Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇
Temp_Vars: S, T, U
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 2 ≤ X₀
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l2(X₀, X₁, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₁+1 ≤ X₀
t₂₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₀ ≤ X₁ ∧ S+1 ≤ 0
t₂₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₀ ≤ X₁
t₁₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l1(X₀, X₁+1, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, 0) :|: 1+X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l2(X₀, X₁, X₂, X₃+1, X₂, S, S, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+S ≤ X₂ ∧ X₃ ≤ X₀
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l2(X₀, X₁, S, X₃+1, X₂, S, S, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₂ ≤ S ∧ X₃ ≤ X₀
t₁₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₂+1 ≤ 0 ∧ 1+X₀ ≤ X₃
t₁₉: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1 ≤ X₂ ∧ 1+X₀ ≤ X₃
t₁₃: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l1(X₀, X₁+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₁₀
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₁₀ ≤ X₀
t₄: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l5(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₃ ≤ X₀
t₁₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₃
t₁₄: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, S, T, T, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₃
t₁₅: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, -S, T, S, X₁₇) :|: U+1 ≤ 0 ∧ 1+X₀ ≤ X₃
t₅: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l6(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆, 0, 0, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₃ ≤ X₀
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l6(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆, S, T, X₉+T, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: S+1 ≤ 0 ∧ X₃ ≤ X₀
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l6(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆, S, T, X₉+T, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1 ≤ S ∧ X₃ ≤ X₀
t₉: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l7(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆, X₇, X₈, S, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₃ ≤ X₀
t₁₂: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, S, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₃
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀+1, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₃
t₁₀: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l8(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₃ ≤ X₀

Preprocessing

Cut unsatisfiable transition t₄: l5→l5

Cut unsatisfiable transition t₁₀: l8→l8

Eliminate variables {T,X₄,X₅,X₆,X₇,X₈,X₉,X₁₁,X₁₂,X₁₃,X₁₄,X₁₅,X₁₆,X₁₇} that do not contribute to the problem

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

Found invariant 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l6

Found invariant 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 1+X₁₀ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁₀ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l7

Found invariant 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l5

Found invariant 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 1+X₁₀ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁₀ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l8

Found invariant 2 ≤ X₀ for location l1

Found invariant 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l4

Found invariant 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location l3

Cut unsatisfiable transition t₅₇: l2→l5

Cut unsatisfiable transition t₆₂: l6→l6

Cut unsatisfiable transition t₆₃: l6→l6

Cut unsatisfiable transition t₆₄: l6→l6

Cut unsatisfiable transition t₆₇: l7→l7

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₁₀
Temp_Vars: S, U
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₅₀: l0(X₀, X₁, X₂, X₃, X₁₀) → l1(X₀, X₁, X₂, X₃, X₁₀) :|: 2 ≤ X₀
t₅₁: l1(X₀, X₁, X₂, X₃, X₁₀) → l2(X₀, X₁, 0, X₃, X₁₀) :|: X₁+1 ≤ X₀ ∧ 2 ≤ X₀
t₅₂: l1(X₀, X₁, X₂, X₃, X₁₀) → l3(X₀, X₁, X₂, X₃, X₁₀) :|: X₀ ≤ X₁ ∧ S+1 ≤ 0 ∧ 2 ≤ X₀
t₅₃: l1(X₀, X₁, X₂, X₃, X₁₀) → l3(X₀, X₁, X₂, X₃, X₁₀) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀
t₅₆: l2(X₀, X₁, X₂, X₃, X₁₀) → l1(X₀, X₁+1, 0, X₃, X₁₀) :|: 1+X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₅₄: l2(X₀, X₁, X₂, X₃, X₁₀) → l2(X₀, X₁, X₂, X₃+1, X₁₀) :|: 1+S ≤ X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₅₅: l2(X₀, X₁, X₂, X₃, X₁₀) → l2(X₀, X₁, S, X₃+1, X₁₀) :|: X₂ ≤ S ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₅₈: l2(X₀, X₁, X₂, X₃, X₁₀) → l5(X₀, X₁, X₂, X₃, X₁₀) :|: 1 ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₆₀: l4(X₀, X₁, X₂, X₃, X₁₀) → l1(X₀, X₁+1, X₂, X₃, X₁₀) :|: 1+X₀ ≤ X₁₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₅₉: l4(X₀, X₁, X₂, X₃, X₁₀) → l7(X₀, X₁, X₂, X₃, X₁₀) :|: X₁₀ ≤ X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₆₁: l5(X₀, X₁, X₂, X₃, X₁₀) → l6(X₀, X₁, X₂, X₃, X₁₀) :|: 1+X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₆₅: l6(X₀, X₁, X₂, X₃, X₁₀) → l4(X₀, X₁, X₂, X₃, X₁₀) :|: 1+X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₆₆: l6(X₀, X₁, X₂, X₃, X₁₀) → l4(X₀, X₁, X₂, X₃, X₁₀) :|: U+1 ≤ 0 ∧ 1+X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₆₈: l7(X₀, X₁, X₂, X₃, X₁₀) → l8(X₀, X₁, X₂, X₃, X₁₀) :|: 1+X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 1+X₁₀ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁₀ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₆₉: l8(X₀, X₁, X₂, X₃, X₁₀) → l4(X₀, X₁, X₂, X₃, X₁₀+1) :|: 1+X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 1+X₁₀ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁₀ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀

MPRF for transition t₅₁: l1(X₀, X₁, X₂, X₃, X₁₀) → l2(X₀, X₁, 0, X₃, X₁₀) :|: X₁+1 ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

l2 [X₀-X₁ ]
l1 [X₀+1-X₁ ]
l5 [X₀-X₁ ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l8 [X₀-X₁ ]
l4 [X₀-X₁ ]

MPRF for transition t₅₄: l2(X₀, X₁, X₂, X₃, X₁₀) → l2(X₀, X₁, X₂, X₃+1, X₁₀) :|: 1+S ≤ X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₀+X₃ {O(n)}

MPRF:

l2 [2⋅X₀-X₃ ]
l1 [2⋅X₀-X₃ ]
l5 [2⋅X₀-X₃ ]
l6 [2⋅X₀-X₃ ]
l7 [2⋅X₀-X₃ ]
l8 [2⋅X₀-X₃ ]
l4 [2⋅X₀-X₃ ]

MPRF for transition t₅₅: l2(X₀, X₁, X₂, X₃, X₁₀) → l2(X₀, X₁, S, X₃+1, X₁₀) :|: X₂ ≤ S ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₀+X₃ {O(n)}

MPRF:

l2 [2⋅X₀-X₃ ]
l1 [2⋅X₀-X₃ ]
l5 [2⋅X₀-X₃ ]
l6 [2⋅X₀-X₃ ]
l7 [2⋅X₀-X₃ ]
l8 [2⋅X₀-X₃ ]
l4 [2⋅X₀-X₃ ]

MPRF for transition t₅₆: l2(X₀, X₁, X₂, X₃, X₁₀) → l1(X₀, X₁+1, 0, X₃, X₁₀) :|: 1+X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF:

l2 [X₀-X₁ ]
l1 [X₀-X₁ ]
l5 [X₀-X₁ ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l8 [X₀-X₁ ]
l4 [X₀-X₁ ]

MPRF for transition t₅₈: l2(X₀, X₁, X₂, X₃, X₁₀) → l5(X₀, X₁, X₂, X₃, X₁₀) :|: 1 ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+X₁+2 {O(n)}

MPRF:

l2 [X₀+2-X₁ ]
l1 [X₀+2-X₁ ]
l5 [X₀+1-X₁ ]
l6 [X₀+1-X₁ ]
l7 [X₀+1-X₁ ]
l8 [X₀+1-X₁ ]
l4 [X₀+1-X₁ ]

MPRF for transition t₅₉: l4(X₀, X₁, X₂, X₃, X₁₀) → l7(X₀, X₁, X₂, X₃, X₁₀) :|: X₁₀ ≤ X₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₀+X₁₀ {O(n)}

MPRF:

l2 [2⋅X₀-X₁₀ ]
l1 [2⋅X₀-X₁₀ ]
l5 [2⋅X₀-X₁₀ ]
l6 [2⋅X₀-X₁₀ ]
l7 [2⋅X₀-X₁₀-1 ]
l8 [2⋅X₀-X₁₀-1 ]
l4 [2⋅X₀-X₁₀ ]

MPRF for transition t₆₀: l4(X₀, X₁, X₂, X₃, X₁₀) → l1(X₀, X₁+1, X₂, X₃, X₁₀) :|: 1+X₀ ≤ X₁₀ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF:

l2 [X₀-X₁ ]
l1 [X₀-X₁ ]
l5 [X₀-X₁ ]
l6 [X₀-X₁ ]
l7 [X₀-X₁ ]
l8 [X₀-X₁ ]
l4 [X₀-X₁ ]

MPRF for transition t₆₁: l5(X₀, X₁, X₂, X₃, X₁₀) → l6(X₀, X₁, X₂, X₃, X₁₀) :|: 1+X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF:

l2 [X₀-X₁ ]
l1 [X₀-X₁ ]
l5 [X₀-X₁ ]
l6 [X₀-X₁-1 ]
l7 [X₀-X₁-1 ]
l8 [X₀-X₁-1 ]
l4 [X₀-X₁-1 ]

MPRF for transition t₆₅: l6(X₀, X₁, X₂, X₃, X₁₀) → l4(X₀, X₁, X₂, X₃, X₁₀) :|: 1+X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF:

l2 [X₀-X₁ ]
l1 [X₀-X₁ ]
l5 [X₀-X₁ ]
l6 [X₀-X₁ ]
l7 [X₀-X₁-1 ]
l8 [X₀-X₁-1 ]
l4 [X₀-X₁-1 ]

MPRF for transition t₆₆: l6(X₀, X₁, X₂, X₃, X₁₀) → l4(X₀, X₁, X₂, X₃, X₁₀) :|: U+1 ≤ 0 ∧ 1+X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

l2 [X₀+1-X₁ ]
l1 [X₀+1-X₁ ]
l5 [X₀+1-X₁ ]
l6 [X₀+1-X₁ ]
l7 [X₀-X₁ ]
l8 [X₀-X₁ ]
l4 [X₀-X₁ ]

MPRF for transition t₆₈: l7(X₀, X₁, X₂, X₃, X₁₀) → l8(X₀, X₁, X₂, X₃, X₁₀) :|: 1+X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 1+X₁₀ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁₀ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+X₁₀+1 {O(n)}

MPRF:

l2 [X₀+1-X₁₀ ]
l1 [X₀+1-X₁₀ ]
l5 [X₀+1-X₁₀ ]
l6 [X₀+1-X₁₀ ]
l7 [X₀+1-X₁₀ ]
l8 [X₀-X₁₀ ]
l4 [X₀+1-X₁₀ ]

MPRF for transition t₆₉: l8(X₀, X₁, X₂, X₃, X₁₀) → l4(X₀, X₁, X₂, X₃, X₁₀+1) :|: 1+X₀ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 1+X₁₀ ≤ X₃ ∧ 2+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁₀ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₀+X₁₀ {O(n)}

MPRF:

l2 [2⋅X₀-X₁₀ ]
l1 [2⋅X₀-X₁₀ ]
l5 [2⋅X₀-X₁₀ ]
l6 [2⋅X₀-X₁₀ ]
l7 [2⋅X₀-X₁₀ ]
l8 [2⋅X₀-X₁₀ ]
l4 [2⋅X₀-X₁₀ ]

All Bounds

Timebounds

Overall timebound:16⋅X₀+2⋅X₃+3⋅X₁₀+7⋅X₁+8 {O(n)}
t₅₀: 1 {O(1)}
t₅₁: X₀+X₁+1 {O(n)}
t₅₂: 1 {O(1)}
t₅₃: 1 {O(1)}
t₅₄: 2⋅X₀+X₃ {O(n)}
t₅₅: 2⋅X₀+X₃ {O(n)}
t₅₆: X₀+X₁ {O(n)}
t₅₈: X₀+X₁+2 {O(n)}
t₅₉: 2⋅X₀+X₁₀ {O(n)}
t₆₀: X₀+X₁ {O(n)}
t₆₁: X₀+X₁ {O(n)}
t₆₅: X₀+X₁ {O(n)}
t₆₆: X₀+X₁+1 {O(n)}
t₆₈: X₀+X₁₀+1 {O(n)}
t₆₉: 2⋅X₀+X₁₀ {O(n)}

Costbounds

Overall costbound: 16⋅X₀+2⋅X₃+3⋅X₁₀+7⋅X₁+8 {O(n)}
t₅₀: 1 {O(1)}
t₅₁: X₀+X₁+1 {O(n)}
t₅₂: 1 {O(1)}
t₅₃: 1 {O(1)}
t₅₄: 2⋅X₀+X₃ {O(n)}
t₅₅: 2⋅X₀+X₃ {O(n)}
t₅₆: X₀+X₁ {O(n)}
t₅₈: X₀+X₁+2 {O(n)}
t₅₉: 2⋅X₀+X₁₀ {O(n)}
t₆₀: X₀+X₁ {O(n)}
t₆₁: X₀+X₁ {O(n)}
t₆₅: X₀+X₁ {O(n)}
t₆₆: X₀+X₁+1 {O(n)}
t₆₈: X₀+X₁₀+1 {O(n)}
t₆₉: 2⋅X₀+X₁₀ {O(n)}

Sizebounds

t₅₀, X₀: X₀ {O(n)}
t₅₀, X₁: X₁ {O(n)}
t₅₀, X₂: X₂ {O(n)}
t₅₀, X₃: X₃ {O(n)}
t₅₀, X₁₀: X₁₀ {O(n)}
t₅₁, X₀: X₀ {O(n)}
t₅₁, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₁, X₂: 0 {O(1)}
t₅₁, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₁, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₅₂, X₀: 3⋅X₀ {O(n)}
t₅₂, X₁: 4⋅X₀+7⋅X₁ {O(n)}
t₅₂, X₃: 7⋅X₃+8⋅X₀ {O(n)}
t₅₂, X₁₀: 4⋅X₀+5⋅X₁₀ {O(n)}
t₅₃, X₀: 3⋅X₀ {O(n)}
t₅₃, X₁: 4⋅X₀+7⋅X₁ {O(n)}
t₅₃, X₃: 7⋅X₃+8⋅X₀ {O(n)}
t₅₃, X₁₀: 4⋅X₀+5⋅X₁₀ {O(n)}
t₅₄, X₀: X₀ {O(n)}
t₅₄, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₄, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₄, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₅₅, X₀: X₀ {O(n)}
t₅₅, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₅, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₅, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₅₆, X₀: X₀ {O(n)}
t₅₆, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₆, X₂: 0 {O(1)}
t₅₆, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₆, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₅₈, X₀: X₀ {O(n)}
t₅₈, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₈, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₈, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₅₉, X₀: X₀ {O(n)}
t₅₉, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₉, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₉, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₆₀, X₀: X₀ {O(n)}
t₆₀, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₀, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₀, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₆₁, X₀: X₀ {O(n)}
t₆₁, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₁, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₁, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₆₅, X₀: X₀ {O(n)}
t₆₅, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₅, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₅, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₆₆, X₀: X₀ {O(n)}
t₆₆, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₆, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₆, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₆₈, X₀: X₀ {O(n)}
t₆₈, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₈, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₈, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₆₉, X₀: X₀ {O(n)}
t₆₉, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₉, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₉, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}