Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₁, X₃, X₄, X₅) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₅, X₂, X₃, X₄, X₅)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ 0
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₂
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-1, X₂, X₂, X₃, X₄, X₅)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂-1, X₃, X₄, X₅)

Preprocessing

Eliminate variables {X₃} that do not contribute to the problem

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6

Found invariant X₁ ≤ X₄ ∧ X₀ ≤ X₃ ∧ X₀ ≤ 0 for location l7

Found invariant X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location l5

Found invariant X₁ ≤ X₄ ∧ X₀ ≤ X₃ for location l1

Found invariant X₁ ≤ X₄ ∧ X₀ ≤ X₃ ∧ X₀ ≤ 0 for location l4

Found invariant X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₇: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₁₈: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₁, X₃, X₄) :|: 0 < X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃
t₁₉: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃
t₂₀: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₂₁: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0 ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀
t₂₂: l3(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₂ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀
t₂₃: l4(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₄ ∧ X₀ ≤ X₃ ∧ X₀ ≤ 0
t₂₄: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₂, X₂, X₃, X₄) :|: X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀
t₂₅: l6(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂-1, X₃, X₄) :|: 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₁₈: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₁, X₃, X₄) :|: 0 < X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃ of depth 1:

new bound:

X₃ {O(n)}

MPRF for transition t₂₁: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0 ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF for transition t₂₂: l3(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₂ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF for transition t₂₄: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₂, X₂, X₃, X₄) :|: X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF for transition t₂₅: l6(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂-1, X₃, X₄) :|: 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₄+3⋅X₃+4 {O(n)}
t₁₇: 1 {O(1)}
t₁₈: X₃ {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₃ {O(n)}
t₂₂: X₄ {O(n)}
t₂₃: 1 {O(1)}
t₂₄: X₃ {O(n)}
t₂₅: X₄ {O(n)}

Costbounds

Overall costbound: 2⋅X₄+3⋅X₃+4 {O(n)}
t₁₇: 1 {O(1)}
t₁₈: X₃ {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₃ {O(n)}
t₂₂: X₄ {O(n)}
t₂₃: 1 {O(1)}
t₂₄: X₃ {O(n)}
t₂₅: X₄ {O(n)}

Sizebounds

t₁₇, X₀: X₀ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: X₄ {O(n)}
t₁₈, X₀: X₃ {O(n)}
t₁₈, X₁: 2⋅X₄ {O(n)}
t₁₈, X₂: X₄ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₉, X₀: 2⋅X₃ {O(n)}
t₁₉, X₁: 2⋅X₄ {O(n)}
t₁₉, X₂: X₂+X₄ {O(n)}
t₁₉, X₃: 2⋅X₃ {O(n)}
t₁₉, X₄: 2⋅X₄ {O(n)}
t₂₀, X₀: X₃ {O(n)}
t₂₀, X₁: X₄ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₀, X₄: X₄ {O(n)}
t₂₁, X₀: X₃ {O(n)}
t₂₁, X₁: 4⋅X₄ {O(n)}
t₂₁, X₂: X₄ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₁, X₄: X₄ {O(n)}
t₂₂, X₀: X₃ {O(n)}
t₂₂, X₁: 2⋅X₄ {O(n)}
t₂₂, X₂: X₄ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₃, X₀: 2⋅X₃ {O(n)}
t₂₃, X₁: 2⋅X₄ {O(n)}
t₂₃, X₂: X₂+X₄ {O(n)}
t₂₃, X₃: 2⋅X₃ {O(n)}
t₂₃, X₄: 2⋅X₄ {O(n)}
t₂₄, X₀: X₃ {O(n)}
t₂₄, X₁: X₄ {O(n)}
t₂₄, X₂: X₄ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₄, X₄: X₄ {O(n)}
t₂₅, X₀: X₃ {O(n)}
t₂₅, X₁: 2⋅X₄ {O(n)}
t₂₅, X₂: X₄ {O(n)}
t₂₅, X₃: X₃ {O(n)}
t₂₅, X₄: X₄ {O(n)}