Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₂+X₁
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₀ ∧ X₁+X₂ ≤ 0
t₉: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₁, X₃, X₁, X₃, X₄, X₅, X₆)
t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, nondef.0, X₄, X₅, X₆)
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₅, X₆, X₄, X₃, X₄, X₅, X₆)

Preprocessing

Found invariant X₁+X₂ ≤ 0 ∧ 1 ≤ X₀ for location l6

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

Found invariant X₁+X₂ ≤ 0 ∧ 1 ≤ X₀ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₂+X₁
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₀ ∧ X₁+X₂ ≤ 0
t₉: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₁, X₃, X₁, X₃, X₄, X₅, X₆) :|: X₁+X₂ ≤ 0 ∧ 1 ≤ X₀
t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁+X₂ ≤ 0 ∧ 1 ≤ X₀
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, nondef.0, X₄, X₅, X₆) :|: X₁+X₂ ≤ 0 ∧ 1 ≤ X₀
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₅, X₆, X₄, X₃, X₄, X₅, X₆)

MPRF for transition t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₀ ∧ X₁+X₂ ≤ 0 of depth 2:

new bound:

24⋅X₅+8⋅X₄+17 {O(n)}

MPRF for transition t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁+X₂ ≤ 0 ∧ 1 ≤ X₀ of depth 2:

new bound:

24⋅X₅+8⋅X₄+17 {O(n)}

MPRF for transition t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, nondef.0, X₄, X₅, X₆) :|: X₁+X₂ ≤ 0 ∧ 1 ≤ X₀ of depth 2:

new bound:

24⋅X₅+8⋅X₄+17 {O(n)}

MPRF for transition t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₁, X₃, X₁, X₃, X₄, X₅, X₆) :|: X₁+X₂ ≤ 0 ∧ 1 ≤ X₀ of depth 2:

new bound:

24⋅X₅+8⋅X₄+9 {O(n)}

All Bounds

Timebounds

Overall timebound:32⋅X₄+96⋅X₅+65 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 24⋅X₅+8⋅X₄+17 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 24⋅X₅+8⋅X₄+17 {O(n)}
t₇: 24⋅X₅+8⋅X₄+17 {O(n)}
t₈: 24⋅X₅+8⋅X₄+9 {O(n)}
t₉: 1 {O(1)}

Costbounds

Overall costbound: 32⋅X₄+96⋅X₅+65 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 24⋅X₅+8⋅X₄+17 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 24⋅X₅+8⋅X₄+17 {O(n)}
t₇: 24⋅X₅+8⋅X₄+17 {O(n)}
t₈: 24⋅X₅+8⋅X₄+9 {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)}
t₀, X₅: X₅ {O(n)}
t₀, X₆: X₆ {O(n)}
t₁, X₀: X₅ {O(n)}
t₁, X₁: X₆ {O(n)}
t₁, X₂: X₄ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₃, X₆: 2⋅X₆ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅X₅ {O(n)}
t₄, X₆: 2⋅X₆ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₆ {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₅ {O(n)}
t₇, X₆: X₆ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₈, X₆: X₆ {O(n)}
t₉, X₄: 4⋅X₄ {O(n)}
t₉, X₅: 4⋅X₅ {O(n)}
t₉, X₆: 4⋅X₆ {O(n)}