Initial Problem

Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f10, f3
Transitions:
t₀: f0(X₀, X₁) → f3(1, X₁)
t₂: f3(X₀, X₁) → f10(X₀, X₁) :|: 11 ≤ X₀
t₁: f3(X₀, X₁) → f3(1+X₀, 10-X₀) :|: X₀ ≤ 10

Preprocessing

Eliminate variables [X₁] that do not contribute to the problem

Found invariant X₀ ≤ 11 ∧ 1 ≤ X₀ for location f3

Found invariant X₀ ≤ 11 ∧ 11 ≤ X₀ for location f10

Problem after Preprocessing

Start: f0
Program_Vars: X₀
Temp_Vars:
Locations: f0, f10, f3
Transitions:
t₆: f0(X₀) → f3(1)
t₇: f3(X₀) → f10(X₀) :|: 11 ≤ X₀ ∧ X₀ ≤ 11 ∧ 1 ≤ X₀
t₈: f3(X₀) → f3(1+X₀) :|: X₀ ≤ 10 ∧ X₀ ≤ 11 ∧ 1 ≤ X₀

MPRF for transition t₈: f3(X₀) → f3(1+X₀) :|: X₀ ≤ 10 ∧ X₀ ≤ 11 ∧ 1 ≤ X₀ of depth 1:

new bound:

12 {O(1)}

• f3: [11-X₀]

All Bounds

Timebounds

Overall timebound:14 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 12 {O(1)}

Costbounds

Overall costbound: 14 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 12 {O(1)}

Sizebounds

t₆, X₀: 1 {O(1)}
t₇, X₀: 11 {O(1)}
t₈, X₀: 11 {O(1)}