Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₁₃: l2(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₁₁: l2(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₁ < 0
t₁₂: l2(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₁
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₂ < 0
t₃: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₂
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₂ ∧ X₂ < X₃
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₂ ∧ X₂ ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₀ < X₂
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₂ < X₀
t₁₆: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₈: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₁₀: l7(X₀, X₁, X₂, X₃, X₄) → l2(X₀, nondef.0, X₂, X₃, X₄)
t₁₄: l8(X₀, X₁, X₂, X₃, X₄) → l4(X₀+1, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃
t₁₅: l8(X₀, X₁, X₂, X₃, X₄) → l4(0, X₁, X₂, X₃, X₄) :|: X₃ < X₀
t₄: l9(X₀, X₁, X₂, X₃, X₄) → l4(X₂+1, X₁, X₂, X₃, X₄)
Preprocessing
Eliminate variables {X₄} that do not contribute to the problem
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ for location l2
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ for location l6
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ for location l7
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ for location l8
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ for location l4
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l9
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₃₅: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₃₈: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂
t₃₆: l2(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ < 0 ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂
t₃₇: l2(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂
t₄₀: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ < 0
t₄₁: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₃₉: l3(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: 0 ≤ X₂ ∧ X₂ < X₃
t₄₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂
t₄₂: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₀ < X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂
t₄₃: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₂ < X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂
t₄₅: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂
t₄₇: l7(X₀, X₁, X₂, X₃) → l2(X₀, nondef.0, X₂, X₃) :|: 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂
t₄₈: l8(X₀, X₁, X₂, X₃) → l4(X₀+1, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂
t₄₉: l8(X₀, X₁, X₂, X₃) → l4(0, X₁, X₂, X₃) :|: X₃ < X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂
t₅₀: l9(X₀, X₁, X₂, X₃) → l4(X₂+1, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂
Analysing control-flow refined program
Cut unsatisfiable transition t₄₄: l4→l5
Cut unsatisfiable transition t₈₈₆: n_l4___11→n_l6___9
Cut unsatisfiable transition t₉₃₀: n_l4___23→l5
Cut unreachable locations [n_l2___3; n_l6___9; n_l7___4; n_l8___1; n_l8___2] from the program graph
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location n_l8___19
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀ for location n_l2___20
Found invariant 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l2___7
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l2___14
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___17
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l7___15
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l8___13
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀ for location n_l4___23
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l6___16
Found invariant 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l6___10
Found invariant 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l8___5
Found invariant 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location n_l8___6
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀ for location n_l6___28
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l8___12
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀ for location n_l6___22
Found invariant 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l7___8
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀ for location n_l7___27
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l8___18
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location n_l8___25
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀ for location n_l7___21
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀ for location n_l2___26
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀ for location l4
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l9
Found invariant 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l8___24
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l4___11
MPRF for transition t₈₇₇: n_l2___20(X₀, X₁, X₂, X₃) → n_l8___18(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 < X₁ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₂+2⋅X₃+10 {O(n)}
MPRF:
n_l6___22 [X₃+3-X₀ ]
n_l7___21 [X₃+3-X₀ ]
n_l2___20 [X₃+3-X₀ ]
n_l8___18 [X₃+2-X₀ ]
n_l8___19 [X₃+2-X₀ ]
n_l4___23 [X₃+3-X₀ ]
MPRF for transition t₈₇₈: n_l2___20(X₀, X₁, X₂, X₃) → n_l8___19(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ < 0 ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₂+2⋅X₃+8 {O(n)}
MPRF:
n_l6___22 [X₃+2-X₀ ]
n_l7___21 [X₃+2-X₀ ]
n_l2___20 [X₃+2-X₀ ]
n_l8___18 [X₃+2-X₀ ]
n_l8___19 [X₃+1-X₀ ]
n_l4___23 [X₃+2-X₀ ]
MPRF for transition t₈₈₈: n_l4___23(X₀, X₁, X₂, X₃) → n_l6___22(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ < X₀ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ ∧ X₂ < X₀ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₂+2⋅X₃+8 {O(n)}
MPRF:
n_l6___22 [X₃+1-X₀ ]
n_l7___21 [X₃+1-X₀ ]
n_l2___20 [X₃+1-X₀ ]
n_l8___18 [X₃+1-X₀ ]
n_l8___19 [X₃+1-X₀ ]
n_l4___23 [X₃+2-X₀ ]
MPRF for transition t₈₉₂: n_l6___22(X₀, X₁, X₂, X₃) → n_l7___21(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₂+4⋅X₃+6 {O(n)}
MPRF:
n_l6___22 [2⋅X₃+1-X₀ ]
n_l7___21 [2⋅X₃-X₀ ]
n_l2___20 [2⋅X₃-X₀ ]
n_l8___18 [2⋅X₃-X₀ ]
n_l8___19 [2⋅X₃-X₀ ]
n_l4___23 [2⋅X₃+1-X₀ ]
MPRF for transition t₈₉₆: n_l7___21(X₀, X₁, X₂, X₃) → n_l2___20(X₀, NoDet0, Arg2_P, Arg3_P) :|: X₀ ≤ 1+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ 1+Arg3_P ∧ 1+Arg2_P ≤ Arg3_P ∧ 0 ≤ Arg2_P ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₂+2⋅X₃+8 {O(n)}
MPRF:
n_l6___22 [X₃+2-X₀ ]
n_l7___21 [X₃+2-X₀ ]
n_l2___20 [X₃+1-X₀ ]
n_l8___18 [X₃+1-X₀ ]
n_l8___19 [X₃+1-X₀ ]
n_l4___23 [X₃+2-X₀ ]
MPRF for transition t₉₀₄: n_l8___18(X₀, X₁, X₂, X₃) → n_l4___23(X₀+1, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 0 < X₁ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₂+4⋅X₃+4 {O(n)}
MPRF:
n_l6___22 [2⋅X₃-X₀ ]
n_l7___21 [2⋅X₃-X₀ ]
n_l2___20 [2⋅X₃-X₀ ]
n_l8___18 [2⋅X₃-X₀ ]
n_l8___19 [2⋅X₃-X₀ ]
n_l4___23 [2⋅X₃-X₀ ]
MPRF for transition t₉₀₆: n_l8___19(X₀, X₁, X₂, X₃) → n_l4___23(X₀+1, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ X₁ < 0 ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₂+4⋅X₃+6 {O(n)}
MPRF:
n_l6___22 [2⋅X₃+1-X₀ ]
n_l7___21 [2⋅X₃+1-X₀ ]
n_l2___20 [2⋅X₃+1-X₀ ]
n_l8___18 [2⋅X₃-X₀ ]
n_l8___19 [2⋅X₃+1-X₀ ]
n_l4___23 [2⋅X₃+1-X₀ ]
MPRF for transition t₈₈₃: n_l2___7(X₀, X₁, X₂, X₃) → n_l8___5(X₀, X₁, X₂, X₃) :|: X₀ < X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 < X₁ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
8⋅X₃+4 {O(n)}
MPRF:
n_l6___10 [X₃-X₀-1 ]
n_l7___8 [X₃-X₀-1 ]
n_l2___7 [X₃-X₀-1 ]
n_l8___5 [X₃-X₀-2 ]
n_l8___6 [X₃-X₀-1 ]
n_l4___11 [X₃-X₀-1 ]
MPRF for transition t₈₈₄: n_l2___7(X₀, X₁, X₂, X₃) → n_l8___6(X₀, X₁, X₂, X₃) :|: X₀ < X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ < 0 ∧ X₀ ≤ 1+X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
8⋅X₂+2 {O(n)}
MPRF:
n_l6___10 [X₂-X₀ ]
n_l7___8 [X₂-X₀ ]
n_l2___7 [X₂-X₀ ]
n_l8___5 [X₂-X₀ ]
n_l8___6 [X₂-X₀-1 ]
n_l4___11 [X₂-X₀ ]
MPRF for transition t₈₈₅: n_l4___11(X₀, X₁, X₂, X₃) → n_l6___10(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ < X₂ ∧ 0 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
8⋅X₃+4 {O(n)}
MPRF:
n_l6___10 [X₃-X₀ ]
n_l7___8 [X₃-X₀ ]
n_l2___7 [X₃-X₀ ]
n_l8___5 [X₃-X₀ ]
n_l8___6 [X₃-X₀ ]
n_l4___11 [X₃+1-X₀ ]
MPRF for transition t₈₉₀: n_l6___10(X₀, X₁, X₂, X₃) → n_l7___8(X₀, X₁, X₂, X₃) :|: X₀ < X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
8⋅X₂+4 {O(n)}
MPRF:
n_l6___10 [X₂+1-X₀ ]
n_l7___8 [X₂-X₀ ]
n_l2___7 [X₂-X₀ ]
n_l8___5 [X₂-X₀ ]
n_l8___6 [X₂-X₀ ]
n_l4___11 [X₂+1-X₀ ]
MPRF for transition t₈₉₉: n_l7___8(X₀, X₁, X₂, X₃) → n_l2___7(X₀, NoDet0, Arg2_P, Arg3_P) :|: X₀ < X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ 1+Arg3_P ∧ 1+Arg2_P ≤ Arg3_P ∧ 0 ≤ Arg2_P ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
8⋅X₃+6 {O(n)}
MPRF:
n_l6___10 [X₃+2-X₀ ]
n_l7___8 [X₃+2-X₀ ]
n_l2___7 [X₃+1-X₀ ]
n_l8___5 [X₃+1-X₀ ]
n_l8___6 [X₃+1-X₀ ]
n_l4___11 [X₃+2-X₀ ]
MPRF for transition t₉₁₀: n_l8___5(X₀, X₁, X₂, X₃) → n_l4___11(X₀+1, X₁, X₂, X₃) :|: X₀ < X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 < X₁ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
8⋅X₃+4 {O(n)}
MPRF:
n_l6___10 [X₃-X₀-1 ]
n_l7___8 [X₃-X₀-1 ]
n_l2___7 [X₃-X₀-1 ]
n_l8___5 [X₃-X₀-1 ]
n_l8___6 [X₃-X₀-1 ]
n_l4___11 [X₃-X₀-1 ]
MPRF for transition t₉₁₁: n_l8___6(X₀, X₁, X₂, X₃) → n_l4___11(X₀+1, X₁, X₂, X₃) :|: X₀ < X₂ ∧ X₁ < 0 ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 1 ≤ X₀ of depth 1:
new bound:
32⋅X₃+2 {O(n)}
MPRF:
n_l6___10 [4⋅X₃-X₀ ]
n_l7___8 [4⋅X₃-X₀ ]
n_l2___7 [4⋅X₃-X₀ ]
n_l8___5 [4⋅X₃-X₀ ]
n_l8___6 [4⋅X₃-X₀ ]
n_l4___11 [4⋅X₃-X₀ ]
CFR: Improvement to new bound with the following program:
new bound:
30⋅X₂+84⋅X₃+76 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: Arg2_P, Arg3_P, NoDet0
Locations: l0, l1, l3, l4, l5, l9, n_l2___14, n_l2___20, n_l2___26, n_l2___7, n_l4___11, n_l4___17, n_l4___23, n_l6___10, n_l6___16, n_l6___22, n_l6___28, n_l7___15, n_l7___21, n_l7___27, n_l7___8, n_l8___12, n_l8___13, n_l8___18, n_l8___19, n_l8___24, n_l8___25, n_l8___5, n_l8___6
Transitions:
t₃₅: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₄₀: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ < 0
t₄₁: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₃₉: l3(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: 0 ≤ X₂ ∧ X₂ < X₃
t₈₈₉: l4(X₀, X₁, X₂, X₃) → n_l6___28(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₂ < X₀ ∧ X₀ ≤ 1+X₃ ∧ X₀ ≤ 1+X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ ∧ X₂ < X₀ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀
t₄₅: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₅₀: l9(X₀, X₁, X₂, X₃) → l4(X₂+1, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂
t₉₃₁: n_l2___14(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₈₇₅: n_l2___14(X₀, X₁, X₂, X₃) → n_l8___12(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 0 < X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 < X₁ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₈₇₆: n_l2___14(X₀, X₁, X₂, X₃) → n_l8___13(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 0 < X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ < 0 ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₉₃₂: n_l2___20(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀
t₈₇₇: n_l2___20(X₀, X₁, X₂, X₃) → n_l8___18(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 < X₁ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀
t₈₇₈: n_l2___20(X₀, X₁, X₂, X₃) → n_l8___19(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ < 0 ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀
t₉₃₃: n_l2___26(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀
t₈₇₉: n_l2___26(X₀, X₁, X₂, X₃) → n_l8___24(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂+1 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 < X₁ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀
t₈₈₀: n_l2___26(X₀, X₁, X₂, X₃) → n_l8___25(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂+1 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ < 0 ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀
t₉₃₅: n_l2___7(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀
t₈₈₃: n_l2___7(X₀, X₁, X₂, X₃) → n_l8___5(X₀, X₁, X₂, X₃) :|: X₀ < X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 < X₁ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀
t₈₈₄: n_l2___7(X₀, X₁, X₂, X₃) → n_l8___6(X₀, X₁, X₂, X₃) :|: X₀ < X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ < 0 ∧ X₀ ≤ 1+X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀
t₉₂₈: n_l4___11(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₈₈₅: n_l4___11(X₀, X₁, X₂, X₃) → n_l6___10(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ < X₂ ∧ 0 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₉₂₉: n_l4___17(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₈₈₇: n_l4___17(X₀, X₁, X₂, X₃) → n_l6___16(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ X₀ < X₂ ∧ 0 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₈₈₈: n_l4___23(X₀, X₁, X₂, X₃) → n_l6___22(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₂ < X₀ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 0 ≤ X₂ ∧ X₂ < X₀ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀
t₈₉₀: n_l6___10(X₀, X₁, X₂, X₃) → n_l7___8(X₀, X₁, X₂, X₃) :|: X₀ < X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀
t₈₉₁: n_l6___16(X₀, X₁, X₂, X₃) → n_l7___15(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 0 < X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₈₉₂: n_l6___22(X₀, X₁, X₂, X₃) → n_l7___21(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀
t₈₉₃: n_l6___28(X₀, X₁, X₂, X₃) → n_l7___27(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂+1 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀
t₈₉₅: n_l7___15(X₀, X₁, X₂, X₃) → n_l2___14(X₀, NoDet0, Arg2_P, Arg3_P) :|: 1+X₂ ≤ X₃ ∧ 0 < X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 1+Arg3_P ∧ 1+Arg2_P ≤ Arg3_P ∧ 0 ≤ Arg2_P ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₈₉₆: n_l7___21(X₀, X₁, X₂, X₃) → n_l2___20(X₀, NoDet0, Arg2_P, Arg3_P) :|: X₀ ≤ 1+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ 1+Arg3_P ∧ 1+Arg2_P ≤ Arg3_P ∧ 0 ≤ Arg2_P ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀
t₈₉₇: n_l7___27(X₀, X₁, X₂, X₃) → n_l2___26(X₀, NoDet0, Arg2_P, Arg3_P) :|: 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂+1 ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ 1+Arg3_P ∧ 1+Arg2_P ≤ Arg3_P ∧ 0 ≤ Arg2_P ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀
t₈₉₉: n_l7___8(X₀, X₁, X₂, X₃) → n_l2___7(X₀, NoDet0, Arg2_P, Arg3_P) :|: X₀ < X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ 1+Arg3_P ∧ 1+Arg2_P ≤ Arg3_P ∧ 0 ≤ Arg2_P ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀
t₉₀₁: n_l8___12(X₀, X₁, X₂, X₃) → n_l4___11(X₀+1, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 0 < X₂ ∧ 0 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₉₀₂: n_l8___13(X₀, X₁, X₂, X₃) → n_l4___11(X₀+1, X₁, X₂, X₃) :|: X₁ < 0 ∧ 1+X₂ ≤ X₃ ∧ 0 < X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₉₀₃: n_l8___18(X₀, X₁, X₂, X₃) → n_l4___17(0, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 0 < X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ X₃ < X₀ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₉₀₄: n_l8___18(X₀, X₁, X₂, X₃) → n_l4___23(X₀+1, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 0 < X₁ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₉₀₅: n_l8___19(X₀, X₁, X₂, X₃) → n_l4___17(0, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ X₁ < 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ X₃ < X₀ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₉₀₆: n_l8___19(X₀, X₁, X₂, X₃) → n_l4___23(X₀+1, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ X₁ < 0 ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₉₀₈: n_l8___24(X₀, X₁, X₂, X₃) → n_l4___23(X₀+1, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 0 < X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂+1 ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₉₀₉: n_l8___25(X₀, X₁, X₂, X₃) → n_l4___23(X₀+1, X₁, X₂, X₃) :|: X₁ < 0 ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂+1 ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 1 ≤ X₀
t₉₁₀: n_l8___5(X₀, X₁, X₂, X₃) → n_l4___11(X₀+1, X₁, X₂, X₃) :|: X₀ < X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 < X₁ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₉₁₁: n_l8___6(X₀, X₁, X₂, X₃) → n_l4___11(X₀+1, X₁, X₂, X₃) :|: X₀ < X₂ ∧ X₁ < 0 ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 1 ≤ X₀
All Bounds
Timebounds
Overall timebound:30⋅X₂+84⋅X₃+104 {O(n)}
t₃₅: 1 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 1 {O(1)}
t₄₁: 1 {O(1)}
t₈₈₉: 1 {O(1)}
t₄₅: 1 {O(1)}
t₅₀: 1 {O(1)}
t₈₇₅: 1 {O(1)}
t₈₇₆: 1 {O(1)}
t₉₃₁: 1 {O(1)}
t₈₇₇: 2⋅X₂+2⋅X₃+10 {O(n)}
t₈₇₈: 2⋅X₂+2⋅X₃+8 {O(n)}
t₉₃₂: 1 {O(1)}
t₈₇₉: 1 {O(1)}
t₈₈₀: 1 {O(1)}
t₉₃₃: 1 {O(1)}
t₈₈₃: 8⋅X₃+4 {O(n)}
t₈₈₄: 8⋅X₂+2 {O(n)}
t₉₃₅: 1 {O(1)}
t₈₈₅: 8⋅X₃+4 {O(n)}
t₉₂₈: 1 {O(1)}
t₈₈₇: 1 {O(1)}
t₉₂₉: 1 {O(1)}
t₈₈₈: 2⋅X₂+2⋅X₃+8 {O(n)}
t₈₉₀: 8⋅X₂+4 {O(n)}
t₈₉₁: 1 {O(1)}
t₈₉₂: 2⋅X₂+4⋅X₃+6 {O(n)}
t₈₉₃: 1 {O(1)}
t₈₉₅: 1 {O(1)}
t₈₉₆: 2⋅X₂+2⋅X₃+8 {O(n)}
t₈₉₇: 1 {O(1)}
t₈₉₉: 8⋅X₃+6 {O(n)}
t₉₀₁: 1 {O(1)}
t₉₀₂: 1 {O(1)}
t₉₀₃: 1 {O(1)}
t₉₀₄: 2⋅X₂+4⋅X₃+4 {O(n)}
t₉₀₅: 1 {O(1)}
t₉₀₆: 2⋅X₂+4⋅X₃+6 {O(n)}
t₉₀₈: 1 {O(1)}
t₉₀₉: 1 {O(1)}
t₉₁₀: 8⋅X₃+4 {O(n)}
t₉₁₁: 32⋅X₃+2 {O(n)}
Costbounds
Overall costbound: 30⋅X₂+84⋅X₃+104 {O(n)}
t₃₅: 1 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 1 {O(1)}
t₄₁: 1 {O(1)}
t₈₈₉: 1 {O(1)}
t₄₅: 1 {O(1)}
t₅₀: 1 {O(1)}
t₈₇₅: 1 {O(1)}
t₈₇₆: 1 {O(1)}
t₉₃₁: 1 {O(1)}
t₈₇₇: 2⋅X₂+2⋅X₃+10 {O(n)}
t₈₇₈: 2⋅X₂+2⋅X₃+8 {O(n)}
t₉₃₂: 1 {O(1)}
t₈₇₉: 1 {O(1)}
t₈₈₀: 1 {O(1)}
t₉₃₃: 1 {O(1)}
t₈₈₃: 8⋅X₃+4 {O(n)}
t₈₈₄: 8⋅X₂+2 {O(n)}
t₉₃₅: 1 {O(1)}
t₈₈₅: 8⋅X₃+4 {O(n)}
t₉₂₈: 1 {O(1)}
t₈₈₇: 1 {O(1)}
t₉₂₉: 1 {O(1)}
t₈₈₈: 2⋅X₂+2⋅X₃+8 {O(n)}
t₈₉₀: 8⋅X₂+4 {O(n)}
t₈₉₁: 1 {O(1)}
t₈₉₂: 2⋅X₂+4⋅X₃+6 {O(n)}
t₈₉₃: 1 {O(1)}
t₈₉₅: 1 {O(1)}
t₈₉₆: 2⋅X₂+2⋅X₃+8 {O(n)}
t₈₉₇: 1 {O(1)}
t₈₉₉: 8⋅X₃+6 {O(n)}
t₉₀₁: 1 {O(1)}
t₉₀₂: 1 {O(1)}
t₉₀₃: 1 {O(1)}
t₉₀₄: 2⋅X₂+4⋅X₃+4 {O(n)}
t₉₀₅: 1 {O(1)}
t₉₀₆: 2⋅X₂+4⋅X₃+6 {O(n)}
t₉₀₈: 1 {O(1)}
t₉₀₉: 1 {O(1)}
t₉₁₀: 8⋅X₃+4 {O(n)}
t₉₁₁: 32⋅X₃+2 {O(n)}
Sizebounds
t₃₅, X₀: X₀ {O(n)}
t₃₅, X₁: X₁ {O(n)}
t₃₅, X₂: X₂ {O(n)}
t₃₅, X₃: X₃ {O(n)}
t₃₉, X₀: X₀ {O(n)}
t₃₉, X₁: X₁ {O(n)}
t₃₉, X₂: X₂ {O(n)}
t₃₉, X₃: X₃ {O(n)}
t₄₀, X₀: X₀ {O(n)}
t₄₀, X₁: X₁ {O(n)}
t₄₀, X₂: X₂ {O(n)}
t₄₀, X₃: X₃ {O(n)}
t₄₁, X₀: X₀ {O(n)}
t₄₁, X₁: X₁ {O(n)}
t₄₁, X₂: X₂ {O(n)}
t₄₁, X₃: X₃ {O(n)}
t₈₈₉, X₀: X₂+1 {O(n)}
t₈₈₉, X₁: X₁ {O(n)}
t₈₈₉, X₂: X₂ {O(n)}
t₈₈₉, X₃: X₃ {O(n)}
t₄₅, X₀: 128⋅X₃+2⋅X₀+7⋅X₂+41 {O(n)}
t₄₅, X₂: 5⋅X₂ {O(n)}
t₄₅, X₃: 5⋅X₃ {O(n)}
t₅₀, X₀: X₂+1 {O(n)}
t₅₀, X₁: X₁ {O(n)}
t₅₀, X₂: X₂ {O(n)}
t₅₀, X₃: X₃ {O(n)}
t₈₇₅, X₀: 0 {O(1)}
t₈₇₅, X₂: 4⋅X₂ {O(n)}
t₈₇₅, X₃: 4⋅X₃ {O(n)}
t₈₇₆, X₀: 0 {O(1)}
t₈₇₆, X₂: 4⋅X₂ {O(n)}
t₈₇₆, X₃: 4⋅X₃ {O(n)}
t₉₃₁, X₀: 0 {O(1)}
t₉₃₁, X₁: 0 {O(1)}
t₉₃₁, X₂: 4⋅X₂ {O(n)}
t₉₃₁, X₃: 4⋅X₃ {O(n)}
t₈₇₇, X₀: 6⋅X₂+8⋅X₃+14 {O(n)}
t₈₇₇, X₂: 2⋅X₂ {O(n)}
t₈₇₇, X₃: 2⋅X₃ {O(n)}
t₈₇₈, X₀: 6⋅X₂+8⋅X₃+14 {O(n)}
t₈₇₈, X₂: 2⋅X₂ {O(n)}
t₈₇₈, X₃: 2⋅X₃ {O(n)}
t₉₃₂, X₀: 6⋅X₂+8⋅X₃+14 {O(n)}
t₉₃₂, X₁: 0 {O(1)}
t₉₃₂, X₂: 2⋅X₂ {O(n)}
t₉₃₂, X₃: 2⋅X₃ {O(n)}
t₈₇₉, X₀: X₂+1 {O(n)}
t₈₇₉, X₂: X₂ {O(n)}
t₈₇₉, X₃: X₃ {O(n)}
t₈₈₀, X₀: X₂+1 {O(n)}
t₈₈₀, X₂: X₂ {O(n)}
t₈₈₀, X₃: X₃ {O(n)}
t₉₃₃, X₀: X₂+1 {O(n)}
t₉₃₃, X₁: 0 {O(1)}
t₉₃₃, X₂: X₂ {O(n)}
t₉₃₃, X₃: X₃ {O(n)}
t₈₈₃, X₀: 40⋅X₃+8 {O(n)}
t₈₈₃, X₂: 8⋅X₂ {O(n)}
t₈₈₃, X₃: 8⋅X₃ {O(n)}
t₈₈₄, X₀: 40⋅X₃+8 {O(n)}
t₈₈₄, X₂: 8⋅X₂ {O(n)}
t₈₈₄, X₃: 8⋅X₃ {O(n)}
t₉₃₅, X₀: 40⋅X₃+8 {O(n)}
t₉₃₅, X₁: 0 {O(1)}
t₉₃₅, X₂: 8⋅X₂ {O(n)}
t₉₃₅, X₃: 8⋅X₃ {O(n)}
t₈₈₅, X₀: 40⋅X₃+8 {O(n)}
t₈₈₅, X₂: 8⋅X₂ {O(n)}
t₈₈₅, X₃: 8⋅X₃ {O(n)}
t₉₂₈, X₀: 80⋅X₃+18 {O(n)}
t₉₂₈, X₂: 24⋅X₂ {O(n)}
t₉₂₈, X₃: 24⋅X₃ {O(n)}
t₈₈₇, X₀: 0 {O(1)}
t₈₈₇, X₂: 4⋅X₂ {O(n)}
t₈₈₇, X₃: 4⋅X₃ {O(n)}
t₉₂₉, X₀: 0 {O(1)}
t₉₂₉, X₂: 0 {O(1)}
t₉₂₉, X₃: 4⋅X₃ {O(n)}
t₈₈₈, X₀: 6⋅X₂+8⋅X₃+14 {O(n)}
t₈₈₈, X₂: 2⋅X₂ {O(n)}
t₈₈₈, X₃: 2⋅X₃ {O(n)}
t₈₉₀, X₀: 40⋅X₃+8 {O(n)}
t₈₉₀, X₂: 8⋅X₂ {O(n)}
t₈₉₀, X₃: 8⋅X₃ {O(n)}
t₈₉₁, X₀: 0 {O(1)}
t₈₉₁, X₂: 4⋅X₂ {O(n)}
t₈₉₁, X₃: 4⋅X₃ {O(n)}
t₈₉₂, X₀: 6⋅X₂+8⋅X₃+14 {O(n)}
t₈₉₂, X₂: 2⋅X₂ {O(n)}
t₈₉₂, X₃: 2⋅X₃ {O(n)}
t₈₉₃, X₀: X₂+1 {O(n)}
t₈₉₃, X₁: X₁ {O(n)}
t₈₉₃, X₂: X₂ {O(n)}
t₈₉₃, X₃: X₃ {O(n)}
t₈₉₅, X₀: 0 {O(1)}
t₈₉₅, X₂: 4⋅X₂ {O(n)}
t₈₉₅, X₃: 4⋅X₃ {O(n)}
t₈₉₆, X₀: 6⋅X₂+8⋅X₃+14 {O(n)}
t₈₉₆, X₂: 2⋅X₂ {O(n)}
t₈₉₆, X₃: 2⋅X₃ {O(n)}
t₈₉₇, X₀: X₂+1 {O(n)}
t₈₉₇, X₂: X₂ {O(n)}
t₈₉₇, X₃: X₃ {O(n)}
t₈₉₉, X₀: 40⋅X₃+8 {O(n)}
t₈₉₉, X₂: 8⋅X₂ {O(n)}
t₈₉₉, X₃: 8⋅X₃ {O(n)}
t₉₀₁, X₀: 1 {O(1)}
t₉₀₁, X₂: 4⋅X₂ {O(n)}
t₉₀₁, X₃: 4⋅X₃ {O(n)}
t₉₀₂, X₀: 1 {O(1)}
t₉₀₂, X₂: 4⋅X₂ {O(n)}
t₉₀₂, X₃: 4⋅X₃ {O(n)}
t₉₀₃, X₀: 0 {O(1)}
t₉₀₃, X₂: 2⋅X₂ {O(n)}
t₉₀₃, X₃: 2⋅X₃ {O(n)}
t₉₀₄, X₀: 6⋅X₂+8⋅X₃+14 {O(n)}
t₉₀₄, X₂: 2⋅X₂ {O(n)}
t₉₀₄, X₃: 2⋅X₃ {O(n)}
t₉₀₅, X₀: 0 {O(1)}
t₉₀₅, X₂: 2⋅X₂ {O(n)}
t₉₀₅, X₃: 2⋅X₃ {O(n)}
t₉₀₆, X₀: 6⋅X₂+8⋅X₃+14 {O(n)}
t₉₀₆, X₂: 2⋅X₂ {O(n)}
t₉₀₆, X₃: 2⋅X₃ {O(n)}
t₉₀₈, X₀: X₂+2 {O(n)}
t₉₀₈, X₂: X₂ {O(n)}
t₉₀₈, X₃: X₃ {O(n)}
t₉₀₉, X₀: X₂+2 {O(n)}
t₉₀₉, X₂: X₂ {O(n)}
t₉₀₉, X₃: X₃ {O(n)}
t₉₁₀, X₀: 40⋅X₃+8 {O(n)}
t₉₁₀, X₂: 8⋅X₂ {O(n)}
t₉₁₀, X₃: 8⋅X₃ {O(n)}
t₉₁₁, X₀: 40⋅X₃+8 {O(n)}
t₉₁₁, X₂: 8⋅X₂ {O(n)}
t₉₁₁, X₃: 8⋅X₃ {O(n)}