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, X₀, X₂, X₃, X₄, X₅) :|: 1 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 1
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₁, X₂, X₃, X₄, X₅)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ 1
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 < X₁
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₁, X₁, X₂, X₃, X₄, X₅)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁-2, X₂, X₃, X₄, X₅)

Preprocessing

Eliminate variables {X₂,X₃,X₅} that do not contribute to the problem

Found invariant 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l6

Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 1 for location l7

Found invariant 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l5

Found invariant X₀ ≤ X₂ for location l1

Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 1 for location l4

Found invariant 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₇: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁₈: l1(X₀, X₁, X₂) → l3(X₀, X₀, X₂) :|: 1 < X₀ ∧ X₀ ≤ X₂
t₁₉: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 1 ∧ X₀ ≤ X₂
t₂₀: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₂₁: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ 1 ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₂: l3(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 1 < X₁ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₃: l4(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ X₀ ≤ 1
t₂₄: l5(X₀, X₁, X₂) → l1(X₁, X₁, X₂) :|: 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₅: l6(X₀, X₁, X₂) → l3(X₀, X₁-2, X₂) :|: 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₈: l1(X₀, X₁, X₂) → l3(X₀, X₀, X₂) :|: 1 < X₀ ∧ X₀ ≤ X₂

MPRF for transition t₂₁: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ 1 ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₂₂: l3(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 1 < X₁ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₂₄: l5(X₀, X₁, X₂) → l1(X₁, X₁, X₂) :|: 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF for transition t₂₅: l6(X₀, X₁, X₂) → l3(X₀, X₁-2, X₂) :|: 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

All Bounds

Timebounds

Overall timebound:4⋅X₂+9 {O(n)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₂+1 {O(n)}
t₂₂: X₂+1 {O(n)}
t₂₃: 1 {O(1)}
t₂₄: X₂+1 {O(n)}
t₂₅: X₂+1 {O(n)}

Costbounds

Overall costbound: 4⋅X₂+9 {O(n)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₂+1 {O(n)}
t₂₂: X₂+1 {O(n)}
t₂₃: 1 {O(1)}
t₂₄: X₂+1 {O(n)}
t₂₅: X₂+1 {O(n)}

Sizebounds

t₁₇, X₀: X₀ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₈, X₀: X₂ {O(n)}
t₁₈, X₁: X₂ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₉, X₀: X₂+1 {O(n)}
t₁₉, X₁: X₁+1 {O(n)}
t₁₉, X₂: 2⋅X₂ {O(n)}
t₂₀, X₀: X₂ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₁, X₀: X₂ {O(n)}
t₂₁, X₁: 1 {O(1)}
t₂₁, X₂: X₂ {O(n)}
t₂₂, X₀: X₂ {O(n)}
t₂₂, X₁: X₂ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₃, X₀: X₂+1 {O(n)}
t₂₃, X₁: X₁+1 {O(n)}
t₂₃, X₂: 2⋅X₂ {O(n)}
t₂₄, X₀: 1 {O(1)}
t₂₄, X₁: 1 {O(1)}
t₂₄, X₂: X₂ {O(n)}
t₂₅, X₀: X₂ {O(n)}
t₂₅, X₁: X₂ {O(n)}
t₂₅, X₂: X₂ {O(n)}