KoAT2 Proof Output

Initial Problem

Start: eval_twn15_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars:
Locations: eval_twn15_.critedge_in, eval_twn15_bb0_in, eval_twn15_bb10_in, eval_twn15_bb1_in, eval_twn15_bb2_in, eval_twn15_bb3_in, eval_twn15_bb4_in, eval_twn15_bb5_in, eval_twn15_bb6_in, eval_twn15_bb7_in, eval_twn15_bb8_in, eval_twn15_bb9_in, eval_twn15_start, eval_twn15_stop
Transitions:
t₂₁: eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_bb1_in(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₁: eval_twn15_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_bb1_in(X₅, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₂₂: eval_twn15_bb10_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₃: eval_twn15_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_bb10_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₀ ≤ 0
t₂: eval_twn15_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀
t₄: eval_twn15_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_bb3_in(X₀, X₀, X₉, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 ≤ 5+X₈ ∧ X₈ ≤ 5
t₅: eval_twn15_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 6+X₈ ≤ 0
t₆: eval_twn15_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 6 ≤ X₈
t₉: eval_twn15_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 ≤ X₁ ∧ X₁ ≤ 0
t₇: eval_twn15_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1+X₁ ≤ 0
t₈: eval_twn15_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₁
t₁₁: eval_twn15_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₂ ≤ (X₁)²+(X₈)⁵
t₁₀: eval_twn15_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1+(X₁)²+(X₈)⁵ ≤ X₂
t₁₂: eval_twn15_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_bb3_in(X₀, -2⋅X₁, 3⋅X₂-(X₈)³, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₁₄: eval_twn15_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₈ ≤ 0
t₁₃: eval_twn15_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_bb7_in(X₀, X₁, X₂, X₀, X₉, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₈
t₁₇: eval_twn15_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 ≤ X₃ ∧ X₃ ≤ 0
t₁₅: eval_twn15_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1+X₃ ≤ 0
t₁₆: eval_twn15_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₃
t₁₉: eval_twn15_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₄ ≤ (X₃)²+(X₈)⁵
t₁₈: eval_twn15_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_bb9_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1+(X₃)²+(X₈)⁵ ≤ X₄
t₂₀: eval_twn15_bb9_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_bb7_in(X₀, X₁, X₂, -2⋅X₃, 3⋅X₄-(X₈)³, X₅, X₆, X₇, X₈, X₉)
t₀: eval_twn15_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → eval_twn15_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)

Preprocessing

Eliminate variables [X₆; X₇] that do not contribute to the problem

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location eval_twn15_bb10_in

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_twn15_bb7_in

Found invariant X₀ ≤ X₅ for location eval_twn15_bb1_in

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location eval_twn15_stop

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_twn15_.critedge_in

Found invariant X₆ ≤ 5 ∧ X₆ ≤ 4+X₅ ∧ X₆ ≤ 4+X₀ ∧ 0 ≤ 5+X₆ ∧ 0 ≤ 4+X₅+X₆ ∧ 0 ≤ 4+X₀+X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_twn15_bb4_in

Found invariant X₆ ≤ 5 ∧ X₆ ≤ 4+X₅ ∧ X₆ ≤ 4+X₀ ∧ 0 ≤ 5+X₆ ∧ 0 ≤ 4+X₅+X₆ ∧ 0 ≤ 4+X₀+X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_twn15_bb3_in

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_twn15_bb6_in

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_twn15_bb8_in

Found invariant X₆ ≤ 5 ∧ X₆ ≤ 4+X₅ ∧ X₆ ≤ 4+X₀ ∧ 0 ≤ 5+X₆ ∧ 0 ≤ 4+X₅+X₆ ∧ 0 ≤ 4+X₀+X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_twn15_bb5_in

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_twn15_bb2_in

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_twn15_bb9_in

Problem after Preprocessing

Start: eval_twn15_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: eval_twn15_.critedge_in, eval_twn15_bb0_in, eval_twn15_bb10_in, eval_twn15_bb1_in, eval_twn15_bb2_in, eval_twn15_bb3_in, eval_twn15_bb4_in, eval_twn15_bb5_in, eval_twn15_bb6_in, eval_twn15_bb7_in, eval_twn15_bb8_in, eval_twn15_bb9_in, eval_twn15_start, eval_twn15_stop
Transitions:
t₄₆: eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb1_in(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₄₇: eval_twn15_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb1_in(X₅, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₄₈: eval_twn15_bb10_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0 ∧ X₀ ≤ X₅
t₄₉: eval_twn15_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb10_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0 ∧ X₀ ≤ X₅
t₅₀: eval_twn15_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ X₀ ≤ X₅
t₅₁: eval_twn15_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb3_in(X₀, X₀, X₇, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 5+X₆ ∧ X₆ ≤ 5 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₅₂: eval_twn15_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 6+X₆ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₅₃: eval_twn15_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 6 ≤ X₆ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₅₄: eval_twn15_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ 5+X₆ ∧ X₆ ≤ 5 ∧ 0 ≤ 4+X₀+X₆ ∧ X₆ ≤ 4+X₀ ∧ 0 ≤ 4+X₅+X₆ ∧ X₆ ≤ 4+X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₅₅: eval_twn15_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₁ ≤ 0 ∧ 0 ≤ 5+X₆ ∧ X₆ ≤ 5 ∧ 0 ≤ 4+X₀+X₆ ∧ X₆ ≤ 4+X₀ ∧ 0 ≤ 4+X₅+X₆ ∧ X₆ ≤ 4+X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₅₆: eval_twn15_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₁ ∧ 0 ≤ 5+X₆ ∧ X₆ ≤ 5 ∧ 0 ≤ 4+X₀+X₆ ∧ X₆ ≤ 4+X₀ ∧ 0 ≤ 4+X₅+X₆ ∧ X₆ ≤ 4+X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₅₇: eval_twn15_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂ ≤ (X₁)²+(X₆)⁵ ∧ 0 ≤ 5+X₆ ∧ X₆ ≤ 5 ∧ 0 ≤ 4+X₀+X₆ ∧ X₆ ≤ 4+X₀ ∧ 0 ≤ 4+X₅+X₆ ∧ X₆ ≤ 4+X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₅₈: eval_twn15_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+(X₁)²+(X₆)⁵ ≤ X₂ ∧ 0 ≤ 5+X₆ ∧ X₆ ≤ 5 ∧ 0 ≤ 4+X₀+X₆ ∧ X₆ ≤ 4+X₀ ∧ 0 ≤ 4+X₅+X₆ ∧ X₆ ≤ 4+X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₅₉: eval_twn15_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb3_in(X₀, -2⋅X₁, 3⋅X₂-(X₆)³, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 5+X₆ ∧ X₆ ≤ 5 ∧ 0 ≤ 4+X₀+X₆ ∧ X₆ ≤ 4+X₀ ∧ 0 ≤ 4+X₅+X₆ ∧ X₆ ≤ 4+X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₆₀: eval_twn15_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₆ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₆₁: eval_twn15_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb7_in(X₀, X₁, X₂, X₀, X₇, X₅, X₆, X₇) :|: 1 ≤ X₆ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅
t₆₂: eval_twn15_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₃ ∧ X₃ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₅+X₆ ∧ X₀ ≤ X₅
t₆₃: eval_twn15_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₃ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₅+X₆ ∧ X₀ ≤ X₅
t₆₄: eval_twn15_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₅+X₆ ∧ X₀ ≤ X₅
t₆₅: eval_twn15_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₄ ≤ (X₃)²+(X₆)⁵ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₅+X₆ ∧ X₀ ≤ X₅
t₆₆: eval_twn15_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb9_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+(X₃)²+(X₆)⁵ ≤ X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₅+X₆ ∧ X₀ ≤ X₅
t₆₇: eval_twn15_bb9_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb7_in(X₀, X₁, X₂, -2⋅X₃, 3⋅X₄-(X₆)³, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₅+X₆ ∧ X₀ ≤ X₅
t₆₈: eval_twn15_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)

MPRF for transition t₄₆: eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb1_in(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_twn15_.critedge_in: [X₀]
• eval_twn15_bb1_in: [X₀]
• eval_twn15_bb2_in: [X₀]
• eval_twn15_bb3_in: [X₀]
• eval_twn15_bb4_in: [X₀]
• eval_twn15_bb5_in: [X₀]
• eval_twn15_bb6_in: [X₀]
• eval_twn15_bb7_in: [X₀]
• eval_twn15_bb8_in: [X₀]
• eval_twn15_bb9_in: [X₀]

MPRF for transition t₅₀: eval_twn15_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₀ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_twn15_.critedge_in: [X₀-1]
• eval_twn15_bb1_in: [X₀]
• eval_twn15_bb2_in: [X₀-1]
• eval_twn15_bb3_in: [X₀-1]
• eval_twn15_bb4_in: [X₀-1]
• eval_twn15_bb5_in: [X₀-1]
• eval_twn15_bb6_in: [X₀-1]
• eval_twn15_bb7_in: [X₀-1]
• eval_twn15_bb8_in: [X₀-1]
• eval_twn15_bb9_in: [X₀-1]

MPRF for transition t₅₁: eval_twn15_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb3_in(X₀, X₀, X₇, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 5+X₆ ∧ X₆ ≤ 5 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

2⋅X₅+1 {O(n)}

MPRF:

• eval_twn15_.critedge_in: [X₀+X₅-2]
• eval_twn15_bb1_in: [X₀+X₅-1]
• eval_twn15_bb2_in: [X₀+X₅-1]
• eval_twn15_bb3_in: [X₀+X₅-2]
• eval_twn15_bb4_in: [X₀+X₅-2]
• eval_twn15_bb5_in: [X₀+X₅-2]
• eval_twn15_bb6_in: [X₀+X₅-1]
• eval_twn15_bb7_in: [X₀+X₅-1]
• eval_twn15_bb8_in: [X₀+X₅-1]
• eval_twn15_bb9_in: [X₀+X₅-1]

MPRF for transition t₅₂: eval_twn15_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 6+X₆ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

• eval_twn15_.critedge_in: [X₀]
• eval_twn15_bb1_in: [1+X₀]
• eval_twn15_bb2_in: [1+X₀]
• eval_twn15_bb3_in: [1+X₀]
• eval_twn15_bb4_in: [1+X₀]
• eval_twn15_bb5_in: [1+X₀]
• eval_twn15_bb6_in: [X₀]
• eval_twn15_bb7_in: [X₀]
• eval_twn15_bb8_in: [X₀]
• eval_twn15_bb9_in: [X₀]

MPRF for transition t₅₃: eval_twn15_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 6 ≤ X₆ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

MPRF for transition t₅₄: eval_twn15_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ 5+X₆ ∧ X₆ ≤ 5 ∧ 0 ≤ 4+X₀+X₆ ∧ X₆ ≤ 4+X₀ ∧ 0 ≤ 4+X₅+X₆ ∧ X₆ ≤ 4+X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

2⋅X₅+1 {O(n)}

MPRF:

• eval_twn15_.critedge_in: [X₀+X₅-2]
• eval_twn15_bb1_in: [X₀+X₅-1]
• eval_twn15_bb2_in: [X₀+X₅-1]
• eval_twn15_bb3_in: [X₀+X₅-1]
• eval_twn15_bb4_in: [X₀+X₅-1]
• eval_twn15_bb5_in: [X₀+X₅-1]
• eval_twn15_bb6_in: [X₀+X₅-1]
• eval_twn15_bb7_in: [X₀+X₅-1]
• eval_twn15_bb8_in: [X₀+X₅-1]
• eval_twn15_bb9_in: [X₀+X₅-1]

MPRF for transition t₅₇: eval_twn15_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂ ≤ (X₁)²+(X₆)⁵ ∧ 0 ≤ 5+X₆ ∧ X₆ ≤ 5 ∧ 0 ≤ 4+X₀+X₆ ∧ X₆ ≤ 4+X₀ ∧ 0 ≤ 4+X₅+X₆ ∧ X₆ ≤ 4+X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_twn15_.critedge_in: [X₀-1]
• eval_twn15_bb1_in: [X₀]
• eval_twn15_bb2_in: [X₀]
• eval_twn15_bb3_in: [X₀]
• eval_twn15_bb4_in: [X₀]
• eval_twn15_bb5_in: [X₀]
• eval_twn15_bb6_in: [X₀]
• eval_twn15_bb7_in: [X₀]
• eval_twn15_bb8_in: [X₀]
• eval_twn15_bb9_in: [X₀]

MPRF for transition t₆₀: eval_twn15_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₆ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

MPRF for transition t₆₁: eval_twn15_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_bb7_in(X₀, X₁, X₂, X₀, X₇, X₅, X₆, X₇) :|: 1 ≤ X₆ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅+X₆+1 {O(n)}

MPRF:

• eval_twn15_.critedge_in: [X₀+X₆]
• eval_twn15_bb1_in: [1+X₀+X₆]
• eval_twn15_bb2_in: [1+X₀+X₆]
• eval_twn15_bb3_in: [X₀+X₆]
• eval_twn15_bb4_in: [X₀+X₆]
• eval_twn15_bb5_in: [X₀+X₆]
• eval_twn15_bb6_in: [1+X₀+X₆]
• eval_twn15_bb7_in: [X₀+X₆]
• eval_twn15_bb8_in: [X₀+X₆]
• eval_twn15_bb9_in: [X₀+X₆]

MPRF for transition t₆₂: eval_twn15_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₃ ∧ X₃ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₅+X₆ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

MPRF for transition t₆₅: eval_twn15_bb8_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_twn15_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₄ ≤ (X₃)²+(X₆)⁵ ∧ 1 ≤ X₀ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₅+X₆ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

Cut unreachable locations [eval_twn15_bb4_in; eval_twn15_bb8_in] from the program graph

Cut unsatisfiable transition [t₅₄: eval_twn15_bb3_in→eval_twn15_.critedge_in; t₆₂: eval_twn15_bb7_in→eval_twn15_.critedge_in; t₁₃₂: eval_twn15_bb3_in→eval_twn15_bb4_in_v2; t₁₃₃: eval_twn15_bb3_in→eval_twn15_.critedge_in; t₁₄₃: eval_twn15_bb7_in→eval_twn15_bb8_in_v2; t₁₄₄: eval_twn15_bb7_in→eval_twn15_.critedge_in]

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 3+X₃ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 3+X₃ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2+X₃ ≤ 0 ∧ 3+X₃ ≤ X₀ ∧ 1+X₀+X₃ ≤ 0 ∧ 1 ≤ X₀ for location eval_twn15_bb8_in_v2

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location eval_twn15_bb10_in

Found invariant X₆ ≤ 5 ∧ X₆ ≤ 4+X₅ ∧ X₆ ≤ 4+X₁ ∧ X₆ ≤ 4+X₀ ∧ 0 ≤ 5+X₆ ∧ 0 ≤ 4+X₅+X₆ ∧ 0 ≤ 4+X₁+X₆ ∧ 0 ≤ 4+X₀+X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_twn15_bb4_in_v1

Found invariant X₇ ≤ X₄ ∧ X₄ ≤ X₇ ∧ 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location eval_twn15_bb7_in

Found invariant X₀ ≤ X₅ for location eval_twn15_bb1_in

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location eval_twn15_stop

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location eval_twn15_bb8_in_v1

Found invariant X₆ ≤ 5 ∧ X₆ ≤ 4+X₅ ∧ X₆ ≤ 3128+X₂ ∧ X₆ ≤ 4+X₁ ∧ X₆ ≤ 4+X₀ ∧ 0 ≤ 5+X₆ ∧ 0 ≤ 4+X₅+X₆ ∧ 0 ≤ 3128+X₂+X₆ ∧ 0 ≤ 4+X₁+X₆ ∧ 0 ≤ 4+X₀+X₆ ∧ 1 ≤ X₅ ∧ 0 ≤ 3122+X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ 3123+X₂ ∧ 0 ≤ 3122+X₁+X₂ ∧ X₁ ≤ 3124+X₂ ∧ 0 ≤ 3122+X₀+X₂ ∧ X₀ ≤ 3124+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_twn15_bb5_in_v2

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_twn15_.critedge_in

Found invariant X₆ ≤ 5 ∧ X₆ ≤ 4+X₅ ∧ X₆ ≤ 1+X₁ ∧ X₆ ≤ 4+X₀ ∧ 0 ≤ 5+X₆ ∧ 0 ≤ 4+X₅+X₆ ∧ 0 ≤ 1+X₁+X₆ ∧ 0 ≤ 4+X₀+X₆ ∧ 1 ≤ X₅ ∧ 5 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_twn15_bb3_in_v1

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_twn15_bb6_in

Found invariant X₆ ≤ 5 ∧ X₆ ≤ 4+X₅ ∧ X₆ ≤ 3125+X₂ ∧ X₁+X₆ ≤ 3 ∧ X₆ ≤ 4+X₀ ∧ 0 ≤ 5+X₆ ∧ 0 ≤ 4+X₅+X₆ ∧ 0 ≤ 3125+X₂+X₆ ∧ X₁ ≤ 3+X₆ ∧ 0 ≤ 4+X₀+X₆ ∧ 1 ≤ X₅ ∧ 0 ≤ 3119+X₂+X₅ ∧ 3+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 0 ≤ 3120+X₂ ∧ 0 ≤ 3122+X₁+X₂ ∧ X₁ ≤ 3118+X₂ ∧ 0 ≤ 3119+X₀+X₂ ∧ X₀ ≤ 3121+X₂ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location eval_twn15_bb5_in_v1

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location eval_twn15_bb2_in

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 5 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 5 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 4 ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 3+X₀ ≤ X₃ ∧ 1 ≤ X₀ for location eval_twn15_bb7_in_v1

Found invariant 2+X₆ ≤ X₄ ∧ 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 4 ≤ X₄+X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 3 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 2+X₃ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ 2+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location eval_twn15_bb9_in_v2

Found invariant 5+X₆ ≤ X₄ ∧ 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 7 ≤ X₄+X₆ ∧ 3+X₃ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 7 ≤ X₄+X₅ ∧ 3+X₃ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 6 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 8+X₃ ≤ X₄ ∧ 7 ≤ X₀+X₄ ∧ 5+X₀ ≤ X₄ ∧ 2+X₃ ≤ 0 ∧ 3+X₃ ≤ X₀ ∧ 1+X₀+X₃ ≤ 0 ∧ 1 ≤ X₀ for location eval_twn15_bb9_in_v1

Found invariant X₆ ≤ 5 ∧ X₆ ≤ 4+X₅ ∧ X₁+X₆ ≤ 3 ∧ X₆ ≤ 4+X₀ ∧ 0 ≤ 5+X₆ ∧ 0 ≤ 4+X₅+X₆ ∧ X₁ ≤ 3+X₆ ∧ 0 ≤ 4+X₀+X₆ ∧ 1 ≤ X₅ ∧ 3+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location eval_twn15_bb3_in_v2

Found invariant X₇ ≤ X₂ ∧ X₂ ≤ X₇ ∧ X₆ ≤ 5 ∧ X₆ ≤ 4+X₅ ∧ X₆ ≤ 4+X₁ ∧ X₆ ≤ 4+X₀ ∧ 0 ≤ 5+X₆ ∧ 0 ≤ 4+X₅+X₆ ∧ 0 ≤ 4+X₁+X₆ ∧ 0 ≤ 4+X₀+X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_twn15_bb3_in

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 3+X₃ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 3+X₃ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2+X₃ ≤ 0 ∧ 3+X₃ ≤ X₀ ∧ 1+X₀+X₃ ≤ 0 ∧ 1 ≤ X₀ for location eval_twn15_bb7_in_v2

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₄₆: X₅ {O(n)}
t₄₇: 1 {O(1)}
t₄₈: 1 {O(1)}
t₄₉: 1 {O(1)}
t₅₀: X₅ {O(n)}
t₅₁: 2⋅X₅+1 {O(n)}
t₅₂: X₅+1 {O(n)}
t₅₃: X₅+1 {O(n)}
t₅₄: 2⋅X₅+1 {O(n)}
t₅₅: inf {Infinity}
t₅₆: inf {Infinity}
t₅₇: X₅ {O(n)}
t₅₈: inf {Infinity}
t₅₉: inf {Infinity}
t₆₀: X₅ {O(n)}
t₆₁: X₅+X₆+1 {O(n)}
t₆₂: X₅ {O(n)}
t₆₃: inf {Infinity}
t₆₄: inf {Infinity}
t₆₅: X₅ {O(n)}
t₆₆: inf {Infinity}
t₆₇: inf {Infinity}
t₆₈: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₄₆: X₅ {O(n)}
t₄₇: 1 {O(1)}
t₄₈: 1 {O(1)}
t₄₉: 1 {O(1)}
t₅₀: X₅ {O(n)}
t₅₁: 2⋅X₅+1 {O(n)}
t₅₂: X₅+1 {O(n)}
t₅₃: X₅+1 {O(n)}
t₅₄: 2⋅X₅+1 {O(n)}
t₅₅: inf {Infinity}
t₅₆: inf {Infinity}
t₅₇: X₅ {O(n)}
t₅₈: inf {Infinity}
t₅₉: inf {Infinity}
t₆₀: X₅ {O(n)}
t₆₁: X₅+X₆+1 {O(n)}
t₆₂: X₅ {O(n)}
t₆₃: inf {Infinity}
t₆₄: inf {Infinity}
t₆₅: X₅ {O(n)}
t₆₆: inf {Infinity}
t₆₇: inf {Infinity}
t₆₈: 1 {O(1)}

Sizebounds

t₄₆, X₀: X₅ {O(n)}
t₄₆, X₅: X₅ {O(n)}
t₄₆, X₆: X₆+10 {O(n)}
t₄₆, X₇: X₇ {O(n)}
t₄₇, X₀: X₅ {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)}
t₄₈, X₀: 2⋅X₅ {O(n)}
t₄₈, X₅: 2⋅X₅ {O(n)}
t₄₈, X₆: 2⋅X₆+10 {O(n)}
t₄₈, X₇: 2⋅X₇ {O(n)}
t₄₉, X₀: 2⋅X₅ {O(n)}
t₄₉, X₅: 2⋅X₅ {O(n)}
t₄₉, X₆: 2⋅X₆+10 {O(n)}
t₄₉, X₇: 2⋅X₇ {O(n)}
t₅₀, X₀: X₅ {O(n)}
t₅₀, X₅: X₅ {O(n)}
t₅₀, X₆: X₆+10 {O(n)}
t₅₀, X₇: X₇ {O(n)}
t₅₁, X₀: X₅ {O(n)}
t₅₁, X₁: X₅ {O(n)}
t₅₁, X₂: X₇ {O(n)}
t₅₁, X₅: X₅ {O(n)}
t₅₁, X₆: 5 {O(1)}
t₅₁, X₇: X₇ {O(n)}
t₅₂, X₀: X₅ {O(n)}
t₅₂, X₅: X₅ {O(n)}
t₅₂, X₆: X₆+10 {O(n)}
t₅₂, X₇: X₇ {O(n)}
t₅₃, X₀: X₅ {O(n)}
t₅₃, X₅: X₅ {O(n)}
t₅₃, X₆: X₆+10 {O(n)}
t₅₃, X₇: X₇ {O(n)}
t₅₄, X₀: X₅ {O(n)}
t₅₄, X₁: 0 {O(1)}
t₅₄, X₅: X₅ {O(n)}
t₅₄, X₆: 5 {O(1)}
t₅₄, X₇: X₇ {O(n)}
t₅₅, X₀: X₅ {O(n)}
t₅₅, X₅: X₅ {O(n)}
t₅₅, X₆: 5 {O(1)}
t₅₅, X₇: X₇ {O(n)}
t₅₆, X₀: X₅ {O(n)}
t₅₆, X₅: X₅ {O(n)}
t₅₆, X₆: 5 {O(1)}
t₅₆, X₇: X₇ {O(n)}
t₅₇, X₀: X₅ {O(n)}
t₅₇, X₅: X₅ {O(n)}
t₅₇, X₆: 5 {O(1)}
t₅₇, X₇: X₇ {O(n)}
t₅₈, X₀: X₅ {O(n)}
t₅₈, X₅: X₅ {O(n)}
t₅₈, X₆: 5 {O(1)}
t₅₈, X₇: X₇ {O(n)}
t₅₉, X₀: X₅ {O(n)}
t₅₉, X₅: X₅ {O(n)}
t₅₉, X₆: 5 {O(1)}
t₅₉, X₇: X₇ {O(n)}
t₆₀, X₀: X₅ {O(n)}
t₆₀, X₅: X₅ {O(n)}
t₆₀, X₆: X₆+10 {O(n)}
t₆₀, X₇: X₇ {O(n)}
t₆₁, X₀: X₅ {O(n)}
t₆₁, X₃: X₅ {O(n)}
t₆₁, X₄: X₇ {O(n)}
t₆₁, X₅: X₅ {O(n)}
t₆₁, X₆: X₆+10 {O(n)}
t₆₁, X₇: X₇ {O(n)}
t₆₂, X₀: X₅ {O(n)}
t₆₂, X₃: 0 {O(1)}
t₆₂, X₅: X₅ {O(n)}
t₆₂, X₆: X₆+10 {O(n)}
t₆₂, X₇: X₇ {O(n)}
t₆₃, X₀: X₅ {O(n)}
t₆₃, X₅: X₅ {O(n)}
t₆₃, X₆: X₆+10 {O(n)}
t₆₃, X₇: X₇ {O(n)}
t₆₄, X₀: X₅ {O(n)}
t₆₄, X₅: X₅ {O(n)}
t₆₄, X₆: X₆+10 {O(n)}
t₆₄, X₇: X₇ {O(n)}
t₆₅, X₀: X₅ {O(n)}
t₆₅, X₅: X₅ {O(n)}
t₆₅, X₆: X₆+10 {O(n)}
t₆₅, X₇: X₇ {O(n)}
t₆₆, X₀: X₅ {O(n)}
t₆₆, X₅: X₅ {O(n)}
t₆₆, X₆: X₆+10 {O(n)}
t₆₆, X₇: X₇ {O(n)}
t₆₇, X₀: X₅ {O(n)}
t₆₇, X₅: X₅ {O(n)}
t₆₇, X₆: X₆+10 {O(n)}
t₆₇, X₇: X₇ {O(n)}
t₆₈, X₀: X₀ {O(n)}
t₆₈, X₁: X₁ {O(n)}
t₆₈, X₂: X₂ {O(n)}
t₆₈, X₃: X₃ {O(n)}
t₆₈, X₄: X₄ {O(n)}
t₆₈, X₅: X₅ {O(n)}
t₆₈, X₆: X₆ {O(n)}
t₆₈, X₇: X₇ {O(n)}