Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ ≤ 42 ∧ 0 < X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: 42 < X₀
t₄: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₅: l3(X₀, X₁) → l1(2⋅X₀, X₁)
t₆: l4(X₀, X₁) → l5(X₀, X₁)

Preprocessing

Found invariant X₁ ≤ X₀ for location l5

Found invariant X₁ ≤ X₀ for location l1

Found invariant X₁ ≤ X₀ for location l4

Found invariant X₁ ≤ 42 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 84 ∧ X₀ ≤ 42 ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ ≤ 42 ∧ 0 < X₀ ∧ X₁ ≤ X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: 42 < X₀ ∧ X₁ ≤ X₀
t₄: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0 ∧ X₁ ≤ X₀
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₅: l3(X₀, X₁) → l1(2⋅X₀, X₁) :|: X₁ ≤ 42 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 84 ∧ X₀ ≤ 42 ∧ 1 ≤ X₀
t₆: l4(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ X₀

MPRF for transition t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ ≤ 42 ∧ 0 < X₀ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₁+43 {O(n)}

MPRF for transition t₅: l3(X₀, X₁) → l1(2⋅X₀, X₁) :|: X₁ ≤ 42 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 84 ∧ X₀ ≤ 42 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+43 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₁+91 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+43 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₁+43 {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₁+91 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+43 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₁+43 {O(n)}
t₆: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: 42 {O(1)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁+84 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: 84 {O(1)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: 2⋅X₁+84 {O(n)}
t₆, X₁: 3⋅X₁ {O(n)}