Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ < 40
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 40 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ 0 ≤ X₃
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀+2, X₁, X₂, X₃) :|: X₃ < 0
t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀+2, X₁, X₂, X₃) :|: 0 < X₃
t₇: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)

Preprocessing

Eliminate variables {X₁,X₂} that do not contribute to the problem

Found invariant 40 ≤ X₀ for location l5

Found invariant 0 ≤ X₀ for location l1

Found invariant 40 ≤ X₀ for location l4

Found invariant X₀ ≤ 39 ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₅: l0(X₀, X₁) → l2(X₀, X₁)
t₁₆: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ < 40 ∧ 0 ≤ X₀
t₁₇: l1(X₀, X₁) → l4(X₀, X₁) :|: 40 ≤ X₀ ∧ 0 ≤ X₀
t₁₈: l2(X₀, X₁) → l1(0, X₁)
t₁₉: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀
t₂₀: l3(X₀, X₁) → l1(X₀+2, X₁) :|: X₁ < 0 ∧ X₀ ≤ 39 ∧ 0 ≤ X₀
t₂₁: l3(X₀, X₁) → l1(X₀+2, X₁) :|: 0 < X₁ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀
t₂₂: l4(X₀, X₁) → l5(X₀, X₁) :|: 40 ≤ X₀

MPRF for transition t₁₆: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ < 40 ∧ 0 ≤ X₀ of depth 1:

new bound:

40 {O(1)}

MPRF for transition t₁₉: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀ of depth 1:

new bound:

40 {O(1)}

MPRF for transition t₂₀: l3(X₀, X₁) → l1(X₀+2, X₁) :|: X₁ < 0 ∧ X₀ ≤ 39 ∧ 0 ≤ X₀ of depth 1:

new bound:

40 {O(1)}

MPRF for transition t₂₁: l3(X₀, X₁) → l1(X₀+2, X₁) :|: 0 < X₁ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀ of depth 1:

new bound:

40 {O(1)}

All Bounds

Timebounds

Overall timebound:164 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 40 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 40 {O(1)}
t₂₀: 40 {O(1)}
t₂₁: 40 {O(1)}
t₂₂: 1 {O(1)}

Costbounds

Overall costbound: 164 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 40 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 40 {O(1)}
t₂₀: 40 {O(1)}
t₂₁: 40 {O(1)}
t₂₂: 1 {O(1)}

Sizebounds

t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₆, X₀: 39 {O(1)}
t₁₆, X₁: X₁ {O(n)}
t₁₇, X₀: 122 {O(1)}
t₁₇, X₁: 2⋅X₁ {O(n)}
t₁₈, X₀: 0 {O(1)}
t₁₈, X₁: X₁ {O(n)}
t₁₉, X₀: 40 {O(1)}
t₁₉, X₁: 0 {O(1)}
t₂₀, X₀: 41 {O(1)}
t₂₀, X₁: X₁ {O(n)}
t₂₁, X₀: 41 {O(1)}
t₂₁, X₁: X₁ {O(n)}
t₂₂, X₀: 122 {O(1)}
t₂₂, X₁: 2⋅X₁ {O(n)}