KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₆ ≤ X₂ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₂+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location eval_rank1_3

Found invariant 0 ≤ X₇ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 0 ≤ 1+X₄+X₇ ∧ 0 ≤ X₃+X₇ ∧ 0 ≤ X₂+X₇ ∧ 0 ≤ X₅ ∧ 0 ≤ 1+X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ 1+X₄ ∧ 0 ≤ 1+X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 0 ≤ 1+X₂+X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ for location eval_rank1_bb6_in

Found invariant 0 ≤ 1+X₅ ∧ X₃ ≤ X₂ for location eval_rank1_bb7_in

Found invariant 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₂+X₆ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location eval_rank1_.critedge_in

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ for location eval_rank1_bb2_in

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ for location eval_rank1_0

Found invariant 0 ≤ 1+X₅ ∧ X₃ ≤ X₂ for location eval_rank1_bb1_in

Found invariant 0 ≤ 1+X₅ ∧ X₃ ≤ X₂ for location eval_rank1_stop

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ for location eval_rank1_1

Found invariant X₆ ≤ X₂ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₂+X₆ ∧ 1 ≤ X₁+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_rank1_bb5_in

Problem after Preprocessing

Start: eval_rank1_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: nondef.0, nondef.1
Locations: eval_rank1_.critedge_in, eval_rank1_0, eval_rank1_1, eval_rank1_2, eval_rank1_3, eval_rank1_bb0_in, eval_rank1_bb1_in, eval_rank1_bb2_in, eval_rank1_bb3_in, eval_rank1_bb4_in, eval_rank1_bb5_in, eval_rank1_bb6_in, eval_rank1_bb7_in, eval_rank1_start, eval_rank1_stop
Transitions:
t₁₈: eval_rank1_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb6_in(X₀, X₁, X₂, X₃, X₃-1, X₅, X₆, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆
t₇: eval_rank1_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_1(nondef.0, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₅
t₈: eval_rank1_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₅, X₇) :|: 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₅
t₉: eval_rank1_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb6_in(X₀, X₁, X₂, X₃, X₃, X₅, X₆, X₅) :|: X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₅
t₁₄: eval_rank1_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_3(X₀, nondef.1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₂+X₆ ∧ X₆ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆
t₁₆: eval_rank1_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₂+X₆ ∧ X₆ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆
t₁₅: eval_rank1_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₂+X₆ ∧ X₆ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆
t₁: eval_rank1_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb1_in(X₀, X₁, X₂, X₂, X₄, 0, X₆, X₇)
t₂: eval_rank1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ 1+X₅ ∧ X₃ ≤ X₂
t₃: eval_rank1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₃ ≤ 0 ∧ 0 ≤ 1+X₅ ∧ X₃ ≤ X₂
t₄: eval_rank1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₅ ≤ 0 ∧ 0 ≤ 1+X₅ ∧ X₃ ≤ X₂
t₅: eval_rank1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₅
t₁₁: eval_rank1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₂ ≤ X₆ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆
t₁₀: eval_rank1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₆ ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆
t₁₂: eval_rank1_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₂+X₆ ∧ X₆ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆
t₁₇: eval_rank1_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₂+X₆ ∧ X₆ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆
t₁₉: eval_rank1_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb1_in(X₀, X₁, X₂, X₄, X₄, X₇-1, X₆, X₇) :|: 0 ≤ 1+X₂+X₄ ∧ 0 ≤ 1+X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 0 ≤ 1+X₄ ∧ 0 ≤ 1+X₄+X₅ ∧ 0 ≤ 1+X₄+X₇ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₇ ∧ 0 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₇ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 0 ≤ X₇
t₂₀: eval_rank1_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₅ ∧ X₃ ≤ X₂
t₀: eval_rank1_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)

MPRF for transition t₈: eval_rank1_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₅, X₇) :|: 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• eval_rank1_.critedge_in: [X₃]
• eval_rank1_0: [1+X₃]
• eval_rank1_1: [1+X₃]
• eval_rank1_2: [X₃]
• eval_rank1_3: [X₃]
• eval_rank1_bb1_in: [1+X₃]
• eval_rank1_bb2_in: [1+X₃]
• eval_rank1_bb3_in: [X₃]
• eval_rank1_bb4_in: [X₃]
• eval_rank1_bb5_in: [X₃]
• eval_rank1_bb6_in: [1+X₄]

MPRF for transition t₁₁: eval_rank1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₂ ≤ X₆ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆ of depth 1:

new bound:

2⋅X₂+1 {O(n)}

MPRF:

• eval_rank1_.critedge_in: [X₂+X₃]
• eval_rank1_0: [1+X₂+X₃]
• eval_rank1_1: [1+X₂+X₃]
• eval_rank1_2: [1+X₂+X₃]
• eval_rank1_3: [1+X₂+X₃]
• eval_rank1_bb1_in: [1+X₂+X₃]
• eval_rank1_bb2_in: [1+X₂+X₃]
• eval_rank1_bb3_in: [1+X₂+X₃]
• eval_rank1_bb4_in: [1+X₂+X₃]
• eval_rank1_bb5_in: [1+X₂+X₃]
• eval_rank1_bb6_in: [1+X₂+X₄]

MPRF for transition t₁₆: eval_rank1_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₂+X₆ ∧ X₆ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• eval_rank1_.critedge_in: [X₃]
• eval_rank1_0: [1+X₃]
• eval_rank1_1: [1+X₃]
• eval_rank1_2: [1+X₃]
• eval_rank1_3: [1+X₃]
• eval_rank1_bb1_in: [1+X₃]
• eval_rank1_bb2_in: [1+X₃]
• eval_rank1_bb3_in: [1+X₃]
• eval_rank1_bb4_in: [1+X₃]
• eval_rank1_bb5_in: [1+X₃]
• eval_rank1_bb6_in: [1+X₄]

MPRF for transition t₁₈: eval_rank1_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb6_in(X₀, X₁, X₂, X₃, X₃-1, X₅, X₆, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• eval_rank1_.critedge_in: [1+X₃]
• eval_rank1_0: [1+X₃]
• eval_rank1_1: [1+X₃]
• eval_rank1_2: [1+X₃]
• eval_rank1_3: [1+X₃]
• eval_rank1_bb1_in: [1+X₃]
• eval_rank1_bb2_in: [1+X₃]
• eval_rank1_bb3_in: [1+X₃]
• eval_rank1_bb4_in: [1+X₃]
• eval_rank1_bb5_in: [1+X₃]
• eval_rank1_bb6_in: [1+X₄]

MPRF for transition t₁₀: eval_rank1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₆ ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₆ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆ of depth 1:

new bound:

4⋅X₂⋅X₂+9⋅X₂+2 {O(n^2)}

MPRF:

• eval_rank1_.critedge_in: [X₂-X₆]
• eval_rank1_0: [1+4⋅X₂]
• eval_rank1_1: [1+4⋅X₂]
• eval_rank1_2: [X₂-X₆]
• eval_rank1_3: [X₂-X₆]
• eval_rank1_bb1_in: [1+4⋅X₂]
• eval_rank1_bb2_in: [1+4⋅X₂]
• eval_rank1_bb3_in: [1+X₂-X₆]
• eval_rank1_bb4_in: [X₂-X₆]
• eval_rank1_bb5_in: [X₂-X₆]
• eval_rank1_bb6_in: [1+4⋅X₂]

MPRF for transition t₁₂: eval_rank1_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₂+X₆ ∧ X₆ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆ of depth 1:

new bound:

X₂⋅X₂+3⋅X₂+2 {O(n^2)}

MPRF:

• eval_rank1_.critedge_in: [X₂-X₆]
• eval_rank1_0: [1+X₂]
• eval_rank1_1: [1+X₂]
• eval_rank1_2: [X₂-X₆]
• eval_rank1_3: [X₂-X₆]
• eval_rank1_bb1_in: [1+X₂]
• eval_rank1_bb2_in: [1+X₂]
• eval_rank1_bb3_in: [1+X₂-X₆]
• eval_rank1_bb4_in: [1+X₂-X₆]
• eval_rank1_bb5_in: [X₂-X₆]
• eval_rank1_bb6_in: [1+X₂]

MPRF for transition t₁₄: eval_rank1_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_3(X₀, nondef.1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₂+X₆ ∧ X₆ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆ of depth 1:

new bound:

7⋅X₂⋅X₂+24⋅X₂+14 {O(n^2)}

MPRF:

• eval_rank1_.critedge_in: [X₂-X₆]
• eval_rank1_0: [1+X₂+3⋅X₃]
• eval_rank1_1: [1+X₂+3⋅X₃]
• eval_rank1_2: [1+X₂-X₆]
• eval_rank1_3: [X₂-X₆]
• eval_rank1_bb1_in: [1+X₂+3⋅X₃]
• eval_rank1_bb2_in: [1+X₂+3⋅X₃]
• eval_rank1_bb3_in: [1+X₂-X₆]
• eval_rank1_bb4_in: [1+X₂-X₆]
• eval_rank1_bb5_in: [X₂-X₆]
• eval_rank1_bb6_in: [1+X₂+3⋅X₄]

MPRF for transition t₁₅: eval_rank1_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₂+X₆ ∧ X₆ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆ of depth 1:

new bound:

X₂⋅X₂+3⋅X₂+2 {O(n^2)}

MPRF:

• eval_rank1_.critedge_in: [1+X₂-X₆]
• eval_rank1_0: [1+X₂]
• eval_rank1_1: [1+X₂]
• eval_rank1_2: [1+X₂-X₆]
• eval_rank1_3: [1+X₂-X₆]
• eval_rank1_bb1_in: [1+X₂]
• eval_rank1_bb2_in: [1+X₂]
• eval_rank1_bb3_in: [1+X₂-X₆]
• eval_rank1_bb4_in: [1+X₂-X₆]
• eval_rank1_bb5_in: [X₂-X₆]
• eval_rank1_bb6_in: [1+X₂]

MPRF for transition t₁₇: eval_rank1_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, 1+X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₂+X₆ ∧ X₆ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₆ of depth 1:

new bound:

X₂⋅X₂+3⋅X₂+2 {O(n^2)}

MPRF:

MPRF for transition t₂: eval_rank1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₃ ∧ 0 ≤ X₅ ∧ 0 ≤ 1+X₅ ∧ X₃ ≤ X₂ of depth 1:

new bound:

X₂⋅X₂⋅X₂+4⋅X₂⋅X₂+6⋅X₂+4 {O(n^3)}

MPRF:

• eval_rank1_.critedge_in: [0]
• eval_rank1_0: [X₅]
• eval_rank1_1: [X₅]
• eval_rank1_2: [0]
• eval_rank1_3: [0]
• eval_rank1_bb1_in: [1+X₅]
• eval_rank1_bb2_in: [X₅]
• eval_rank1_bb3_in: [0]
• eval_rank1_bb4_in: [0]
• eval_rank1_bb5_in: [0]
• eval_rank1_bb6_in: [X₇]

MPRF for transition t₅: eval_rank1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₂⋅X₂⋅X₂+4⋅X₂⋅X₂+6⋅X₂+4 {O(n^3)}

MPRF:

• eval_rank1_.critedge_in: [0]
• eval_rank1_0: [X₅]
• eval_rank1_1: [X₅]
• eval_rank1_2: [0]
• eval_rank1_3: [0]
• eval_rank1_bb1_in: [1+X₅]
• eval_rank1_bb2_in: [1+X₅]
• eval_rank1_bb3_in: [0]
• eval_rank1_bb4_in: [0]
• eval_rank1_bb5_in: [0]
• eval_rank1_bb6_in: [X₇]

MPRF for transition t₇: eval_rank1_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_1(nondef.0, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₂⋅X₂⋅X₂+4⋅X₂⋅X₂+6⋅X₂+4 {O(n^3)}

MPRF:

• eval_rank1_.critedge_in: [0]
• eval_rank1_0: [1+X₅]
• eval_rank1_1: [X₅]
• eval_rank1_2: [0]
• eval_rank1_3: [0]
• eval_rank1_bb1_in: [1+X₅]
• eval_rank1_bb2_in: [1+X₅]
• eval_rank1_bb3_in: [0]
• eval_rank1_bb4_in: [0]
• eval_rank1_bb5_in: [0]
• eval_rank1_bb6_in: [X₇]

MPRF for transition t₉: eval_rank1_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb6_in(X₀, X₁, X₂, X₃, X₃, X₅, X₆, X₅) :|: X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₂⋅X₂⋅X₂+4⋅X₂⋅X₂+6⋅X₂+4 {O(n^3)}

MPRF:

• eval_rank1_.critedge_in: [0]
• eval_rank1_0: [1+X₅]
• eval_rank1_1: [1+X₅]
• eval_rank1_2: [0]
• eval_rank1_3: [0]
• eval_rank1_bb1_in: [1+X₅]
• eval_rank1_bb2_in: [1+X₅]
• eval_rank1_bb3_in: [0]
• eval_rank1_bb4_in: [0]
• eval_rank1_bb5_in: [0]
• eval_rank1_bb6_in: [X₇]

MPRF for transition t₁₉: eval_rank1_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_rank1_bb1_in(X₀, X₁, X₂, X₄, X₄, X₇-1, X₆, X₇) :|: 0 ≤ 1+X₂+X₄ ∧ 0 ≤ 1+X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 0 ≤ 1+X₄ ∧ 0 ≤ 1+X₄+X₅ ∧ 0 ≤ 1+X₄+X₇ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₂+X₅ ∧ 0 ≤ X₂+X₇ ∧ 0 ≤ X₃ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₃+X₇ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 0 ≤ X₇ of depth 1:

new bound:

X₂⋅X₂⋅X₂+4⋅X₂⋅X₂+7⋅X₂+5 {O(n^3)}

MPRF:

Cut unreachable locations [eval_rank1_1; eval_rank1_3] from the program graph

Cut unsatisfiable transition [t₄: eval_rank1_bb1_in→eval_rank1_bb7_in; t₁₀₀: eval_rank1_bb1_in→eval_rank1_bb7_in]

Found invariant X₇ ≤ X₆ ∧ X₇ ≤ 1+X₂ ∧ 0 ≤ X₇ ∧ 0 ≤ X₆+X₇ ∧ X₆ ≤ X₇ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 0 ≤ 1+X₄+X₇ ∧ 0 ≤ X₃+X₇ ∧ 0 ≤ X₂+X₇ ∧ 1 ≤ X₀+X₇ ∧ X₆ ≤ 1+X₂ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ 1+X₄+X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₂+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ 1+X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ 1+X₄ ∧ 0 ≤ 1+X₃+X₄ ∧ X₃ ≤ 1+X₄ ∧ 0 ≤ 1+X₂+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location eval_rank1_bb6_in

Found invariant 0 ≤ 1+X₅ ∧ X₃ ≤ X₂ for location eval_rank1_bb7_in

Found invariant X₆ ≤ 1+X₂ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₂+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location eval_rank1_.critedge_in

Found invariant X₇ ≤ 1+X₅ ∧ X₇ ≤ 1+X₂ ∧ 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 1 ≤ X₄+X₇ ∧ 1 ≤ X₃+X₇ ∧ 2 ≤ X₂+X₇ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ 1 ≤ X₂+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location eval_rank1_0_v2

Found invariant X₇ ≤ X₆ ∧ X₇ ≤ 1+X₅ ∧ X₇ ≤ 1+X₂ ∧ 0 ≤ X₇ ∧ 0 ≤ X₆+X₇ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 0 ≤ 1+X₄+X₇ ∧ 0 ≤ 1+X₃+X₇ ∧ 0 ≤ X₂+X₇ ∧ 1 ≤ X₀+X₇ ∧ X₆ ≤ 1+X₅ ∧ X₆ ≤ 1+X₂ ∧ 0 ≤ X₆ ∧ 0 ≤ 1+X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 0 ≤ 1+X₄+X₆ ∧ 0 ≤ 1+X₃+X₆ ∧ 0 ≤ X₂+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₂ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 2+X₄+X₅ ∧ 0 ≤ 2+X₃+X₅ ∧ 0 ≤ 1+X₂+X₅ ∧ 0 ≤ X₀+X₅ ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 0 ≤ 1+X₄ ∧ 0 ≤ 2+X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ 1+X₂+X₄ ∧ 0 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ 1+X₂+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location eval_rank1_bb1_in_v2

Found invariant X₅ ≤ 0 ∧ 0 ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location eval_rank1_bb1_in

Found invariant X₆ ≤ X₂ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1+X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_rank1_2_v2

Found invariant X₆ ≤ X₅ ∧ X₆ ≤ X₂ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₂+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location eval_rank1_bb3_in

Found invariant X₅ ≤ 0 ∧ X₅ ≤ X₃ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ for location eval_rank1_1_v1

Found invariant 0 ≤ 1+X₅ ∧ X₃ ≤ X₂ for location eval_rank1_stop

Found invariant X₇ ≤ X₅ ∧ X₇ ≤ X₂ ∧ 0 ≤ X₇ ∧ 0 ≤ X₅+X₇ ∧ X₅ ≤ X₇ ∧ 0 ≤ X₄+X₇ ∧ 0 ≤ X₃+X₇ ∧ 0 ≤ X₂+X₇ ∧ X₀ ≤ X₇ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ X₄+X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ X₀ ≤ X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 for location eval_rank1_bb6_in_v1

Found invariant X₆ ≤ X₅ ∧ X₆ ≤ X₂ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 0 ≤ X₃+X₆ ∧ 0 ≤ X₂+X₆ ∧ 1 ≤ X₁+X₆ ∧ 1 ≤ X₀+X₆ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_rank1_bb5_in_v1

Found invariant X₅ ≤ 0 ∧ X₅ ≤ X₃ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ for location eval_rank1_0_v1

Found invariant X₆ ≤ 1+X₂ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₂+X₆ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_rank1_bb3_in_v1

Found invariant X₅ ≤ 0 ∧ X₅ ≤ X₃ ∧ X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ for location eval_rank1_bb2_in_v1

Found invariant X₇ ≤ 1+X₅ ∧ X₇ ≤ X₂ ∧ 0 ≤ X₇ ∧ 0 ≤ 1+X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 0 ≤ X₄+X₇ ∧ 0 ≤ X₃+X₇ ∧ 0 ≤ X₂+X₇ ∧ X₀ ≤ X₇ ∧ 1+X₅ ≤ X₂ ∧ 0 ≤ 1+X₅ ∧ 0 ≤ 1+X₄+X₅ ∧ 0 ≤ 1+X₃+X₅ ∧ 0 ≤ 1+X₂+X₅ ∧ X₀ ≤ 1+X₅ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 for location eval_rank1_bb1_in_v1

Found invariant X₆ ≤ X₂ ∧ 1 ≤ X₆ ∧ 1 ≤ X₅+X₆ ∧ 1+X₅ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1+X₅ ≤ X₂ ∧ 0 ≤ X₅ ∧ 0 ≤ X₃+X₅ ∧ 1 ≤ X₂+X₅ ∧ 1 ≤ X₀+X₅ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location eval_rank1_3_v2

Cut unsatisfiable transition [t₁₁: eval_rank1_bb3_in→eval_rank1_.critedge_in; t₁₁₅: eval_rank1_bb3_in→eval_rank1_.critedge_in]

All Bounds

Timebounds

Overall timebound:5⋅X₂⋅X₂⋅X₂+34⋅X₂⋅X₂+78⋅X₂+52 {O(n^3)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂⋅X₂⋅X₂+4⋅X₂⋅X₂+6⋅X₂+4 {O(n^3)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₂⋅X₂⋅X₂+4⋅X₂⋅X₂+6⋅X₂+4 {O(n^3)}
t₇: X₂⋅X₂⋅X₂+4⋅X₂⋅X₂+6⋅X₂+4 {O(n^3)}
t₈: X₂+1 {O(n)}
t₉: X₂⋅X₂⋅X₂+4⋅X₂⋅X₂+6⋅X₂+4 {O(n^3)}
t₁₀: 4⋅X₂⋅X₂+9⋅X₂+2 {O(n^2)}
t₁₁: 2⋅X₂+1 {O(n)}
t₁₂: X₂⋅X₂+3⋅X₂+2 {O(n^2)}
t₁₄: 7⋅X₂⋅X₂+24⋅X₂+14 {O(n^2)}
t₁₅: X₂⋅X₂+3⋅X₂+2 {O(n^2)}
t₁₆: X₂+1 {O(n)}
t₁₇: X₂⋅X₂+3⋅X₂+2 {O(n^2)}
t₁₈: X₂+1 {O(n)}
t₁₉: X₂⋅X₂⋅X₂+4⋅X₂⋅X₂+7⋅X₂+5 {O(n^3)}
t₂₀: 1 {O(1)}

Costbounds

Overall costbound: 5⋅X₂⋅X₂⋅X₂+34⋅X₂⋅X₂+78⋅X₂+52 {O(n^3)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂⋅X₂⋅X₂+4⋅X₂⋅X₂+6⋅X₂+4 {O(n^3)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₂⋅X₂⋅X₂+4⋅X₂⋅X₂+6⋅X₂+4 {O(n^3)}
t₇: X₂⋅X₂⋅X₂+4⋅X₂⋅X₂+6⋅X₂+4 {O(n^3)}
t₈: X₂+1 {O(n)}
t₉: X₂⋅X₂⋅X₂+4⋅X₂⋅X₂+6⋅X₂+4 {O(n^3)}
t₁₀: 4⋅X₂⋅X₂+9⋅X₂+2 {O(n^2)}
t₁₁: 2⋅X₂+1 {O(n)}
t₁₂: X₂⋅X₂+3⋅X₂+2 {O(n^2)}
t₁₄: 7⋅X₂⋅X₂+24⋅X₂+14 {O(n^2)}
t₁₅: X₂⋅X₂+3⋅X₂+2 {O(n^2)}
t₁₆: X₂+1 {O(n)}
t₁₇: X₂⋅X₂+3⋅X₂+2 {O(n^2)}
t₁₈: X₂+1 {O(n)}
t₁₉: X₂⋅X₂⋅X₂+4⋅X₂⋅X₂+7⋅X₂+5 {O(n^3)}
t₂₀: 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)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₂ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: 0 {O(1)}
t₁, X₆: X₆ {O(n)}
t₁, X₇: X₇ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₂+1 {O(n)}
t₂, X₄: 3⋅X₂+X₄+5 {O(n)}
t₂, X₅: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₂, X₆: 2⋅X₂⋅X₂+6⋅X₂+X₆+6 {O(n^2)}
t₂, X₇: 2⋅X₂⋅X₂+6⋅X₂+X₇+6 {O(n^2)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₂+1 {O(n)}
t₃, X₄: 3⋅X₂+X₄+5 {O(n)}
t₃, X₅: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₃, X₆: 2⋅X₂⋅X₂+2⋅X₆+6⋅X₂+6 {O(n^2)}
t₃, X₇: 2⋅X₂⋅X₂+6⋅X₂+X₇+6 {O(n^2)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₂+1 {O(n)}
t₄, X₄: 3⋅X₂+5 {O(n)}
t₄, X₅: 1 {O(1)}
t₄, X₆: 2⋅X₂⋅X₂+6⋅X₂+X₆+6 {O(n^2)}
t₄, X₇: 2⋅X₂⋅X₂+6⋅X₂+6 {O(n^2)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₂+1 {O(n)}
t₅, X₄: 3⋅X₂+X₄+5 {O(n)}
t₅, X₅: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₅, X₆: 2⋅X₂⋅X₂+6⋅X₂+X₆+6 {O(n^2)}
t₅, X₇: 2⋅X₂⋅X₂+6⋅X₂+X₇+6 {O(n^2)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₂+1 {O(n)}
t₇, X₄: 3⋅X₂+X₄+5 {O(n)}
t₇, X₅: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₇, X₆: 2⋅X₂⋅X₂+6⋅X₂+X₆+6 {O(n^2)}
t₇, X₇: 2⋅X₂⋅X₂+6⋅X₂+X₇+6 {O(n^2)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₂+1 {O(n)}
t₈, X₄: 3⋅X₂+X₄+5 {O(n)}
t₈, X₅: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₈, X₆: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₈, X₇: 2⋅X₂⋅X₂+6⋅X₂+X₇+6 {O(n^2)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₂+1 {O(n)}
t₉, X₄: X₂+1 {O(n)}
t₉, X₅: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₉, X₆: 2⋅X₂⋅X₂+6⋅X₂+X₆+6 {O(n^2)}
t₉, X₇: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₂+1 {O(n)}
t₁₀, X₄: 3⋅X₂+X₄+5 {O(n)}
t₁₀, X₅: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₁₀, X₆: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₁₀, X₇: 2⋅X₂⋅X₂+6⋅X₂+X₇+6 {O(n^2)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₂+1 {O(n)}
t₁₁, X₄: 2⋅X₄+6⋅X₂+10 {O(n)}
t₁₁, X₅: 2⋅X₂⋅X₂+6⋅X₂+6 {O(n^2)}
t₁₁, X₆: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₁₁, X₇: 4⋅X₂⋅X₂+12⋅X₂+2⋅X₇+12 {O(n^2)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₂+1 {O(n)}
t₁₂, X₄: 3⋅X₂+X₄+5 {O(n)}
t₁₂, X₅: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₁₂, X₆: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₁₂, X₇: 2⋅X₂⋅X₂+6⋅X₂+X₇+6 {O(n^2)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₂+1 {O(n)}
t₁₄, X₄: 3⋅X₂+X₄+5 {O(n)}
t₁₄, X₅: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₁₄, X₆: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₁₄, X₇: 2⋅X₂⋅X₂+6⋅X₂+X₇+6 {O(n^2)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₂+1 {O(n)}
t₁₅, X₄: 3⋅X₂+X₄+5 {O(n)}
t₁₅, X₅: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₁₅, X₆: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₁₅, X₇: 2⋅X₂⋅X₂+6⋅X₂+X₇+6 {O(n^2)}
t₁₆, X₂: X₂ {O(n)}
t₁₆, X₃: X₂+1 {O(n)}
t₁₆, X₄: 3⋅X₂+X₄+5 {O(n)}
t₁₆, X₅: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₁₆, X₆: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₁₆, X₇: 2⋅X₂⋅X₂+6⋅X₂+X₇+6 {O(n^2)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₂+1 {O(n)}
t₁₇, X₄: 3⋅X₂+X₄+5 {O(n)}
t₁₇, X₅: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₁₇, X₆: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₁₇, X₇: 2⋅X₂⋅X₂+6⋅X₂+X₇+6 {O(n^2)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₂+1 {O(n)}
t₁₈, X₄: 2⋅X₂+4 {O(n)}
t₁₈, X₅: 3⋅X₂⋅X₂+9⋅X₂+9 {O(n^2)}
t₁₈, X₆: 2⋅X₂⋅X₂+6⋅X₂+6 {O(n^2)}
t₁₈, X₇: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₂+1 {O(n)}
t₁₉, X₄: 3⋅X₂+5 {O(n)}
t₁₉, X₅: X₂⋅X₂+3⋅X₂+3 {O(n^2)}
t₁₉, X₆: 2⋅X₂⋅X₂+6⋅X₂+X₆+6 {O(n^2)}
t₁₉, X₇: 2⋅X₂⋅X₂+6⋅X₂+6 {O(n^2)}
t₂₀, X₂: 3⋅X₂ {O(n)}
t₂₀, X₃: 3⋅X₂+2 {O(n)}
t₂₀, X₄: 6⋅X₂+X₄+10 {O(n)}
t₂₀, X₅: X₂⋅X₂+3⋅X₂+4 {O(n^2)}
t₂₀, X₆: 4⋅X₂⋅X₂+12⋅X₂+3⋅X₆+12 {O(n^2)}
t₂₀, X₇: 4⋅X₂⋅X₂+12⋅X₂+X₇+12 {O(n^2)}