Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l11, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₁₄: l10(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄)
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄)
t₆: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₇: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₃, X₄, X₂, X₃, X₄)
t₉: l8(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₀
t₈: l8(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: X₀ < X₂
t₁₀: l9(X₀, X₁, X₂, X₃, X₄) → l8(X₀+1, X₁, X₂, X₃, X₄) :|: X₀ < X₁ ∧ X₀ < X₁
t₁₁: l9(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄) :|: X₀ < X₁ ∧ X₁ ≤ X₀
t₁₂: l9(X₀, X₁, X₂, X₃, X₄) → l8(X₀+1, X₁+1, X₂, X₃, X₄) :|: X₁ ≤ X₀ ∧ X₀ < X₁
t₁₃: l9(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁+1, X₂, X₃, X₄) :|: X₁ ≤ X₀ ∧ X₁ ≤ X₀

Preprocessing

Cut unsatisfiable transition t₁₁: l9→l8

Cut unsatisfiable transition t₁₂: l9→l8

Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ for location l11

Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₀ for location l8

Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ for location l10

Found invariant X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₂ for location l9

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l11, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₁₄: l10(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄)
t₆: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₇: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₃, X₄, X₂, X₃, X₄)
t₉: l8(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀
t₈: l8(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: X₀ < X₂ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀
t₁₀: l9(X₀, X₁, X₂, X₃, X₄) → l8(X₀+1, X₁, X₂, X₃, X₄) :|: X₀ < X₁ ∧ X₀ < X₁ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₂
t₁₃: l9(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁+1, X₂, X₃, X₄) :|: X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₂

MPRF for transition t₁₀: l9(X₀, X₁, X₂, X₃, X₄) → l8(X₀+1, X₁, X₂, X₃, X₄) :|: X₀ < X₁ ∧ X₀ < X₁ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₂ of depth 1:

new bound:

X₂+X₃ {O(n)}

MPRF for transition t₁₃: l9(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁+1, X₂, X₃, X₄) :|: X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₂ of depth 1:

new bound:

X₂+X₄ {O(n)}

knowledge_propagation leads to new time bound 2⋅X₂+X₃+X₄+1 {O(n)} for transition t₈: l8(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: X₀ < X₂ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀

All Bounds

Timebounds

Overall timebound:2⋅X₃+2⋅X₄+4⋅X₂+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 2⋅X₂+X₃+X₄+1 {O(n)}
t₉: 1 {O(1)}
t₁₀: X₂+X₃ {O(n)}
t₁₃: X₂+X₄ {O(n)}
t₁₄: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₃+2⋅X₄+4⋅X₂+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 2⋅X₂+X₃+X₄+1 {O(n)}
t₉: 1 {O(1)}
t₁₀: X₂+X₃ {O(n)}
t₁₃: X₂+X₄ {O(n)}
t₁₄: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₇, X₀: X₃ {O(n)}
t₇, X₁: X₄ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₈, X₀: 2⋅X₃+X₂ {O(n)}
t₈, X₁: 2⋅X₄+X₂ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₉, X₀: 3⋅X₃+X₂ {O(n)}
t₉, X₁: 3⋅X₄+X₂ {O(n)}
t₉, X₂: 2⋅X₂ {O(n)}
t₉, X₃: 2⋅X₃ {O(n)}
t₉, X₄: 2⋅X₄ {O(n)}
t₁₀, X₀: 2⋅X₃+X₂ {O(n)}
t₁₀, X₁: 2⋅X₄+X₂ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₃, X₀: 2⋅X₃+X₂ {O(n)}
t₁₃, X₁: 2⋅X₄+X₂ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₄, X₀: 3⋅X₃+X₂ {O(n)}
t₁₄, X₁: 3⋅X₄+X₂ {O(n)}
t₁₄, X₂: 2⋅X₂ {O(n)}
t₁₄, X₃: 2⋅X₃ {O(n)}
t₁₄, X₄: 2⋅X₄ {O(n)}