Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 1
t₄: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₁ < 2⋅X₀
t₂: l2(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 1 < X₀ ∧ 2⋅X₀ ≤ X₁
t₉: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₂, X₀, X₂, X₃, X₄)
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄)
t₇: l6(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, nondef.0, X₃, X₄)
t₁: l7(X₀, X₁, X₂, X₃, X₄) → l2(X₄, X₃, X₂, X₃, X₄)

Preprocessing

Found invariant X₁ ≤ X₃ for location l2

Found invariant 4 ≤ X₃ ∧ 8 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 6 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 4 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location l6

Found invariant 4 ≤ X₃ ∧ 8 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 6 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 4 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location l5

Found invariant X₁ ≤ X₃ for location l1

Found invariant 4 ≤ X₃ ∧ 8 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 6 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 4 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location l4

Found invariant X₁ ≤ X₃ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 1 ∧ X₁ ≤ X₃
t₄: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₁ < 2⋅X₀ ∧ X₁ ≤ X₃
t₂: l2(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 1 < X₀ ∧ 2⋅X₀ ≤ X₁ ∧ X₁ ≤ X₃
t₉: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₃
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₂, X₀, X₂, X₃, X₄) :|: 4 ≤ X₃ ∧ 8 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 6 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 4 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₀
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 4 ≤ X₃ ∧ 8 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 6 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 4 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₀
t₇: l6(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, nondef.0, X₃, X₄) :|: 4 ≤ X₃ ∧ 8 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 6 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 4 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₀
t₁: l7(X₀, X₁, X₂, X₃, X₄) → l2(X₄, X₃, X₂, X₃, X₄)

MPRF for transition t₂: l2(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 1 < X₀ ∧ 2⋅X₀ ≤ X₁ ∧ X₁ ≤ X₃ of depth 1:

new bound:

X₃+3 {O(n)}

MPRF for transition t₅: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 4 ≤ X₃ ∧ 8 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 6 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 4 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₃+3 {O(n)}

MPRF for transition t₇: l6(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, nondef.0, X₃, X₄) :|: 4 ≤ X₃ ∧ 8 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 6 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 4 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₃+7 {O(n)}

MPRF for transition t₈: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₂, X₀, X₂, X₃, X₄) :|: 4 ≤ X₃ ∧ 8 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 6 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 4 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₃+3 {O(n)}

All Bounds

Timebounds

Overall timebound:5⋅X₃+21 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₃+3 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₃+3 {O(n)}
t₇: 2⋅X₃+7 {O(n)}
t₈: X₃+3 {O(n)}
t₉: 1 {O(1)}

Costbounds

Overall costbound: 5⋅X₃+21 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₃+3 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₃+3 {O(n)}
t₇: 2⋅X₃+7 {O(n)}
t₈: X₃+3 {O(n)}
t₉: 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: X₄ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₉, X₃: 4⋅X₃ {O(n)}
t₉, X₄: 4⋅X₄ {O(n)}