Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef_0
Locations: l0, l1, l10, l11, l12, 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)
t₁₀: l10(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, nondef_0, X₃, X₄)
t₁₅: l11(X₀, X₁, X₂, X₃, X₄) → l12(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(X₃, X₄, X₂, X₃, X₄)
t₈: l7(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁
t₇: l7(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: X₁ < X₀
t₁₁: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁+1, X₂, X₃, X₄) :|: 0 < X₂ ∧ 0 < X₂
t₁₂: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀-1, X₁+1, X₂, X₃, X₄) :|: 0 < X₂ ∧ X₂ ≤ 0
t₁₃: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0 ∧ 0 < X₂
t₁₄: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀-1, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0 ∧ X₂ ≤ 0
t₉: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Cut unsatisfiable transition t₁₂: l8→l7

Cut unsatisfiable transition t₁₃: l8→l7

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

Found invariant X₄ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₁ for location l12

Found invariant X₄ ≤ X₁ ∧ X₀ ≤ X₃ for location l7

Found invariant 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location l8

Found invariant 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location l10

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef_0
Locations: l0, l1, l10, l11, l12, 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)
t₁₀: l10(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, nondef_0, X₃, X₄) :|: 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀
t₁₅: l11(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₁
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(X₃, X₄, X₂, X₃, X₄)
t₈: l7(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₃
t₇: l7(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: X₁ < X₀ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₃
t₁₁: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁+1, X₂, X₃, X₄) :|: 0 < X₂ ∧ 0 < X₂ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀
t₁₄: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀-1, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0 ∧ X₂ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀
t₉: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀

MPRF for transition t₇: l7(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: X₁ < X₀ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₃ of depth 1:

new bound:

X₃+X₄ {O(n)}

MPRF for transition t₉: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₃+X₄ {O(n)}

MPRF for transition t₁₀: l10(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, nondef_0, X₃, X₄) :|: 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

2⋅X₃+2⋅X₄+1 {O(n)}

MPRF for transition t₁₁: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁+1, X₂, X₃, X₄) :|: 0 < X₂ ∧ 0 < X₂ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₃+X₄ {O(n)}

MPRF for transition t₁₄: l8(X₀, X₁, X₂, X₃, X₄) → l7(X₀-1, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0 ∧ X₂ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₃+X₄ {O(n)}

All Bounds

Timebounds

Overall timebound:6⋅X₃+6⋅X₄+10 {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: X₃+X₄ {O(n)}
t₈: 1 {O(1)}
t₉: X₃+X₄ {O(n)}
t₁₀: 2⋅X₃+2⋅X₄+1 {O(n)}
t₁₁: X₃+X₄ {O(n)}
t₁₄: X₃+X₄ {O(n)}
t₁₅: 1 {O(1)}

Costbounds

Overall costbound: 6⋅X₃+6⋅X₄+10 {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: X₃+X₄ {O(n)}
t₈: 1 {O(1)}
t₉: X₃+X₄ {O(n)}
t₁₀: 2⋅X₃+2⋅X₄+1 {O(n)}
t₁₁: X₃+X₄ {O(n)}
t₁₄: X₃+X₄ {O(n)}
t₁₅: 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: X₃ {O(n)}
t₆, X₁: X₄ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₇, X₀: 2⋅X₃+X₄ {O(n)}
t₇, X₁: 2⋅X₄+X₃ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₈, X₀: 2⋅X₄+5⋅X₃ {O(n)}
t₈, X₁: 2⋅X₃+5⋅X₄ {O(n)}
t₈, X₃: 3⋅X₃ {O(n)}
t₈, X₄: 3⋅X₄ {O(n)}
t₉, X₀: 2⋅X₃+X₄ {O(n)}
t₉, X₁: 2⋅X₄+X₃ {O(n)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: X₄ {O(n)}
t₁₀, X₀: 2⋅X₃+X₄ {O(n)}
t₁₀, X₁: 2⋅X₄+X₃ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₁, X₀: 2⋅X₃+X₄ {O(n)}
t₁₁, X₁: 2⋅X₄+X₃ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₁₄, X₀: 2⋅X₃+X₄ {O(n)}
t₁₄, X₁: 2⋅X₄+X₃ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₅, X₀: 2⋅X₄+5⋅X₃ {O(n)}
t₁₅, X₁: 2⋅X₃+5⋅X₄ {O(n)}
t₁₅, X₃: 3⋅X₃ {O(n)}
t₁₅, X₄: 3⋅X₄ {O(n)}