Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: nondef.0
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l18, l19, l2, l20, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l18(X₀, X₁, X₂, X₃)
t₈: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀) :|: X₁ < 0
t₉: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀) :|: 3 < X₁
t₇: l1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ X₁ ≤ 3
t₂₈: l10(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀)
t₂₃: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₁ < 3
t₂₄: l11(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃) :|: 3 ≤ X₁
t₂₅: l12(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: X₁ ≤ 2 ∧ 2 ≤ X₁
t₂₆: l12(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ < 2
t₂₇: l12(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 2 < X₁
t₃₂: l13(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀)
t₂₉: l14(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: X₁ ≤ 3 ∧ 3 ≤ X₁
t₃₀: l14(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ < 3
t₃₁: l14(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 3 < X₁
t₁₈: l15(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀)
t₁₅: l16(X₀, X₁, X₂, X₃) → l15(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₁₆: l16(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ < 0
t₁₇: l16(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 0 < X₁
t₁₂: l17(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: 2 ≤ X₁
t₁₁: l17(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ < 2
t₁: l18(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, 0)
t₃₄: l19(X₀, X₁, X₂, X₃) → l20(X₀, X₁, X₂, X₃)
t₄: l2(X₀, X₁, X₂, X₃) → l3(X₃+1, X₁, X₂, X₃)
t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀, nondef.0, X₂, X₃)
t₃: l4(X₀, X₁, X₂, X₃) → l19(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃
t₂: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ < X₂
t₁₀: l5(X₀, X₁, X₂, X₃) → l17(X₀, X₁, X₂, X₃)
t₃₃: l6(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀)
t₂₂: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀)
t₁₃: l8(X₀, X₁, X₂, X₃) → l16(X₀, X₁, X₂, X₃) :|: X₁ < 1
t₁₄: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁
t₂₀: l9(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ < 1
t₂₁: l9(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 1 < X₁
t₁₉: l9(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1 ∧ 1 ≤ X₁
Preprocessing
Cut unsatisfiable transition t₂₇: l12→l6
Cut unsatisfiable transition t₃₀: l14→l6
Cut unsatisfiable transition t₁₇: l16→l6
Cut unsatisfiable transition t₂₀: l9→l6
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l11
Found invariant 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location l2
Found invariant 1 ≤ 0 for location l6
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l15
Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l19
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l12
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l17
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l7
Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l20
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l13
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l8
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l1
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l10
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l16
Found invariant 0 ≤ X₃ for location l4
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l9
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l3
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l14
Cut unsatisfiable transition t₂₆: l12→l6
Cut unsatisfiable transition t₃₁: l14→l6
Cut unsatisfiable transition t₁₆: l16→l6
Cut unsatisfiable transition t₃₃: l6→l4
Cut unsatisfiable transition t₂₁: l9→l6
Cut unreachable locations [l6] from the program graph
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: nondef.0
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l18, l19, l2, l20, l3, l4, l5, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l18(X₀, X₁, X₂, X₃)
t₈: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀) :|: X₁ < 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₉: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀) :|: 3 < X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₇: l1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₂₈: l10(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₃: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₁ < 3 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₄: l11(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃) :|: 3 ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₅: l12(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: X₁ ≤ 2 ∧ 2 ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃₂: l13(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₉: l14(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: X₁ ≤ 3 ∧ 3 ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₈: l15(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₅: l16(X₀, X₁, X₂, X₃) → l15(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₂: l17(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: 2 ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₁: l17(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ < 2 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁: l18(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, 0)
t₃₄: l19(X₀, X₁, X₂, X₃) → l20(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ X₂ ≤ X₃
t₄: l2(X₀, X₁, X₂, X₃) → l3(X₃+1, X₁, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂
t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀, nondef.0, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₃: l4(X₀, X₁, X₂, X₃) → l19(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ 0 ≤ X₃
t₂: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ < X₂ ∧ 0 ≤ X₃
t₁₀: l5(X₀, X₁, X₂, X₃) → l17(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₂: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₃: l8(X₀, X₁, X₂, X₃) → l16(X₀, X₁, X₂, X₃) :|: X₁ < 1 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₄: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₉: l9(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
MPRF for transition t₇: l1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
3⋅X₂ {O(n)}
MPRF:
l12 [3⋅X₂-3⋅X₀ ]
l10 [3⋅X₂-3⋅X₀ ]
l14 [3⋅X₂-3⋅X₃-3 ]
l13 [3⋅X₂-X₁-3⋅X₃ ]
l15 [3⋅X₂-3⋅X₀ ]
l11 [3⋅X₂-3⋅X₃-3 ]
l3 [3⋅X₂-3⋅X₃ ]
l1 [3⋅X₂-3⋅X₃ ]
l2 [3⋅X₂-3⋅X₃ ]
l5 [3⋅X₂-3⋅X₀ ]
l17 [3⋅X₂-3⋅X₀ ]
l4 [3⋅X₂-3⋅X₃ ]
l16 [3⋅X₂-3⋅X₀ ]
l8 [3⋅X₂-3⋅X₀ ]
l9 [3⋅X₂-3⋅X₀ ]
l7 [3⋅X₂-3⋅X₀ ]
MPRF for transition t₈: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀) :|: X₁ < 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
3⋅X₂+2 {O(n)}
MPRF:
l12 [3⋅X₂-3⋅X₃-5 ]
l10 [3⋅X₂-3⋅X₀-X₁ ]
l14 [3⋅X₂+2⋅X₃-5⋅X₀ ]
l13 [3⋅X₂+2⋅X₃-5⋅X₀ ]
l15 [3⋅X₂-3⋅X₀ ]
l11 [3⋅X₂-3⋅X₃-5 ]
l3 [3⋅X₂-3⋅X₃-2 ]
l1 [3⋅X₂+1-3⋅X₀ ]
l2 [3⋅X₂-3⋅X₃-2 ]
l5 [3⋅X₂+1-3⋅X₀-X₁ ]
l17 [3⋅X₂+1-3⋅X₀-X₁ ]
l4 [3⋅X₂-3⋅X₃-2 ]
l16 [3⋅X₂-3⋅X₀ ]
l8 [3⋅X₂-3⋅X₀-X₁ ]
l9 [3⋅X₂-3⋅X₀-X₁ ]
l7 [3⋅X₂-3⋅X₀-1 ]
MPRF for transition t₉: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀) :|: 3 < X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l12 [X₂-X₃ ]
l10 [X₂-X₃-1 ]
l14 [X₂-X₃ ]
l13 [X₂-X₃ ]
l15 [X₂-X₃ ]
l11 [X₂-X₃ ]
l3 [X₂-X₃ ]
l1 [X₂+1-X₀ ]
l2 [X₂-X₃ ]
l5 [X₂+1-X₀ ]
l17 [X₂-X₃ ]
l4 [X₂-X₃ ]
l16 [X₂-X₃ ]
l8 [X₂-X₃ ]
l9 [X₂-X₃ ]
l7 [X₂-X₀ ]
MPRF for transition t₂₈: l10(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l12 [X₂+1-X₀ ]
l10 [X₂+1-X₀ ]
l14 [X₂-X₀ ]
l13 [X₂-X₀ ]
l15 [X₂-X₃ ]
l11 [X₂+1-X₀ ]
l3 [X₂-X₃ ]
l1 [X₂+1-X₀ ]
l2 [X₂-X₃ ]
l5 [X₂-X₃ ]
l17 [X₂-X₃ ]
l4 [X₂-X₃ ]
l16 [X₂-X₃ ]
l8 [X₂-X₃ ]
l9 [X₂-X₀ ]
l7 [X₂-X₀ ]
MPRF for transition t₂₃: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₁ < 3 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l12 [X₂-X₃-1 ]
l10 [X₂-X₀ ]
l14 [X₂-X₀ ]
l13 [X₂-X₀ ]
l15 [X₂-X₀ ]
l11 [X₂-X₃ ]
l3 [X₂-X₃ ]
l1 [X₂-X₃ ]
l2 [X₂-X₃ ]
l5 [X₂+1-X₀ ]
l17 [X₂+1-X₀ ]
l4 [X₂-X₃ ]
l16 [X₂-X₀ ]
l8 [X₂-X₀ ]
l9 [X₂-X₀ ]
l7 [X₂-X₀ ]
MPRF for transition t₂₄: l11(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃) :|: 3 ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l12 [X₂-X₃-1 ]
l10 [X₂-X₀ ]
l14 [X₂-X₃-1 ]
l13 [X₂-X₀ ]
l15 [X₂-X₃-1 ]
l11 [X₂-X₃ ]
l3 [X₂-X₃ ]
l1 [X₂-X₃ ]
l2 [X₂-X₃ ]
l5 [X₂+1-X₀ ]
l17 [X₂-X₃ ]
l4 [X₂-X₃ ]
l16 [X₂-X₃-1 ]
l8 [X₂-X₃ ]
l9 [X₂-X₃ ]
l7 [X₂-X₃ ]
MPRF for transition t₂₅: l12(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: X₁ ≤ 2 ∧ 2 ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l12 [X₂+1-X₀ ]
l10 [X₂-X₀ ]
l14 [X₂-X₀ ]
l13 [X₂-X₀ ]
l15 [X₂-X₃ ]
l11 [X₂+1-X₀ ]
l3 [X₂-X₃ ]
l1 [X₂-X₃ ]
l2 [X₂-X₃ ]
l5 [X₂-X₃ ]
l17 [X₂-X₃ ]
l4 [X₂-X₃ ]
l16 [X₂-X₃ ]
l8 [X₂-X₃ ]
l9 [X₂-X₀ ]
l7 [X₂-X₀ ]
MPRF for transition t₃₂: l13(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l12 [X₂-X₃ ]
l10 [X₂+1-X₀ ]
l14 [X₂+4-X₀-X₁ ]
l13 [X₂+1-X₀ ]
l15 [X₂-X₃ ]
l11 [X₂-X₃ ]
l3 [X₂-X₃ ]
l1 [X₂-X₃ ]
l2 [X₂-X₃ ]
l5 [X₂+1-X₀ ]
l17 [X₂-X₃ ]
l4 [X₂-X₃ ]
l16 [X₂-X₃ ]
l8 [X₂-X₃ ]
l9 [X₂-X₃ ]
l7 [X₂-X₀ ]
MPRF for transition t₂₉: l14(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: X₁ ≤ 3 ∧ 3 ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l12 [X₂-X₃ ]
l10 [X₂-X₃ ]
l14 [X₂-X₃ ]
l13 [X₂-X₃-1 ]
l15 [X₂-X₃ ]
l11 [X₂-X₃ ]
l3 [X₂-X₃ ]
l1 [X₂-X₃ ]
l2 [X₂-X₃ ]
l5 [X₂-X₃ ]
l17 [X₂-X₃ ]
l4 [X₂-X₃ ]
l16 [X₂-X₃ ]
l8 [X₂-X₃ ]
l9 [X₂-X₃ ]
l7 [X₂-X₀ ]
MPRF for transition t₁₈: l15(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l12 [X₂-X₀ ]
l10 [X₂-X₀ ]
l14 [X₂-X₀ ]
l13 [X₂-X₀ ]
l15 [X₂+1-X₀ ]
l11 [X₂-X₀ ]
l3 [X₂-X₃ ]
l1 [X₂-X₃ ]
l2 [X₂-X₃ ]
l5 [X₂-X₃ ]
l17 [X₂-X₃ ]
l4 [X₂-X₃ ]
l16 [X₂-X₃ ]
l8 [X₂-X₃ ]
l9 [X₂-X₃ ]
l7 [X₂-X₀ ]
MPRF for transition t₁₅: l16(X₀, X₁, X₂, X₃) → l15(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l12 [X₂-X₃ ]
l10 [X₂-X₃ ]
l14 [X₂-X₃ ]
l13 [X₂-X₀ ]
l15 [X₂-X₀ ]
l11 [X₂-X₃ ]
l3 [X₂-X₃ ]
l1 [X₂+1-X₀ ]
l2 [X₂-X₃ ]
l5 [X₂-X₃ ]
l17 [X₂-X₃ ]
l4 [X₂-X₃ ]
l16 [X₂+1-X₀ ]
l8 [X₂+1-X₀ ]
l9 [X₂-X₀ ]
l7 [X₂-X₀ ]
MPRF for transition t₁₁: l17(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ < 2 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂+1 {O(n)}
MPRF:
l12 [X₂+1-X₀ ]
l10 [X₂+1-X₀ ]
l14 [X₂-X₃ ]
l13 [X₂-X₃ ]
l15 [X₂-X₃ ]
l11 [X₂-X₃ ]
l3 [X₀+X₂-2⋅X₃ ]
l1 [X₀+X₂-2⋅X₃ ]
l2 [X₂+1-X₃ ]
l5 [X₀+X₂-2⋅X₃ ]
l17 [X₂+2-X₀ ]
l4 [X₂+1-X₃ ]
l16 [X₂-X₃ ]
l8 [X₂-X₃ ]
l9 [X₂-X₃ ]
l7 [X₂-X₃ ]
MPRF for transition t₁₂: l17(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: 2 ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l12 [X₂-X₀ ]
l10 [X₂-X₀ ]
l14 [X₂-X₃-1 ]
l13 [X₂-X₀ ]
l15 [X₂-X₃-1 ]
l11 [X₂-X₃-1 ]
l3 [X₂-X₃ ]
l1 [X₂-X₃ ]
l2 [X₂-X₃ ]
l5 [X₂-X₃ ]
l17 [X₂-X₃ ]
l4 [X₂-X₃ ]
l16 [X₂-X₃-1 ]
l8 [X₂-X₃ ]
l9 [X₂-X₀ ]
l7 [X₂-X₀ ]
MPRF for transition t₄: l2(X₀, X₁, X₂, X₃) → l3(X₃+1, X₁, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l12 [X₂-X₃-1 ]
l10 [X₂-X₃-1 ]
l14 [X₂-X₃-1 ]
l13 [X₂-X₃-1 ]
l15 [X₂-X₀ ]
l11 [X₂-X₃-1 ]
l3 [X₂-X₀ ]
l1 [X₂-X₀ ]
l2 [X₂-X₃ ]
l5 [X₂-X₀ ]
l17 [X₂-X₀ ]
l4 [X₂-X₃ ]
l16 [X₂-X₀ ]
l8 [X₂-X₀ ]
l9 [X₂-X₀ ]
l7 [X₂-X₀ ]
MPRF for transition t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀, nondef.0, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l12 [X₂-X₀ ]
l10 [X₂-X₀ ]
l14 [X₂-X₃-1 ]
l13 [X₂-X₀ ]
l15 [X₂-X₀ ]
l11 [X₂-X₃-1 ]
l3 [X₂-X₃ ]
l1 [X₂-X₀ ]
l2 [X₂-X₃ ]
l5 [X₂-X₀ ]
l17 [X₂-X₀ ]
l4 [X₂-X₃ ]
l16 [X₂-X₀ ]
l8 [X₂-X₀ ]
l9 [X₂-X₀ ]
l7 [X₂-X₀ ]
MPRF for transition t₂: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ < X₂ ∧ 0 ≤ X₃ of depth 1:
new bound:
X₂+1 {O(n)}
MPRF:
l12 [X₁+X₂+X₃-2⋅X₀ ]
l10 [X₂+1-X₀ ]
l14 [X₂+1-X₀ ]
l13 [X₂-X₃ ]
l15 [X₂-X₃ ]
l11 [X₂+1-X₀ ]
l3 [X₂-X₃ ]
l1 [X₂-X₃ ]
l2 [X₂-X₃ ]
l5 [X₂-X₃ ]
l17 [X₂-X₃ ]
l4 [X₂+1-X₃ ]
l16 [X₂-X₃ ]
l8 [X₂-X₃ ]
l9 [X₂-X₃ ]
l7 [X₂+1-X₀ ]
MPRF for transition t₁₀: l5(X₀, X₁, X₂, X₃) → l17(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ 3+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 3 ∧ X₁ ≤ 2+X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂+1 {O(n)}
MPRF:
l12 [X₂-X₃ ]
l10 [X₂-X₃ ]
l14 [X₂-X₃ ]
l13 [X₂-X₃ ]
l15 [X₂-X₃ ]
l11 [X₂-X₃ ]
l3 [X₂+1-X₃ ]
l1 [X₂+2-X₀ ]
l2 [X₂+1-X₃ ]
l5 [X₂+2-X₀ ]
l17 [X₂+1-X₀ ]
l4 [X₂+1-X₃ ]
l16 [X₂+1-X₀ ]
l8 [X₂+1-X₀ ]
l9 [X₂-X₃ ]
l7 [X₂-X₃ ]
MPRF for transition t₂₂: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l12 [X₂-X₃ ]
l10 [X₂-X₃ ]
l14 [X₂+1-X₀ ]
l13 [X₂-X₀ ]
l15 [X₂-X₃ ]
l11 [X₂-X₃ ]
l3 [X₂+1-X₀ ]
l1 [X₂-X₃ ]
l2 [X₂-X₃ ]
l5 [X₂-X₃ ]
l17 [X₂-X₃ ]
l4 [X₂-X₃ ]
l16 [X₂-X₃ ]
l8 [X₂-X₃ ]
l9 [X₂-X₃ ]
l7 [X₂-X₃ ]
MPRF for transition t₁₃: l8(X₀, X₁, X₂, X₃) → l16(X₀, X₁, X₂, X₃) :|: X₁ < 1 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l12 [X₂-X₀ ]
l10 [X₂-X₀ ]
l14 [X₂-X₀ ]
l13 [X₂-X₀ ]
l15 [X₂-X₀ ]
l11 [X₂-X₀ ]
l3 [X₂+1-X₀ ]
l1 [X₂-X₃ ]
l2 [X₂-X₃ ]
l5 [X₂-X₃ ]
l17 [X₂+1-X₀ ]
l4 [X₂-X₃ ]
l16 [X₂-X₀ ]
l8 [X₂+1-X₀ ]
l9 [X₂-X₀ ]
l7 [X₂-X₀ ]
MPRF for transition t₁₄: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
3⋅X₂+3 {O(n)}
MPRF:
l12 [3⋅X₂+6-3⋅X₀ ]
l10 [3⋅X₁+3⋅X₂-3⋅X₀ ]
l14 [3⋅X₂-3⋅X₃ ]
l13 [3⋅X₂-3⋅X₃ ]
l15 [3⋅X₂-3⋅X₃ ]
l11 [3⋅X₂+3-3⋅X₃ ]
l3 [3⋅X₂+3-3⋅X₃ ]
l1 [3⋅X₂+3-3⋅X₃ ]
l2 [3⋅X₂+3-3⋅X₃ ]
l5 [3⋅X₀+3⋅X₂-6⋅X₃ ]
l17 [3⋅X₂+3-3⋅X₃ ]
l4 [3⋅X₂+3-3⋅X₃ ]
l16 [3⋅X₂-3⋅X₃ ]
l8 [3⋅X₂+3-3⋅X₃ ]
l9 [3⋅X₂-3⋅X₃ ]
l7 [3⋅X₂-3⋅X₃ ]
MPRF for transition t₁₉: l9(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l12 [X₂-X₀ ]
l10 [X₂-X₀ ]
l14 [X₂+1-X₀ ]
l13 [X₂-X₃ ]
l15 [X₂-X₃ ]
l11 [X₂+1-X₀ ]
l3 [X₂-X₃ ]
l1 [X₂-X₃ ]
l2 [X₂-X₃ ]
l5 [X₂-X₃ ]
l17 [X₂-X₃ ]
l4 [X₂-X₃ ]
l16 [X₂-X₃ ]
l8 [X₂-X₃ ]
l9 [X₂+1-X₀ ]
l7 [X₂-X₀ ]
All Bounds
Timebounds
Overall timebound:27⋅X₂+12 {O(n)}
t₀: 1 {O(1)}
t₇: 3⋅X₂ {O(n)}
t₈: 3⋅X₂+2 {O(n)}
t₉: X₂ {O(n)}
t₂₈: X₂ {O(n)}
t₂₃: X₂ {O(n)}
t₂₄: X₂ {O(n)}
t₂₅: X₂ {O(n)}
t₃₂: X₂ {O(n)}
t₂₉: X₂ {O(n)}
t₁₈: X₂ {O(n)}
t₁₅: X₂ {O(n)}
t₁₁: X₂+1 {O(n)}
t₁₂: X₂ {O(n)}
t₁: 1 {O(1)}
t₃₄: 1 {O(1)}
t₄: X₂ {O(n)}
t₆: X₂ {O(n)}
t₂: X₂+1 {O(n)}
t₃: 1 {O(1)}
t₁₀: X₂+1 {O(n)}
t₂₂: X₂ {O(n)}
t₁₃: X₂ {O(n)}
t₁₄: 3⋅X₂+3 {O(n)}
t₁₉: X₂ {O(n)}
Costbounds
Overall costbound: 27⋅X₂+12 {O(n)}
t₀: 1 {O(1)}
t₇: 3⋅X₂ {O(n)}
t₈: 3⋅X₂+2 {O(n)}
t₉: X₂ {O(n)}
t₂₈: X₂ {O(n)}
t₂₃: X₂ {O(n)}
t₂₄: X₂ {O(n)}
t₂₅: X₂ {O(n)}
t₃₂: X₂ {O(n)}
t₂₉: X₂ {O(n)}
t₁₈: X₂ {O(n)}
t₁₅: X₂ {O(n)}
t₁₁: X₂+1 {O(n)}
t₁₂: X₂ {O(n)}
t₁: 1 {O(1)}
t₃₄: 1 {O(1)}
t₄: X₂ {O(n)}
t₆: X₂ {O(n)}
t₂: X₂+1 {O(n)}
t₃: 1 {O(1)}
t₁₀: X₂+1 {O(n)}
t₂₂: X₂ {O(n)}
t₁₃: X₂ {O(n)}
t₁₄: 3⋅X₂+3 {O(n)}
t₁₉: X₂ {O(n)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₇, X₀: X₂ {O(n)}
t₇, X₁: 3 {O(1)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₂ {O(n)}
t₈, X₀: X₂ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₂ {O(n)}
t₉, X₀: X₂ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₂ {O(n)}
t₂₈, X₀: X₂ {O(n)}
t₂₈, X₁: 2 {O(1)}
t₂₈, X₂: X₂ {O(n)}
t₂₈, X₃: X₂ {O(n)}
t₂₃, X₀: X₂ {O(n)}
t₂₃, X₁: 2 {O(1)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₂ {O(n)}
t₂₄, X₀: X₂ {O(n)}
t₂₄, X₁: 3 {O(1)}
t₂₄, X₂: X₂ {O(n)}
t₂₄, X₃: X₂ {O(n)}
t₂₅, X₀: X₂ {O(n)}
t₂₅, X₁: 2 {O(1)}
t₂₅, X₂: X₂ {O(n)}
t₂₅, X₃: X₂ {O(n)}
t₃₂, X₀: X₂ {O(n)}
t₃₂, X₁: 3 {O(1)}
t₃₂, X₂: X₂ {O(n)}
t₃₂, X₃: X₂ {O(n)}
t₂₉, X₀: X₂ {O(n)}
t₂₉, X₁: 3 {O(1)}
t₂₉, X₂: X₂ {O(n)}
t₂₉, X₃: X₂ {O(n)}
t₁₈, X₀: X₂ {O(n)}
t₁₈, X₁: 0 {O(1)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₂ {O(n)}
t₁₅, X₀: X₂ {O(n)}
t₁₅, X₁: 0 {O(1)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₂ {O(n)}
t₁₁, X₀: X₂ {O(n)}
t₁₁, X₁: 1 {O(1)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₂ {O(n)}
t₁₂, X₀: X₂ {O(n)}
t₁₂, X₁: 3 {O(1)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: 0 {O(1)}
t₃₄, X₀: 6⋅X₂+X₀ {O(n)}
t₃₄, X₂: 7⋅X₂ {O(n)}
t₃₄, X₃: 6⋅X₂ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₂ {O(n)}
t₆, X₀: X₂ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₂ {O(n)}
t₂, X₀: 6⋅X₂+X₀ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₂ {O(n)}
t₃, X₀: 6⋅X₂+X₀ {O(n)}
t₃, X₂: 7⋅X₂ {O(n)}
t₃, X₃: 6⋅X₂ {O(n)}
t₁₀, X₀: X₂ {O(n)}
t₁₀, X₁: 3 {O(1)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₂ {O(n)}
t₂₂, X₀: X₂ {O(n)}
t₂₂, X₁: 1 {O(1)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₂ {O(n)}
t₁₃, X₀: X₂ {O(n)}
t₁₃, X₁: 0 {O(1)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₂ {O(n)}
t₁₄, X₀: X₂ {O(n)}
t₁₄, X₁: 1 {O(1)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₂ {O(n)}
t₁₉, X₀: X₂ {O(n)}
t₁₉, X₁: 1 {O(1)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₂ {O(n)}