KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ for location eval_ex1_10

Found invariant 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location eval_ex1_bb5_in

Found invariant X₅ ≤ X₂ ∧ 0 ≤ X₂ for location eval_ex1_bb6_in

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 0 ≤ X₂ for location eval_ex1_bb2_in

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location eval_ex1_16

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ for location eval_ex1_bb3_in

Found invariant 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ for location eval_ex1_9

Found invariant 0 ≤ X₂ for location eval_ex1_bb1_in

Found invariant 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ for location eval_ex1_bb4_in

Found invariant X₅ ≤ X₂ ∧ 0 ≤ X₂ for location eval_ex1_stop

Found invariant 1 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₄ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 0 ≤ X₂+X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ for location eval_ex1__critedge_in

Problem after Preprocessing

Start: eval_ex1_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef_0
Locations: eval_ex1_0, eval_ex1_1, eval_ex1_10, eval_ex1_15, eval_ex1_16, eval_ex1_2, eval_ex1_3, eval_ex1_4, eval_ex1_5, eval_ex1_6, eval_ex1_9, eval_ex1__critedge_in, eval_ex1_bb0_in, eval_ex1_bb1_in, eval_ex1_bb2_in, eval_ex1_bb3_in, eval_ex1_bb4_in, eval_ex1_bb5_in, eval_ex1_bb6_in, eval_ex1_start, eval_ex1_stop
Transitions:
t₂: eval_ex1_0(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_1(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: eval_ex1_1(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_2(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₇: eval_ex1_10(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₄
t₁₆: eval_ex1_10(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₄
t₂₀: eval_ex1_15(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_16(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ 1+X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄
t₂₁: eval_ex1_16(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_bb1_in(X₀, X₁, X₁, X₃, X₄, X₅) :|: 1 ≤ X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄
t₂₂: eval_ex1_16(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_bb1_in(X₀, X₁, X₃, X₃, X₄, X₅) :|: X₄ ≤ 0 ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄
t₄: eval_ex1_2(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_3(X₀, X₁, X₂, X₃, X₄, X₅)
t₅: eval_ex1_3(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_4(X₀, X₁, X₂, X₃, X₄, X₅)
t₆: eval_ex1_4(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_5(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: eval_ex1_5(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_6(X₀, X₁, X₂, X₃, X₄, X₅)
t₈: eval_ex1_6(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_bb1_in(X₀, X₁, 0, X₃, X₄, X₅)
t₁₅: eval_ex1_9(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_10(nondef_0, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₄
t₁₉: eval_ex1__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_15(X₀, X₃-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄
t₁: eval_ex1_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_0(X₀, X₁, X₂, X₃, X₄, X₅)
t₉: eval_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₂ ≤ X₅ ∧ 0 ≤ X₂
t₁₀: eval_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₂ ∧ 0 ≤ X₂
t₁₁: eval_ex1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_bb3_in(X₀, X₁, X₂, 1+X₂, 0, X₅) :|: 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₅ ∧ 0 ≤ X₂
t₁₃: eval_ex1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄
t₁₂: eval_ex1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₃ ≤ X₅ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄
t₁₄: eval_ex1_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_9(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₄
t₁₈: eval_ex1_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_bb3_in(X₀, X₁, X₂, 1+X₃, 1+X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 3 ≤ X₃+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₄
t₂₃: eval_ex1_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₂ ∧ X₅ ≤ X₂
t₀: eval_ex1_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

MPRF for transition t₉: eval_ex1_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₂ ≤ X₅ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_ex1_10: [X₄+X₅-X₃]
• eval_ex1_15: [X₄+X₅-X₃]
• eval_ex1_16: [X₄+X₅-X₃]
• eval_ex1_9: [X₄+X₅-X₃]
• eval_ex1__critedge_in: [X₄+X₅-X₃]
• eval_ex1_bb1_in: [X₅-X₂]
• eval_ex1_bb2_in: [X₅-1-X₂]
• eval_ex1_bb3_in: [X₄+X₅-X₃]
• eval_ex1_bb4_in: [X₄+X₅-X₃]
• eval_ex1_bb5_in: [X₄+X₅-X₃]

MPRF for transition t₁₁: eval_ex1_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_bb3_in(X₀, X₁, X₂, 1+X₂, 0, X₅) :|: 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₅ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_ex1_10: [X₄+X₅-X₃]
• eval_ex1_15: [X₄+X₅-X₃]
• eval_ex1_16: [X₄+X₅-1-X₁]
• eval_ex1_9: [X₄+X₅-X₃]
• eval_ex1__critedge_in: [X₄+X₅-X₃]
• eval_ex1_bb1_in: [X₅-X₂]
• eval_ex1_bb2_in: [X₅-X₂]
• eval_ex1_bb3_in: [X₄+X₅-X₃]
• eval_ex1_bb4_in: [X₄+X₅-X₃]
• eval_ex1_bb5_in: [X₄+X₅-X₃]

MPRF for transition t₁₂: eval_ex1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₃ ≤ X₅ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄ of depth 1:

new bound:

3⋅X₅+2 {O(n)}

MPRF:

• eval_ex1_10: [X₄+3⋅X₅-1-2⋅X₃]
• eval_ex1_15: [X₄+3⋅X₅-1-2⋅X₃]
• eval_ex1_16: [X₄+3⋅X₅-1-2⋅X₃]
• eval_ex1_9: [X₄+3⋅X₅-1-2⋅X₃]
• eval_ex1__critedge_in: [X₄+3⋅X₅-1-2⋅X₃]
• eval_ex1_bb1_in: [3⋅X₅-2-2⋅X₂]
• eval_ex1_bb2_in: [3⋅X₅-2-2⋅X₂]
• eval_ex1_bb3_in: [X₄+3⋅X₅-2⋅X₃]
• eval_ex1_bb4_in: [X₄+3⋅X₅-1-2⋅X₃]
• eval_ex1_bb5_in: [X₄+3⋅X₅-1-2⋅X₃]

MPRF for transition t₁₃: eval_ex1_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄ of depth 1:

new bound:

2⋅X₅+1 {O(n)}

MPRF:

• eval_ex1_10: [X₄+2⋅X₅-X₃]
• eval_ex1_15: [X₄+2⋅X₅-2-X₁]
• eval_ex1_16: [X₄+2⋅X₅-2-X₁]
• eval_ex1_9: [X₄+2⋅X₅-X₃]
• eval_ex1__critedge_in: [X₄+2⋅X₅-1-X₃]
• eval_ex1_bb1_in: [2⋅X₅-1-X₂]
• eval_ex1_bb2_in: [2⋅X₅-1-X₂]
• eval_ex1_bb3_in: [X₄+2⋅X₅-X₃]
• eval_ex1_bb4_in: [X₄+2⋅X₅-X₃]
• eval_ex1_bb5_in: [X₄+2⋅X₅-X₃]

MPRF for transition t₁₄: eval_ex1_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_9(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

2⋅X₅+1 {O(n)}

MPRF:

• eval_ex1_10: [X₄+2⋅X₅-2⋅X₃]
• eval_ex1_15: [X₄+2⋅X₅-2⋅X₃]
• eval_ex1_16: [X₄+2⋅X₅-2⋅X₃]
• eval_ex1_9: [X₄+2⋅X₅-2⋅X₃]
• eval_ex1__critedge_in: [X₄+2⋅X₅-2⋅X₃]
• eval_ex1_bb1_in: [2⋅X₅-1-2⋅X₂]
• eval_ex1_bb2_in: [2⋅X₅-1-2⋅X₂]
• eval_ex1_bb3_in: [1+X₄+2⋅X₅-2⋅X₃]
• eval_ex1_bb4_in: [1+X₄+2⋅X₅-2⋅X₃]
• eval_ex1_bb5_in: [X₄+2⋅X₅-2⋅X₃]

MPRF for transition t₁₅: eval_ex1_9(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_10(nondef_0, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

2⋅X₅+1 {O(n)}

MPRF:

• eval_ex1_10: [X₄+2⋅X₅-2⋅X₃]
• eval_ex1_15: [X₄+2⋅X₅-2⋅X₃]
• eval_ex1_16: [X₄+2⋅X₅-2⋅X₃]
• eval_ex1_9: [1+X₄+2⋅X₅-2⋅X₃]
• eval_ex1__critedge_in: [X₄+2⋅X₅-2⋅X₃]
• eval_ex1_bb1_in: [2⋅X₅-1-2⋅X₂]
• eval_ex1_bb2_in: [2⋅X₅-1-2⋅X₂]
• eval_ex1_bb3_in: [1+X₄+2⋅X₅-2⋅X₃]
• eval_ex1_bb4_in: [1+X₄+2⋅X₅-2⋅X₃]
• eval_ex1_bb5_in: [X₄+2⋅X₅-2⋅X₃]

MPRF for transition t₁₆: eval_ex1_10(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

• eval_ex1_10: [X₅-X₃]
• eval_ex1_15: [X₅-X₃]
• eval_ex1_16: [X₅-X₃]
• eval_ex1_9: [X₅-X₃]
• eval_ex1__critedge_in: [X₅-X₃]
• eval_ex1_bb1_in: [X₅-1-X₂]
• eval_ex1_bb2_in: [X₅-1-X₂]
• eval_ex1_bb3_in: [X₅-X₃]
• eval_ex1_bb4_in: [X₅-X₃]
• eval_ex1_bb5_in: [X₅-1-X₃]

MPRF for transition t₁₇: eval_ex1_10(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 2 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_ex1_10: [1+X₄+X₅-X₃]
• eval_ex1_15: [X₄+X₅-X₃]
• eval_ex1_16: [X₄+X₅-X₃]
• eval_ex1_9: [1+X₄+X₅-X₃]
• eval_ex1__critedge_in: [X₄+X₅-X₃]
• eval_ex1_bb1_in: [X₅-X₂]
• eval_ex1_bb2_in: [X₅-X₂]
• eval_ex1_bb3_in: [1+X₄+X₅-X₃]
• eval_ex1_bb4_in: [1+X₄+X₅-X₃]
• eval_ex1_bb5_in: [1+X₄+X₅-X₃]

MPRF for transition t₁₈: eval_ex1_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_bb3_in(X₀, X₁, X₂, 1+X₃, 1+X₄, X₅) :|: 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂+X₅ ∧ 2+X₂ ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2+X₄ ≤ X₅ ∧ 2 ≤ X₅ ∧ 3 ≤ X₀+X₅ ∧ 3 ≤ X₃+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

MPRF for transition t₁₉: eval_ex1__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_15(X₀, X₃-1, X₂, X₃, X₄, X₅) :|: 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_ex1_10: [1+X₄+X₅-X₃]
• eval_ex1_15: [X₄+X₅-X₃]
• eval_ex1_16: [X₄+X₅-1-X₁]
• eval_ex1_9: [1+X₄+X₅-X₃]
• eval_ex1__critedge_in: [1+X₄+X₅-X₃]
• eval_ex1_bb1_in: [X₅-X₂]
• eval_ex1_bb2_in: [X₅-X₂]
• eval_ex1_bb3_in: [1+X₄+X₅-X₃]
• eval_ex1_bb4_in: [1+X₄+X₅-X₃]
• eval_ex1_bb5_in: [1+X₄+X₅-X₃]

MPRF for transition t₂₀: eval_ex1_15(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_16(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ 1+X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_ex1_10: [1+X₄+X₅-X₃]
• eval_ex1_15: [1+X₄+X₅-X₃]
• eval_ex1_16: [X₄+X₅-1-X₁]
• eval_ex1_9: [1+X₄+X₅-X₃]
• eval_ex1__critedge_in: [1+X₄+X₅-X₃]
• eval_ex1_bb1_in: [X₅-X₂]
• eval_ex1_bb2_in: [X₅-X₂]
• eval_ex1_bb3_in: [1+X₄+X₅-X₃]
• eval_ex1_bb4_in: [1+X₄+X₅-X₃]
• eval_ex1_bb5_in: [1+X₄+X₅-X₃]

MPRF for transition t₂₁: eval_ex1_16(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_bb1_in(X₀, X₁, X₁, X₃, X₄, X₅) :|: 1 ≤ X₄ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_ex1_10: [1+X₄+X₅-X₃]
• eval_ex1_15: [X₄+X₅-X₁]
• eval_ex1_16: [X₄+X₅-X₁]
• eval_ex1_9: [1+X₄+X₅-X₃]
• eval_ex1__critedge_in: [1+X₄+X₅-X₃]
• eval_ex1_bb1_in: [X₅-X₂]
• eval_ex1_bb2_in: [X₅-X₂]
• eval_ex1_bb3_in: [1+X₄+X₅-X₃]
• eval_ex1_bb4_in: [1+X₄+X₅-X₃]
• eval_ex1_bb5_in: [1+X₄+X₅-X₃]

MPRF for transition t₂₂: eval_ex1_16(X₀, X₁, X₂, X₃, X₄, X₅) → eval_ex1_bb1_in(X₀, X₁, X₃, X₃, X₄, X₅) :|: X₄ ≤ 0 ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂+X₅ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄+X₅ ∧ 1+X₄ ≤ X₅ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₁+X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₄ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

• eval_ex1_10: [X₅-X₂]
• eval_ex1_15: [X₅-X₂]
• eval_ex1_16: [1+X₅-X₃]
• eval_ex1_9: [X₅-X₂]
• eval_ex1__critedge_in: [X₅-X₂]
• eval_ex1_bb1_in: [X₅-X₂]
• eval_ex1_bb2_in: [X₅-X₂]
• eval_ex1_bb3_in: [X₅-X₂]
• eval_ex1_bb4_in: [X₅-X₂]
• eval_ex1_bb5_in: [X₅-X₂]

All Bounds

Timebounds

Overall timebound:18⋅X₅+18 {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: X₅ {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₅ {O(n)}
t₁₂: 3⋅X₅+2 {O(n)}
t₁₃: 2⋅X₅+1 {O(n)}
t₁₄: 2⋅X₅+1 {O(n)}
t₁₅: 2⋅X₅+1 {O(n)}
t₁₆: X₅+1 {O(n)}
t₁₇: X₅ {O(n)}
t₁₈: X₅+1 {O(n)}
t₁₉: X₅ {O(n)}
t₂₀: X₅ {O(n)}
t₂₁: X₅ {O(n)}
t₂₂: X₅ {O(n)}
t₂₃: 1 {O(1)}

Costbounds

Overall costbound: 18⋅X₅+18 {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: X₅ {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₅ {O(n)}
t₁₂: 3⋅X₅+2 {O(n)}
t₁₃: 2⋅X₅+1 {O(n)}
t₁₄: 2⋅X₅+1 {O(n)}
t₁₅: 2⋅X₅+1 {O(n)}
t₁₆: X₅+1 {O(n)}
t₁₇: X₅ {O(n)}
t₁₈: X₅+1 {O(n)}
t₁₉: X₅ {O(n)}
t₂₀: X₅ {O(n)}
t₂₁: X₅ {O(n)}
t₂₂: X₅ {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)}
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)}
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)}
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)}
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)}
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)}
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)}
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)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: 0 {O(1)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₉, X₁: 4⋅X₅+X₁+2 {O(n)}
t₉, X₂: 2⋅X₅+1 {O(n)}
t₉, X₃: 4⋅X₅+X₃+2 {O(n)}
t₉, X₄: 2⋅X₅+X₄+2 {O(n)}
t₉, X₅: X₅ {O(n)}
t₁₀, X₁: 2⋅X₅+X₁+1 {O(n)}
t₁₀, X₂: 2⋅X₅+1 {O(n)}
t₁₀, X₃: 2⋅X₅+X₃+1 {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: 2⋅X₅ {O(n)}
t₁₁, X₁: 4⋅X₅+X₁+2 {O(n)}
t₁₁, X₂: 2⋅X₅+1 {O(n)}
t₁₁, X₃: 2⋅X₅+1 {O(n)}
t₁₁, X₄: 0 {O(1)}
t₁₁, X₅: X₅ {O(n)}
t₁₂, X₁: 4⋅X₅+X₁+2 {O(n)}
t₁₂, X₂: 2⋅X₅+1 {O(n)}
t₁₂, X₃: 2⋅X₅+1 {O(n)}
t₁₂, X₄: X₅+1 {O(n)}
t₁₂, X₅: X₅ {O(n)}
t₁₃, X₁: 2⋅X₁+8⋅X₅+4 {O(n)}
t₁₃, X₂: 4⋅X₅+2 {O(n)}
t₁₃, X₃: 2⋅X₅+1 {O(n)}
t₁₃, X₄: X₅+1 {O(n)}
t₁₃, X₅: X₅ {O(n)}
t₁₄, X₁: 4⋅X₅+X₁+2 {O(n)}
t₁₄, X₂: 2⋅X₅+1 {O(n)}
t₁₄, X₃: 2⋅X₅+1 {O(n)}
t₁₄, X₄: X₅+1 {O(n)}
t₁₄, X₅: X₅ {O(n)}
t₁₅, X₁: 4⋅X₅+X₁+2 {O(n)}
t₁₅, X₂: 2⋅X₅+1 {O(n)}
t₁₅, X₃: 2⋅X₅+1 {O(n)}
t₁₅, X₄: X₅+1 {O(n)}
t₁₅, X₅: X₅ {O(n)}
t₁₆, X₁: 4⋅X₅+X₁+2 {O(n)}
t₁₆, X₂: 2⋅X₅+1 {O(n)}
t₁₆, X₃: 2⋅X₅+1 {O(n)}
t₁₆, X₄: X₅+1 {O(n)}
t₁₆, X₅: X₅ {O(n)}
t₁₇, X₁: 4⋅X₅+X₁+2 {O(n)}
t₁₇, X₂: 2⋅X₅+1 {O(n)}
t₁₇, X₃: 2⋅X₅+1 {O(n)}
t₁₇, X₄: X₅+1 {O(n)}
t₁₇, X₅: X₅ {O(n)}
t₁₈, X₁: 4⋅X₅+X₁+2 {O(n)}
t₁₈, X₂: 2⋅X₅+1 {O(n)}
t₁₈, X₃: 2⋅X₅+1 {O(n)}
t₁₈, X₄: X₅+1 {O(n)}
t₁₈, X₅: X₅ {O(n)}
t₁₉, X₁: 2⋅X₅+1 {O(n)}
t₁₉, X₂: 6⋅X₅+3 {O(n)}
t₁₉, X₃: 2⋅X₅+1 {O(n)}
t₁₉, X₄: 2⋅X₅+2 {O(n)}
t₁₉, X₅: X₅ {O(n)}
t₂₀, X₁: 2⋅X₅+1 {O(n)}
t₂₀, X₂: 6⋅X₅+3 {O(n)}
t₂₀, X₃: 2⋅X₅+1 {O(n)}
t₂₀, X₄: 2⋅X₅+2 {O(n)}
t₂₀, X₅: X₅ {O(n)}
t₂₁, X₁: 2⋅X₅+1 {O(n)}
t₂₁, X₂: 2⋅X₅+1 {O(n)}
t₂₁, X₃: 2⋅X₅+1 {O(n)}
t₂₁, X₄: 2⋅X₅+2 {O(n)}
t₂₁, X₅: X₅ {O(n)}
t₂₂, X₁: 2⋅X₅+1 {O(n)}
t₂₂, X₂: 2⋅X₅+1 {O(n)}
t₂₂, X₃: 2⋅X₅+1 {O(n)}
t₂₂, X₄: 0 {O(1)}
t₂₂, X₅: X₅ {O(n)}
t₂₃, X₁: 2⋅X₅+X₁+1 {O(n)}
t₂₃, X₂: 2⋅X₅+1 {O(n)}
t₂₃, X₃: 2⋅X₅+X₃+1 {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₃, X₅: 2⋅X₅ {O(n)}