Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ X₀
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 2⋅X₂
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₀ ∧ X₀ < X₁ ∧ 2⋅X₂ < X₀
t₁₀: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₃, X₇, X₀, X₃, X₄, X₅, X₆, X₇)
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, nondef.0, X₄, X₅, X₆, X₇)
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₅, X₆, X₄, X₃, X₄, X₅, X₆, X₇)

Preprocessing

Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l6

Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l5

Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ X₀
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 2⋅X₂
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₀ ∧ X₀ < X₁ ∧ 2⋅X₂ < X₀
t₁₀: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₃, X₇, X₀, X₃, X₄, X₅, X₆, X₇) :|: 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, nondef.0, X₄, X₅, X₆, X₇) :|: 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₅, X₆, X₄, X₃, X₄, X₅, X₆, X₇)

MPRF for transition t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₀ ∧ X₀ < X₁ ∧ 2⋅X₂ < X₀ of depth 2:

new bound:

16⋅X₄+8⋅X₆+8⋅X₇+9 {O(n)}

MPRF for transition t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 2:

new bound:

32⋅X₄+8⋅X₆+8⋅X₇+1 {O(n)}

MPRF for transition t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, nondef.0, X₄, X₅, X₆, X₇) :|: 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 2:

new bound:

16⋅X₄+16⋅X₆+16⋅X₇+9 {O(n)}

MPRF for transition t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₃, X₇, X₀, X₃, X₄, X₅, X₆, X₇) :|: 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 2:

new bound:

48⋅X₄+8⋅X₆+8⋅X₇+41 {O(n)}

All Bounds

Timebounds

Overall timebound:112⋅X₄+40⋅X₆+40⋅X₇+66 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 16⋅X₄+8⋅X₆+8⋅X₇+9 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 32⋅X₄+8⋅X₆+8⋅X₇+1 {O(n)}
t₈: 16⋅X₄+16⋅X₆+16⋅X₇+9 {O(n)}
t₉: 48⋅X₄+8⋅X₆+8⋅X₇+41 {O(n)}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: 112⋅X₄+40⋅X₆+40⋅X₇+66 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 16⋅X₄+8⋅X₆+8⋅X₇+9 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 32⋅X₄+8⋅X₆+8⋅X₇+1 {O(n)}
t₈: 16⋅X₄+16⋅X₆+16⋅X₇+9 {O(n)}
t₉: 48⋅X₄+8⋅X₆+8⋅X₇+41 {O(n)}
t₁₀: 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)}
t₀, X₇: X₇ {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)}
t₁, X₇: X₇ {O(n)}
t₂, X₁: X₆+X₇ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₂, X₇: X₇ {O(n)}
t₃, X₁: X₆+X₇ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₃, X₆: 2⋅X₆ {O(n)}
t₃, X₇: 2⋅X₇ {O(n)}
t₄, X₁: X₆+X₇ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅X₅ {O(n)}
t₄, X₆: 2⋅X₆ {O(n)}
t₄, X₇: 2⋅X₇ {O(n)}
t₅, X₁: X₆+X₇ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₅, X₅: 2⋅X₅ {O(n)}
t₅, X₆: 2⋅X₆ {O(n)}
t₅, X₇: 2⋅X₇ {O(n)}
t₆, X₁: X₆+X₇ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₆, X₆: X₆ {O(n)}
t₆, X₇: X₇ {O(n)}
t₈, X₁: X₆+X₇ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₈, X₆: X₆ {O(n)}
t₈, X₇: X₇ {O(n)}
t₉, X₁: X₇ {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: X₅ {O(n)}
t₉, X₆: X₆ {O(n)}
t₉, X₇: X₇ {O(n)}
t₁₀, X₁: 3⋅X₆+3⋅X₇ {O(n)}
t₁₀, X₄: 6⋅X₄ {O(n)}
t₁₀, X₅: 6⋅X₅ {O(n)}
t₁₀, X₆: 6⋅X₆ {O(n)}
t₁₀, X₇: 6⋅X₇ {O(n)}