KoAT2 Proof Output

Initial Problem

Start: eval_size13_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄
Temp_Vars:
Locations: eval_size13_bb0_in, eval_size13_bb1_in, eval_size13_bb2_in, eval_size13_bb3_in, eval_size13_bb4_in, eval_size13_bb5_in, eval_size13_bb6_in, eval_size13_bb7_in, eval_size13_start, eval_size13_stop
Transitions:
t₁: eval_size13_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb1_in(X₈, X₉, X₁₀, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₇, X₁₂, 0, X₁₄)
t₂: eval_size13_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₁₁
t₃: eval_size13_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₃) :|: X₁₁ ≤ 0
t₄: eval_size13_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb3_in(X₀, X₁, X₂, X₀, X₁, X₁₁-1, 1+(X₁₁)²+X₁₃-2⋅X₁₁, X₇, X₈, X₉, X₁₀, X₁₁, X₀+X₁, X₁₃, X₁₄)
t₆: eval_size13_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb1_in(X₃, X₄, X₃, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₅, X₁₂, X₆, X₁₄) :|: X₁₂ ≤ 0
t₅: eval_size13_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₁₂
t₇: eval_size13_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb3_in(X₀, X₁, X₂, X₂, X₇, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂-1, X₁₃, X₁₄)
t₈: eval_size13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₁₄
t₉: eval_size13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₁₄ ≤ 0
t₁₀: eval_size13_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄-1)
t₁₁: eval_size13_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄)
t₀: eval_size13_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄)

Preprocessing

Found invariant X₁₁ ≤ X₇ for location eval_size13_bb1_in

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₇+X₁₁ ∧ X₁₁ ≤ X₇ ∧ 1 ≤ X₁₁ for location eval_size13_bb2_in

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ 0 ∧ X₁₄ ≤ X₁₃ ∧ X₁₁+X₁₄ ≤ 0 ∧ X₁₁ ≤ 0 for location eval_size13_stop

Found invariant 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₇+X₁₁ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₅+X₁₁ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₁₁ for location eval_size13_bb3_in

Found invariant 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₇+X₁₂ ∧ 2 ≤ X₇+X₁₁ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₅+X₁₂ ∧ 1 ≤ X₅+X₁₁ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₁₂ ∧ 2 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁ for location eval_size13_bb4_in

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ X₁₃ ∧ X₁₁ ≤ 0 for location eval_size13_bb5_in

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ X₁₃ ∧ 1 ≤ X₁₄ ∧ 2 ≤ X₁₃+X₁₄ ∧ 1+X₁₁ ≤ X₁₄ ∧ 1 ≤ X₁₃ ∧ 1+X₁₁ ≤ X₁₃ ∧ X₁₁ ≤ 0 for location eval_size13_bb6_in

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ 0 ∧ X₁₄ ≤ X₁₃ ∧ X₁₁+X₁₄ ≤ 0 ∧ X₁₁ ≤ 0 for location eval_size13_bb7_in

Problem after Preprocessing

Start: eval_size13_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄
Temp_Vars:
Locations: eval_size13_bb0_in, eval_size13_bb1_in, eval_size13_bb2_in, eval_size13_bb3_in, eval_size13_bb4_in, eval_size13_bb5_in, eval_size13_bb6_in, eval_size13_bb7_in, eval_size13_start, eval_size13_stop
Transitions:
t₁: eval_size13_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb1_in(X₈, X₉, X₁₀, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₇, X₁₂, 0, X₁₄)
t₂: eval_size13_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₁₁ ∧ X₁₁ ≤ X₇
t₃: eval_size13_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₃) :|: X₁₁ ≤ 0 ∧ X₁₁ ≤ X₇
t₄: eval_size13_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb3_in(X₀, X₁, X₂, X₀, X₁, X₁₁-1, 1+(X₁₁)²+X₁₃-2⋅X₁₁, X₇, X₈, X₉, X₁₀, X₁₁, X₀+X₁, X₁₃, X₁₄) :|: 1 ≤ X₇ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₇+X₁₁ ∧ X₁₁ ≤ X₇
t₆: eval_size13_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb1_in(X₃, X₄, X₃, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₅, X₁₂, X₆, X₁₄) :|: X₁₂ ≤ 0 ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₅+X₇ ∧ 1 ≤ X₅+X₁₁ ∧ 1+X₅ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 1 ≤ X₇ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₇+X₁₁ ∧ 0 ≤ X₅ ∧ X₁₁ ≤ X₇
t₅: eval_size13_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₁₂ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₅+X₇ ∧ 1 ≤ X₅+X₁₁ ∧ 1+X₅ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 1 ≤ X₇ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₇+X₁₁ ∧ 0 ≤ X₅ ∧ X₁₁ ≤ X₇
t₇: eval_size13_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb3_in(X₀, X₁, X₂, X₂, X₇, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂-1, X₁₃, X₁₄) :|: X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₅+X₇ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₅+X₁₂ ∧ 1+X₅ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 1 ≤ X₇ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₂ ∧ 2 ≤ X₇+X₁₁ ∧ 2 ≤ X₇+X₁₂ ∧ 2 ≤ X₁₁+X₁₂ ∧ 0 ≤ X₅ ∧ X₁₁ ≤ X₇
t₈: eval_size13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₁₄ ∧ X₁₁ ≤ X₇ ∧ X₁₁ ≤ 0 ∧ X₁₄ ≤ X₁₃
t₉: eval_size13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₁₄ ≤ 0 ∧ X₁₁ ≤ X₇ ∧ X₁₁ ≤ 0 ∧ X₁₄ ≤ X₁₃
t₁₀: eval_size13_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄-1) :|: 1+X₁₁ ≤ X₁₃ ∧ 1+X₁₁ ≤ X₁₄ ∧ 1 ≤ X₁₃ ∧ 1 ≤ X₁₄ ∧ 2 ≤ X₁₃+X₁₄ ∧ X₁₁ ≤ X₇ ∧ X₁₁ ≤ 0 ∧ X₁₄ ≤ X₁₃
t₁₁: eval_size13_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₁₁ ≤ X₇ ∧ X₁₁ ≤ 0 ∧ X₁₁+X₁₄ ≤ 0 ∧ X₁₄ ≤ X₁₃ ∧ X₁₄ ≤ 0
t₀: eval_size13_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄)

MPRF for transition t₂: eval_size13_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₁₁ ∧ X₁₁ ≤ X₇ of depth 1:

new bound:

X₇+1 {O(n)}

MPRF:

• eval_size13_bb1_in: [1+X₁₁]
• eval_size13_bb2_in: [X₁₁]
• eval_size13_bb3_in: [X₁₁]
• eval_size13_bb4_in: [X₁₁]

MPRF for transition t₄: eval_size13_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb3_in(X₀, X₁, X₂, X₀, X₁, X₁₁-1, Temp_Int₉₅₆+Temp_Int₉₅₇+X₁₃-2⋅X₁₁, X₇, X₈, X₉, X₁₀, X₁₁, X₀+X₁, X₁₃, X₁₄) :|: 1 ≤ Temp_Int₉₅₇ ∧ X₁₁ ≤ Temp_Int₉₅₇ ∧ 1 ≤ X₇ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₇+X₁₁ ∧ X₁₁ ≤ X₇ of depth 1:

new bound:

X₇ {O(n)}

MPRF:

• eval_size13_bb1_in: [X₁₁]
• eval_size13_bb2_in: [X₁₁]
• eval_size13_bb3_in: [X₁₁-1]
• eval_size13_bb4_in: [X₁₁-1]

MPRF for transition t₆: eval_size13_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb1_in(X₃, X₄, X₃, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₅, X₁₂, X₆, X₁₄) :|: X₁₂ ≤ 0 ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₅+X₇ ∧ 1 ≤ X₅+X₁₁ ∧ 1+X₅ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 1 ≤ X₇ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₇+X₁₁ ∧ 0 ≤ X₅ ∧ X₁₁ ≤ X₇ of depth 1:

new bound:

X₇ {O(n)}

MPRF:

• eval_size13_bb1_in: [X₁₁]
• eval_size13_bb2_in: [X₁₁]
• eval_size13_bb3_in: [1+X₅]
• eval_size13_bb4_in: [1+X₅]

MPRF for transition t₅: eval_size13_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₁₂ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₅+X₇ ∧ 1 ≤ X₅+X₁₁ ∧ 1+X₅ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 1 ≤ X₇ ∧ 1 ≤ X₁₁ ∧ 2 ≤ X₇+X₁₁ ∧ 0 ≤ X₅ ∧ X₁₁ ≤ X₇ of depth 1:

new bound:

X₁₀⋅X₇+X₇⋅X₇+X₇⋅X₈+X₇⋅X₉+X₈+X₉ {O(n^2)}

MPRF:

• eval_size13_bb1_in: [X₀+X₁]
• eval_size13_bb2_in: [X₀+X₁]
• eval_size13_bb3_in: [X₁₂]
• eval_size13_bb4_in: [X₁₂-1]

MPRF for transition t₇: eval_size13_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_size13_bb3_in(X₀, X₁, X₂, X₂, X₇, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂-1, X₁₃, X₁₄) :|: X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₅+X₇ ∧ 1 ≤ X₅+X₁₁ ∧ 1 ≤ X₅+X₁₂ ∧ 1+X₅ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 1 ≤ X₇ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₂ ∧ 2 ≤ X₇+X₁₁ ∧ 2 ≤ X₇+X₁₂ ∧ 2 ≤ X₁₁+X₁₂ ∧ 0 ≤ X₅ ∧ X₁₁ ≤ X₇ of depth 1:

new bound:

X₁₀⋅X₇+X₇⋅X₇+X₇⋅X₈+X₇⋅X₉+X₈+X₉ {O(n^2)}

MPRF:

• eval_size13_bb1_in: [X₀+X₁]
• eval_size13_bb2_in: [X₀+X₁]
• eval_size13_bb3_in: [X₁₂]
• eval_size13_bb4_in: [X₁₂]

Found invariant X₁₁ ≤ X₇ for location eval_size13_bb1_in

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₇+X₁₁ ∧ X₁₁ ≤ X₇ ∧ 1 ≤ X₁₁ for location eval_size13_bb2_in

Found invariant 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₇+X₁₂ ∧ 2 ≤ X₇+X₁₁ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₅+X₁₂ ∧ 1 ≤ X₅+X₁₁ ∧ X₁₁ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁₂ ∧ 2 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁ for location eval_size13_bb4_in_v1

Found invariant X₇ ≤ X₄ ∧ 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₄+X₇ ∧ X₄ ≤ X₇ ∧ 2 ≤ X₇+X₁₂ ∧ 2 ≤ X₇+X₁₁ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₅+X₁₂ ∧ 1 ≤ X₅+X₁₁ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₄+X₁₂ ∧ 2 ≤ X₄+X₁₁ ∧ X₁₁ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁₂ ∧ 2 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁ for location eval_size13_bb4_in_v2

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ 0 ∧ X₁₄ ≤ X₁₃ ∧ X₁₁+X₁₄ ≤ 0 ∧ X₁₁ ≤ 0 for location eval_size13_stop

Found invariant X₇ ≤ X₄ ∧ 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₄+X₇ ∧ X₄ ≤ X₇ ∧ 1 ≤ X₇+X₁₂ ∧ 2 ≤ X₇+X₁₁ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 0 ≤ X₅+X₁₂ ∧ 1 ≤ X₅+X₁₁ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₁₂ ∧ 2 ≤ X₄+X₁₁ ∧ X₁₁ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁₂ ∧ 1 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁ for location eval_size13_bb3_in_v1

Found invariant 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₇+X₁₁ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₅+X₁₁ ∧ X₁₁ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁₁ for location eval_size13_bb3_in

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ X₁₃ ∧ X₁₁ ≤ 0 for location eval_size13_bb5_in

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ 0 ∧ X₁₄ ≤ X₁₃ ∧ X₁₁+X₁₄ ≤ 0 ∧ X₁₁ ≤ 0 for location eval_size13_bb7_in

Found invariant X₁₁ ≤ X₇ for location eval_size13_bb1_in

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ X₁₃ ∧ 1 ≤ X₁₄ ∧ 2 ≤ X₁₃+X₁₄ ∧ X₁₃ ≤ X₁₄ ∧ 1+X₁₁ ≤ X₁₄ ∧ 1 ≤ X₁₃ ∧ 1+X₁₁ ≤ X₁₃ ∧ X₁₁ ≤ 0 for location eval_size13_bb6_in_v1

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₇+X₁₁ ∧ X₁₁ ≤ X₇ ∧ 1 ≤ X₁₁ for location eval_size13_bb2_in

Found invariant X₁₁ ≤ X₇ ∧ 1+X₁₄ ≤ X₁₃ ∧ 1 ≤ X₁₄ ∧ 3 ≤ X₁₃+X₁₄ ∧ 1+X₁₁ ≤ X₁₄ ∧ 2 ≤ X₁₃ ∧ 2+X₁₁ ≤ X₁₃ ∧ X₁₁ ≤ 0 for location eval_size13_bb6_in_v2

Found invariant X₁₁ ≤ X₇ ∧ 1+X₁₄ ≤ X₁₃ ∧ 0 ≤ X₁₄ ∧ 1 ≤ X₁₃+X₁₄ ∧ X₁₁ ≤ X₁₄ ∧ 1 ≤ X₁₃ ∧ 1+X₁₁ ≤ X₁₃ ∧ X₁₁ ≤ 0 for location eval_size13_bb5_in_v1

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ 0 ∧ X₁₄ ≤ X₁₃ ∧ X₁₁+X₁₄ ≤ 0 ∧ X₁₁ ≤ 0 for location eval_size13_stop

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ X₁₃ ∧ X₁₃ ≤ X₁₄ ∧ X₁₁ ≤ 0 for location eval_size13_bb5_in

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ 0 ∧ X₁₄ ≤ X₁₃ ∧ X₁₁+X₁₄ ≤ 0 ∧ X₁₁ ≤ 0 for location eval_size13_bb7_in

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₇+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₇ {O(n)}
t₅: X₁₀⋅X₇+X₇⋅X₇+X₇⋅X₈+X₇⋅X₉+X₈+X₉ {O(n^2)}
t₆: X₇ {O(n)}
t₇: X₁₀⋅X₇+X₇⋅X₇+X₇⋅X₈+X₇⋅X₉+X₈+X₉ {O(n^2)}
t₈: inf {Infinity}
t₉: 1 {O(1)}
t₁₀: inf {Infinity}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₇+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₇ {O(n)}
t₅: X₁₀⋅X₇+X₇⋅X₇+X₇⋅X₈+X₇⋅X₉+X₈+X₉ {O(n^2)}
t₆: X₇ {O(n)}
t₇: X₁₀⋅X₇+X₇⋅X₇+X₇⋅X₈+X₇⋅X₉+X₈+X₉ {O(n^2)}
t₈: inf {Infinity}
t₉: 1 {O(1)}
t₁₀: inf {Infinity}
t₁₁: 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)}
t₀, X₁₃: X₁₃ {O(n)}
t₀, X₁₄: X₁₄ {O(n)}
t₁, X₀: X₈ {O(n)}
t₁, X₁: X₉ {O(n)}
t₁, X₂: X₁₀ {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: X₇ {O(n)}
t₁, X₁₂: X₁₂ {O(n)}
t₁, X₁₃: 0 {O(1)}
t₁, X₁₄: X₁₄ {O(n)}
t₂, X₀: X₁₀+X₈ {O(n)}
t₂, X₁: X₇+X₉ {O(n)}
t₂, X₂: X₁₀+X₈ {O(n)}
t₂, X₃: 2⋅X₁₀+2⋅X₈+X₃ {O(n)}
t₂, X₄: 2⋅X₇+X₄+X₉ {O(n)}
t₂, X₅: 2⋅X₇+X₅ {O(n)}
t₂, X₇: X₇ {O(n)}
t₂, X₈: X₈ {O(n)}
t₂, X₉: X₉ {O(n)}
t₂, X₁₀: X₁₀ {O(n)}
t₂, X₁₁: X₇ {O(n)}
t₂, X₁₂: 2⋅X₁₀+2⋅X₇+2⋅X₈+2⋅X₉+X₁₂ {O(n)}
t₂, X₁₄: X₁₄ {O(n)}
t₃, X₀: 2⋅X₈+X₁₀ {O(n)}
t₃, X₁: 2⋅X₉+X₇ {O(n)}
t₃, X₂: 2⋅X₁₀+X₈ {O(n)}
t₃, X₃: 2⋅X₁₀+2⋅X₈+X₃ {O(n)}
t₃, X₄: 2⋅X₇+X₄+X₉ {O(n)}
t₃, X₅: 2⋅X₇+X₅ {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⋅X₇ {O(n)}
t₃, X₁₂: 2⋅X₁₀+2⋅X₇+2⋅X₈+2⋅X₉+X₁₂ {O(n)}
t₄, X₀: X₁₀+X₈ {O(n)}
t₄, X₁: X₇+X₉ {O(n)}
t₄, X₂: X₁₀+X₈ {O(n)}
t₄, X₃: X₁₀+X₈ {O(n)}
t₄, X₄: X₇+X₉ {O(n)}
t₄, X₅: X₇ {O(n)}
t₄, X₇: X₇ {O(n)}
t₄, X₈: X₈ {O(n)}
t₄, X₉: X₉ {O(n)}
t₄, X₁₀: X₁₀ {O(n)}
t₄, X₁₁: X₇ {O(n)}
t₄, X₁₂: X₁₀+X₇+X₈+X₉ {O(n)}
t₄, X₁₄: X₁₄ {O(n)}
t₅, X₀: X₁₀+X₈ {O(n)}
t₅, X₁: X₇+X₉ {O(n)}
t₅, X₂: X₁₀+X₈ {O(n)}
t₅, X₃: 2⋅X₁₀+2⋅X₈ {O(n)}
t₅, X₄: 2⋅X₇+X₉ {O(n)}
t₅, X₅: X₇ {O(n)}
t₅, X₇: X₇ {O(n)}
t₅, X₈: X₈ {O(n)}
t₅, X₉: X₉ {O(n)}
t₅, X₁₀: X₁₀ {O(n)}
t₅, X₁₁: X₇ {O(n)}
t₅, X₁₂: X₁₀+X₇+X₈+X₉ {O(n)}
t₅, X₁₄: X₁₄ {O(n)}
t₆, X₀: X₁₀+X₈ {O(n)}
t₆, X₁: X₇+X₉ {O(n)}
t₆, X₂: X₁₀+X₈ {O(n)}
t₆, X₃: 2⋅X₁₀+2⋅X₈ {O(n)}
t₆, X₄: 2⋅X₇+X₉ {O(n)}
t₆, X₅: 2⋅X₇ {O(n)}
t₆, X₇: X₇ {O(n)}
t₆, X₈: X₈ {O(n)}
t₆, X₉: X₉ {O(n)}
t₆, X₁₀: X₁₀ {O(n)}
t₆, X₁₁: X₇ {O(n)}
t₆, X₁₂: 2⋅X₁₀+2⋅X₇+2⋅X₈+2⋅X₉ {O(n)}
t₆, X₁₄: X₁₄ {O(n)}
t₇, X₀: X₁₀+X₈ {O(n)}
t₇, X₁: X₇+X₉ {O(n)}
t₇, X₂: X₁₀+X₈ {O(n)}
t₇, X₃: X₁₀+X₈ {O(n)}
t₇, X₄: X₇ {O(n)}
t₇, X₅: X₇ {O(n)}
t₇, X₇: X₇ {O(n)}
t₇, X₈: X₈ {O(n)}
t₇, X₉: X₉ {O(n)}
t₇, X₁₀: X₁₀ {O(n)}
t₇, X₁₁: X₇ {O(n)}
t₇, X₁₂: X₁₀+X₇+X₈+X₉ {O(n)}
t₇, X₁₄: X₁₄ {O(n)}
t₈, X₀: 2⋅X₈+X₁₀ {O(n)}
t₈, X₁: 2⋅X₉+X₇ {O(n)}
t₈, X₂: 2⋅X₁₀+X₈ {O(n)}
t₈, X₃: 2⋅X₁₀+2⋅X₈+X₃ {O(n)}
t₈, X₄: 2⋅X₇+X₄+X₉ {O(n)}
t₈, X₅: 2⋅X₇+X₅ {O(n)}
t₈, X₇: 2⋅X₇ {O(n)}
t₈, X₈: 2⋅X₈ {O(n)}
t₈, X₉: 2⋅X₉ {O(n)}
t₈, X₁₀: 2⋅X₁₀ {O(n)}
t₈, X₁₁: 2⋅X₇ {O(n)}
t₈, X₁₂: 2⋅X₁₀+2⋅X₇+2⋅X₈+2⋅X₉+X₁₂ {O(n)}
t₉, X₀: 2⋅X₁₀+4⋅X₈ {O(n)}
t₉, X₁: 2⋅X₇+4⋅X₉ {O(n)}
t₉, X₂: 2⋅X₈+4⋅X₁₀ {O(n)}
t₉, X₃: 2⋅X₃+4⋅X₁₀+4⋅X₈ {O(n)}
t₉, X₄: 2⋅X₄+2⋅X₉+4⋅X₇ {O(n)}
t₉, X₅: 2⋅X₅+4⋅X₇ {O(n)}
t₉, X₇: 4⋅X₇ {O(n)}
t₉, X₈: 4⋅X₈ {O(n)}
t₉, X₉: 4⋅X₉ {O(n)}
t₉, X₁₀: 4⋅X₁₀ {O(n)}
t₉, X₁₁: 4⋅X₇ {O(n)}
t₉, X₁₂: 2⋅X₁₂+4⋅X₁₀+4⋅X₇+4⋅X₈+4⋅X₉ {O(n)}
t₁₀, X₀: 2⋅X₈+X₁₀ {O(n)}
t₁₀, X₁: 2⋅X₉+X₇ {O(n)}
t₁₀, X₂: 2⋅X₁₀+X₈ {O(n)}
t₁₀, X₃: 2⋅X₁₀+2⋅X₈+X₃ {O(n)}
t₁₀, X₄: 2⋅X₇+X₄+X₉ {O(n)}
t₁₀, X₅: 2⋅X₇+X₅ {O(n)}
t₁₀, X₇: 2⋅X₇ {O(n)}
t₁₀, X₈: 2⋅X₈ {O(n)}
t₁₀, X₉: 2⋅X₉ {O(n)}
t₁₀, X₁₀: 2⋅X₁₀ {O(n)}
t₁₀, X₁₁: 2⋅X₇ {O(n)}
t₁₀, X₁₂: 2⋅X₁₀+2⋅X₇+2⋅X₈+2⋅X₉+X₁₂ {O(n)}
t₁₁, X₀: 2⋅X₁₀+4⋅X₈ {O(n)}
t₁₁, X₁: 2⋅X₇+4⋅X₉ {O(n)}
t₁₁, X₂: 2⋅X₈+4⋅X₁₀ {O(n)}
t₁₁, X₃: 2⋅X₃+4⋅X₁₀+4⋅X₈ {O(n)}
t₁₁, X₄: 2⋅X₄+2⋅X₉+4⋅X₇ {O(n)}
t₁₁, X₅: 2⋅X₅+4⋅X₇ {O(n)}
t₁₁, X₇: 4⋅X₇ {O(n)}
t₁₁, X₈: 4⋅X₈ {O(n)}
t₁₁, X₉: 4⋅X₉ {O(n)}
t₁₁, X₁₀: 4⋅X₁₀ {O(n)}
t₁₁, X₁₁: 4⋅X₇ {O(n)}
t₁₁, X₁₂: 2⋅X₁₂+4⋅X₁₀+4⋅X₇+4⋅X₈+4⋅X₉ {O(n)}