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) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l2(X₀, X₁, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₁ ≤ X₀
t₂₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₁
t₁₀: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l10(X₀, X₁, X₂, X₃, X₄, X₅, L, X₇+1, X₈, X₉, X₁₀) :|: X₇+1 ≤ X₃
t₁₈: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l9(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇, M, L, X₁₀) :|: M+1 ≤ X₂ ∧ X₃ ≤ X₇
t₁₉: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l9(X₀, X₁+1, L, X₃, X₄, X₅, X₆, X₇, L, M, X₁) :|: X₂ ≤ L ∧ X₃ ≤ X₇
t₁₁: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇+1, L, X₉, X₁₀) :|: X₇ ≤ X₀
t₁₇: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₇
t₀: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: L+1 ≤ 0
t₁: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀)
t₂₆: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l1(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₂+1 ≤ 0 ∧ 1+X₀ ≤ X₃
t₂₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l1(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1 ≤ X₂ ∧ 1+X₀ ≤ X₃
t₂₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l1(X₀, X₁+1, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l2(X₀, X₁, X₂, X₃+1, L, L, X₆, X₇, X₈, X₉, X₁₀) :|: L ≤ X₂ ∧ X₃ ≤ X₀
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l2(X₀, X₁, L, X₃+1, L, L, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₂ ≤ L ∧ X₃ ≤ X₀
t₆: l3(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
t₂₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₃
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l8(X₀, X₁, X₂, X₃, X₄, X₅, L, X₇, X₈, X₉, X₁₀) :|: X₁+1 ≤ X₃
t₂₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l9(X₀, X₁, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₃ ≤ X₁
t₁₅: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l3(X₀, X₁, X₂, X₀+1, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₀ ≤ X₃ ∧ X₃ ≤ X₀
t₁₂: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, L, X₉, X₁₀) :|: X₃+1 ≤ X₀
t₁₃: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, L, X₉, X₁₀) :|: 1+X₀ ≤ X₃
t₁₆: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l3(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1+X₀ ≤ X₁
t₁₄: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l7(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₁ ≤ X₀
t₂₃: l8(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: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l8(X₀, X₁, X₂, X₃, X₄, X₅, L, X₇+1, X₈, X₉, X₁₀) :|: X₇+1 ≤ X₁
t₉: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l10(X₀, X₁, X₂, X₃, X₄, X₅, L, X₇, X₈, X₉, X₁₀) :|: X₁ ≤ X₀
t₂₀: l9(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 ≤ X₁ ∧ X₃+1 ≤ X₁₀
t₂₁: l9(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 ≤ X₁ ∧ 1+X₁₀ ≤ X₃
t₂₂: l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₃) :|: 1+X₀ ≤ X₁ ∧ X₃ ≤ X₁₀ ∧ X₁₀ ≤ 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 0 ≤ X₂ ∧ X₁ ≤ X₀ for location l2
Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l6
Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l12
Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l7
Found invariant 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ for location l5
Found invariant 1 ≤ 0 for location l8
Found invariant 1 ≤ 0 for location l10
Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location l4
Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location l9
Found invariant 1+X₀ ≤ X₁ for location l3
Cut unsatisfiable transition t₆₆: l10→l10
Cut unsatisfiable transition t₆₇: l10→l9
Cut unsatisfiable transition t₆₈: l10→l9
Cut unsatisfiable transition t₇₅: l2→l1
Cut unsatisfiable transition t₈₀: l4→l8
Cut unsatisfiable transition t₈₃: l6→l7
Cut unsatisfiable transition t₈₅: l7→l7
Cut unsatisfiable transition t₈₇: l8→l8
Cut unsatisfiable transition t₈₈: l8→l4
Cut unsatisfiable transition t₈₉: l9→l10
Cut unreachable locations [l10; l8] from the program graph
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₇, X₁₀
Temp_Vars: L
Locations: l0, l1, l11, l12, l2, l3, l4, l5, l6, l7, l9
Transitions:
t₆₃: l0(X₀, X₁, X₂, X₃, X₇, X₁₀) → l1(X₀, X₁, X₂, X₃, X₇, X₁₀)
t₆₄: l1(X₀, X₁, X₂, X₃, X₇, X₁₀) → l2(X₀, X₁, 0, X₃, X₇, X₁₀) :|: X₁ ≤ X₀
t₆₅: l1(X₀, X₁, X₂, X₃, X₇, X₁₀) → l3(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1+X₀ ≤ X₁
t₆₉: l11(X₀, X₁, X₂, X₃, X₇, X₁₀) → l11(X₀, X₁, X₂, X₃, X₇+1, X₁₀) :|: X₇ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₇₀: l11(X₀, X₁, X₂, X₃, X₇, X₁₀) → l12(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1+X₀ ≤ X₇ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₇₁: l12(X₀, X₁, X₂, X₃, X₇, X₁₀) → l6(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: L+1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₇₂: l12(X₀, X₁, X₂, X₃, X₇, X₁₀) → l6(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₇₆: l2(X₀, X₁, X₂, X₃, X₇, X₁₀) → l1(X₀, X₁+1, X₂, X₃, X₇, X₁₀) :|: 1 ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀
t₇₇: l2(X₀, X₁, X₂, X₃, X₇, X₁₀) → l1(X₀, X₁+1, 0, X₃, X₇, X₁₀) :|: 1+X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀
t₇₃: l2(X₀, X₁, X₂, X₃, X₇, X₁₀) → l2(X₀, X₁, X₂, X₃+1, X₇, X₁₀) :|: L ≤ X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀
t₇₄: l2(X₀, X₁, X₂, X₃, X₇, X₁₀) → l2(X₀, X₁, L, X₃+1, X₇, X₁₀) :|: 1+X₂ ≤ L ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀
t₇₈: l3(X₀, X₁, X₂, X₃, X₇, X₁₀) → l4(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁
t₇₉: l3(X₀, X₁, X₂, X₃, X₇, X₁₀) → l5(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁
t₈₁: l4(X₀, X₁, X₂, X₃, X₇, X₁₀) → l9(X₀, X₁, 0, X₃, X₇, X₁₀) :|: X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁
t₈₄: l6(X₀, X₁, X₂, X₃, X₇, X₁₀) → l3(X₀, X₁, X₂, X₀+1, X₇, X₁₀) :|: X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₈₂: l6(X₀, X₁, X₂, X₃, X₇, X₁₀) → l7(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: X₃+1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₈₆: l7(X₀, X₁, X₂, X₃, X₇, X₁₀) → l3(X₀, X₁, X₂, X₃+1, X₇, X₁₀) :|: 1+X₀ ≤ X₁ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₉₀: l9(X₀, X₁, X₂, X₃, X₇, X₁₀) → l11(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1+X₀ ≤ X₁ ∧ X₃+1 ≤ X₁₀ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₉₁: l9(X₀, X₁, X₂, X₃, X₇, X₁₀) → l11(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: 1+X₀ ≤ X₁ ∧ 1+X₁₀ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₉₂: l9(X₀, X₁, X₂, X₃, X₇, X₁₀) → l12(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 t₆₄: l1(X₀, X₁, X₂, X₃, X₇, X₁₀) → l2(X₀, X₁, 0, X₃, X₇, X₁₀) :|: X₁ ≤ X₀ of depth 1:
new bound:
X₀+X₁+1 {O(n)}
MPRF:
l2 [X₀-X₁ ]
l1 [X₀+1-X₁ ]
MPRF for transition t₇₃: l2(X₀, X₁, X₂, X₃, X₇, X₁₀) → l2(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:
l2 [X₀+1-X₃ ]
l1 [X₀+1-X₃ ]
MPRF for transition t₇₄: l2(X₀, X₁, X₂, X₃, X₇, X₁₀) → l2(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:
l2 [X₀+1-X₃ ]
l1 [X₀+1-X₃ ]
MPRF for transition t₇₆: l2(X₀, X₁, X₂, X₃, X₇, X₁₀) → l1(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:
l2 [X₀+1-X₁ ]
l1 [X₀+1-X₁ ]
MPRF for transition t₇₇: l2(X₀, X₁, X₂, X₃, X₇, X₁₀) → l1(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:
l2 [X₀+1-X₁ ]
l1 [X₀+1-X₁ ]
MPRF for transition t₆₉: l11(X₀, X₁, X₂, X₃, X₇, X₁₀) → l11(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 ]
l6 [2⋅X₀-X₃-X₇ ]
l7 [2⋅X₀-X₃-X₇ ]
l3 [2⋅X₀+1-X₃-X₇ ]
l11 [2⋅X₀+1-X₃-X₇ ]
l9 [2⋅X₀+1-X₃-X₇ ]
l12 [2⋅X₀-X₃-X₇ ]
MPRF for transition t₇₀: l11(X₀, X₁, X₂, X₃, X₇, X₁₀) → l12(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 ]
l6 [X₀-X₃ ]
l7 [X₀-X₃ ]
l3 [X₀+1-X₃ ]
l11 [X₀+1-X₃ ]
l9 [X₀+1-X₃ ]
l12 [X₀-X₃ ]
MPRF for transition t₇₁: l12(X₀, X₁, X₂, X₃, X₇, X₁₀) → l6(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 ]
l6 [X₁-X₃-1 ]
l7 [X₁-X₃-1 ]
l3 [X₁-X₃ ]
l11 [X₁-X₃ ]
l9 [X₁-X₃ ]
l12 [X₁-X₃ ]
MPRF for transition t₇₂: l12(X₀, X₁, X₂, X₃, X₇, X₁₀) → l6(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 ]
l6 [X₁-X₃-1 ]
l7 [X₁-X₃-1 ]
l3 [X₁-X₃ ]
l11 [X₁-X₃ ]
l9 [X₁-X₃ ]
l12 [X₁-X₃ ]
MPRF for transition t₇₈: l3(X₀, X₁, X₂, X₃, X₇, X₁₀) → l4(X₀, X₁, X₂, X₃, X₇, X₁₀) :|: X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
7⋅X₀+7⋅X₃+5 {O(n)}
MPRF:
l4 [X₀-X₃ ]
l6 [X₀-X₃ ]
l7 [X₀-X₃ ]
l3 [X₀+1-X₃ ]
l11 [X₀-X₃ ]
l9 [X₀-X₃ ]
l12 [X₀-X₃ ]
MPRF for transition t₈₁: l4(X₀, X₁, X₂, X₃, X₇, X₁₀) → l9(X₀, X₁, 0, X₃, X₇, X₁₀) :|: X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
MPRF:
l4 [X₁-X₃ ]
l6 [X₁-X₃-1 ]
l7 [X₁-X₃-1 ]
l3 [X₁-X₃ ]
l11 [X₁-X₃-1 ]
l9 [X₁-X₃-1 ]
l12 [X₁-X₃-1 ]
MPRF for transition t₈₂: l6(X₀, X₁, X₂, X₃, X₇, X₁₀) → l7(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⋅X₁+7⋅X₃+8⋅X₀+9 {O(n)}
MPRF:
l4 [X₁+1-X₃ ]
l6 [X₁+1-X₃ ]
l7 [X₁-X₃ ]
l3 [X₁+1-X₃ ]
l11 [X₁+1-X₃ ]
l9 [X₁+1-X₃ ]
l12 [X₁+1-X₃ ]
MPRF for transition t₈₄: l6(X₀, X₁, X₂, X₃, X₇, X₁₀) → l3(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 ]
l6 [X₀+1-X₃ ]
l7 [X₀-X₃ ]
l3 [X₀+1-X₃ ]
l11 [X₀+1-X₃ ]
l9 [X₀+1-X₃ ]
l12 [X₀+1-X₃ ]
MPRF for transition t₈₆: l7(X₀, X₁, X₂, X₃, X₇, X₁₀) → l3(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⋅X₀+7⋅X₃+4 {O(n)}
MPRF:
l4 [X₀-X₃ ]
l6 [X₀-X₃ ]
l7 [X₀-X₃ ]
l3 [X₀-X₃ ]
l11 [X₀-X₃ ]
l9 [X₀-X₃ ]
l12 [X₀-X₃ ]
MPRF for transition t₉₀: l9(X₀, X₁, X₂, X₃, X₇, X₁₀) → l11(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⋅X₀+7⋅X₃+5 {O(n)}
MPRF:
l4 [X₀+1-X₃ ]
l6 [X₀-X₃ ]
l7 [X₀-X₃ ]
l3 [X₀+1-X₃ ]
l11 [X₀-X₃ ]
l9 [X₀+1-X₃ ]
l12 [X₀-X₃ ]
MPRF for transition t₉₁: l9(X₀, X₁, X₂, X₃, X₇, X₁₀) → l11(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 ]
l6 [X₀-X₃ ]
l7 [X₀-X₃ ]
l3 [X₀+1-X₃ ]
l11 [X₀-X₃ ]
l9 [X₀+1-X₃ ]
l12 [X₀-X₃ ]
MPRF for transition t₉₂: l9(X₀, X₁, X₂, X₃, X₇, X₁₀) → l12(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:
3⋅X₁₀+4⋅X₀+7⋅X₃+5 {O(n)}
MPRF:
l4 [X₁₀+1-X₃ ]
l6 [X₁₀-X₃ ]
l7 [X₁₀-X₃ ]
l3 [X₁₀+1-X₃ ]
l11 [X₁₀-X₃ ]
l9 [X₁₀+1-X₃ ]
l12 [X₁₀-X₃ ]
All Bounds
Timebounds
Overall timebound:3⋅X₁₀+3⋅X₇+31⋅X₁+86⋅X₃+93⋅X₀+80 {O(n)}
t₆₃: 1 {O(1)}
t₆₄: X₀+X₁+1 {O(n)}
t₆₅: 1 {O(1)}
t₆₉: 10⋅X₀+3⋅X₇+7⋅X₃+5 {O(n)}
t₇₀: 7⋅X₀+7⋅X₃+5 {O(n)}
t₇₁: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₇₂: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₇₃: X₀+X₃+1 {O(n)}
t₇₄: X₀+X₃+1 {O(n)}
t₇₆: X₀+X₁+1 {O(n)}
t₇₇: X₀+X₁+1 {O(n)}
t₇₈: 7⋅X₀+7⋅X₃+5 {O(n)}
t₇₉: 1 {O(1)}
t₈₁: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₈₂: 7⋅X₁+7⋅X₃+8⋅X₀+9 {O(n)}
t₈₄: 7⋅X₀+7⋅X₃+5 {O(n)}
t₈₆: 7⋅X₀+7⋅X₃+4 {O(n)}
t₉₀: 7⋅X₀+7⋅X₃+5 {O(n)}
t₉₁: 7⋅X₀+7⋅X₃+5 {O(n)}
t₉₂: 3⋅X₁₀+4⋅X₀+7⋅X₃+5 {O(n)}
Costbounds
Overall costbound: 3⋅X₁₀+3⋅X₇+31⋅X₁+86⋅X₃+93⋅X₀+80 {O(n)}
t₆₃: 1 {O(1)}
t₆₄: X₀+X₁+1 {O(n)}
t₆₅: 1 {O(1)}
t₆₉: 10⋅X₀+3⋅X₇+7⋅X₃+5 {O(n)}
t₇₀: 7⋅X₀+7⋅X₃+5 {O(n)}
t₇₁: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₇₂: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₇₃: X₀+X₃+1 {O(n)}
t₇₄: X₀+X₃+1 {O(n)}
t₇₆: X₀+X₁+1 {O(n)}
t₇₇: X₀+X₁+1 {O(n)}
t₇₈: 7⋅X₀+7⋅X₃+5 {O(n)}
t₇₉: 1 {O(1)}
t₈₁: 7⋅X₁+7⋅X₃+8⋅X₀+8 {O(n)}
t₈₂: 7⋅X₁+7⋅X₃+8⋅X₀+9 {O(n)}
t₈₄: 7⋅X₀+7⋅X₃+5 {O(n)}
t₈₆: 7⋅X₀+7⋅X₃+4 {O(n)}
t₉₀: 7⋅X₀+7⋅X₃+5 {O(n)}
t₉₁: 7⋅X₀+7⋅X₃+5 {O(n)}
t₉₂: 3⋅X₁₀+4⋅X₀+7⋅X₃+5 {O(n)}
Sizebounds
t₆₃, X₀: X₀ {O(n)}
t₆₃, X₁: X₁ {O(n)}
t₆₃, X₂: X₂ {O(n)}
t₆₃, X₃: X₃ {O(n)}
t₆₃, X₇: X₇ {O(n)}
t₆₃, X₁₀: X₁₀ {O(n)}
t₆₄, X₀: X₀ {O(n)}
t₆₄, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₆₄, X₂: 0 {O(1)}
t₆₄, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₆₄, X₇: X₇ {O(n)}
t₆₄, X₁₀: X₁₀ {O(n)}
t₆₅, X₀: 3⋅X₀ {O(n)}
t₆₅, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₆₅, X₃: 4⋅X₀+7⋅X₃+4 {O(n)}
t₆₅, X₇: 3⋅X₇ {O(n)}
t₆₅, X₁₀: 3⋅X₁₀ {O(n)}
t₆₉, X₀: 3⋅X₀ {O(n)}
t₆₉, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₆₉, X₂: 0 {O(1)}
t₆₉, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₆₉, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₆₉, X₁₀: 22⋅X₀+28⋅X₃+3⋅X₁₀+16 {O(n)}
t₇₀, X₀: 3⋅X₀ {O(n)}
t₇₀, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₇₀, X₂: 0 {O(1)}
t₇₀, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₇₀, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₇₀, X₁₀: 22⋅X₀+28⋅X₃+3⋅X₁₀+16 {O(n)}
t₇₁, X₀: 3⋅X₀ {O(n)}
t₇₁, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₇₁, X₂: 0 {O(1)}
t₇₁, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₇₁, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₇₁, X₁₀: 22⋅X₀+28⋅X₃+3⋅X₁₀+16 {O(n)}
t₇₂, X₀: 3⋅X₀ {O(n)}
t₇₂, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₇₂, X₂: 0 {O(1)}
t₇₂, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₇₂, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₇₂, X₁₀: 22⋅X₀+28⋅X₃+3⋅X₁₀+16 {O(n)}
t₇₃, X₀: X₀ {O(n)}
t₇₃, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₇₃, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₇₃, X₇: X₇ {O(n)}
t₇₃, X₁₀: X₁₀ {O(n)}
t₇₄, X₀: X₀ {O(n)}
t₇₄, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₇₄, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₇₄, X₇: X₇ {O(n)}
t₇₄, 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)}
t₇₇, X₀: X₀ {O(n)}
t₇₇, X₁: 2⋅X₀+3⋅X₁+2 {O(n)}
t₇₇, X₂: 0 {O(1)}
t₇₇, X₃: 2⋅X₀+3⋅X₃+2 {O(n)}
t₇₇, X₇: X₇ {O(n)}
t₇₇, X₁₀: X₁₀ {O(n)}
t₇₈, X₀: 3⋅X₀ {O(n)}
t₇₈, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₇₈, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₇₈, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₇₈, X₁₀: 22⋅X₀+28⋅X₃+3⋅X₁₀+16 {O(n)}
t₇₉, X₀: 9⋅X₀ {O(n)}
t₇₉, X₁: 12⋅X₀+21⋅X₁+12 {O(n)}
t₇₉, X₃: 10⋅X₀+7⋅X₃+6 {O(n)}
t₇₉, X₇: 14⋅X₃+15⋅X₇+20⋅X₀+10 {O(n)}
t₇₉, X₁₀: 44⋅X₀+56⋅X₃+9⋅X₁₀+32 {O(n)}
t₈₁, X₀: 3⋅X₀ {O(n)}
t₈₁, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₁, X₂: 0 {O(1)}
t₈₁, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₈₁, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₈₁, X₁₀: 22⋅X₀+28⋅X₃+3⋅X₁₀+16 {O(n)}
t₈₂, X₀: 3⋅X₀ {O(n)}
t₈₂, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₂, X₂: 0 {O(1)}
t₈₂, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₈₂, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₈₂, X₁₀: 22⋅X₀+28⋅X₃+3⋅X₁₀+16 {O(n)}
t₈₄, X₀: 6⋅X₀ {O(n)}
t₈₄, X₁: 14⋅X₁+8⋅X₀+8 {O(n)}
t₈₄, X₂: 0 {O(1)}
t₈₄, X₃: 6⋅X₀+2 {O(n)}
t₈₄, X₇: 12⋅X₇+14⋅X₃+20⋅X₀+10 {O(n)}
t₈₄, X₁₀: 44⋅X₀+56⋅X₃+6⋅X₁₀+32 {O(n)}
t₈₆, X₀: 3⋅X₀ {O(n)}
t₈₆, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₈₆, X₂: 0 {O(1)}
t₈₆, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₈₆, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₈₆, X₁₀: 22⋅X₀+28⋅X₃+3⋅X₁₀+16 {O(n)}
t₉₀, X₀: 3⋅X₀ {O(n)}
t₉₀, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₉₀, X₂: 0 {O(1)}
t₉₀, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₉₀, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₉₀, X₁₀: 22⋅X₀+28⋅X₃+3⋅X₁₀+16 {O(n)}
t₉₁, X₀: 3⋅X₀ {O(n)}
t₉₁, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₉₁, X₂: 0 {O(1)}
t₉₁, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₉₁, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₉₁, X₁₀: 22⋅X₀+28⋅X₃+3⋅X₁₀+16 {O(n)}
t₉₂, X₀: 3⋅X₀ {O(n)}
t₉₂, X₁: 4⋅X₀+7⋅X₁+4 {O(n)}
t₉₂, X₂: 0 {O(1)}
t₉₂, X₃: 11⋅X₀+14⋅X₃+8 {O(n)}
t₉₂, X₇: 10⋅X₀+6⋅X₇+7⋅X₃+5 {O(n)}
t₉₂, X₁₀: 11⋅X₀+14⋅X₃+8 {O(n)}