Initial Problem

Start: f0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: f0, f15, f6
Transitions:
t₀: f0(X₀, X₁) → f6(C, 0)
t₂: f6(X₀, X₁) → f15(X₀, X₁) :|: 10 ≤ X₁
t₁: f6(X₀, X₁) → f6(X₀, 1+X₁) :|: X₁ ≤ 9

Preprocessing

Eliminate variables [C; X₀] that do not contribute to the problem

Found invariant X₀ ≤ 10 ∧ 10 ≤ X₀ for location f15

Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location f6

Problem after Preprocessing

Start: f0
Program_Vars: X₀
Temp_Vars:
Locations: f0, f15, f6
Transitions:
t₆: f0(X₀) → f6(0)
t₇: f6(X₀) → f15(X₀) :|: 10 ≤ X₀ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₈: f6(X₀) → f6(1+X₀) :|: X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀

MPRF for transition t₈: f6(X₀) → f6(1+X₀) :|: X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

11 {O(1)}

• f6: [11-X₀]

All Bounds

Timebounds

Overall timebound:13 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 11 {O(1)}

Costbounds

Overall costbound: 13 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 11 {O(1)}

Sizebounds

t₆, X₀: 0 {O(1)}
t₇, X₀: 10 {O(1)}
t₈, X₀: 10 {O(1)}