location eval_non_linear09_stop

Found invariant X₄ ≤ X₉ for location eval_non_linear09_bb1_in

Found invariant 1 ≤ X₉ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₉ ∧ 2 ≤ X₃+X₉ ∧ 3 ≤ X₂+X₉ ∧ 1+X₇ ≤ X₄ ∧ 1+X₇ ≤ X₃ ∧ 0 ≤ X₇ ∧ 1 ≤ X₄+X₇ ∧ X₄ ≤ 1+X₇ ∧ 1 ≤ X₃+X₇ ∧ 2 ≤ X₂+X₇ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 3 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₂ for location eval_non_linear09_bb4_in_v1

Found invariant 1 ≤ X₉ ∧ 1 ≤ X₇+X₉ ∧ 1+X₇ ≤ X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₉ ∧ 8 ≤ X₃+X₉ ∧ 5+X₂ ≤ X₉ ∧ 1+X₇ ≤ X₄ ∧ 7+X₇ ≤ X₃ ∧ 0 ≤ X₇ ∧ 1 ≤ X₄+X₇ ∧ X₄ ≤ 1+X₇ ∧ 7 ≤ X₃+X₇ ∧ 4+X₂ ≤ X₇ ∧ 6+X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 8 ≤ X₃+X₄ ∧ 5+X₂ ≤ X₄ ∧ 7 ≤ X₃ ∧ 11+X₂ ≤ X₃ ∧ 4+X₂ ≤ 0 for location eval_non_linear09_bb4_in_v2

Found invariant X₄ ≤ X₉ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₆ ∧ 1+X₄ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀ for location eval_non_linear09_bb6_in

Found invariant X₄ ≤ X₉ ∧ X₆ ≤ 0 ∧ X₄+X₆ ≤ 0 ∧ X₆ ≤ X₀ ∧ X₄ ≤ 0 for location eval_non_linear09_bb7_in

Found invariant 1 ≤ X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₉ ∧ 1 ≤ X₄ for location eval_non_linear09_bb2_in

Found invariant X₄ ≤ X₉ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₆ ∧ X₄ ≤ 0 for location eval_non_linear09_bb5_in

Found invariant X₄ ≤ X₉ ∧ X₆ ≤ 0 ∧ X₄+X₆ ≤ 0 ∧ X₆ ≤ X₀ ∧ X₄ ≤ 0 for location eval_non_linear09_stop

Found invariant X₄ ≤ X₉ for location eval_non_linear09_bb1_in

Found invariant X₄ ≤ X₉ ∧ 1+X₆ ≤ X₀ ∧ 0 ≤ X₆ ∧ X₄ ≤ X₆ ∧ 1 ≤ X₀+X₆ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀ for location eval_non_linear09_bb5_in_v1

Found invariant X₄ ≤ X₉ ∧ 1+X₆ ≤ X₀ ∧ 1 ≤ X₆ ∧ 1+X₄ ≤ X₆ ∧ 3 ≤ X₀+X₆ ∧ X₄ ≤ 0 ∧ 2+X₄ ≤ X₀ ∧ 2 ≤ X₀ for location eval_non_linear09_bb6_in_v2

Found invariant X₄ ≤ X₉ ∧ X₆ ≤ 0 ∧ X₄+X₆ ≤ 0 ∧ X₆ ≤ X₀ ∧ X₄ ≤ 0 for location eval_non_linear09_bb7_in

Found invariant 1 ≤ X₉ ∧ 2 ≤ X₄+X₉ ∧ X₄ ≤ X₉ ∧ 1 ≤ X₄ for location eval_non_linear09_bb2_in

Found invariant X₄ ≤ X₉ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₆ ∧ 1+X₄ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₀ ≤ X₆ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₀ for location eval_non_linear09_bb6_in_v1

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₃₂: X₉ {O(n)}
t₃₃: X₉ {O(n)}
t₃₄: 1 {O(1)}
t₃₅: X₉ {O(n)}
t₃₆: 1 {O(1)}
t₃₇: X₉ {O(n)}
t₃₈: X₉ {O(n)}
t₃₉: X₉ {O(n)}
t₄₀: inf {Infinity}
t₄₁: inf {Infinity}
t₄₂: inf {Infinity}
t₄₃: inf {Infinity}
t₄₄: 1 {O(1)}
t₄₅: inf {Infinity}
t₄₆: 1 {O(1)}
t₄₇: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₃₂: X₉ {O(n)}
t₃₃: X₉ {O(n)}
t₃₄: 1 {O(1)}
t₃₅: X₉ {O(n)}
t₃₆: 1 {O(1)}
t₃₇: X₉ {O(n)}
t₃₈: X₉ {O(n)}
t₃₉: X₉ {O(n)}
t₄₀: inf {Infinity}
t₄₁: inf {Infinity}
t₄₂: inf {Infinity}
t₄₃: inf {Infinity}
t₄₄: 1 {O(1)}
t₄₅: inf {Infinity}
t₄₆: 1 {O(1)}
t₄₇: 1 {O(1)}

Sizebounds

t₃₂, X₄: X₉ {O(n)}
t₃₂, X₆: X₆ {O(n)}
t₃₂, X₇: X₉ {O(n)}
t₃₂, X₈: X₈ {O(n)}
t₃₂, X₉: X₉ {O(n)}
t₃₃, X₁: X₉ {O(n)}
t₃₃, X₂: 2 {O(1)}
t₃₃, X₃: X₉ {O(n)}
t₃₃, X₄: X₉ {O(n)}
t₃₃, X₅: X₉ {O(n)}
t₃₃, X₆: X₆ {O(n)}
t₃₃, X₇: X₉ {O(n)}
t₃₃, X₈: X₈ {O(n)}
t₃₃, X₉: X₉ {O(n)}
t₃₄, X₀: X₈ {O(n)}
t₃₄, X₁: X₁ {O(n)}
t₃₄, X₂: X₂ {O(n)}
t₃₄, X₃: X₃ {O(n)}
t₃₄, X₄: X₉ {O(n)}
t₃₄, X₅: X₅ {O(n)}
t₃₄, X₆: X₆ {O(n)}
t₃₄, X₇: X₇ {O(n)}
t₃₄, X₈: X₈ {O(n)}
t₃₄, X₉: X₉ {O(n)}
t₃₅, X₄: X₉ {O(n)}
t₃₅, X₆: X₆ {O(n)}
t₃₅, X₇: 2⋅X₉+X₇ {O(n)}
t₃₅, X₈: X₈ {O(n)}
t₃₅, X₉: X₉ {O(n)}
t₃₆, X₄: 3⋅X₉ {O(n)}
t₃₆, X₇: 2⋅X₉+X₇ {O(n)}
t₃₆, X₈: 3⋅X₈ {O(n)}
t₃₆, X₉: 3⋅X₉ {O(n)}
t₃₇, X₄: X₉ {O(n)}
t₃₇, X₆: X₆ {O(n)}
t₃₇, X₇: X₉ {O(n)}
t₃₇, X₈: X₈ {O(n)}
t₃₇, X₉: X₉ {O(n)}
t₃₈, X₄: X₉ {O(n)}
t₃₈, X₆: X₆ {O(n)}
t₃₈, X₇: X₉ {O(n)}
t₃₈, X₈: X₈ {O(n)}
t₃₈, X₉: X₉ {O(n)}
t₃₉, X₂: 0 {O(1)}
t₃₉, X₄: X₉ {O(n)}
t₃₉, X₆: X₆ {O(n)}
t₃₉, X₇: X₉ {O(n)}
t₃₉, X₈: X₈ {O(n)}
t₃₉, X₉: X₉ {O(n)}
t₄₀, X₄: X₉ {O(n)}
t₄₀, X₆: X₆ {O(n)}
t₄₀, X₇: X₉ {O(n)}
t₄₀, X₈: X₈ {O(n)}
t₄₀, X₉: X₉ {O(n)}
t₄₁, X₄: X₉ {O(n)}
t₄₁, X₆: X₆ {O(n)}
t₄₁, X₇: X₉ {O(n)}
t₄₁, X₈: X₈ {O(n)}
t₄₁, X₉: X₉ {O(n)}
t₄₂, X₄: X₉ {O(n)}
t₄₂, X₆: X₆ {O(n)}
t₄₂, X₇: X₉ {O(n)}
t₄₂, X₈: X₈ {O(n)}
t₄₂, X₉: X₉ {O(n)}
t₄₃, X₄: 3⋅X₉ {O(n)}
t₄₃, X₇: 2⋅X₉+X₇ {O(n)}
t₄₃, X₈: 3⋅X₈ {O(n)}
t₄₃, X₉: 3⋅X₉ {O(n)}
t₄₄, X₄: 6⋅X₉ {O(n)}
t₄₄, X₇: 2⋅X₇+4⋅X₉ {O(n)}
t₄₄, X₈: 6⋅X₈ {O(n)}
t₄₄, X₉: 6⋅X₉ {O(n)}
t₄₅, X₄: 3⋅X₉ {O(n)}
t₄₅, X₇: 2⋅X₉+X₇ {O(n)}
t₄₅, X₈: 3⋅X₈ {O(n)}
t₄₅, X₉: 3⋅X₉ {O(n)}
t₄₆, X₄: 6⋅X₉ {O(n)}
t₄₆, X₇: 2⋅X₇+4⋅X₉ {O(n)}
t₄₆, X₈: 6⋅X₈ {O(n)}
t₄₆, X₉: 6⋅X₉ {O(n)}
t₄₇, X₀: X₀ {O(n)}
t₄₇, X₁: X₁ {O(n)}
t₄₇, X₂: X₂ {O(n)}
t₄₇, X₃: X₃ {O(n)}
t₄₇, X₄: X₄ {O(n)}
t₄₇, X₅: X₅ {O(n)}
t₄₇, X₆: X₆ {O(n)}
t₄₇, X₇: X₇ {O(n)}
t₄₇, X₈: X₈ {O(n)}
t₄₇, X₉: X₉ {O(n)}