Initial Problem

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

Preprocessing

Found invariant 1+X₁ ≤ X₂ for location l2

Found invariant X₂ ≤ X₁ for location l7

Found invariant X₂ ≤ X₁ for location l5

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

Found invariant 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ 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:
t₀: l0(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁+1 ≤ X₂
t₃: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ X₁
t₄: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁+1 ≤ X₀ ∧ 1+X₁ ≤ X₂
t₅: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 1+X₁ ≤ X₂
t₆: l3(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂) :|: 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₇: l4(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ X₁
t₈: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ X₁
t₁: l6(X₀, X₁, X₂) → l1(X₁, X₀, X₂)

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

new bound:

X₀+X₂ {O(n)}

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

new bound:

X₁+X₂ {O(n)}

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

new bound:

X₀+X₂ {O(n)}

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

new bound:

X₁+X₂ {O(n)}

knowledge_propagation leads to new time bound 2⋅X₂+X₀+X₁+1 {O(n)} for transition t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁+1 ≤ X₂

All Bounds

Timebounds

Overall timebound:3⋅X₀+3⋅X₁+6⋅X₂+5 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 2⋅X₂+X₀+X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₀+X₂ {O(n)}
t₅: X₁+X₂ {O(n)}
t₆: X₀+X₂ {O(n)}
t₇: X₁+X₂ {O(n)}
t₈: 1 {O(1)}

Costbounds

Overall costbound: 3⋅X₀+3⋅X₁+6⋅X₂+5 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 2⋅X₂+X₀+X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₀+X₂ {O(n)}
t₅: X₁+X₂ {O(n)}
t₆: X₀+X₂ {O(n)}
t₇: X₁+X₂ {O(n)}
t₈: 1 {O(1)}

Sizebounds

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