Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l1(C, 0)
t₁: l1(X₀, X₁) → l1(X₀, X₁+1) :|: X₁ ≤ 9
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: 10 ≤ X₁

Preprocessing

Eliminate variables {C,X₀} that do not contribute to the problem

Found invariant X₀ ≤ 10 ∧ 10 ≤ X₀ for location l2

Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₆: l0(X₀) → l1(0)
t₇: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₈: l1(X₀) → l2(X₀) :|: 10 ≤ X₀ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀

MPRF for transition t₇: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

10 {O(1)}

All Bounds

Timebounds

Overall timebound:12 {O(1)}
t₆: 1 {O(1)}
t₇: 10 {O(1)}
t₈: 1 {O(1)}

Costbounds

Overall costbound: 12 {O(1)}
t₆: 1 {O(1)}
t₇: 10 {O(1)}
t₈: 1 {O(1)}

Sizebounds

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