KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ 1+X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_textbook_ex3_bb5_in

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ 1+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ for location eval_textbook_ex3_bb2_in

Found invariant X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ X₀ ≤ 1+X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_textbook_ex3_bb6_in

Found invariant 1 ≤ X₁ for location eval_textbook_ex3_bb1_in

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ 2+X₂ ∧ X₄ ≤ 1+X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_textbook_ex3_bb4_in

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location eval_textbook_ex3_bb3_in

Found invariant 1+X₅ ≤ X₁ ∧ 1 ≤ X₁ for location eval_textbook_ex3_bb8_in

Found invariant 1 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ X₃ ≤ 1+X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₁ for location eval_textbook_ex3_bb7_in

Found invariant 1+X₅ ≤ X₁ ∧ 1 ≤ X₁ for location eval_textbook_ex3_stop

Problem after Preprocessing

Start: eval_textbook_ex3_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: eval_textbook_ex3_bb0_in, eval_textbook_ex3_bb1_in, eval_textbook_ex3_bb2_in, eval_textbook_ex3_bb3_in, eval_textbook_ex3_bb4_in, eval_textbook_ex3_bb5_in, eval_textbook_ex3_bb6_in, eval_textbook_ex3_bb7_in, eval_textbook_ex3_bb8_in, eval_textbook_ex3_start, eval_textbook_ex3_stop
Transitions:
t₁: eval_textbook_ex3_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb1_in(X₀, 1, X₂, X₃, X₄, X₅)
t₂: eval_textbook_ex3_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb2_in(X₀, X₁, X₂, 1, X₄, X₅) :|: X₁ ≤ X₅ ∧ 1 ≤ X₁
t₃: eval_textbook_ex3_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₅ ≤ X₁ ∧ 1 ≤ X₁
t₄: eval_textbook_ex3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb3_in(X₀, X₁, X₁, X₃, X₄, X₅) :|: X₃ ≤ X₁ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₁ ≤ X₅
t₅: eval_textbook_ex3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₁ ≤ X₅
t₆: eval_textbook_ex3_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb4_in(1+X₂, X₁, X₂, X₃, 1, X₅) :|: 1+X₂ ≤ X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₃ ≤ X₅
t₇: eval_textbook_ex3_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb6_in(1+X₂, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₃ ≤ X₅
t₉: eval_textbook_ex3_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb3_in(X₀, X₁, X₀, X₃, X₄, X₅) :|: 1+X₀ ≤ X₄ ∧ X₄ ≤ 2+X₂ ∧ X₄ ≤ 1+X₀ ∧ X₀ ≤ 1+X₂ ∧ X₄ ≤ 1+X₅ ∧ 1+X₁ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₄+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₂
t₈: eval_textbook_ex3_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₀ ∧ X₄ ≤ 2+X₂ ∧ X₄ ≤ 1+X₀ ∧ X₀ ≤ 1+X₂ ∧ X₄ ≤ 1+X₅ ∧ 1+X₁ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₄+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₂
t₁₀: eval_textbook_ex3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb4_in(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₀ ≤ 1+X₂ ∧ X₄ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₄+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₅
t₁₁: eval_textbook_ex3_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb2_in(X₀, X₁, X₂, 1+X₃, X₄, X₅) :|: X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₅ ∧ 1+X₁ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₃ ≤ X₅
t₁₂: eval_textbook_ex3_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb1_in(X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₃+X₅ ∧ X₁ ≤ X₅
t₁₃: eval_textbook_ex3_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₁ ∧ 1+X₅ ≤ X₁
t₀: eval_textbook_ex3_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

MPRF for transition t₂: eval_textbook_ex3_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb2_in(X₀, X₁, X₂, 1, X₄, X₅) :|: X₁ ≤ X₅ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₅+2 {O(n)}

MPRF:

• eval_textbook_ex3_bb1_in: [1+X₅-X₁]
• eval_textbook_ex3_bb2_in: [X₅-X₁]
• eval_textbook_ex3_bb3_in: [X₅-X₁]
• eval_textbook_ex3_bb4_in: [X₅-X₁]
• eval_textbook_ex3_bb5_in: [X₅-X₁]
• eval_textbook_ex3_bb6_in: [X₂-X₁]
• eval_textbook_ex3_bb7_in: [X₅-X₁]

MPRF for transition t₅: eval_textbook_ex3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₁ ≤ X₅ of depth 1:

new bound:

X₅+3 {O(n)}

MPRF:

• eval_textbook_ex3_bb1_in: [2+X₅-X₁]
• eval_textbook_ex3_bb2_in: [2+X₅-X₁]
• eval_textbook_ex3_bb3_in: [2+X₅-X₁]
• eval_textbook_ex3_bb4_in: [2+X₅-X₁]
• eval_textbook_ex3_bb5_in: [2+X₅-X₁]
• eval_textbook_ex3_bb6_in: [2⋅X₀-X₁-X₂]
• eval_textbook_ex3_bb7_in: [1+X₅-X₁]

MPRF for transition t₁₂: eval_textbook_ex3_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb1_in(X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₃+X₅ ∧ X₁ ≤ X₅ of depth 1:

new bound:

X₅+2 {O(n)}

MPRF:

• eval_textbook_ex3_bb1_in: [1+X₅-X₁]
• eval_textbook_ex3_bb2_in: [1+X₅-X₁]
• eval_textbook_ex3_bb3_in: [1+X₅-X₁]
• eval_textbook_ex3_bb4_in: [1+X₅-X₁]
• eval_textbook_ex3_bb5_in: [1+X₅-X₁]
• eval_textbook_ex3_bb6_in: [1+X₅-X₁]
• eval_textbook_ex3_bb7_in: [1+X₅-X₁]

MPRF for transition t₄: eval_textbook_ex3_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb3_in(X₀, X₁, X₁, X₃, X₄, X₅) :|: X₃ ≤ X₁ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₁ ≤ X₅ of depth 1:

new bound:

X₅⋅X₅+3⋅X₅ {O(n^2)}

MPRF:

• eval_textbook_ex3_bb1_in: [X₅]
• eval_textbook_ex3_bb2_in: [1+X₅-X₃]
• eval_textbook_ex3_bb3_in: [X₅-X₃]
• eval_textbook_ex3_bb4_in: [X₅-X₃]
• eval_textbook_ex3_bb5_in: [X₅-X₃]
• eval_textbook_ex3_bb6_in: [X₀-1-X₃]
• eval_textbook_ex3_bb7_in: [X₅-X₃]

MPRF for transition t₇: eval_textbook_ex3_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb6_in(1+X₂, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₃ ≤ X₅ of depth 1:

new bound:

X₅⋅X₅+3⋅X₅ {O(n^2)}

MPRF:

• eval_textbook_ex3_bb1_in: [X₅]
• eval_textbook_ex3_bb2_in: [1+X₅-X₃]
• eval_textbook_ex3_bb3_in: [1+X₅-X₃]
• eval_textbook_ex3_bb4_in: [1+X₅-X₃]
• eval_textbook_ex3_bb5_in: [1+X₅-X₃]
• eval_textbook_ex3_bb6_in: [X₅-X₃]
• eval_textbook_ex3_bb7_in: [X₅-X₃]

MPRF for transition t₁₁: eval_textbook_ex3_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb2_in(X₀, X₁, X₂, 1+X₃, X₄, X₅) :|: X₀ ≤ 1+X₂ ∧ X₀ ≤ 1+X₅ ∧ 1+X₁ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₃+X₅ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₃ ≤ X₅ of depth 1:

new bound:

5⋅X₅⋅X₅+19⋅X₅+14 {O(n^2)}

MPRF:

• eval_textbook_ex3_bb1_in: [3⋅X₅-2⋅X₁]
• eval_textbook_ex3_bb2_in: [1+3⋅X₅-2⋅X₁-X₃]
• eval_textbook_ex3_bb3_in: [1+3⋅X₅-2⋅X₁-X₃]
• eval_textbook_ex3_bb4_in: [1+3⋅X₅-2⋅X₁-X₃]
• eval_textbook_ex3_bb5_in: [X₀+3⋅X₅-2⋅X₁-X₂-X₃]
• eval_textbook_ex3_bb6_in: [2⋅X₀+X₅-1-2⋅X₁-X₃]
• eval_textbook_ex3_bb7_in: [3⋅X₅-2⋅X₁-X₃]

MPRF for transition t₆: eval_textbook_ex3_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb4_in(1+X₂, X₁, X₂, X₃, 1, X₅) :|: 1+X₂ ≤ X₅ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₃ ≤ X₅ of depth 1:

new bound:

30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+315⋅X₅+174 {O(n^3)}

MPRF:

• eval_textbook_ex3_bb1_in: [3+3⋅X₅-3⋅X₁]
• eval_textbook_ex3_bb2_in: [3+3⋅X₅-3⋅X₁]
• eval_textbook_ex3_bb3_in: [2+X₅-X₂]
• eval_textbook_ex3_bb4_in: [2+X₅-X₀]
• eval_textbook_ex3_bb5_in: [2+X₅-X₀]
• eval_textbook_ex3_bb6_in: [X₅-X₂]
• eval_textbook_ex3_bb7_in: [3⋅X₅-3⋅X₁]

MPRF for transition t₉: eval_textbook_ex3_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb3_in(X₀, X₁, X₀, X₃, X₄, X₅) :|: 1+X₀ ≤ X₄ ∧ X₄ ≤ 2+X₂ ∧ X₄ ≤ 1+X₀ ∧ X₀ ≤ 1+X₂ ∧ X₄ ≤ 1+X₅ ∧ 1+X₁ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₄+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₂ of depth 1:

new bound:

10⋅X₅⋅X₅⋅X₅+53⋅X₅⋅X₅+86⋅X₅+43 {O(n^3)}

MPRF:

• eval_textbook_ex3_bb1_in: [X₅-X₁]
• eval_textbook_ex3_bb2_in: [X₅-X₁]
• eval_textbook_ex3_bb3_in: [X₅-X₂]
• eval_textbook_ex3_bb4_in: [X₅-X₂]
• eval_textbook_ex3_bb5_in: [X₅-X₂]
• eval_textbook_ex3_bb6_in: [X₅-X₂]
• eval_textbook_ex3_bb7_in: [X₅-X₁]

MPRF for transition t₈: eval_textbook_ex3_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₀ ∧ X₄ ≤ 2+X₂ ∧ X₄ ≤ 1+X₀ ∧ X₀ ≤ 1+X₂ ∧ X₄ ≤ 1+X₅ ∧ 1+X₁ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₄+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₂ of depth 1:

new bound:

600⋅X₅⋅X₅⋅X₅⋅X₅⋅X₅⋅X₅+6660⋅X₅⋅X₅⋅X₅⋅X₅⋅X₅+29944⋅X₅⋅X₅⋅X₅⋅X₅+69710⋅X₅⋅X₅⋅X₅+88568⋅X₅⋅X₅+58224⋅X₅+15480 {O(n^6)}

MPRF:

• eval_textbook_ex3_bb1_in: [2⋅X₅]
• eval_textbook_ex3_bb2_in: [2⋅X₅]
• eval_textbook_ex3_bb3_in: [2⋅X₂]
• eval_textbook_ex3_bb4_in: [X₀+X₁-X₄]
• eval_textbook_ex3_bb5_in: [X₀+X₁-1-X₄]
• eval_textbook_ex3_bb6_in: [X₀+X₂-1]
• eval_textbook_ex3_bb7_in: [2⋅X₅]

MPRF for transition t₁₀: eval_textbook_ex3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb4_in(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₀ ≤ 1+X₂ ∧ X₄ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₄+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₅ of depth 1:

new bound:

10⋅X₅⋅X₅⋅X₅⋅X₅+53⋅X₅⋅X₅⋅X₅+86⋅X₅⋅X₅+44⋅X₅ {O(n^4)}

MPRF:

• eval_textbook_ex3_bb1_in: [X₅]
• eval_textbook_ex3_bb2_in: [X₅]
• eval_textbook_ex3_bb3_in: [X₅]
• eval_textbook_ex3_bb4_in: [1+X₀-X₄]
• eval_textbook_ex3_bb5_in: [1+X₀-X₄]
• eval_textbook_ex3_bb6_in: [X₅]
• eval_textbook_ex3_bb7_in: [X₅]

knowledge_propagation leads to new time bound 10⋅X₅⋅X₅⋅X₅⋅X₅+83⋅X₅⋅X₅⋅X₅+260⋅X₅⋅X₅+359⋅X₅+174 {O(n^4)} for transition t₈: eval_textbook_ex3_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_textbook_ex3_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₀ ∧ X₄ ≤ 2+X₂ ∧ X₄ ≤ 1+X₀ ∧ X₀ ≤ 1+X₂ ∧ X₄ ≤ 1+X₅ ∧ 1+X₁ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₄+X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₂

Cut unsatisfiable transition [t₅: eval_textbook_ex3_bb2_in→eval_textbook_ex3_bb7_in; t₇₄: eval_textbook_ex3_bb2_in→eval_textbook_ex3_bb7_in]

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ for location eval_textbook_ex3_bb2_in

Found invariant X₅ ≤ X₂ ∧ X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 5 ≤ X₃+X₅ ∧ X₃ ≤ 1+X₅ ∧ 4 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 4 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 5 ≤ X₀+X₅ ∧ X₀ ≤ 1+X₅ ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 5 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 3 ≤ X₀ for location eval_textbook_ex3_bb2_in_v3

Found invariant 1+X₅ ≤ X₄ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 4 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 5 ≤ X₀+X₅ ∧ X₀ ≤ 1+X₅ ∧ X₄ ≤ 1+X₂ ∧ X₄ ≤ X₀ ∧ 3 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 5 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 6 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location eval_textbook_ex3_bb6_in_v2

Found invariant 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ 2 ∧ X₄ ≤ 1+X₃ ∧ X₄ ≤ 1+X₂ ∧ X₄ ≤ 1+X₁ ∧ X₄ ≤ X₀ ∧ 2 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 4 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_textbook_ex3_bb5_in_v2

Found invariant 1+X₅ ≤ X₄ ∧ X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 4 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 5 ≤ X₀+X₅ ∧ X₀ ≤ 1+X₅ ∧ X₄ ≤ 1+X₂ ∧ X₄ ≤ X₀ ∧ 3 ≤ X₄ ∧ 5 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 5 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 6 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₁ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location eval_textbook_ex3_bb2_in_v1

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location eval_textbook_ex3_bb3_in_v1

Found invariant 2 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 4 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ 1+X₂ ∧ X₄ ≤ 1+X₀ ∧ 3 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 5 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 5 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_textbook_ex3_bb3_in_v2

Found invariant 1 ≤ X₁ for location eval_textbook_ex3_bb1_in

Found invariant X₅ ≤ X₂ ∧ X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ X₃ ≤ 1+X₅ ∧ 2 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ X₀ ≤ 1+X₅ ∧ X₃ ≤ 2 ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location eval_textbook_ex3_bb2_in_v2

Found invariant 2 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ 1 ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_textbook_ex3_bb4_in_v1

Found invariant X₅ ≤ X₂ ∧ X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ 2 ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 4 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 4 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 5 ≤ X₀+X₅ ∧ X₀ ≤ 1+X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 3 ≤ X₀ for location eval_textbook_ex3_bb3_in_v4

Found invariant 1+X₅ ≤ X₁ ∧ 1 ≤ X₁ for location eval_textbook_ex3_stop

Found invariant 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₀ ∧ 3 ≤ X₅ ∧ 7 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 5 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 5 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 5 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 7 ≤ X₀+X₅ ∧ X₀ ≤ 1+X₅ ∧ X₄ ≤ X₀ ∧ 4 ≤ X₄ ∧ 6 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 6 ≤ X₂+X₄ ∧ 2+X₂ ≤ X₄ ∧ 6 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 8 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 6 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 6 ≤ X₀+X₂ ∧ 2+X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location eval_textbook_ex3_bb3_in_v3

Found invariant X₅ ≤ X₂ ∧ X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ X₀ ≤ 1+X₅ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location eval_textbook_ex3_bb6_in_v1

Found invariant 3 ≤ X₅ ∧ 6 ≤ X₄+X₅ ∧ X₄ ≤ X₅ ∧ 4 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 5 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 4 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 6 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ 1+X₂ ∧ X₄ ≤ X₀ ∧ 3 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 5 ≤ X₂+X₄ ∧ 4 ≤ X₁+X₄ ∧ 6 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location eval_textbook_ex3_bb5_in_v3

Found invariant 1+X₅ ≤ X₁ ∧ 1 ≤ X₁ for location eval_textbook_ex3_bb8_in

Found invariant 2 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 3 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 4 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ 2+X₂ ∧ X₄ ≤ 1+X₀ ∧ 3 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 4 ≤ X₂+X₄ ∧ 4 ≤ X₁+X₄ ∧ 5 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_textbook_ex3_bb4_in_v3

Found invariant X₅ ≤ X₂ ∧ 1+X₅ ≤ X₀ ∧ 1 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ X₃ ≤ 1+X₅ ∧ 2 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ X₀ ≤ 1+X₅ ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_textbook_ex3_bb7_in

All Bounds

Timebounds

Overall timebound:20⋅X₅⋅X₅⋅X₅⋅X₅+176⋅X₅⋅X₅⋅X₅+580⋅X₅⋅X₅+832⋅X₅+416 {O(n^4)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₅+2 {O(n)}
t₃: 1 {O(1)}
t₄: X₅⋅X₅+3⋅X₅ {O(n^2)}
t₅: X₅+3 {O(n)}
t₆: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+315⋅X₅+174 {O(n^3)}
t₇: X₅⋅X₅+3⋅X₅ {O(n^2)}
t₈: 10⋅X₅⋅X₅⋅X₅⋅X₅+83⋅X₅⋅X₅⋅X₅+260⋅X₅⋅X₅+359⋅X₅+174 {O(n^4)}
t₉: 10⋅X₅⋅X₅⋅X₅+53⋅X₅⋅X₅+86⋅X₅+43 {O(n^3)}
t₁₀: 10⋅X₅⋅X₅⋅X₅⋅X₅+53⋅X₅⋅X₅⋅X₅+86⋅X₅⋅X₅+44⋅X₅ {O(n^4)}
t₁₁: 5⋅X₅⋅X₅+19⋅X₅+14 {O(n^2)}
t₁₂: X₅+2 {O(n)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 20⋅X₅⋅X₅⋅X₅⋅X₅+176⋅X₅⋅X₅⋅X₅+580⋅X₅⋅X₅+832⋅X₅+416 {O(n^4)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₅+2 {O(n)}
t₃: 1 {O(1)}
t₄: X₅⋅X₅+3⋅X₅ {O(n^2)}
t₅: X₅+3 {O(n)}
t₆: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+315⋅X₅+174 {O(n^3)}
t₇: X₅⋅X₅+3⋅X₅ {O(n^2)}
t₈: 10⋅X₅⋅X₅⋅X₅⋅X₅+83⋅X₅⋅X₅⋅X₅+260⋅X₅⋅X₅+359⋅X₅+174 {O(n^4)}
t₉: 10⋅X₅⋅X₅⋅X₅+53⋅X₅⋅X₅+86⋅X₅+43 {O(n^3)}
t₁₀: 10⋅X₅⋅X₅⋅X₅⋅X₅+53⋅X₅⋅X₅⋅X₅+86⋅X₅⋅X₅+44⋅X₅ {O(n^4)}
t₁₁: 5⋅X₅⋅X₅+19⋅X₅+14 {O(n^2)}
t₁₂: X₅+2 {O(n)}
t₁₃: 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)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 1 {O(1)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+319⋅X₅+X₀+188 {O(n^3)}
t₂, X₁: X₅+3 {O(n)}
t₂, X₂: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+319⋅X₅+X₂+186 {O(n^3)}
t₂, X₃: 1 {O(1)}
t₂, X₄: X₄+X₅+4 {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+319⋅X₅+X₀+188 {O(n^3)}
t₃, X₁: X₅+4 {O(n)}
t₃, X₂: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+319⋅X₅+X₂+186 {O(n^3)}
t₃, X₃: 5⋅X₅⋅X₅+19⋅X₅+X₃+15 {O(n^2)}
t₃, X₄: 2⋅X₄+X₅+4 {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₄, X₀: 60⋅X₅⋅X₅⋅X₅+348⋅X₅⋅X₅+638⋅X₅+X₀+376 {O(n^3)}
t₄, X₁: X₅+3 {O(n)}
t₄, X₂: 2⋅X₅+6 {O(n)}
t₄, X₃: 5⋅X₅⋅X₅+19⋅X₅+15 {O(n^2)}
t₄, X₄: X₄+X₅+4 {O(n)}
t₄, X₅: X₅ {O(n)}
t₅, X₀: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+319⋅X₅+188 {O(n^3)}
t₅, X₁: X₅+3 {O(n)}
t₅, X₂: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+319⋅X₅+186 {O(n^3)}
t₅, X₃: 5⋅X₅⋅X₅+19⋅X₅+15 {O(n^2)}
t₅, X₄: X₄+X₅+4 {O(n)}
t₅, X₅: X₅ {O(n)}
t₆, X₀: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+317⋅X₅+180 {O(n^3)}
t₆, X₁: X₅+3 {O(n)}
t₆, X₂: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+319⋅X₅+186 {O(n^3)}
t₆, X₃: 5⋅X₅⋅X₅+19⋅X₅+15 {O(n^2)}
t₆, X₄: 1 {O(1)}
t₆, X₅: X₅ {O(n)}
t₇, X₀: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+319⋅X₅+188 {O(n^3)}
t₇, X₁: X₅+3 {O(n)}
t₇, X₂: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+319⋅X₅+186 {O(n^3)}
t₇, X₃: 5⋅X₅⋅X₅+19⋅X₅+15 {O(n^2)}
t₇, X₄: X₄+X₅+4 {O(n)}
t₇, X₅: X₅ {O(n)}
t₈, X₀: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+317⋅X₅+180 {O(n^3)}
t₈, X₁: X₅+3 {O(n)}
t₈, X₂: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+319⋅X₅+186 {O(n^3)}
t₈, X₃: 5⋅X₅⋅X₅+19⋅X₅+15 {O(n^2)}
t₈, X₄: X₅+4 {O(n)}
t₈, X₅: X₅ {O(n)}
t₉, X₀: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+317⋅X₅+180 {O(n^3)}
t₉, X₁: X₅+3 {O(n)}
t₉, X₂: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+317⋅X₅+180 {O(n^3)}
t₉, X₃: 5⋅X₅⋅X₅+19⋅X₅+15 {O(n^2)}
t₉, X₄: X₅+4 {O(n)}
t₉, X₅: X₅ {O(n)}
t₁₀, X₀: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+317⋅X₅+180 {O(n^3)}
t₁₀, X₁: X₅+3 {O(n)}
t₁₀, X₂: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+319⋅X₅+186 {O(n^3)}
t₁₀, X₃: 5⋅X₅⋅X₅+19⋅X₅+15 {O(n^2)}
t₁₀, X₄: X₅+4 {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₁, X₀: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+319⋅X₅+188 {O(n^3)}
t₁₁, X₁: X₅+3 {O(n)}
t₁₁, X₂: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+319⋅X₅+186 {O(n^3)}
t₁₁, X₃: 5⋅X₅⋅X₅+19⋅X₅+15 {O(n^2)}
t₁₁, X₄: X₄+X₅+4 {O(n)}
t₁₁, X₅: X₅ {O(n)}
t₁₂, X₀: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+319⋅X₅+188 {O(n^3)}
t₁₂, X₁: X₅+3 {O(n)}
t₁₂, X₂: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+319⋅X₅+186 {O(n^3)}
t₁₂, X₃: 5⋅X₅⋅X₅+19⋅X₅+15 {O(n^2)}
t₁₂, X₄: X₄+X₅+4 {O(n)}
t₁₂, X₅: X₅ {O(n)}
t₁₃, X₀: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+319⋅X₅+X₀+188 {O(n^3)}
t₁₃, X₁: X₅+4 {O(n)}
t₁₃, X₂: 30⋅X₅⋅X₅⋅X₅+174⋅X₅⋅X₅+319⋅X₅+X₂+186 {O(n^3)}
t₁₃, X₃: 5⋅X₅⋅X₅+19⋅X₅+X₃+15 {O(n^2)}
t₁₃, X₄: 2⋅X₄+X₅+4 {O(n)}
t₁₃, X₅: 2⋅X₅ {O(n)}