KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₆ ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₃+X₆ ∧ 1+X₁ ≤ X₆ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location eval_start_12

Found invariant 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₃ for location eval_start_bb1_in

Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₃ ≤ 0 for location eval_start_stop

Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₃ ≤ 0 for location eval_start_bb6_in

Found invariant X₆ ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₅+X₆ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₂+X₆ ∧ 1+X₁ ≤ X₆ ∧ 1 ≤ X₀+X₆ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₂+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location eval_start_bb5_in

Found invariant 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 0 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₀ for location eval_start_8

Found invariant X₆ ≤ X₅ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1 ≤ X₃+X₆ ∧ X₁ ≤ X₆ ∧ 0 ≤ X₀+X₆ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ X₁ ≤ X₅ ∧ 0 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location eval_start_bb3_in

Found invariant 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 0 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₀ for location eval_start_9

Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₄ for location eval_start__critedge_in

Found invariant 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₁+X₅ ∧ 0 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_start_bb2_in

Problem after Preprocessing

Start: eval_start_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef_0, nondef_1
Locations: eval_start_0, eval_start_1, eval_start_12, eval_start_13, eval_start_2, eval_start_3, eval_start_4, eval_start_5, eval_start_6, eval_start_8, eval_start_9, eval_start__critedge_in, eval_start_bb0_in, eval_start_bb1_in, eval_start_bb2_in, eval_start_bb3_in, eval_start_bb4_in, eval_start_bb5_in, eval_start_bb6_in, eval_start_start, eval_start_stop
Transitions:
t₂: eval_start_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: eval_start_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₉: eval_start_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_13(X₀, X₁, nondef_1, X₃, X₄, X₅, X₆) :|: X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₅+X₆ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 0 ∧ X₃ ≤ X₄ ∧ X₆ ≤ X₅
t₂₁: eval_start_13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start__critedge_in(X₀, X₁, X₂, X₀, X₄, X₆, X₆) :|: X₂ ≤ 0 ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₅+X₆ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 0 ∧ X₃ ≤ X₄ ∧ X₆ ≤ X₅
t₂₀: eval_start_13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₅+X₆ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 0 ∧ X₃ ≤ X₄ ∧ X₆ ≤ X₅
t₄: eval_start_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₅: eval_start_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₆: eval_start_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₇: eval_start_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: eval_start_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start__critedge_in(X₀, X₁, X₂, X₄, X₄, 0, X₆)
t₁₂: eval_start_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_9(X₀, nondef_0, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₄ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅
t₁₃: eval_start_9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₄ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅
t₁₄: eval_start_9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₅) :|: X₁ ≤ 0 ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₄ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅
t₉: eval_start__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅
t₁₀: eval_start__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 0 ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅
t₁: eval_start_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₁: eval_start_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_8(X₃-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅
t₁₅: eval_start_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start__critedge_in(X₀, X₁, X₂, X₀, X₄, 1+X₅, X₆) :|: X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₃+X₄ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅
t₁₇: eval_start_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start__critedge_in(X₀, X₁, X₂, X₀, X₄, X₆, X₆) :|: X₆ ≤ 0 ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₄+X₆ ∧ 2 ≤ X₃+X₄ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀+X₆ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₆ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆
t₁₆: eval_start_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₆ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₄+X₆ ∧ 2 ≤ X₃+X₄ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀+X₆ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₆ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆
t₁₈: eval_start_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₅+X₆ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 0 ∧ X₃ ≤ X₄ ∧ X₆ ≤ X₅
t₂₂: eval_start_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1) :|: X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₅+X₆ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 0 ∧ X₃ ≤ X₄ ∧ X₆ ≤ X₅
t₂₃: eval_start_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 0 ∧ X₃ ≤ X₄ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₅
t₀: eval_start_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

MPRF for transition t₉: eval_start__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_start_12: [X₃-1]
• eval_start_13: [X₃-1]
• eval_start_8: [X₀]
• eval_start_9: [X₀]
• eval_start__critedge_in: [X₃]
• eval_start_bb1_in: [X₃-1]
• eval_start_bb2_in: [X₃-1]
• eval_start_bb3_in: [X₀]
• eval_start_bb4_in: [X₀]
• eval_start_bb5_in: [X₀]

MPRF for transition t₁₁: eval_start_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_8(X₃-1, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

• eval_start_12: [1+X₀]
• eval_start_13: [X₃]
• eval_start_8: [1+X₀]
• eval_start_9: [1+X₀]
• eval_start__critedge_in: [1+X₃]
• eval_start_bb1_in: [1+X₃]
• eval_start_bb2_in: [X₃]
• eval_start_bb3_in: [1+X₀]
• eval_start_bb4_in: [1+X₀]
• eval_start_bb5_in: [X₃]

MPRF for transition t₁₂: eval_start_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_9(X₀, nondef_0, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₄ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_start_12: [X₃-1]
• eval_start_13: [X₃-1]
• eval_start_8: [X₃]
• eval_start_9: [X₃-1]
• eval_start__critedge_in: [X₃]
• eval_start_bb1_in: [X₃]
• eval_start_bb2_in: [X₃-1]
• eval_start_bb3_in: [X₀]
• eval_start_bb4_in: [X₀]
• eval_start_bb5_in: [X₃-1]

MPRF for transition t₁₃: eval_start_9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₄ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_start_12: [X₃]
• eval_start_13: [X₃]
• eval_start_8: [1+X₀]
• eval_start_9: [1+X₀]
• eval_start__critedge_in: [X₃]
• eval_start_bb1_in: [X₃]
• eval_start_bb2_in: [X₀]
• eval_start_bb3_in: [X₃]
• eval_start_bb4_in: [X₃]
• eval_start_bb5_in: [X₃]

MPRF for transition t₁₄: eval_start_9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₅) :|: X₁ ≤ 0 ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₄ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_start_12: [X₀]
• eval_start_13: [X₀]
• eval_start_8: [1+X₀]
• eval_start_9: [1+X₀]
• eval_start__critedge_in: [X₃]
• eval_start_bb1_in: [X₃]
• eval_start_bb2_in: [X₃]
• eval_start_bb3_in: [X₀]
• eval_start_bb4_in: [X₀]
• eval_start_bb5_in: [X₀]

MPRF for transition t₁₅: eval_start_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start__critedge_in(X₀, X₁, X₂, X₀, X₄, 1+X₅, X₆) :|: X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₃+X₄ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_start_12: [1+X₀]
• eval_start_13: [1+X₀]
• eval_start_8: [1+X₀]
• eval_start_9: [X₃]
• eval_start__critedge_in: [X₃]
• eval_start_bb1_in: [X₃]
• eval_start_bb2_in: [1+X₀]
• eval_start_bb3_in: [X₃]
• eval_start_bb4_in: [1+X₀]
• eval_start_bb5_in: [1+X₀]

MPRF for transition t₁₆: eval_start_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₆ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₄+X₆ ∧ 2 ≤ X₃+X₄ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀+X₆ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₆ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_start_12: [X₀+X₆]
• eval_start_13: [X₀+X₆]
• eval_start_8: [1+X₀+X₅]
• eval_start_9: [1+X₀+X₅]
• eval_start__critedge_in: [X₃+X₅]
• eval_start_bb1_in: [X₃+X₅]
• eval_start_bb2_in: [1+X₀+X₅]
• eval_start_bb3_in: [X₃+X₆]
• eval_start_bb4_in: [X₀+X₆]
• eval_start_bb5_in: [X₀+X₆]

MPRF for transition t₁₇: eval_start_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start__critedge_in(X₀, X₁, X₂, X₀, X₄, X₆, X₆) :|: X₆ ≤ 0 ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃+X₆ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₄+X₆ ∧ 2 ≤ X₃+X₄ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀+X₅ ∧ 0 ≤ X₀+X₆ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₆ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_start_12: [X₃]
• eval_start_13: [X₃]
• eval_start_8: [X₃]
• eval_start_9: [X₃]
• eval_start__critedge_in: [X₃]
• eval_start_bb1_in: [X₃]
• eval_start_bb2_in: [X₃]
• eval_start_bb3_in: [1+X₀]
• eval_start_bb4_in: [1+X₀]
• eval_start_bb5_in: [X₃]

MPRF for transition t₁₈: eval_start_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₅+X₆ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 0 ∧ X₃ ≤ X₄ ∧ X₆ ≤ X₅ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

• eval_start_12: [1+X₀+X₆]
• eval_start_13: [X₃+X₆]
• eval_start_8: [1+X₃+X₅]
• eval_start_9: [1+X₃+X₅]
• eval_start__critedge_in: [1+X₃+X₅]
• eval_start_bb1_in: [1+X₃+X₅]
• eval_start_bb2_in: [2⋅X₃+X₅-X₀]
• eval_start_bb3_in: [1+X₃+X₆]
• eval_start_bb4_in: [2+X₀+X₆]
• eval_start_bb5_in: [X₃+X₆]

MPRF for transition t₁₉: eval_start_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_13(X₀, X₁, nondef_1, X₃, X₄, X₅, X₆) :|: X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₅+X₆ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 0 ∧ X₃ ≤ X₄ ∧ X₆ ≤ X₅ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_start_12: [X₃+X₆]
• eval_start_13: [X₃+X₆-1]
• eval_start_8: [1+X₀+X₅]
• eval_start_9: [1+X₀+X₅]
• eval_start__critedge_in: [X₃+X₅]
• eval_start_bb1_in: [X₃+X₅]
• eval_start_bb2_in: [X₃+X₅]
• eval_start_bb3_in: [1+X₀+X₆]
• eval_start_bb4_in: [X₃+X₆]
• eval_start_bb5_in: [X₃+X₆-1]

MPRF for transition t₂₀: eval_start_13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₅+X₆ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 0 ∧ X₃ ≤ X₄ ∧ X₆ ≤ X₅ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

• eval_start_12: [1+X₃+X₆]
• eval_start_13: [1+X₃+X₆]
• eval_start_8: [1+X₃+X₅]
• eval_start_9: [2+X₀+X₅]
• eval_start__critedge_in: [1+X₃+X₅]
• eval_start_bb1_in: [1+X₃+X₅]
• eval_start_bb2_in: [1+X₃+X₅]
• eval_start_bb3_in: [1+X₃+X₆]
• eval_start_bb4_in: [2+X₀+X₆]
• eval_start_bb5_in: [1+X₀+X₆]

MPRF for transition t₂₁: eval_start_13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start__critedge_in(X₀, X₁, X₂, X₀, X₄, X₆, X₆) :|: X₂ ≤ 0 ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₅+X₆ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 0 ∧ X₃ ≤ X₄ ∧ X₆ ≤ X₅ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_start_12: [1+X₀]
• eval_start_13: [1+X₀]
• eval_start_8: [X₃]
• eval_start_9: [X₃]
• eval_start__critedge_in: [X₃]
• eval_start_bb1_in: [X₃]
• eval_start_bb2_in: [X₀]
• eval_start_bb3_in: [1+X₀]
• eval_start_bb4_in: [1+X₀]
• eval_start_bb5_in: [X₃]

MPRF for transition t₂₂: eval_start_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_start_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1) :|: X₃ ≤ 1+X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₀+X₆ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 1 ≤ X₆ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₂+X₅ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₄+X₆ ∧ 2 ≤ X₅+X₆ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 0 ∧ X₃ ≤ X₄ ∧ X₆ ≤ X₅ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_start_12: [X₃+X₆-1]
• eval_start_13: [X₃+X₆-1]
• eval_start_8: [X₃+X₅]
• eval_start_9: [X₃+X₅]
• eval_start__critedge_in: [X₃+X₅]
• eval_start_bb1_in: [X₃+X₅]
• eval_start_bb2_in: [X₃+X₅]
• eval_start_bb3_in: [X₃+X₆-1]
• eval_start_bb4_in: [X₀+X₆]
• eval_start_bb5_in: [X₃+X₆-1]

All Bounds

Timebounds

Overall timebound:13⋅X₄+14 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₄ {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₄+1 {O(n)}
t₁₂: X₄ {O(n)}
t₁₃: X₄ {O(n)}
t₁₄: X₄ {O(n)}
t₁₅: X₄ {O(n)}
t₁₆: X₄ {O(n)}
t₁₇: X₄ {O(n)}
t₁₈: X₄+1 {O(n)}
t₁₉: X₄ {O(n)}
t₂₀: X₄+1 {O(n)}
t₂₁: X₄ {O(n)}
t₂₂: X₄ {O(n)}
t₂₃: 1 {O(1)}

Costbounds

Overall costbound: 13⋅X₄+14 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₄ {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₄+1 {O(n)}
t₁₂: X₄ {O(n)}
t₁₃: X₄ {O(n)}
t₁₄: X₄ {O(n)}
t₁₅: X₄ {O(n)}
t₁₆: X₄ {O(n)}
t₁₇: X₄ {O(n)}
t₁₈: X₄+1 {O(n)}
t₁₉: X₄ {O(n)}
t₂₀: X₄+1 {O(n)}
t₂₁: X₄ {O(n)}
t₂₂: X₄ {O(n)}
t₂₃: 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)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₃, X₅: X₅ {O(n)}
t₃, X₆: X₆ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₆ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₆, X₆: X₆ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₅ {O(n)}
t₇, X₆: X₆ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₄ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: 0 {O(1)}
t₈, X₆: X₆ {O(n)}
t₉, X₀: 4⋅X₄+X₀ {O(n)}
t₉, X₃: X₄ {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: X₄ {O(n)}
t₉, X₆: X₄+X₆ {O(n)}
t₁₀, X₀: 4⋅X₄+X₀ {O(n)}
t₁₀, X₃: 4⋅X₄ {O(n)}
t₁₀, X₄: 4⋅X₄ {O(n)}
t₁₀, X₅: 2⋅X₄ {O(n)}
t₁₀, X₆: 2⋅X₄+2⋅X₆ {O(n)}
t₁₁, X₀: X₄ {O(n)}
t₁₁, X₃: X₄ {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₁₁, X₅: X₄ {O(n)}
t₁₁, X₆: X₄+X₆ {O(n)}
t₁₂, X₀: X₄ {O(n)}
t₁₂, X₃: X₄ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₂, X₅: X₄ {O(n)}
t₁₂, X₆: X₄+X₆ {O(n)}
t₁₃, X₀: X₄ {O(n)}
t₁₃, X₃: X₄ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₃, X₅: X₄ {O(n)}
t₁₃, X₆: X₄+X₆ {O(n)}
t₁₄, X₀: X₄ {O(n)}
t₁₄, X₃: X₄ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₄, X₅: X₄ {O(n)}
t₁₄, X₆: X₄ {O(n)}
t₁₅, X₀: X₄ {O(n)}
t₁₅, X₃: X₄ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₅, X₅: X₄ {O(n)}
t₁₅, X₆: X₄+X₆ {O(n)}
t₁₆, X₀: X₄ {O(n)}
t₁₆, X₃: X₄ {O(n)}
t₁₆, X₄: X₄ {O(n)}
t₁₆, X₅: X₄ {O(n)}
t₁₆, X₆: X₄ {O(n)}
t₁₇, X₀: 2⋅X₄ {O(n)}
t₁₇, X₃: X₄ {O(n)}
t₁₇, X₄: X₄ {O(n)}
t₁₇, X₅: 0 {O(1)}
t₁₇, X₆: 0 {O(1)}
t₁₈, X₀: X₄ {O(n)}
t₁₈, X₃: X₄ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₈, X₅: X₄ {O(n)}
t₁₈, X₆: X₄ {O(n)}
t₁₉, X₀: X₄ {O(n)}
t₁₉, X₃: X₄ {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₁₉, X₅: X₄ {O(n)}
t₁₉, X₆: X₄ {O(n)}
t₂₀, X₀: X₄ {O(n)}
t₂₀, X₃: X₄ {O(n)}
t₂₀, X₄: X₄ {O(n)}
t₂₀, X₅: X₄ {O(n)}
t₂₀, X₆: X₄ {O(n)}
t₂₁, X₀: X₄ {O(n)}
t₂₁, X₃: X₄ {O(n)}
t₂₁, X₄: X₄ {O(n)}
t₂₁, X₅: X₄ {O(n)}
t₂₁, X₆: X₄ {O(n)}
t₂₂, X₀: X₄ {O(n)}
t₂₂, X₃: X₄ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₂, X₅: X₄ {O(n)}
t₂₂, X₆: X₄ {O(n)}
t₂₃, X₀: 4⋅X₄+X₀ {O(n)}
t₂₃, X₃: 4⋅X₄ {O(n)}
t₂₃, X₄: 4⋅X₄ {O(n)}
t₂₃, X₅: 2⋅X₄ {O(n)}
t₂₃, X₆: 2⋅X₄+2⋅X₆ {O(n)}