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:
t₁₂: l0(X₀, X₁) → l2(X₀, X₁)
t₁₃: l1(X₀, X₁) → l3(X₀, X₁) :|: 23 ≤ X₀ ∧ X₀ ≤ X₁
t₁₄: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ < 23 ∧ X₀ ≤ X₁
t₁₅: l2(X₀, X₁) → l1(X₁, X₁)
t₁₆: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 23 ≤ X₁ ∧ 46 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 23 ≤ X₀
t₁₇: l4(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₀ ≤ 22

MPRF for transition t₁₃: l1(X₀, X₁) → l3(X₀, X₁) :|: 23 ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₁+22 {O(n)}

MPRF:

l3 [X₀-23 ]
l1 [X₀-22 ]

MPRF for transition t₁₆: 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)}

MPRF:

l3 [X₀-22 ]
l1 [X₀-22 ]

All Bounds

Timebounds

Overall timebound:2⋅X₁+48 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: X₁+22 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: X₁+22 {O(n)}
t₁₇: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₁+48 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: X₁+22 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: X₁+22 {O(n)}
t₁₇: 1 {O(1)}

Sizebounds

t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₃, X₀: X₁ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₀: 2⋅X₁ {O(n)}
t₁₄, X₁: 2⋅X₁ {O(n)}
t₁₅, X₀: X₁ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₆, X₀: X₁ {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₇, X₀: 2⋅X₁ {O(n)}
t₁₇, X₁: 2⋅X₁ {O(n)}