KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₃ for location eval_Loopus2014_ex2_bb1_in

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_Loopus2014_ex2_5

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_Loopus2014_ex2_2

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_Loopus2014_ex2_bb2_in

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_Loopus2014_ex2_bb3_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_Loopus2014_ex2_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_Loopus2014_ex2_1

Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₄ for location eval_Loopus2014_ex2_.critedge_in

Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₃ ≤ 0 for location eval_Loopus2014_ex2_bb6_in

Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₃ ≤ 0 for location eval_Loopus2014_ex2_stop

Problem after Preprocessing

Start: eval_Loopus2014_ex2_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef.0, nondef.1
Locations: eval_Loopus2014_ex2_.critedge_in, eval_Loopus2014_ex2_1, eval_Loopus2014_ex2_2, eval_Loopus2014_ex2_5, eval_Loopus2014_ex2_6, eval_Loopus2014_ex2_bb0_in, eval_Loopus2014_ex2_bb1_in, eval_Loopus2014_ex2_bb2_in, eval_Loopus2014_ex2_bb3_in, eval_Loopus2014_ex2_bb4_in, eval_Loopus2014_ex2_bb5_in, eval_Loopus2014_ex2_bb6_in, eval_Loopus2014_ex2_start, eval_Loopus2014_ex2_stop
Transitions:
t₂: eval_Loopus2014_ex2_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₃ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅
t₃: eval_Loopus2014_ex2_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 0 ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅
t₆: eval_Loopus2014_ex2_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_2(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
t₇: eval_Loopus2014_ex2_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_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
t₈: eval_Loopus2014_ex2_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_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
t₁₄: eval_Loopus2014_ex2_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_6(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
t₁₆: eval_Loopus2014_ex2_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_.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
t₁₅: eval_Loopus2014_ex2_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_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
t₁: eval_Loopus2014_ex2_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_.critedge_in(X₀, X₁, X₂, X₄, X₄, 0, X₆)
t₄: eval_Loopus2014_ex2_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_1(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
t₉: eval_Loopus2014_ex2_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_.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
t₁₁: eval_Loopus2014_ex2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_.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
t₁₀: eval_Loopus2014_ex2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_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
t₁₂: eval_Loopus2014_ex2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_5(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
t₁₇: eval_Loopus2014_ex2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_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
t₁₈: eval_Loopus2014_ex2_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 0 ∧ X₃ ≤ X₄ ∧ X₃ ≤ X₅ ∧ 0 ≤ X₅
t₀: eval_Loopus2014_ex2_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

MPRF for transition t₂: eval_Loopus2014_ex2_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_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_Loopus2014_ex2_.critedge_in: [X₃]
• eval_Loopus2014_ex2_1: [X₃-1]
• eval_Loopus2014_ex2_2: [X₃-1]
• eval_Loopus2014_ex2_5: [X₀]
• eval_Loopus2014_ex2_6: [X₀]
• eval_Loopus2014_ex2_bb1_in: [X₃-1]
• eval_Loopus2014_ex2_bb2_in: [X₀]
• eval_Loopus2014_ex2_bb3_in: [X₃-1]
• eval_Loopus2014_ex2_bb4_in: [X₀]
• eval_Loopus2014_ex2_bb5_in: [X₀]

MPRF for transition t₄: eval_Loopus2014_ex2_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_1(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 {O(n)}

MPRF:

• eval_Loopus2014_ex2_.critedge_in: [X₃]
• eval_Loopus2014_ex2_1: [X₀]
• eval_Loopus2014_ex2_2: [X₀]
• eval_Loopus2014_ex2_5: [X₃-1]
• eval_Loopus2014_ex2_6: [X₃-1]
• eval_Loopus2014_ex2_bb1_in: [X₃]
• eval_Loopus2014_ex2_bb2_in: [X₃-1]
• eval_Loopus2014_ex2_bb3_in: [X₃-1]
• eval_Loopus2014_ex2_bb4_in: [X₃-1]
• eval_Loopus2014_ex2_bb5_in: [X₃-1]

MPRF for transition t₆: eval_Loopus2014_ex2_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_2(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+1 {O(n)}

MPRF:

• eval_Loopus2014_ex2_.critedge_in: [1+X₃]
• eval_Loopus2014_ex2_1: [1+X₃]
• eval_Loopus2014_ex2_2: [X₃]
• eval_Loopus2014_ex2_5: [X₃]
• eval_Loopus2014_ex2_6: [X₃]
• eval_Loopus2014_ex2_bb1_in: [1+X₃]
• eval_Loopus2014_ex2_bb2_in: [X₃]
• eval_Loopus2014_ex2_bb3_in: [X₃]
• eval_Loopus2014_ex2_bb4_in: [X₃]
• eval_Loopus2014_ex2_bb5_in: [X₃]

MPRF for transition t₇: eval_Loopus2014_ex2_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_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_Loopus2014_ex2_.critedge_in: [X₃]
• eval_Loopus2014_ex2_1: [1+X₀]
• eval_Loopus2014_ex2_2: [1+X₀]
• eval_Loopus2014_ex2_5: [1+X₀]
• eval_Loopus2014_ex2_6: [1+X₀]
• eval_Loopus2014_ex2_bb1_in: [X₃]
• eval_Loopus2014_ex2_bb2_in: [X₀]
• eval_Loopus2014_ex2_bb3_in: [X₃]
• eval_Loopus2014_ex2_bb4_in: [X₃]
• eval_Loopus2014_ex2_bb5_in: [1+X₀]

MPRF for transition t₈: eval_Loopus2014_ex2_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_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_Loopus2014_ex2_.critedge_in: [X₃]
• eval_Loopus2014_ex2_1: [1+X₀]
• eval_Loopus2014_ex2_2: [1+X₀]
• eval_Loopus2014_ex2_5: [X₀]
• eval_Loopus2014_ex2_6: [X₀]
• eval_Loopus2014_ex2_bb1_in: [X₃]
• eval_Loopus2014_ex2_bb2_in: [X₃]
• eval_Loopus2014_ex2_bb3_in: [X₀]
• eval_Loopus2014_ex2_bb4_in: [X₀]
• eval_Loopus2014_ex2_bb5_in: [X₀]

MPRF for transition t₉: eval_Loopus2014_ex2_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_.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_Loopus2014_ex2_.critedge_in: [X₃]
• eval_Loopus2014_ex2_1: [1+X₀]
• eval_Loopus2014_ex2_2: [X₃]
• eval_Loopus2014_ex2_5: [X₃]
• eval_Loopus2014_ex2_6: [X₃]
• eval_Loopus2014_ex2_bb1_in: [X₃]
• eval_Loopus2014_ex2_bb2_in: [1+X₀]
• eval_Loopus2014_ex2_bb3_in: [X₃]
• eval_Loopus2014_ex2_bb4_in: [X₃]
• eval_Loopus2014_ex2_bb5_in: [X₃]

MPRF for transition t₁₀: eval_Loopus2014_ex2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_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_Loopus2014_ex2_.critedge_in: [X₃+X₅]
• eval_Loopus2014_ex2_1: [X₃+X₅]
• eval_Loopus2014_ex2_2: [X₃+X₅]
• eval_Loopus2014_ex2_5: [X₃+X₆-1]
• eval_Loopus2014_ex2_6: [X₃+X₆-1]
• eval_Loopus2014_ex2_bb1_in: [X₃+X₅]
• eval_Loopus2014_ex2_bb2_in: [X₃+X₅]
• eval_Loopus2014_ex2_bb3_in: [X₃+X₆]
• eval_Loopus2014_ex2_bb4_in: [X₃+X₆-1]
• eval_Loopus2014_ex2_bb5_in: [X₃+X₆-1]

MPRF for transition t₁₁: eval_Loopus2014_ex2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_.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_Loopus2014_ex2_.critedge_in: [X₃]
• eval_Loopus2014_ex2_1: [X₃]
• eval_Loopus2014_ex2_2: [X₃]
• eval_Loopus2014_ex2_5: [1+X₀]
• eval_Loopus2014_ex2_6: [X₃]
• eval_Loopus2014_ex2_bb1_in: [X₃]
• eval_Loopus2014_ex2_bb2_in: [X₃]
• eval_Loopus2014_ex2_bb3_in: [1+X₀]
• eval_Loopus2014_ex2_bb4_in: [1+X₀]
• eval_Loopus2014_ex2_bb5_in: [X₃]

MPRF for transition t₁₂: eval_Loopus2014_ex2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_5(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_Loopus2014_ex2_.critedge_in: [1+X₃+X₅]
• eval_Loopus2014_ex2_1: [2+X₀+X₅]
• eval_Loopus2014_ex2_2: [2+X₀+X₅]
• eval_Loopus2014_ex2_5: [1+X₀+X₆]
• eval_Loopus2014_ex2_6: [X₃+X₆]
• eval_Loopus2014_ex2_bb1_in: [1+X₃+X₅]
• eval_Loopus2014_ex2_bb2_in: [1+X₃+X₅]
• eval_Loopus2014_ex2_bb3_in: [1+X₃+X₆]
• eval_Loopus2014_ex2_bb4_in: [2+X₀+X₆]
• eval_Loopus2014_ex2_bb5_in: [X₃+X₆]

MPRF for transition t₁₄: eval_Loopus2014_ex2_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_6(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+1 {O(n)}

MPRF:

• eval_Loopus2014_ex2_.critedge_in: [X₃+X₅-1]
• eval_Loopus2014_ex2_1: [X₀+X₅]
• eval_Loopus2014_ex2_2: [X₃+X₅-1]
• eval_Loopus2014_ex2_5: [X₃+X₆-1]
• eval_Loopus2014_ex2_6: [X₃+X₆-2]
• eval_Loopus2014_ex2_bb1_in: [X₃+X₅-1]
• eval_Loopus2014_ex2_bb2_in: [X₃+X₅-1]
• eval_Loopus2014_ex2_bb3_in: [X₃+X₆-1]
• eval_Loopus2014_ex2_bb4_in: [X₀+X₆]
• eval_Loopus2014_ex2_bb5_in: [X₃+X₆-2]

MPRF for transition t₁₅: eval_Loopus2014_ex2_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_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_Loopus2014_ex2_.critedge_in: [1+X₃+X₅]
• eval_Loopus2014_ex2_1: [1+X₃+X₅]
• eval_Loopus2014_ex2_2: [1+X₃+X₅]
• eval_Loopus2014_ex2_5: [2+X₀+X₆]
• eval_Loopus2014_ex2_6: [2+X₀+X₆]
• eval_Loopus2014_ex2_bb1_in: [1+X₃+X₅]
• eval_Loopus2014_ex2_bb2_in: [1+X₃+X₅]
• eval_Loopus2014_ex2_bb3_in: [1+X₃+X₆]
• eval_Loopus2014_ex2_bb4_in: [2+X₀+X₆]
• eval_Loopus2014_ex2_bb5_in: [X₃+X₆]

MPRF for transition t₁₆: eval_Loopus2014_ex2_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_.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_Loopus2014_ex2_.critedge_in: [X₃]
• eval_Loopus2014_ex2_1: [X₃]
• eval_Loopus2014_ex2_2: [X₃]
• eval_Loopus2014_ex2_5: [X₃]
• eval_Loopus2014_ex2_6: [1+X₀]
• eval_Loopus2014_ex2_bb1_in: [X₃]
• eval_Loopus2014_ex2_bb2_in: [X₀]
• eval_Loopus2014_ex2_bb3_in: [1+X₀]
• eval_Loopus2014_ex2_bb4_in: [X₃]
• eval_Loopus2014_ex2_bb5_in: [1+X₀]

MPRF for transition t₁₇: eval_Loopus2014_ex2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_Loopus2014_ex2_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+1 {O(n)}

MPRF:

• eval_Loopus2014_ex2_.critedge_in: [X₃+X₅-1]
• eval_Loopus2014_ex2_1: [X₃+X₅-1]
• eval_Loopus2014_ex2_2: [X₃+X₅-1]
• eval_Loopus2014_ex2_5: [X₀+X₆]
• eval_Loopus2014_ex2_6: [X₀+X₆]
• eval_Loopus2014_ex2_bb1_in: [X₃+X₅-1]
• eval_Loopus2014_ex2_bb2_in: [X₀+X₅]
• eval_Loopus2014_ex2_bb3_in: [X₀+X₆]
• eval_Loopus2014_ex2_bb4_in: [X₀+X₆]
• eval_Loopus2014_ex2_bb5_in: [X₀+X₆]

All Bounds

Timebounds

Overall timebound:13⋅X₄+9 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₄ {O(n)}
t₃: 1 {O(1)}
t₄: X₄ {O(n)}
t₆: X₄+1 {O(n)}
t₇: X₄ {O(n)}
t₈: X₄ {O(n)}
t₉: X₄ {O(n)}
t₁₀: X₄ {O(n)}
t₁₁: X₄ {O(n)}
t₁₂: X₄+1 {O(n)}
t₁₄: X₄+1 {O(n)}
t₁₅: X₄+1 {O(n)}
t₁₆: X₄ {O(n)}
t₁₇: X₄+1 {O(n)}
t₁₈: 1 {O(1)}

Costbounds

Overall costbound: 13⋅X₄+9 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₄ {O(n)}
t₃: 1 {O(1)}
t₄: X₄ {O(n)}
t₆: X₄+1 {O(n)}
t₇: X₄ {O(n)}
t₈: X₄ {O(n)}
t₉: X₄ {O(n)}
t₁₀: X₄ {O(n)}
t₁₁: X₄ {O(n)}
t₁₂: X₄+1 {O(n)}
t₁₄: X₄+1 {O(n)}
t₁₅: X₄+1 {O(n)}
t₁₆: X₄ {O(n)}
t₁₇: X₄+1 {O(n)}
t₁₈: 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: X₄ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: 0 {O(1)}
t₁, X₆: X₆ {O(n)}
t₂, X₀: 4⋅X₄+X₀ {O(n)}
t₂, X₃: X₄ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₄ {O(n)}
t₂, X₆: X₄+X₆ {O(n)}
t₃, X₀: 4⋅X₄+X₀ {O(n)}
t₃, X₃: 4⋅X₄ {O(n)}
t₃, X₄: 4⋅X₄ {O(n)}
t₃, X₅: 2⋅X₄ {O(n)}
t₃, X₆: 2⋅X₄+2⋅X₆ {O(n)}
t₄, X₀: X₄ {O(n)}
t₄, X₃: X₄ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₄ {O(n)}
t₄, X₆: X₄+X₆ {O(n)}
t₆, X₀: X₄ {O(n)}
t₆, X₃: X₄ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₄ {O(n)}
t₆, X₆: X₄+X₆ {O(n)}
t₇, X₀: X₄ {O(n)}
t₇, X₃: X₄ {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₄ {O(n)}
t₇, X₆: X₄+X₆ {O(n)}
t₈, X₀: X₄ {O(n)}
t₈, X₃: X₄ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₄ {O(n)}
t₈, X₆: X₄ {O(n)}
t₉, X₀: X₄ {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: X₄ {O(n)}
t₁₀, X₃: X₄ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: X₄ {O(n)}
t₁₀, X₆: X₄ {O(n)}
t₁₁, X₀: 2⋅X₄ {O(n)}
t₁₁, X₃: X₄ {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₁₁, X₅: 0 {O(1)}
t₁₁, X₆: 0 {O(1)}
t₁₂, X₀: X₄ {O(n)}
t₁₂, X₃: X₄ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₂, X₅: X₄ {O(n)}
t₁₂, X₆: X₄ {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 {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: X₄ {O(n)}
t₁₇, X₃: X₄ {O(n)}
t₁₇, X₄: X₄ {O(n)}
t₁₇, X₅: X₄ {O(n)}
t₁₇, X₆: X₄ {O(n)}
t₁₈, X₀: 4⋅X₄+X₀ {O(n)}
t₁₈, X₃: 4⋅X₄ {O(n)}
t₁₈, X₄: 4⋅X₄ {O(n)}
t₁₈, X₅: 2⋅X₄ {O(n)}
t₁₈, X₆: 2⋅X₄+2⋅X₆ {O(n)}