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
t₂₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l2(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) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₀ ≤ X₁ ∧ 1 ≤ S
t₂₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₀ ≤ X₁
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l5(X₀, X₁, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₁+1 ≤ X₀
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l3(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₃ ≤ X₀
t₁₆: l3(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, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₀ ≤ X₃
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l4(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆, 0, 0, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₃ ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l4(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: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l4(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆, S, T, X₉+T, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1 ≤ S ∧ X₃ ≤ X₀
t₁₄: l4(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, S, T, T, X₁₅, X₁₆, X₁₇) :|: 0 ≤ U ∧ 1+X₀ ≤ X₃
t₁₅: l4(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, -S, T, S, X₁₇) :|: U+1 ≤ 0 ∧ 1+X₀ ≤ X₃
t₁₇: l5(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
t₁₈: l5(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) :|: X₂+1 ≤ 0 ∧ 1+X₀ ≤ X₃
t₁₉: l5(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) :|: 1 ≤ X₂ ∧ 1+X₀ ≤ X₃
t₂: 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, X₂, S, S, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+S ≤ X₂ ∧ X₃ ≤ X₀
t₃: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → l5(X₀, X₁, S, X₃+1, X₂, S, S, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₂ ≤ S ∧ X₃ ≤ X₀
t₁₃: l6(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: l6(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
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) → l6(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: l3→l3

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 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 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 0 ≤ X₂ ∧ 2 ≤ 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 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 l3

Cut unsatisfiable transition t₅₈: l4→l4

Cut unsatisfiable transition t₅₉: l4→l4

Cut unsatisfiable transition t₆₀: l4→l4

Cut unsatisfiable transition t₆₆: l5→l3

Cut unsatisfiable transition t₇₀: 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:
t₅₂: l0(X₀, X₁, X₂, X₃, X₁₀) → l1(X₀, X₁, X₂, X₃, X₁₀) :|: 2 ≤ X₀
t₅₄: l1(X₀, X₁, X₂, X₃, X₁₀) → l2(X₀, X₁, X₂, X₃, X₁₀) :|: X₀ ≤ X₁ ∧ S+1 ≤ 0 ∧ 2 ≤ X₀
t₅₅: l1(X₀, X₁, X₂, X₃, X₁₀) → l2(X₀, X₁, X₂, X₃, X₁₀) :|: X₀ ≤ X₁ ∧ 1 ≤ S ∧ 2 ≤ X₀
t₅₆: l1(X₀, X₁, X₂, X₃, X₁₀) → l2(X₀, X₁, X₂, X₃, X₁₀) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀
t₅₃: l1(X₀, X₁, X₂, X₃, X₁₀) → l5(X₀, X₁, 0, X₃, X₁₀) :|: X₁+1 ≤ X₀ ∧ 2 ≤ X₀
t₅₇: l3(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
t₆₁: l4(X₀, X₁, X₂, X₃, X₁₀) → l6(X₀, X₁, X₂, X₃, X₁₀) :|: 0 ≤ U ∧ 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
t₆₂: l4(X₀, X₁, X₂, X₃, X₁₀) → l6(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
t₆₅: l5(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
t₆₇: l5(X₀, X₁, X₂, X₃, X₁₀) → l3(X₀, X₁, X₂, X₃, X₁₀) :|: 1 ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₆₃: l5(X₀, X₁, X₂, X₃, X₁₀) → l5(X₀, X₁, X₂, X₃+1, X₁₀) :|: 1+S ≤ X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₆₄: l5(X₀, X₁, X₂, X₃, X₁₀) → l5(X₀, X₁, S, X₃+1, X₁₀) :|: X₂ ≤ S ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₆₉: l6(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
t₆₈: l6(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
t₇₁: 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
t₇₂: l8(X₀, X₁, X₂, X₃, X₁₀) → l6(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 t₅₃: l1(X₀, X₁, X₂, X₃, X₁₀) → l5(X₀, X₁, 0, X₃, X₁₀) :|: X₁+1 ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF:

l4 [X₀-X₁ ]
l5 [X₀-X₁ ]
l3 [X₀-X₁ ]
l1 [X₀+1-X₁ ]
l7 [X₀-X₁ ]
l8 [X₀-X₁ ]
l6 [X₀-X₁ ]

MPRF for transition t₅₇: l3(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+1 {O(n)}

MPRF:

l4 [X₀-X₁ ]
l5 [X₀+1-X₁ ]
l3 [X₀+1-X₁ ]
l1 [X₀+1-X₁ ]
l7 [X₀-X₁ ]
l8 [X₀-X₁ ]
l6 [X₀-X₁ ]

MPRF for transition t₆₁: l4(X₀, X₁, X₂, X₃, X₁₀) → l6(X₀, X₁, X₂, X₃, X₁₀) :|: 0 ≤ U ∧ 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:

l4 [X₀+1-X₁ ]
l5 [X₀+1-X₁ ]
l3 [X₀+1-X₁ ]
l1 [X₀+1-X₁ ]
l7 [X₀-X₁ ]
l8 [X₀-X₁ ]
l6 [X₀-X₁ ]

MPRF for transition t₆₂: l4(X₀, X₁, X₂, X₃, X₁₀) → l6(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:

l4 [X₀+1-X₁ ]
l5 [X₀+1-X₁ ]
l3 [X₀+1-X₁ ]
l1 [X₀+1-X₁ ]
l7 [X₀-X₁ ]
l8 [X₀-X₁ ]
l6 [X₀-X₁ ]

MPRF for transition t₆₃: l5(X₀, X₁, X₂, X₃, X₁₀) → l5(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:

l4 [2⋅X₀-X₃ ]
l5 [2⋅X₀-X₃ ]
l3 [2⋅X₀-X₃ ]
l1 [2⋅X₀-X₃ ]
l7 [2⋅X₀-X₃ ]
l8 [2⋅X₀-X₃ ]
l6 [2⋅X₀-X₃ ]

MPRF for transition t₆₄: l5(X₀, X₁, X₂, X₃, X₁₀) → l5(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:

l4 [2⋅X₀-X₃ ]
l5 [2⋅X₀-X₃ ]
l3 [2⋅X₀-X₃ ]
l1 [2⋅X₀-X₃ ]
l7 [2⋅X₀-X₃ ]
l8 [2⋅X₀-X₃ ]
l6 [2⋅X₀-X₃ ]

MPRF for transition t₆₅: l5(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:

l4 [X₀-X₁ ]
l5 [X₀-X₁ ]
l3 [X₀-X₁ ]
l1 [X₀-X₁ ]
l7 [X₀-X₁ ]
l8 [X₀-X₁ ]
l6 [X₀-X₁ ]

MPRF for transition t₆₇: l5(X₀, X₁, X₂, X₃, X₁₀) → l3(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+1 {O(n)}

MPRF:

l4 [X₀-X₁ ]
l5 [X₀+1-X₁ ]
l3 [X₀-X₁ ]
l1 [X₀+1-X₁ ]
l7 [X₀-X₁ ]
l8 [X₀-X₁ ]
l6 [X₀-X₁ ]

MPRF for transition t₆₈: l6(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:

l4 [2⋅X₀-X₁₀ ]
l5 [2⋅X₀-X₁₀ ]
l3 [2⋅X₀-X₁₀ ]
l1 [2⋅X₀-X₁₀ ]
l7 [2⋅X₀-X₁₀-1 ]
l8 [2⋅X₀-X₁₀-1 ]
l6 [2⋅X₀-X₁₀ ]

MPRF for transition t₆₉: l6(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+1 {O(n)}

MPRF:

l4 [X₀+1-X₁ ]
l5 [X₀+1-X₁ ]
l3 [X₀+1-X₁ ]
l1 [X₀+1-X₁ ]
l7 [X₀+1-X₁ ]
l8 [X₀+1-X₁ ]
l6 [X₀+1-X₁ ]

MPRF for transition t₇₁: 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:

2⋅X₀+X₁₀ {O(n)}

MPRF:

l4 [2⋅X₀-X₁₀ ]
l5 [2⋅X₀-X₁₀ ]
l3 [2⋅X₀-X₁₀ ]
l1 [2⋅X₀-X₁₀ ]
l7 [2⋅X₀-X₁₀ ]
l8 [2⋅X₀-X₁₀-1 ]
l6 [2⋅X₀-X₁₀ ]

MPRF for transition t₇₂: l8(X₀, X₁, X₂, X₃, X₁₀) → l6(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:

l4 [2⋅X₀-X₁₀ ]
l5 [2⋅X₀-X₁₀ ]
l3 [2⋅X₀-X₁₀ ]
l1 [2⋅X₀-X₁₀ ]
l7 [2⋅X₀-X₁₀ ]
l8 [2⋅X₀-X₁₀ ]
l6 [2⋅X₀-X₁₀ ]

All Bounds

Timebounds

Overall timebound:17⋅X₀+2⋅X₃+3⋅X₁₀+7⋅X₁+10 {O(n)}
t₅₂: 1 {O(1)}
t₅₃: X₀+X₁+1 {O(n)}
t₅₄: 1 {O(1)}
t₅₅: 1 {O(1)}
t₅₆: 1 {O(1)}
t₅₇: X₀+X₁+1 {O(n)}
t₆₁: X₀+X₁+1 {O(n)}
t₆₂: X₀+X₁+1 {O(n)}
t₆₃: 2⋅X₀+X₃ {O(n)}
t₆₄: 2⋅X₀+X₃ {O(n)}
t₆₅: X₀+X₁ {O(n)}
t₆₇: X₀+X₁+1 {O(n)}
t₆₈: 2⋅X₀+X₁₀ {O(n)}
t₆₉: X₀+X₁+1 {O(n)}
t₇₁: 2⋅X₀+X₁₀ {O(n)}
t₇₂: 2⋅X₀+X₁₀ {O(n)}

Costbounds

Overall costbound: 17⋅X₀+2⋅X₃+3⋅X₁₀+7⋅X₁+10 {O(n)}
t₅₂: 1 {O(1)}
t₅₃: X₀+X₁+1 {O(n)}
t₅₄: 1 {O(1)}
t₅₅: 1 {O(1)}
t₅₆: 1 {O(1)}
t₅₇: X₀+X₁+1 {O(n)}
t₆₁: X₀+X₁+1 {O(n)}
t₆₂: X₀+X₁+1 {O(n)}
t₆₃: 2⋅X₀+X₃ {O(n)}
t₆₄: 2⋅X₀+X₃ {O(n)}
t₆₅: X₀+X₁ {O(n)}
t₆₇: X₀+X₁+1 {O(n)}
t₆₈: 2⋅X₀+X₁₀ {O(n)}
t₆₉: X₀+X₁+1 {O(n)}
t₇₁: 2⋅X₀+X₁₀ {O(n)}
t₇₂: 2⋅X₀+X₁₀ {O(n)}

Sizebounds

t₅₂, X₀: X₀ {O(n)}
t₅₂, X₁: X₁ {O(n)}
t₅₂, X₂: X₂ {O(n)}
t₅₂, X₃: X₃ {O(n)}
t₅₂, X₁₀: X₁₀ {O(n)}
t₅₃, X₀: X₀ {O(n)}
t₅₃, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₅₃, X₂: 0 {O(1)}
t₅₃, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₃, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₅₄, X₀: 3⋅X₀ {O(n)}
t₅₄, X₁: 4⋅X₀+7⋅X₁+2 {O(n)}
t₅₄, X₃: 7⋅X₃+8⋅X₀ {O(n)}
t₅₄, X₁₀: 4⋅X₀+5⋅X₁₀ {O(n)}
t₅₅, X₀: 3⋅X₀ {O(n)}
t₅₅, X₁: 4⋅X₀+7⋅X₁+2 {O(n)}
t₅₅, X₃: 7⋅X₃+8⋅X₀ {O(n)}
t₅₅, X₁₀: 4⋅X₀+5⋅X₁₀ {O(n)}
t₅₆, X₀: 3⋅X₀ {O(n)}
t₅₆, X₁: 4⋅X₀+7⋅X₁+2 {O(n)}
t₅₆, X₃: 7⋅X₃+8⋅X₀ {O(n)}
t₅₆, X₁₀: 4⋅X₀+5⋅X₁₀ {O(n)}
t₅₇, X₀: X₀ {O(n)}
t₅₇, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₅₇, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₇, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₆₁, X₀: X₀ {O(n)}
t₆₁, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₆₁, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₁, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₆₂, X₀: X₀ {O(n)}
t₆₂, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₆₂, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₂, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₆₃, X₀: X₀ {O(n)}
t₆₃, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₆₃, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₃, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₆₄, X₀: X₀ {O(n)}
t₆₄, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₆₄, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₄, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₆₅, X₀: X₀ {O(n)}
t₆₅, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₆₅, X₂: 0 {O(1)}
t₆₅, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₅, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₆₇, X₀: X₀ {O(n)}
t₆₇, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₆₇, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₇, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₆₈, X₀: X₀ {O(n)}
t₆₈, X₁: 2⋅X₀+3⋅X₁+1 {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+1 {O(n)}
t₆₉, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₉, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₇₁, X₀: X₀ {O(n)}
t₇₁, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₇₁, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₇₁, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}
t₇₂, X₀: X₀ {O(n)}
t₇₂, X₁: 2⋅X₀+3⋅X₁+1 {O(n)}
t₇₂, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₇₂, X₁₀: 2⋅X₀+2⋅X₁₀ {O(n)}