Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 23 ≤ X₀
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ < 23
t₁: l2(X₀, X₁, X₂) → l1(X₁, X₁, X₂)
t₄: l3(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂)
t₅: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)

Preprocessing

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

Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 22 for location l5

Found invariant X₀ ≤ X₁ for location l1

Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 22 for location l4

Found invariant 23 ≤ X₁ ∧ 46 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 23 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₁: l0(X₀, X₁) → l2(X₀, X₁)
t₁₂: l1(X₀, X₁) → l3(X₀, X₁) :|: 23 ≤ X₀ ∧ X₀ ≤ X₁
t₁₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ < 23 ∧ X₀ ≤ X₁
t₁₄: l2(X₀, X₁) → l1(X₁, X₁)
t₁₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 23 ≤ X₁ ∧ 46 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 23 ≤ X₀
t₁₆: l4(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₀ ≤ 22

MPRF for transition t₁₂: l1(X₀, X₁) → l3(X₀, X₁) :|: 23 ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₁+22 {O(n)}

MPRF for transition t₁₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 23 ≤ X₁ ∧ 46 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 23 ≤ X₀ of depth 1:

new bound:

X₁+22 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₁+48 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₁+22 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: X₁+22 {O(n)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₁+48 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₁+22 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: X₁+22 {O(n)}
t₁₆: 1 {O(1)}

Sizebounds

t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₂, X₀: X₁ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₃, X₀: 2⋅X₁ {O(n)}
t₁₃, X₁: 2⋅X₁ {O(n)}
t₁₄, X₀: X₁ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₅, X₀: X₁ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₆, X₀: 2⋅X₁ {O(n)}
t₁₆, X₁: 2⋅X₁ {O(n)}