Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l1(2, 4)
t₁: l1(X₀, X₁) → l1(X₀+2, X₀+4) :|: X₀ ≤ 19
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: 20 ≤ X₀

Preprocessing

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

Found invariant X₀ ≤ 21 ∧ 20 ≤ X₀ for location l2

Found invariant X₀ ≤ 21 ∧ 2 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₇: l0(X₀) → l1(2)
t₈: l1(X₀) → l1(X₀+2) :|: X₀ ≤ 19 ∧ X₀ ≤ 21 ∧ 2 ≤ X₀
t₉: l1(X₀) → l2(X₀) :|: 20 ≤ X₀ ∧ X₀ ≤ 21 ∧ 2 ≤ X₀

MPRF for transition t₈: l1(X₀) → l1(X₀+2) :|: X₀ ≤ 19 ∧ X₀ ≤ 21 ∧ 2 ≤ X₀ of depth 1:

new bound:

24 {O(1)}

MPRF:

l1 [22-X₀ ]

All Bounds

Timebounds

Overall timebound:26 {O(1)}
t₇: 1 {O(1)}
t₈: 24 {O(1)}
t₉: 1 {O(1)}

Costbounds

Overall costbound: 26 {O(1)}
t₇: 1 {O(1)}
t₈: 24 {O(1)}
t₉: 1 {O(1)}

Sizebounds

t₇, X₀: 2 {O(1)}
t₈, X₀: 21 {O(1)}
t₉, X₀: 21 {O(1)}