Initial Problem

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

Preprocessing

Found invariant 1+X₁ ≤ X₀ for location l2

Found invariant X₀ ≤ X₁ for location l7

Found invariant X₀ ≤ X₁ for location l5

Found invariant X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location l4

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

Problem after Preprocessing

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

MPRF for transition t₄: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₂+X₃ {O(n)}

MPRF for transition t₅: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF for transition t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃+1) :|: 1+X₃ ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₂+X₃ {O(n)}

MPRF for transition t₇: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

knowledge_propagation leads to new time bound X₀+X₁+X₂+X₃+1 {O(n)} for transition t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₀

All Bounds

Timebounds

Overall timebound:3⋅X₀+3⋅X₁+3⋅X₂+3⋅X₃+5 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁+X₂+X₃+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₂+X₃ {O(n)}
t₅: X₀+X₁ {O(n)}
t₆: X₂+X₃ {O(n)}
t₇: X₀+X₁ {O(n)}
t₈: 1 {O(1)}

Costbounds

Overall costbound: 3⋅X₀+3⋅X₁+3⋅X₂+3⋅X₃+5 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁+X₂+X₃+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₂+X₃ {O(n)}
t₅: X₀+X₁ {O(n)}
t₆: X₂+X₃ {O(n)}
t₇: X₀+X₁ {O(n)}
t₈: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: X₃ {O(n)}
t₁, X₃: X₂ {O(n)}
t₂, X₀: X₁ {O(n)}
t₂, X₁: 2⋅X₀+X₁ {O(n)}
t₂, X₂: X₃ {O(n)}
t₂, X₃: 2⋅X₂+X₃ {O(n)}
t₃, X₀: 2⋅X₁ {O(n)}
t₃, X₁: 3⋅X₀+X₁ {O(n)}
t₃, X₂: 2⋅X₃ {O(n)}
t₃, X₃: 3⋅X₂+X₃ {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: 2⋅X₀+X₁ {O(n)}
t₄, X₂: X₃ {O(n)}
t₄, X₃: 2⋅X₂+X₃ {O(n)}
t₅, X₀: X₁ {O(n)}
t₅, X₁: 2⋅X₀+X₁ {O(n)}
t₅, X₂: X₃ {O(n)}
t₅, X₃: 2⋅X₂+X₃ {O(n)}
t₆, X₀: X₁ {O(n)}
t₆, X₁: 2⋅X₀+X₁ {O(n)}
t₆, X₂: X₃ {O(n)}
t₆, X₃: 2⋅X₂+X₃ {O(n)}
t₇, X₀: X₁ {O(n)}
t₇, X₁: 2⋅X₀+X₁ {O(n)}
t₇, X₂: X₃ {O(n)}
t₇, X₃: 2⋅X₂+X₃ {O(n)}
t₈, X₀: 2⋅X₁ {O(n)}
t₈, X₁: 3⋅X₀+X₁ {O(n)}
t₈, X₂: 2⋅X₃ {O(n)}
t₈, X₃: 3⋅X₂+X₃ {O(n)}