Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀
Temp_Vars: L, M
Locations: l0, l1, l10, l11, l12, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₂: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀)
t₂₆: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₃
t₆: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₃ ≤ X₀
t₁₁: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇+1, L, X₉, X₁₀) :|: X₇ ≤ X₀
t₁₈: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₇
t₀: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: L+1 ≤ 0
t₁: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1 ≤ L
t₁₂: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀)
t₄: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l12(X₀, X₁, X₂, X₃+1, L, L, X₆, X₇, X₈, X₉, X₁₀) :|: L ≤ X₂ ∧ X₃ ≤ X₀
t₅: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l12(X₀, X₁, L, X₃+1, L, L, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₂ ≤ L ∧ X₃ ≤ X₀
t₂₇: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l3(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₂+1 ≤ 0 ∧ 1+X₀ ≤ X₃
t₂₈: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l3(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1 ≤ X₂ ∧ 1+X₀ ≤ X₃
t₂₉: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l3(X₀, X₁+1, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
t₃₀: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₁
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l12(X₀, X₁, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₁ ≤ X₀
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l7(X₀, X₁, X₂, X₃, X₄, X₅, L, X₇, X₈, X₉, X₁₀) :|: X₁+1 ≤ X₃
t₂₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l8(X₀, X₁, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₃ ≤ X₁
t₁₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l1(X₀, X₁, X₂, X₀+1, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₀ ≤ X₃ ∧ X₃ ≤ X₀
t₁₃: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, L, X₉, X₁₀) :|: X₃+1 ≤ X₀
t₁₄: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, L, X₉, X₁₀) :|: 1+X₀ ≤ X₃
t₁₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l1(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₁
t₁₅: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l6(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₁ ≤ X₀
t₂₄: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l4(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₁ ≤ X₇
t₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l7(X₀, X₁, X₂, X₃, X₄, X₅, L, X₇+1, X₈, X₉, X₁₀) :|: X₇+1 ≤ X₁
t₂₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₁ ∧ X₃+1 ≤ X₁₀
t₂₂: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₁ ∧ 1+X₁₀ ≤ X₃
t₂₃: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₃) :|: 1+X₀ ≤ X₁ ∧ X₃ ≤ X₁₀ ∧ X₁₀ ≤ X₃
t₉: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l9(X₀, X₁, X₂, X₃, X₄, X₅, L, X₇, X₈, X₉, X₁₀) :|: X₁ ≤ X₀
t₁₉: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l8(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇, M, L, X₁₀) :|: M+1 ≤ X₂ ∧ X₃ ≤ X₇
t₂₀: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l8(X₀, X₁+1, L, X₃, X₄, X₅, X₆, X₇, L, M, X₁) :|: X₂ ≤ L ∧ X₃ ≤ X₇
t₁₀: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l9(X₀, X₁, X₂, X₃, X₄, X₅, L, X₇+1, X₈, X₉, X₁₀) :|: X₇+1 ≤ X₃
Preprocessing
Eliminate variables {X₄,X₅,X₆,X₈,X₉} that do not contribute to the problem
Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l11
Found invariant 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ for location l2
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l6
Found invariant 0 ≤ X₂ ∧ X₁ ≤ X₀ for location l12
Found invariant 1 ≤ 0 for location l7
Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l5
Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l8
Found invariant 1+X₀ ≤ X₁ for location l1
Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l10
Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location l4
Found invariant 1 ≤ 0 for location l9
Cut unsatisfiable transition t₇₇: l12→l3
Cut unsatisfiable transition t₈₂: l4→l7
Cut unsatisfiable transition t₈₅: l5→l6
Cut unsatisfiable transition t₈₇: l6→l6
Cut unsatisfiable transition t₈₉: l7→l7
Cut unsatisfiable transition t₉₀: l7→l4
Cut unsatisfiable transition t₉₁: l8→l9
Cut unsatisfiable transition t₉₅: l9→l9
Cut unsatisfiable transition t₉₆: l9→l8
Cut unsatisfiable transition t₉₇: l9→l8
Cut unreachable locations [l7; l9] from the program graph
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₇, X₁₀
Temp_Vars: L
Locations: l0, l1, l10, l11, l12, l2, l3, l4, l5, l6, l8
Transitions:
t₆₇: l0(X₀, X₁, X₂, X₃, X₇, X₁₀) → l3(X₀, X₁, X₂, X₃, X₇, X₁₀)
t₆₉: l1(X₀, X₁, X₂, X₃, X₇, X₁₀) → l2(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁
t₆₈: l1(X₀, X₁, X₂, X₃, X₇, X₁₀) → l4(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁
t₇₀: l10(X₀, X₁, X₂, X₃, X₇, X₁₀) → l10(X₀, X₁, X₂, X₃, X₇+1, X₁₀) :|: X₇ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₇₁: l10(X₀, X₁, X₂, X₃, X₇, X₁₀) → l11(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1+X₀ ≤ X₇ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₇₂: l11(X₀, X₁, X₂, X₃, X₇, X₁₀) → l5(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: L+1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₇₃: l11(X₀, X₁, X₂, X₃, X₇, X₁₀) → l5(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1 ≤ L ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₇₄: l11(X₀, X₁, X₂, X₃, X₇, X₁₀) → l5(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₇₅: l12(X₀, X₁, X₂, X₃, X₇, X₁₀) → l12(X₀, X₁, X₂, X₃+1, X₇, X₁₀) :|: L ≤ X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀
t₇₆: l12(X₀, X₁, X₂, X₃, X₇, X₁₀) → l12(X₀, X₁, L, X₃+1, X₇, X₁₀) :|: 1+X₂ ≤ L ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀
t₇₈: l12(X₀, X₁, X₂, X₃, X₇, X₁₀) → l3(X₀, X₁+1, X₂, X₃, X₇, X₁₀) :|: 1 ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀
t₇₉: l12(X₀, X₁, X₂, X₃, X₇, X₁₀) → l3(X₀, X₁+1, 0, X₃, X₇, X₁₀) :|: 1+X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀
t₈₁: l3(X₀, X₁, X₂, X₃, X₇, X₁₀) → l1(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1+X₀ ≤ X₁
t₈₀: l3(X₀, X₁, X₂, X₃, X₇, X₁₀) → l12(X₀, X₁, 0, X₃, X₇, X₁₀) :|: X₁ ≤ X₀
t₈₃: l4(X₀, X₁, X₂, X₃, X₇, X₁₀) → l8(X₀, X₁, 0, X₃, X₇, X₁₀) :|: X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁
t₈₆: l5(X₀, X₁, X₂, X₃, X₇, X₁₀) → l1(X₀, X₁, X₂, X₀+1, X₇, X₁₀) :|: X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₈₄: l5(X₀, X₁, X₂, X₃, X₇, X₁₀) → l6(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: X₃+1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₈₈: l6(X₀, X₁, X₂, X₃, X₇, X₁₀) → l1(X₀, X₁, X₂, X₃+1, X₇, X₁₀) :|: 1+X₀ ≤ X₁ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₉₂: l8(X₀, X₁, X₂, X₃, X₇, X₁₀) → l10(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1+X₀ ≤ X₁ ∧ X₃+1 ≤ X₁₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₉₃: l8(X₀, X₁, X₂, X₃, X₇, X₁₀) → l10(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1+X₀ ≤ X₁ ∧ 1+X₁₀ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₉₄: l8(X₀, X₁, X₂, X₃, X₇, X₁₀) → l11(X₀, X₁, X₂, X₃, X₇, X₃) :|: 1+X₀ ≤ X₁ ∧ X₃ ≤ X₁₀ ∧ X₁₀ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
MPRF for transition t₇₅: l12(X₀, X₁, X₂, X₃, X₇, X₁₀) → l12(X₀, X₁, X₂, X₃+1, X₇, X₁₀) :|: L ≤ X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₃+1 {O(n)}
MPRF:
l3 [X₀+1-X₃ ]
l12 [X₀+1-X₃ ]
MPRF for transition t₇₆: l12(X₀, X₁, X₂, X₃, X₇, X₁₀) → l12(X₀, X₁, L, X₃+1, X₇, X₁₀) :|: 1+X₂ ≤ L ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₃+1 {O(n)}
MPRF:
l3 [X₀+1-X₃ ]
l12 [X₀+1-X₃ ]
MPRF for transition t₇₈: l12(X₀, X₁, X₂, X₃, X₇, X₁₀) → l3(X₀, X₁+1, X₂, X₃, X₇, X₁₀) :|: 1 ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF:
l3 [X₀+1-X₁ ]
l12 [X₀+1-X₁ ]
MPRF for transition t₇₉: l12(X₀, X₁, X₂, X₃, X₇, X₁₀) → l3(X₀, X₁+1, 0, X₃, X₇, X₁₀) :|: 1+X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF:
l3 [X₀+1-X₁ ]
l12 [X₀+1-X₁ ]
MPRF for transition t₈₀: l3(X₀, X₁, X₂, X₃, X₇, X₁₀) → l12(X₀, X₁, 0, X₃, X₇, X₁₀) :|: X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF:
l3 [X₀+1-X₁ ]
l12 [X₀-X₁ ]
MPRF for transition t₆₈: l1(X₀, X₁, X₂, X₃, X₇, X₁₀) → l4(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
MPRF:
l4 [X₁-X₃-1 ]
l5 [X₁-X₃-1 ]
l6 [X₁-X₃-1 ]
l1 [X₁-X₃ ]
l10 [X₁-X₃-1 ]
l8 [X₁-X₃-1 ]
l11 [X₁-X₃-1 ]
MPRF for transition t₇₀: l10(X₀, X₁, X₂, X₃, X₇, X₁₀) → l10(X₀, X₁, X₂, X₃, X₇+1, X₁₀) :|: X₇ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
10⋅X₀+3⋅X₇+7⋅X₃+5 {O(n)}
MPRF:
l4 [2⋅X₀+1-X₃-X₇ ]
l5 [2⋅X₀-X₃-X₇ ]
l6 [2⋅X₀-X₃-X₇ ]
l1 [2⋅X₀+1-X₃-X₇ ]
l10 [2⋅X₀+1-X₃-X₇ ]
l8 [2⋅X₀+1-X₃-X₇ ]
l11 [2⋅X₀-X₃-X₇ ]
MPRF for transition t₇₁: l10(X₀, X₁, X₂, X₃, X₇, X₁₀) → l11(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1+X₀ ≤ X₇ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
7⋅X₀+7⋅X₃+5 {O(n)}
MPRF:
l4 [X₀+1-X₃ ]
l5 [X₀-X₃ ]
l6 [X₀-X₃ ]
l1 [X₀+1-X₃ ]
l10 [X₀+1-X₃ ]
l8 [X₀+1-X₃ ]
l11 [X₀-X₃ ]
MPRF for transition t₇₂: l11(X₀, X₁, X₂, X₃, X₇, X₁₀) → l5(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: L+1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
MPRF:
l4 [X₁-X₃ ]
l5 [X₁-X₃-1 ]
l6 [X₁-X₃-1 ]
l1 [X₁-X₃ ]
l10 [X₁-X₃ ]
l8 [X₁-X₃ ]
l11 [X₁-X₃ ]
MPRF for transition t₇₃: l11(X₀, X₁, X₂, X₃, X₇, X₁₀) → l5(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1 ≤ L ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
7⋅X₀+7⋅X₃+5 {O(n)}
MPRF:
l4 [X₀+1-X₃ ]
l5 [X₀-X₃ ]
l6 [X₀-X₃ ]
l1 [X₀+1-X₃ ]
l10 [X₀+1-X₃ ]
l8 [X₀+1-X₃ ]
l11 [X₀+1-X₃ ]
MPRF for transition t₇₄: l11(X₀, X₁, X₂, X₃, X₇, X₁₀) → l5(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
MPRF:
l4 [X₁-X₃ ]
l5 [X₁-X₃-1 ]
l6 [X₁-X₃-1 ]
l1 [X₁-X₃ ]
l10 [X₁-X₃ ]
l8 [X₁-X₃ ]
l11 [X₁-X₃ ]
MPRF for transition t₈₃: l4(X₀, X₁, X₂, X₃, X₇, X₁₀) → l8(X₀, X₁, 0, X₃, X₇, X₁₀) :|: X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
7⋅X₀+7⋅X₃+5 {O(n)}
MPRF:
l4 [X₀+1-X₃ ]
l5 [X₀-X₃ ]
l6 [X₀-X₃ ]
l1 [X₀+1-X₃ ]
l10 [X₀-X₃ ]
l8 [X₀-X₃ ]
l11 [X₀-X₃ ]
MPRF for transition t₈₄: l5(X₀, X₁, X₂, X₃, X₇, X₁₀) → l6(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: X₃+1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
7⋅X₀+7⋅X₃+5 {O(n)}
MPRF:
l4 [X₀+1-X₃ ]
l5 [X₀+1-X₃ ]
l6 [X₀-X₃ ]
l1 [X₀+1-X₃ ]
l10 [X₀+1-X₃ ]
l8 [X₀+1-X₃ ]
l11 [X₀+1-X₃ ]
MPRF for transition t₈₆: l5(X₀, X₁, X₂, X₃, X₇, X₁₀) → l1(X₀, X₁, X₂, X₀+1, X₇, X₁₀) :|: X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
7⋅X₀+7⋅X₃+5 {O(n)}
MPRF:
l4 [X₀+1-X₃ ]
l5 [X₀+1-X₃ ]
l6 [X₀-X₃ ]
l1 [X₀+1-X₃ ]
l10 [X₀+1-X₃ ]
l8 [X₀+1-X₃ ]
l11 [X₀+1-X₃ ]
MPRF for transition t₈₈: l6(X₀, X₁, X₂, X₃, X₇, X₁₀) → l1(X₀, X₁, X₂, X₃+1, X₇, X₁₀) :|: 1+X₀ ≤ X₁ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
7⋅X₁+7⋅X₃+8⋅X₀+9 {O(n)}
MPRF:
l4 [X₁+1-X₃ ]
l5 [X₁+1-X₃ ]
l6 [X₁+1-X₃ ]
l1 [X₁+1-X₃ ]
l10 [X₁+1-X₃ ]
l8 [X₁+1-X₃ ]
l11 [X₁+1-X₃ ]
MPRF for transition t₉₂: l8(X₀, X₁, X₂, X₃, X₇, X₁₀) → l10(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1+X₀ ≤ X₁ ∧ X₃+1 ≤ X₁₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
MPRF:
l4 [X₁-X₃ ]
l5 [X₁-X₃-1 ]
l6 [X₁-X₃-1 ]
l1 [X₁-X₃ ]
l10 [X₁-X₃-1 ]
l8 [X₁-X₃ ]
l11 [X₁-X₃-1 ]
MPRF for transition t₉₃: l8(X₀, X₁, X₂, X₃, X₇, X₁₀) → l10(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1+X₀ ≤ X₁ ∧ 1+X₁₀ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
7⋅X₀+7⋅X₃+5 {O(n)}
MPRF:
l4 [X₀+1-X₃ ]
l5 [X₀-X₃ ]
l6 [X₀-X₃ ]
l1 [X₀+1-X₃ ]
l10 [X₀-X₃ ]
l8 [X₀+1-X₃ ]
l11 [X₀-X₃ ]
MPRF for transition t₉₄: l8(X₀, X₁, X₂, X₃, X₇, X₁₀) → l11(X₀, X₁, X₂, X₃, X₇, X₃) :|: 1+X₀ ≤ X₁ ∧ X₃ ≤ X₁₀ ∧ X₁₀ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
7⋅X₀+7⋅X₃+5 {O(n)}
MPRF:
l4 [X₀+1-X₃ ]
l5 [X₀-X₃ ]
l6 [X₀-X₃ ]
l1 [X₀+1-X₃ ]
l10 [X₀-X₃ ]
l8 [X₀+1-X₃ ]
l11 [X₀-X₃ ]
All Bounds
Timebounds
Overall timebound:104⋅X₀+3⋅X₇+38⋅X₁+93⋅X₃+89 {O(n)}
t₆₇: 1 {O(1)}
t₆₈: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₆₉: 1 {O(1)}
t₇₀: 10⋅X₀+3⋅X₇+7⋅X₃+5 {O(n)}
t₇₁: 7⋅X₀+7⋅X₃+5 {O(n)}
t₇₂: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₇₃: 7⋅X₀+7⋅X₃+5 {O(n)}
t₇₄: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₇₅: X₀+X₃+1 {O(n)}
t₇₆: X₀+X₃+1 {O(n)}
t₇₈: X₀+X₁+1 {O(n)}
t₇₉: X₀+X₁+1 {O(n)}
t₈₀: X₀+X₁+1 {O(n)}
t₈₁: 1 {O(1)}
t₈₃: 7⋅X₀+7⋅X₃+5 {O(n)}
t₈₄: 7⋅X₀+7⋅X₃+5 {O(n)}
t₈₆: 7⋅X₀+7⋅X₃+5 {O(n)}
t₈₈: 7⋅X₁+7⋅X₃+8⋅X₀+9 {O(n)}
t₉₂: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₉₃: 7⋅X₀+7⋅X₃+5 {O(n)}
t₉₄: 7⋅X₀+7⋅X₃+5 {O(n)}
Costbounds
Overall costbound: 104⋅X₀+3⋅X₇+38⋅X₁+93⋅X₃+89 {O(n)}
t₆₇: 1 {O(1)}
t₆₈: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₆₉: 1 {O(1)}
t₇₀: 10⋅X₀+3⋅X₇+7⋅X₃+5 {O(n)}
t₇₁: 7⋅X₀+7⋅X₃+5 {O(n)}
t₇₂: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₇₃: 7⋅X₀+7⋅X₃+5 {O(n)}
t₇₄: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₇₅: X₀+X₃+1 {O(n)}
t₇₆: X₀+X₃+1 {O(n)}
t₇₈: X₀+X₁+1 {O(n)}
t₇₉: X₀+X₁+1 {O(n)}
t₈₀: X₀+X₁+1 {O(n)}
t₈₁: 1 {O(1)}
t₈₃: 7⋅X₀+7⋅X₃+5 {O(n)}
t₈₄: 7⋅X₀+7⋅X₃+5 {O(n)}
t₈₆: 7⋅X₀+7⋅X₃+5 {O(n)}
t₈₈: 7⋅X₁+7⋅X₃+8⋅X₀+9 {O(n)}
t₉₂: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₉₃: 7⋅X₀+7⋅X₃+5 {O(n)}
t₉₄: 7⋅X₀+7⋅X₃+5 {O(n)}
Sizebounds
t₆₇, X₀: X₀ {O(n)}
t₆₇, X₁: X₁ {O(n)}
t₆₇, X₂: X₂ {O(n)}
t₆₇, X₃: X₃ {O(n)}
t₆₇, X₇: X₇ {O(n)}
t₆₇, X₁₀: X₁₀ {O(n)}
t₆₈, X₀: 3⋅X₀ {O(n)}
t₆₈, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₆₈, X₃: 12⋅X₀+14⋅X₃+7⋅X₁+13 {O(n)}
t₆₈, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₆₈, X₁₀: 21⋅X₁+3⋅X₁₀+36⋅X₀+42⋅X₃+39 {O(n)}
t₆₉, X₀: 12⋅X₀ {O(n)}
t₆₉, X₁: 16⋅X₀+28⋅X₁+16 {O(n)}
t₆₉, X₃: 13⋅X₀+7⋅X₃+7 {O(n)}
t₆₉, X₇: 21⋅X₃+21⋅X₇+30⋅X₀+15 {O(n)}
t₆₉, X₁₀: 108⋅X₀+12⋅X₁₀+126⋅X₃+63⋅X₁+117 {O(n)}
t₇₀, X₀: 3⋅X₀ {O(n)}
t₇₀, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₇₀, X₂: 0 {O(1)}
t₇₀, X₃: 12⋅X₀+14⋅X₃+7⋅X₁+13 {O(n)}
t₇₀, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₇₀, X₁₀: 21⋅X₁+3⋅X₁₀+36⋅X₀+42⋅X₃+39 {O(n)}
t₇₁, X₀: 3⋅X₀ {O(n)}
t₇₁, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₇₁, X₂: 0 {O(1)}
t₇₁, X₃: 12⋅X₀+14⋅X₃+7⋅X₁+13 {O(n)}
t₇₁, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₇₁, X₁₀: 21⋅X₁+3⋅X₁₀+36⋅X₀+42⋅X₃+39 {O(n)}
t₇₂, X₀: 3⋅X₀ {O(n)}
t₇₂, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₇₂, X₂: 0 {O(1)}
t₇₂, X₃: 12⋅X₀+14⋅X₃+7⋅X₁+13 {O(n)}
t₇₂, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₇₂, X₁₀: 21⋅X₁+3⋅X₁₀+36⋅X₀+42⋅X₃+39 {O(n)}
t₇₃, X₀: 3⋅X₀ {O(n)}
t₇₃, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₇₃, X₂: 0 {O(1)}
t₇₃, X₃: 12⋅X₀+14⋅X₃+7⋅X₁+13 {O(n)}
t₇₃, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₇₃, X₁₀: 21⋅X₁+3⋅X₁₀+36⋅X₀+42⋅X₃+39 {O(n)}
t₇₄, X₀: 3⋅X₀ {O(n)}
t₇₄, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₇₄, X₂: 0 {O(1)}
t₇₄, X₃: 12⋅X₀+14⋅X₃+7⋅X₁+13 {O(n)}
t₇₄, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₇₄, X₁₀: 21⋅X₁+3⋅X₁₀+36⋅X₀+42⋅X₃+39 {O(n)}
t₇₅, X₀: X₀ {O(n)}
t₇₅, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₇₅, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₇₅, X₇: X₇ {O(n)}
t₇₅, X₁₀: X₁₀ {O(n)}
t₇₆, X₀: X₀ {O(n)}
t₇₆, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₇₆, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₇₆, X₇: X₇ {O(n)}
t₇₆, X₁₀: X₁₀ {O(n)}
t₇₈, X₀: X₀ {O(n)}
t₇₈, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₇₈, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₇₈, X₇: X₇ {O(n)}
t₇₈, X₁₀: X₁₀ {O(n)}
t₇₉, X₀: X₀ {O(n)}
t₇₉, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₇₉, X₂: 0 {O(1)}
t₇₉, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₇₉, X₇: X₇ {O(n)}
t₇₉, X₁₀: X₁₀ {O(n)}
t₈₀, X₀: X₀ {O(n)}
t₈₀, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₈₀, X₂: 0 {O(1)}
t₈₀, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₈₀, X₇: X₇ {O(n)}
t₈₀, X₁₀: X₁₀ {O(n)}
t₈₁, X₀: 3⋅X₀ {O(n)}
t₈₁, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₁, X₃: 4⋅X₀+7⋅X₃+4 {O(n)}
t₈₁, X₇: 3⋅X₇ {O(n)}
t₈₁, X₁₀: 3⋅X₁₀ {O(n)}
t₈₃, X₀: 3⋅X₀ {O(n)}
t₈₃, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₃, X₂: 0 {O(1)}
t₈₃, X₃: 12⋅X₀+14⋅X₃+7⋅X₁+13 {O(n)}
t₈₃, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₈₃, X₁₀: 21⋅X₁+3⋅X₁₀+36⋅X₀+42⋅X₃+39 {O(n)}
t₈₄, X₀: 3⋅X₀ {O(n)}
t₈₄, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₄, X₂: 0 {O(1)}
t₈₄, X₃: 12⋅X₀+14⋅X₃+7⋅X₁+13 {O(n)}
t₈₄, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₈₄, X₁₀: 21⋅X₁+3⋅X₁₀+36⋅X₀+42⋅X₃+39 {O(n)}
t₈₆, X₀: 9⋅X₀ {O(n)}
t₈₆, X₁: 12⋅X₀+21⋅X₁+12 {O(n)}
t₈₆, X₂: 0 {O(1)}
t₈₆, X₃: 9⋅X₀+3 {O(n)}
t₈₆, X₇: 18⋅X₇+21⋅X₃+30⋅X₀+15 {O(n)}
t₈₆, X₁₀: 108⋅X₀+126⋅X₃+63⋅X₁+9⋅X₁₀+117 {O(n)}
t₈₈, X₀: 3⋅X₀ {O(n)}
t₈₈, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₈, X₂: 0 {O(1)}
t₈₈, X₃: 12⋅X₀+14⋅X₃+7⋅X₁+13 {O(n)}
t₈₈, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₈₈, X₁₀: 21⋅X₁+3⋅X₁₀+36⋅X₀+42⋅X₃+39 {O(n)}
t₉₂, X₀: 3⋅X₀ {O(n)}
t₉₂, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₉₂, X₂: 0 {O(1)}
t₉₂, X₃: 12⋅X₀+14⋅X₃+7⋅X₁+13 {O(n)}
t₉₂, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₉₂, X₁₀: 21⋅X₁+3⋅X₁₀+36⋅X₀+42⋅X₃+39 {O(n)}
t₉₃, X₀: 3⋅X₀ {O(n)}
t₉₃, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₉₃, X₂: 0 {O(1)}
t₉₃, X₃: 12⋅X₀+14⋅X₃+7⋅X₁+13 {O(n)}
t₉₃, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₉₃, X₁₀: 21⋅X₁+3⋅X₁₀+36⋅X₀+42⋅X₃+39 {O(n)}
t₉₄, X₀: 3⋅X₀ {O(n)}
t₉₄, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₉₄, X₂: 0 {O(1)}
t₉₄, X₃: 12⋅X₀+14⋅X₃+7⋅X₁+13 {O(n)}
t₉₄, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₉₄, X₁₀: 12⋅X₀+14⋅X₃+7⋅X₁+13 {O(n)}