Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l18, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l17(X₀, X₁, X₂, X₃)
t₃₀: l1(X₀, X₁, X₂, X₃) → l12(X₂, X₁, X₂, X₃)
t₁₅: l10(X₀, X₁, X₂, X₃) → l12(X₂, X₁, X₂, X₃)
t₁₃: l11(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ 0
t₁₄: l11(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃
t₁₂: l11(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ 0 ≤ X₃
t₂: l12(X₀, X₁, X₂, X₃) → l15(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁
t₃: l12(X₀, X₁, X₂, X₃) → l16(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀
t₈: l13(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1
t₉: l13(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 2 ≤ X₃
t₇: l14(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃)
t₅: l15(X₀, X₁, X₂, X₃) → l12(X₀+1, X₁, X₂, X₃) :|: E+1 ≤ 0
t₆: l15(X₀, X₁, X₂, X₃) → l12(X₀+1, X₁, X₂, X₃) :|: 4 ≤ E
t₄: l15(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₀+1, E) :|: 0 ≤ E ∧ E ≤ 3
t₃₁: l16(X₀, X₁, X₂, X₃) → l18(X₀, X₁, X₂, X₃)
t₁: l17(X₀, X₁, X₂, X₃) → l12(0, X₁, X₂, X₃)
t₁₉: l2(X₀, X₁, X₂, X₃) → l12(X₂, X₁, X₂, X₃)
t₁₀: l3(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0
t₁₁: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃
t₁₇: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0
t₁₈: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 2 ≤ X₃
t₁₆: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1 ∧ 1 ≤ X₃
t₂₅: l5(X₀, X₁, X₂, X₃) → l12(X₂, X₁, X₂, X₃)
t₂₀: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₃ ≤ 2
t₂₁: l6(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: 3 ≤ X₃
t₂₃: l7(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1
t₂₄: l7(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 3 ≤ X₃
t₂₂: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₃ ≤ 2 ∧ 2 ≤ X₃
t₂₉: l8(X₀, X₁, X₂, X₃) → l12(X₂, X₁, X₂, X₃)
t₂₇: l9(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₃ ≤ 2
t₂₈: l9(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 4 ≤ X₃
t₂₆: l9(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₃ ≤ 3 ∧ 3 ≤ X₃

Preprocessing

Cut unsatisfiable transition t₁₄: l11→l1

Cut unsatisfiable transition t₁₇: l4→l1

Cut unsatisfiable transition t₂₄: l7→l1

Cut unsatisfiable transition t₂₇: l9→l1

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l11

Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l2

Found invariant X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l6

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l15

Found invariant 0 ≤ X₀ for location l12

Found invariant X₃ ≤ 2 ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 2+X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l7

Found invariant X₃ ≤ 2 ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 2+X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l13

Found invariant X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l8

Found invariant 1 ≤ 0 for location l1

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l10

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l16

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location l18

Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l4

Found invariant X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l9

Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l3

Found invariant X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l14

Cut unsatisfiable transition t₃₀: l1→l12

Cut unsatisfiable transition t₁₃: l11→l1

Cut unsatisfiable transition t₁₈: l4→l1

Cut unsatisfiable transition t₂₃: l7→l1

Cut unsatisfiable transition t₂₈: l9→l1

Cut unreachable locations [l1] from the program graph

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l10, l11, l12, l13, l14, l15, l16, l17, l18, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l17(X₀, X₁, X₂, X₃)
t₁₅: l10(X₀, X₁, X₂, X₃) → l12(X₂, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₂: l11(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂: l12(X₀, X₁, X₂, X₃) → l15(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₀
t₃: l12(X₀, X₁, X₂, X₃) → l16(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 0 ≤ X₀
t₈: l13(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1 ∧ X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₉: l13(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 2 ≤ X₃ ∧ X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₇: l14(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₅: l15(X₀, X₁, X₂, X₃) → l12(X₀+1, X₁, X₂, X₃) :|: E+1 ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₆: l15(X₀, X₁, X₂, X₃) → l12(X₀+1, X₁, X₂, X₃) :|: 4 ≤ E ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₄: l15(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₀+1, E) :|: 0 ≤ E ∧ E ≤ 3 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃₁: l16(X₀, X₁, X₂, X₃) → l18(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 0 ≤ X₀
t₁: l17(X₀, X₁, X₂, X₃) → l12(0, X₁, X₂, X₃)
t₁₉: l2(X₀, X₁, X₂, X₃) → l12(X₂, X₁, X₂, X₃) :|: X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₀: l3(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₁: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₆: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂₅: l5(X₀, X₁, X₂, X₃) → l12(X₂, X₁, X₂, X₃) :|: X₃ ≤ 2 ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 2+X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂₀: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₃ ≤ 2 ∧ X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂₁: l6(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: 3 ≤ X₃ ∧ X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂₂: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₃ ≤ 2 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2 ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 2+X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂₉: l8(X₀, X₁, X₂, X₃) → l12(X₂, X₁, X₂, X₃) :|: X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₂₆: l9(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₃ ≤ 3 ∧ 3 ≤ X₃ ∧ X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀

MPRF for transition t₁₅: l10(X₀, X₁, X₂, X₃) → l12(X₂, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l10 [X₁-X₀ ]
l13 [X₁-X₀ ]
l14 [X₁-X₀ ]
l15 [X₁-X₀ ]
l11 [X₁+1-X₂ ]
l3 [X₁-X₀ ]
l4 [X₁-X₀ ]
l2 [X₁-X₀ ]
l6 [X₁-X₀ ]
l7 [X₁-X₀ ]
l5 [X₁-X₂ ]
l12 [X₁-X₀ ]
l9 [X₁-X₀ ]
l8 [X₁-X₂ ]

MPRF for transition t₁₂: l11(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l10 [X₁-X₂ ]
l13 [X₁-X₀ ]
l14 [X₁-X₀ ]
l15 [X₁-X₀ ]
l11 [X₁+1-X₂ ]
l3 [X₁-X₀ ]
l4 [X₁-X₀ ]
l2 [X₁-X₂ ]
l6 [X₁-X₀ ]
l7 [X₁-X₀ ]
l5 [X₁-X₂ ]
l12 [X₁-X₀ ]
l9 [X₁-X₀ ]
l8 [X₁-X₂ ]

MPRF for transition t₂: l12(X₀, X₁, X₂, X₃) → l15(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

l10 [X₁-X₀ ]
l13 [X₁+1-X₂ ]
l14 [X₁-X₀ ]
l15 [X₁-X₀ ]
l11 [X₁-X₀ ]
l3 [X₁+1-X₂ ]
l4 [X₁+1-X₂ ]
l2 [X₁+1-X₂ ]
l6 [X₁-X₀ ]
l7 [X₁+3-X₂-X₃ ]
l5 [X₁+1-X₂ ]
l12 [X₁+1-X₀ ]
l9 [X₁-X₀ ]
l8 [X₁-X₀ ]

MPRF for transition t₈: l13(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1 ∧ X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l10 [X₁-X₂ ]
l13 [X₁+1-X₂ ]
l14 [X₁+1-X₂ ]
l15 [X₁-X₀ ]
l11 [X₁-X₂ ]
l3 [X₁-X₂ ]
l4 [X₁-X₂ ]
l2 [X₁-X₂ ]
l6 [X₁-X₂ ]
l7 [X₁-X₂ ]
l5 [X₁-X₂ ]
l12 [X₁-X₀ ]
l9 [X₁-X₂ ]
l8 [X₁-X₂ ]

MPRF for transition t₉: l13(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 2 ≤ X₃ ∧ X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+3 {O(n)}

MPRF:

l10 [X₁+2-X₀ ]
l13 [X₁+3-X₀ ]
l14 [X₁+3-X₀ ]
l15 [X₁+3-X₀ ]
l11 [X₁+2-X₀ ]
l3 [X₁+3-X₀ ]
l4 [X₁+3-X₀-X₃ ]
l2 [X₁+3-X₂ ]
l6 [X₁+2-X₀ ]
l7 [X₁+3-X₂ ]
l5 [X₁+3-X₂ ]
l12 [X₁+3-X₀ ]
l9 [X₁+2-X₀ ]
l8 [X₁+5-X₀-X₃ ]

MPRF for transition t₇: l14(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l10 [X₁-X₂ ]
l13 [X₁-X₂ ]
l14 [X₁+1-X₂ ]
l15 [X₁-X₀ ]
l11 [X₁-X₂ ]
l3 [X₁-X₂ ]
l4 [X₁-X₂ ]
l2 [X₁-X₂ ]
l6 [X₁-X₂ ]
l7 [X₁-X₂ ]
l5 [X₁-X₂ ]
l12 [X₁-X₀ ]
l9 [X₁-X₂ ]
l8 [X₁-X₂ ]

MPRF for transition t₄: l15(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₀+1, E) :|: 0 ≤ E ∧ E ≤ 3 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

l10 [X₁-X₀ ]
l13 [X₁-X₀ ]
l14 [X₁-X₀ ]
l15 [X₁+1-X₀ ]
l11 [X₁-X₀ ]
l3 [X₁-X₀ ]
l4 [X₁-X₀ ]
l2 [X₁-X₀ ]
l6 [X₁-X₀ ]
l7 [X₁-X₀ ]
l5 [X₁-X₀ ]
l12 [X₁+1-X₀ ]
l9 [X₁-X₀ ]
l8 [X₁-X₀ ]

MPRF for transition t₅: l15(X₀, X₁, X₂, X₃) → l12(X₀+1, X₁, X₂, X₃) :|: E+1 ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l10 [X₁-X₀-1 ]
l13 [X₁-X₂ ]
l14 [X₁-X₀ ]
l15 [X₁-X₀ ]
l11 [X₁-X₂ ]
l3 [X₁-X₂ ]
l4 [X₁-X₂ ]
l2 [X₁-X₂ ]
l6 [X₁-X₂ ]
l7 [X₁-X₂ ]
l5 [X₁-X₂ ]
l12 [X₁-X₀ ]
l9 [X₁-X₂ ]
l8 [X₁-X₂ ]

MPRF for transition t₆: l15(X₀, X₁, X₂, X₃) → l12(X₀+1, X₁, X₂, X₃) :|: 4 ≤ E ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l10 [X₁-X₂ ]
l13 [X₁-X₂ ]
l14 [X₁-X₀ ]
l15 [X₁-X₀ ]
l11 [X₁-X₂ ]
l3 [X₁-X₂ ]
l4 [X₁-X₂ ]
l2 [X₁-X₂ ]
l6 [X₁-X₂ ]
l7 [X₁-X₂ ]
l5 [X₁-X₂ ]
l12 [X₁-X₀ ]
l9 [X₁-X₂ ]
l8 [X₁-X₂ ]

MPRF for transition t₁₉: l2(X₀, X₁, X₂, X₃) → l12(X₂, X₁, X₂, X₃) :|: X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l10 [X₁-X₂ ]
l13 [X₁-X₀ ]
l14 [X₁-X₀ ]
l15 [X₁-X₀ ]
l11 [X₁-X₀ ]
l3 [X₁-X₀ ]
l4 [X₁-X₀ ]
l2 [X₁+1-X₂ ]
l6 [X₁-X₀ ]
l7 [X₁-X₀ ]
l5 [X₁-X₂ ]
l12 [X₁-X₀ ]
l9 [X₁-X₀ ]
l8 [X₁-X₂ ]

MPRF for transition t₁₀: l3(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l10 [X₁-X₂ ]
l13 [X₁+1-X₂ ]
l14 [X₁+1-X₂ ]
l15 [X₁-X₀ ]
l11 [X₁-X₂ ]
l3 [X₁+1-X₂ ]
l4 [X₁-X₂ ]
l2 [X₁-X₂ ]
l6 [X₁-X₂ ]
l7 [X₁-X₂ ]
l5 [X₁-X₂ ]
l12 [X₁-X₀ ]
l9 [X₁-X₂ ]
l8 [X₁-X₂ ]

MPRF for transition t₁₁: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l10 [X₁-X₂ ]
l13 [X₁+1-X₂ ]
l14 [X₁+1-X₂ ]
l15 [X₁-X₀ ]
l11 [X₁-X₂ ]
l3 [X₁+1-X₂ ]
l4 [X₁-X₂ ]
l2 [X₁-X₂ ]
l6 [X₁-X₂ ]
l7 [X₁-X₂ ]
l5 [X₁-X₂ ]
l12 [X₁-X₀ ]
l9 [X₁-X₂ ]
l8 [X₁-X₂ ]

MPRF for transition t₁₆: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l10 [X₁-X₂ ]
l13 [X₁-X₀ ]
l14 [X₁-X₀ ]
l15 [X₁-X₀ ]
l11 [X₁-X₂ ]
l3 [X₁-X₀ ]
l4 [X₁-X₀ ]
l2 [X₁-X₀-1 ]
l6 [X₁-X₀ ]
l7 [X₁-X₀ ]
l5 [X₁-X₂ ]
l12 [X₁-X₀ ]
l9 [X₁-X₀ ]
l8 [X₁-X₂ ]

MPRF for transition t₂₅: l5(X₀, X₁, X₂, X₃) → l12(X₂, X₁, X₂, X₃) :|: X₃ ≤ 2 ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 2+X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l10 [X₁-X₀-1 ]
l13 [X₁-X₀ ]
l14 [X₁-X₀ ]
l15 [X₁-X₀ ]
l11 [X₁-X₀ ]
l3 [X₁-X₀ ]
l4 [X₁-X₀ ]
l2 [X₁-X₀ ]
l6 [X₁-X₀ ]
l7 [X₁+1-X₂ ]
l5 [X₁+1-X₂ ]
l12 [X₁-X₀ ]
l9 [X₁-X₀ ]
l8 [X₁-X₂ ]

MPRF for transition t₂₀: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₃ ≤ 2 ∧ X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

l10 [X₁-X₀ ]
l13 [X₁+X₂-2⋅X₀ ]
l14 [X₁+1-X₀ ]
l15 [X₁+1-X₀ ]
l11 [X₁-X₀ ]
l3 [X₁+1-X₀ ]
l4 [X₁-X₀ ]
l2 [X₁+1-X₂ ]
l6 [X₁+1-X₀ ]
l7 [X₁-X₀ ]
l5 [X₁+1-X₂ ]
l12 [X₁+1-X₀ ]
l9 [X₁-X₀ ]
l8 [X₁-X₀ ]

MPRF for transition t₂₁: l6(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: 3 ≤ X₃ ∧ X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

4⋅X₁+1 {O(n)}

MPRF:

l10 [4⋅X₁-X₀-3⋅X₂ ]
l13 [4⋅X₁+X₂-5⋅X₀-X₃ ]
l14 [4⋅X₁+4⋅X₂-8⋅X₀-X₃-3 ]
l15 [4⋅X₁+1-4⋅X₀ ]
l11 [4⋅X₁-X₀-3⋅X₂ ]
l3 [4⋅X₁+X₂-5⋅X₀-X₃ ]
l4 [4⋅X₁+X₂+X₃-5⋅X₀-2 ]
l2 [4⋅X₁+X₃-4⋅X₂ ]
l6 [4⋅X₁+5-4⋅X₂-X₃ ]
l7 [4⋅X₁+1-4⋅X₂ ]
l5 [4⋅X₁+1-4⋅X₂ ]
l12 [4⋅X₁+1-4⋅X₀ ]
l9 [4⋅X₁+1-4⋅X₂ ]
l8 [4⋅X₁+X₃-4⋅X₂-2 ]

MPRF for transition t₂₂: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₃ ≤ 2 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2 ∧ X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 2+X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

3⋅X₁ {O(n)}

MPRF:

l10 [3⋅X₁-2⋅X₀ ]
l13 [3⋅X₁-2⋅X₀ ]
l14 [3⋅X₁+2-2⋅X₂ ]
l15 [3⋅X₁-2⋅X₀ ]
l11 [3⋅X₁-2⋅X₀ ]
l3 [3⋅X₁-2⋅X₀ ]
l4 [3⋅X₁-2⋅X₀ ]
l2 [3⋅X₁-2⋅X₀ ]
l6 [X₀+3⋅X₁+X₃-3⋅X₂ ]
l7 [X₀+3⋅X₁+2-3⋅X₂ ]
l5 [X₀+3⋅X₁+1-3⋅X₂ ]
l12 [3⋅X₁-2⋅X₀ ]
l9 [X₀+3⋅X₁+X₃-3⋅X₂ ]
l8 [3⋅X₁+X₃-2⋅X₂-1 ]

MPRF for transition t₂₉: l8(X₀, X₁, X₂, X₃) → l12(X₂, X₁, X₂, X₃) :|: X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l10 [X₁-X₀ ]
l13 [X₁+1-X₂ ]
l14 [X₁-X₀ ]
l15 [X₁-X₀ ]
l11 [X₁-X₀ ]
l3 [X₁-X₀ ]
l4 [X₁-X₀ ]
l2 [X₁-X₂ ]
l6 [X₁-X₀ ]
l7 [X₁-X₀ ]
l5 [X₁-X₀ ]
l12 [X₁-X₀ ]
l9 [X₁-X₀ ]
l8 [X₁-X₀ ]

MPRF for transition t₂₆: l9(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₃ ≤ 3 ∧ 3 ≤ X₃ ∧ X₃ ≤ 3 ∧ X₃ ≤ 2+X₂ ∧ X₃ ≤ 2+X₁ ∧ X₃ ≤ 3+X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l10 [X₁-X₂ ]
l13 [X₁+1-X₂ ]
l14 [X₁-X₀ ]
l15 [X₁-X₀ ]
l11 [X₁-X₀-1 ]
l3 [X₁-X₂ ]
l4 [X₁-X₂ ]
l2 [X₁-X₂ ]
l6 [X₁+X₃-X₂-2 ]
l7 [X₁+X₃-X₂-2 ]
l5 [X₁-X₂ ]
l12 [X₁-X₀ ]
l9 [X₁+X₃-X₂-2 ]
l8 [X₁+X₃-X₂-3 ]

All Bounds

Timebounds

Overall timebound:24⋅X₁+11 {O(n)}
t₀: 1 {O(1)}
t₁₅: X₁ {O(n)}
t₁₂: X₁ {O(n)}
t₂: X₁+1 {O(n)}
t₃: 1 {O(1)}
t₈: X₁ {O(n)}
t₉: X₁+3 {O(n)}
t₇: X₁ {O(n)}
t₄: X₁+1 {O(n)}
t₅: X₁ {O(n)}
t₆: X₁ {O(n)}
t₃₁: 1 {O(1)}
t₁: 1 {O(1)}
t₁₉: X₁ {O(n)}
t₁₀: X₁ {O(n)}
t₁₁: X₁ {O(n)}
t₁₆: X₁ {O(n)}
t₂₅: X₁ {O(n)}
t₂₀: X₁+1 {O(n)}
t₂₁: 4⋅X₁+1 {O(n)}
t₂₂: 3⋅X₁ {O(n)}
t₂₉: X₁ {O(n)}
t₂₆: X₁ {O(n)}

Costbounds

Overall costbound: 24⋅X₁+11 {O(n)}
t₀: 1 {O(1)}
t₁₅: X₁ {O(n)}
t₁₂: X₁ {O(n)}
t₂: X₁+1 {O(n)}
t₃: 1 {O(1)}
t₈: X₁ {O(n)}
t₉: X₁+3 {O(n)}
t₇: X₁ {O(n)}
t₄: X₁+1 {O(n)}
t₅: X₁ {O(n)}
t₆: X₁ {O(n)}
t₃₁: 1 {O(1)}
t₁: 1 {O(1)}
t₁₉: X₁ {O(n)}
t₁₀: X₁ {O(n)}
t₁₁: X₁ {O(n)}
t₁₆: X₁ {O(n)}
t₂₅: X₁ {O(n)}
t₂₀: X₁+1 {O(n)}
t₂₁: 4⋅X₁+1 {O(n)}
t₂₂: 3⋅X₁ {O(n)}
t₂₉: X₁ {O(n)}
t₂₆: X₁ {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁₅, X₀: 6⋅X₁ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: 6⋅X₁+1 {O(n)}
t₁₅, X₃: 0 {O(1)}
t₁₂, X₀: 6⋅X₁ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: 6⋅X₁+1 {O(n)}
t₁₂, X₃: 0 {O(1)}
t₂, X₀: 6⋅X₁ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 24⋅X₁+X₂+4 {O(n)}
t₂, X₃: X₃+6 {O(n)}
t₃, X₀: 36⋅X₁ {O(n)}
t₃, X₁: 7⋅X₁ {O(n)}
t₃, X₂: 3⋅X₂+72⋅X₁+12 {O(n)}
t₃, X₃: 3⋅X₃+18 {O(n)}
t₈, X₀: 6⋅X₁ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: 6⋅X₁+1 {O(n)}
t₈, X₃: 1 {O(1)}
t₉, X₀: 6⋅X₁ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: 6⋅X₁+1 {O(n)}
t₉, X₃: 3 {O(1)}
t₇, X₀: 6⋅X₁ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: 6⋅X₁+1 {O(n)}
t₇, X₃: 3 {O(1)}
t₄, X₀: 6⋅X₁ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: 6⋅X₁+1 {O(n)}
t₄, X₃: 3 {O(1)}
t₅, X₀: 6⋅X₁ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: 24⋅X₁+X₂+4 {O(n)}
t₅, X₃: X₃+6 {O(n)}
t₆, X₀: 6⋅X₁ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: 24⋅X₁+X₂+4 {O(n)}
t₆, X₃: X₃+6 {O(n)}
t₃₁, X₀: 36⋅X₁ {O(n)}
t₃₁, X₁: 7⋅X₁ {O(n)}
t₃₁, X₂: 3⋅X₂+72⋅X₁+12 {O(n)}
t₃₁, X₃: 3⋅X₃+18 {O(n)}
t₁, X₀: 0 {O(1)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁₉, X₀: 6⋅X₁ {O(n)}
t₁₉, X₁: X₁ {O(n)}
t₁₉, X₂: 6⋅X₁+1 {O(n)}
t₁₉, X₃: 1 {O(1)}
t₁₀, X₀: 6⋅X₁ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: 6⋅X₁+1 {O(n)}
t₁₀, X₃: 0 {O(1)}
t₁₁, X₀: 6⋅X₁ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: 6⋅X₁+1 {O(n)}
t₁₁, X₃: 1 {O(1)}
t₁₆, X₀: 6⋅X₁ {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₆, X₂: 6⋅X₁+1 {O(n)}
t₁₆, X₃: 1 {O(1)}
t₂₅, X₀: 6⋅X₁ {O(n)}
t₂₅, X₁: X₁ {O(n)}
t₂₅, X₂: 6⋅X₁+1 {O(n)}
t₂₅, X₃: 2 {O(1)}
t₂₀, X₀: 6⋅X₁ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: 6⋅X₁+1 {O(n)}
t₂₀, X₃: 2 {O(1)}
t₂₁, X₀: 6⋅X₁ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₂: 6⋅X₁+1 {O(n)}
t₂₁, X₃: 3 {O(1)}
t₂₂, X₀: 6⋅X₁ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₂: 6⋅X₁+1 {O(n)}
t₂₂, X₃: 2 {O(1)}
t₂₉, X₀: 6⋅X₁ {O(n)}
t₂₉, X₁: X₁ {O(n)}
t₂₉, X₂: 6⋅X₁+1 {O(n)}
t₂₉, X₃: 3 {O(1)}
t₂₆, X₀: 6⋅X₁ {O(n)}
t₂₆, X₁: X₁ {O(n)}
t₂₆, X₂: 6⋅X₁+1 {O(n)}
t₂₆, X₃: 3 {O(1)}