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, V
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, (S)², X₉+(S)², 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, (S)², X₉+(S)², 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) :|: 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) :|: 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, X₉+S*T, 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) :|: T*U ≤ X₉ ∧ X₉+1 ≤ T*U+T ∧ S ≤ T ∧ U*V ≤ X₉ ∧ X₉+1 ≤ U*V+V ∧ V ≤ S ∧ 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 {X₄,X₅,X₆,X₇,X₈,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 1+X₅ ≤ X₃ ∧ X₅ ≤ 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 for location l7

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

Found invariant 1+X₅ ≤ X₃ ∧ X₅ ≤ 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 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 t₅₇: l4→l4

Cut unsatisfiable transition t₅₈: l4→l4

Cut unsatisfiable transition t₅₉: l4→l4

Cut unsatisfiable transition t₆₃: l5→l3

Cut unsatisfiable transition t₆₉: l7→l7

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: S, T, U, V
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₅₁: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2 ≤ X₀
t₅₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₁ ∧ S+1 ≤ 0 ∧ 2 ≤ X₀
t₅₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₁ ∧ 1 ≤ S ∧ 2 ≤ X₀
t₅₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₁ ∧ 2 ≤ X₀
t₅₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, 0, X₃, X₄, X₅) :|: X₁+1 ≤ X₀ ∧ 2 ≤ X₀
t₅₆: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 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
t₆₀: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 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, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 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: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁+1, 0, X₃, X₄, X₅) :|: 1+X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₆₄: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₆₅: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃+1, X₄, X₅) :|: 1+S ≤ X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₆₆: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, S, X₃+1, X₄, X₅) :|: X₂ ≤ S ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀
t₆₇: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁+1, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₅ ∧ 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, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ 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
t₇₀: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅) :|: T*U ≤ X₄ ∧ X₄+1 ≤ T*U+T ∧ S ≤ T ∧ U*V ≤ X₄ ∧ X₄+1 ≤ U*V+V ∧ V ≤ S ∧ 1+X₀ ≤ X₃ ∧ 1+X₅ ≤ X₃ ∧ X₅ ≤ 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: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅+1) :|: 1+X₀ ≤ X₃ ∧ 1+X₅ ≤ X₃ ∧ X₅ ≤ 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

MPRF for transition t₅₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, 0, X₃, X₄, X₅) :|: X₁+1 ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF for transition t₅₆: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 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 for transition t₆₀: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 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 for transition t₆₁: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 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 for transition t₆₂: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁+1, 0, X₃, X₄, X₅) :|: 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 for transition t₆₄: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 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 for transition t₆₅: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃+1, X₄, X₅) :|: 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 for transition t₆₆: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, S, X₃+1, X₄, X₅) :|: 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 for transition t₆₇: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁+1, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₅ ∧ 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 for transition t₆₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ 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+X₅ {O(n)}

MPRF for transition t₇₀: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅) :|: T*U ≤ X₄ ∧ X₄+1 ≤ T*U+T ∧ S ≤ T ∧ U*V ≤ X₄ ∧ X₄+1 ≤ U*V+V ∧ V ≤ S ∧ 1+X₀ ≤ X₃ ∧ 1+X₅ ≤ X₃ ∧ X₅ ≤ 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+X₅ {O(n)}

MPRF for transition t₇₁: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅+1) :|: 1+X₀ ≤ X₃ ∧ 1+X₅ ≤ X₃ ∧ X₅ ≤ 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:

X₀+X₅+1 {O(n)}

All Bounds

Timebounds

Overall timebound:16⋅X₀+2⋅X₃+3⋅X₅+7⋅X₁+7 {O(n)}
t₅₁: 1 {O(1)}
t₅₂: 1 {O(1)}
t₅₃: 1 {O(1)}
t₅₄: 1 {O(1)}
t₅₅: X₀+X₁+1 {O(n)}
t₅₆: X₀+X₁ {O(n)}
t₆₀: X₀+X₁ {O(n)}
t₆₁: X₀+X₁ {O(n)}
t₆₂: X₀+X₁ {O(n)}
t₆₄: X₀+X₁+1 {O(n)}
t₆₅: 2⋅X₀+X₃ {O(n)}
t₆₆: 2⋅X₀+X₃ {O(n)}
t₆₇: X₀+X₁ {O(n)}
t₆₈: 2⋅X₀+X₅ {O(n)}
t₇₀: 2⋅X₀+X₅ {O(n)}
t₇₁: X₀+X₅+1 {O(n)}

Costbounds

Overall costbound: 16⋅X₀+2⋅X₃+3⋅X₅+7⋅X₁+7 {O(n)}
t₅₁: 1 {O(1)}
t₅₂: 1 {O(1)}
t₅₃: 1 {O(1)}
t₅₄: 1 {O(1)}
t₅₅: X₀+X₁+1 {O(n)}
t₅₆: X₀+X₁ {O(n)}
t₆₀: X₀+X₁ {O(n)}
t₆₁: X₀+X₁ {O(n)}
t₆₂: X₀+X₁ {O(n)}
t₆₄: X₀+X₁+1 {O(n)}
t₆₅: 2⋅X₀+X₃ {O(n)}
t₆₆: 2⋅X₀+X₃ {O(n)}
t₆₇: X₀+X₁ {O(n)}
t₆₈: 2⋅X₀+X₅ {O(n)}
t₇₀: 2⋅X₀+X₅ {O(n)}
t₇₁: X₀+X₅+1 {O(n)}

Sizebounds

t₅₁, X₀: X₀ {O(n)}
t₅₁, X₁: X₁ {O(n)}
t₅₁, X₂: X₂ {O(n)}
t₅₁, X₃: X₃ {O(n)}
t₅₁, X₄: X₄ {O(n)}
t₅₁, X₅: X₅ {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, X₄: 3⋅X₄ {O(n)}
t₅₂, X₅: 2⋅X₀+5⋅X₅+2 {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, X₄: 3⋅X₄ {O(n)}
t₅₃, X₅: 2⋅X₀+5⋅X₅+2 {O(n)}
t₅₄, X₀: 3⋅X₀ {O(n)}
t₅₄, X₁: 4⋅X₀+7⋅X₁ {O(n)}
t₅₄, X₃: 7⋅X₃+8⋅X₀ {O(n)}
t₅₄, X₄: 3⋅X₄ {O(n)}
t₅₄, X₅: 2⋅X₀+5⋅X₅+2 {O(n)}
t₅₅, X₀: X₀ {O(n)}
t₅₅, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₅, X₂: 0 {O(1)}
t₅₅, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₅, X₄: X₄ {O(n)}
t₅₅, X₅: 2⋅X₅+X₀+1 {O(n)}
t₅₆, X₀: X₀ {O(n)}
t₅₆, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₅₆, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₅₆, X₄: X₄ {O(n)}
t₅₆, X₅: 2⋅X₅+X₀+1 {O(n)}
t₆₀, X₀: X₀ {O(n)}
t₆₀, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₀, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₀, X₄: X₄ {O(n)}
t₆₀, X₅: 2⋅X₅+X₀+1 {O(n)}
t₆₁, X₀: X₀ {O(n)}
t₆₁, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₁, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₁, X₄: X₄ {O(n)}
t₆₁, X₅: 2⋅X₅+X₀+1 {O(n)}
t₆₂, X₀: X₀ {O(n)}
t₆₂, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₂, X₂: 0 {O(1)}
t₆₂, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₂, X₄: X₄ {O(n)}
t₆₂, X₅: 2⋅X₅+X₀+1 {O(n)}
t₆₄, X₀: X₀ {O(n)}
t₆₄, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₄, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₄, X₄: X₄ {O(n)}
t₆₄, X₅: 2⋅X₅+X₀+1 {O(n)}
t₆₅, X₀: X₀ {O(n)}
t₆₅, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₅, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₅, X₄: X₄ {O(n)}
t₆₅, X₅: 2⋅X₅+X₀+1 {O(n)}
t₆₆, X₀: X₀ {O(n)}
t₆₆, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₆, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₆, X₄: X₄ {O(n)}
t₆₆, X₅: 2⋅X₅+X₀+1 {O(n)}
t₆₇, X₀: X₀ {O(n)}
t₆₇, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₇, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₇, X₄: X₄ {O(n)}
t₆₇, X₅: 2⋅X₅+X₀+1 {O(n)}
t₆₈, X₀: X₀ {O(n)}
t₆₈, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₆₈, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₆₈, X₄: X₄ {O(n)}
t₆₈, X₅: 2⋅X₅+X₀+1 {O(n)}
t₇₀, X₀: X₀ {O(n)}
t₇₀, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₇₀, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₇₀, X₄: X₄ {O(n)}
t₇₀, X₅: 2⋅X₅+X₀+1 {O(n)}
t₇₁, X₀: X₀ {O(n)}
t₇₁, X₁: 2⋅X₀+3⋅X₁ {O(n)}
t₇₁, X₃: 3⋅X₃+4⋅X₀ {O(n)}
t₇₁, X₄: X₄ {O(n)}
t₇₁, X₅: 2⋅X₅+X₀+1 {O(n)}