Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l4(X₀, X₁)
t₃: l1(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ X₀
t₄: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀+1 ≤ X₁
t₅: l2(X₀, X₁) → l1(X₀, X₁+1) :|: C+1 ≤ 0
t₆: l2(X₀, X₁) → l1(X₀, X₁+1) :|: 1 ≤ C
t₇: l2(X₀, X₁) → l1(X₀, X₁+1)
t₈: l3(X₀, X₁) → l5(X₀, X₁)
t₁: l4(X₀, X₁) → l1(X₀, 1) :|: 1 ≤ X₀
t₂: l4(X₀, X₁) → l3(X₀, X₁) :|: X₀ ≤ 0
Preprocessing
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2
Found invariant X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l4(X₀, X₁)
t₃: l1(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ X₀ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₄: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀+1 ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₅: l2(X₀, X₁) → l1(X₀, X₁+1) :|: C+1 ≤ 0 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆: l2(X₀, X₁) → l1(X₀, X₁+1) :|: 1 ≤ C ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇: l2(X₀, X₁) → l1(X₀, X₁+1) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈: l3(X₀, X₁) → l5(X₀, X₁)
t₁: l4(X₀, X₁) → l1(X₀, 1) :|: 1 ≤ X₀
t₂: l4(X₀, X₁) → l3(X₀, X₁) :|: X₀ ≤ 0
MPRF for transition t₃: l1(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ X₀ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF for transition t₅: l2(X₀, X₁) → l1(X₀, X₁+1) :|: C+1 ≤ 0 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF for transition t₆: l2(X₀, X₁) → l1(X₀, X₁+1) :|: 1 ≤ C ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
MPRF for transition t₇: l2(X₀, X₁) → l1(X₀, X₁+1) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+2 {O(n)}
All Bounds
Timebounds
Overall timebound:4⋅X₀+13 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₀+2 {O(n)}
t₄: 1 {O(1)}
t₅: X₀+2 {O(n)}
t₆: X₀+2 {O(n)}
t₇: X₀+2 {O(n)}
t₈: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₀+13 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₀+2 {O(n)}
t₄: 1 {O(1)}
t₅: X₀+2 {O(n)}
t₆: X₀+2 {O(n)}
t₇: X₀+2 {O(n)}
t₈: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 1 {O(1)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: 3⋅X₀+7 {O(n)}
t₄, X₀: 3⋅X₀ {O(n)}
t₄, X₁: 9⋅X₀+21 {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: 3⋅X₀+7 {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: 3⋅X₀+7 {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: 3⋅X₀+7 {O(n)}
t₈, X₀: 4⋅X₀ {O(n)}
t₈, X₁: 9⋅X₀+X₁+21 {O(n)}