Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef.0, nondef.1
Locations: l0, l1, l10, l11, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₂
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₃, X₅, X₆) :|: X₂ < X₆
t₁₃: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l9(X₀, nondef.1, X₂, X₃, X₄, X₅, X₆)
t₁₇: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄-X₁, X₅, X₆)
t₁: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, 0, 0, X₄, X₅, X₆)
t₂₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₀: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0
t₉: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₀
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ < 0
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₄
t₁₉: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂+1, X₄+1, X₄, X₅, X₆) :|: X₄+1 < X₅
t₂₀: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂+1, X₄+1, X₄, X₅, X₆) :|: X₅ < X₄+1
t₁₈: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄+1 ≤ X₅ ∧ X₅ ≤ X₄+1
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(nondef.0, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁₆: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₁ ∧ X₁ ≤ 0
t₁₄: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ ≤ 0
t₁₅: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₁
Preprocessing
Cut unsatisfiable transition t₁₇: l11→l4
Cut unsatisfiable transition t₁₆: l9→l11
Cut unreachable locations [l11] from the program graph
Found invariant X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l2
Found invariant 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l6
Found invariant 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l7
Found invariant 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 1+X₀ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l5
Found invariant X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l13
Found invariant 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l8
Found invariant X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l1
Found invariant 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l10
Found invariant 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l4
Found invariant 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l9
Found invariant 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l3
Cut unsatisfiable transition t₅: l4→l5
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef.0, nondef.1
Locations: l0, l1, l10, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₂ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₃, X₅, X₆) :|: X₂ < X₆ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₃: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l9(X₀, nondef.1, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₁: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, 0, 0, X₄, X₅, X₆)
t₂₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₀: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0 ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂
t₉: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₀ ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₄ ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₉: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂+1, X₄+1, X₄, X₅, X₆) :|: X₄+1 < X₅ ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 1+X₀ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0
t₂₀: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂+1, X₄+1, X₄, X₅, X₆) :|: X₅ < X₄+1 ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 1+X₀ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0
t₁₈: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄+1 ≤ X₅ ∧ X₅ ≤ X₄+1 ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 1+X₀ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂
t₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(nondef.0, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₁₄: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ ≤ 0 ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₁₅: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₁ ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀
MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₃, X₅, X₆) :|: X₂ < X₆ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:
new bound:
X₆ {O(n)}
MPRF:
l4 [X₆-X₃-1 ]
l5 [X₆-X₄-1 ]
l1 [X₆-X₃ ]
l6 [X₆-X₄-1 ]
l7 [X₆-X₂-1 ]
l3 [X₃+X₆-X₂-X₄-1 ]
MPRF for transition t₁₀: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0 ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:
new bound:
X₆ {O(n)}
MPRF:
l4 [X₆-X₄ ]
l5 [X₆-X₃-1 ]
l1 [X₆-X₃ ]
l6 [X₆-X₃ ]
l7 [X₆-X₃ ]
l3 [X₆-X₂ ]
MPRF for transition t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₄ ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:
new bound:
X₆ {O(n)}
MPRF:
l4 [X₆-X₂ ]
l5 [X₆-X₃-1 ]
l1 [X₆-X₃ ]
l6 [X₆-X₂-1 ]
l7 [X₆-X₄-1 ]
l3 [X₆-X₂-1 ]
MPRF for transition t₁₉: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂+1, X₄+1, X₄, X₅, X₆) :|: X₄+1 < X₅ ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 1+X₀ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 of depth 1:
new bound:
X₆ {O(n)}
MPRF:
l4 [X₆-X₂ ]
l5 [X₆-X₂ ]
l1 [X₆-X₂ ]
l6 [X₆-X₃ ]
l7 [X₆-X₂ ]
l3 [X₆-X₃ ]
MPRF for transition t₂₀: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂+1, X₄+1, X₄, X₅, X₆) :|: X₅ < X₄+1 ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ 1+X₀ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 of depth 1:
new bound:
X₆ {O(n)}
MPRF:
l4 [X₆-X₂ ]
l5 [X₆-X₃ ]
l1 [X₆-X₂ ]
l6 [X₆-X₃ ]
l7 [X₆-X₄ ]
l3 [X₆-X₂ ]
MPRF for transition t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:
new bound:
X₆ {O(n)}
MPRF:
l4 [X₆-X₂ ]
l5 [X₆-X₄-1 ]
l1 [X₆-X₃ ]
l6 [X₆-X₃ ]
l7 [X₆-X₃-1 ]
l3 [X₆-X₂-1 ]
MPRF for transition t₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(nondef.0, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 1 ≤ X₃+X₆ ∧ 1+X₃ ≤ X₆ ∧ 1 ≤ X₂+X₆ ∧ 1+X₂ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ of depth 1:
new bound:
X₆ {O(n)}
MPRF:
l4 [X₆-X₄ ]
l5 [X₆-X₄-1 ]
l1 [X₆-X₃ ]
l6 [X₆-X₂ ]
l7 [X₆-X₃ ]
l3 [X₆-X₂-1 ]
All Bounds
Timebounds
Overall timebound:7⋅X₆+10 {O(n)}
t₀: 1 {O(1)}
t₂: X₆ {O(n)}
t₃: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂₁: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: X₆ {O(n)}
t₄: X₆ {O(n)}
t₁₈: 1 {O(1)}
t₁₉: X₆ {O(n)}
t₂₀: X₆ {O(n)}
t₆: X₆ {O(n)}
t₈: X₆ {O(n)}
t₁₁: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
Costbounds
Overall costbound: 7⋅X₆+10 {O(n)}
t₀: 1 {O(1)}
t₂: X₆ {O(n)}
t₃: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂₁: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: X₆ {O(n)}
t₄: X₆ {O(n)}
t₁₈: 1 {O(1)}
t₁₉: X₆ {O(n)}
t₂₀: X₆ {O(n)}
t₆: X₆ {O(n)}
t₈: X₆ {O(n)}
t₁₁: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 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)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 2⋅X₆ {O(n)}
t₂, X₃: 2⋅X₆ {O(n)}
t₂, X₄: 4⋅X₆ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₃, X₁: 3⋅X₁ {O(n)}
t₃, X₂: 4⋅X₆ {O(n)}
t₃, X₃: 4⋅X₆ {O(n)}
t₃, X₄: 8⋅X₆+X₄ {O(n)}
t₃, X₅: 3⋅X₅ {O(n)}
t₃, X₆: 3⋅X₆ {O(n)}
t₁₃, X₂: 2⋅X₆ {O(n)}
t₁₃, X₃: 2⋅X₆ {O(n)}
t₁₃, X₄: 4⋅X₆ {O(n)}
t₁₃, X₅: X₅ {O(n)}
t₁₃, X₆: X₆ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: 0 {O(1)}
t₁, X₃: 0 {O(1)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₂₁, X₂: 10⋅X₆ {O(n)}
t₂₁, X₃: 10⋅X₆ {O(n)}
t₂₁, X₄: 20⋅X₆+X₄ {O(n)}
t₂₁, X₅: 6⋅X₅ {O(n)}
t₂₁, X₆: 6⋅X₆ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: 2⋅X₆ {O(n)}
t₉, X₃: 2⋅X₆ {O(n)}
t₉, X₄: 4⋅X₆ {O(n)}
t₉, X₅: X₅ {O(n)}
t₉, X₆: X₆ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: 2⋅X₆ {O(n)}
t₁₀, X₃: 2⋅X₆ {O(n)}
t₁₀, X₄: 4⋅X₆ {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₀, X₆: X₆ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: 2⋅X₆ {O(n)}
t₄, X₃: 2⋅X₆ {O(n)}
t₄, X₄: 4⋅X₆ {O(n)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₈, X₂: 2⋅X₆ {O(n)}
t₁₈, X₃: 2⋅X₆ {O(n)}
t₁₈, X₄: 4⋅X₆ {O(n)}
t₁₈, X₅: X₅ {O(n)}
t₁₈, X₆: X₆ {O(n)}
t₁₉, X₁: X₁ {O(n)}
t₁₉, X₂: 2⋅X₆ {O(n)}
t₁₉, X₃: 2⋅X₆ {O(n)}
t₁₉, X₄: 4⋅X₆ {O(n)}
t₁₉, X₅: X₅ {O(n)}
t₁₉, X₆: X₆ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: 2⋅X₆ {O(n)}
t₂₀, X₃: 2⋅X₆ {O(n)}
t₂₀, X₄: 4⋅X₆ {O(n)}
t₂₀, X₅: X₅ {O(n)}
t₂₀, X₆: X₆ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: 2⋅X₆ {O(n)}
t₆, X₃: 2⋅X₆ {O(n)}
t₆, X₄: 4⋅X₆ {O(n)}
t₆, X₅: X₅ {O(n)}
t₆, X₆: X₆ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: 2⋅X₆ {O(n)}
t₈, X₃: 2⋅X₆ {O(n)}
t₈, X₄: 4⋅X₆ {O(n)}
t₈, X₅: X₅ {O(n)}
t₈, X₆: X₆ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: 2⋅X₆ {O(n)}
t₁₁, X₃: 2⋅X₆ {O(n)}
t₁₁, X₄: 4⋅X₆ {O(n)}
t₁₁, X₅: X₅ {O(n)}
t₁₁, X₆: X₆ {O(n)}
t₁₄, X₂: 2⋅X₆ {O(n)}
t₁₄, X₃: 2⋅X₆ {O(n)}
t₁₄, X₄: 4⋅X₆ {O(n)}
t₁₄, X₅: X₅ {O(n)}
t₁₄, X₆: X₆ {O(n)}
t₁₅, X₂: 2⋅X₆ {O(n)}
t₁₅, X₃: 2⋅X₆ {O(n)}
t₁₅, X₄: 4⋅X₆ {O(n)}
t₁₅, X₅: X₅ {O(n)}
t₁₅, X₆: X₆ {O(n)}