Initial Problem

Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f5, f8
Transitions:
t₀: f0(X₀, X₁) → f5(2, 4)
t₁: f5(X₀, X₁) → f5(2+X₀, 4+X₀) :|: X₀ ≤ 19
t₂: f5(X₀, X₁) → f8(X₀, X₁) :|: 20 ≤ X₀

Preprocessing

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

Found invariant X₀ ≤ 21 ∧ 20 ≤ X₀ for location f8

Found invariant X₀ ≤ 21 ∧ 2 ≤ X₀ for location f5

Problem after Preprocessing

Start: f0
Program_Vars: X₀
Temp_Vars:
Locations: f0, f5, f8
Transitions:
t₆: f0(X₀) → f5(2)
t₇: f5(X₀) → f5(2+X₀) :|: X₀ ≤ 19 ∧ X₀ ≤ 21 ∧ 2 ≤ X₀
t₈: f5(X₀) → f8(X₀) :|: 20 ≤ X₀ ∧ X₀ ≤ 21 ∧ 2 ≤ X₀

MPRF for transition t₇: f5(X₀) → f5(2+X₀) :|: X₀ ≤ 19 ∧ X₀ ≤ 21 ∧ 2 ≤ X₀ of depth 1:

new bound:

190 {O(1)}

• f5: [172-9⋅X₀]

All Bounds

Timebounds

Overall timebound:192 {O(1)}
t₆: 1 {O(1)}
t₇: 190 {O(1)}
t₈: 1 {O(1)}

Costbounds

Overall costbound: 192 {O(1)}
t₆: 1 {O(1)}
t₇: 190 {O(1)}
t₈: 1 {O(1)}

Sizebounds

t₆, X₀: 2 {O(1)}
t₇, X₀: 21 {O(1)}
t₈, X₀: 21 {O(1)}