Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4
Transitions:
t₄: l0(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(1+X₀, X₁, X₀, X₃) :|: X₀ ≤ 9
t₀: l1(X₀, X₁, X₂, X₃) → l2(X₀, E, X₂, X₃) :|: 10 ≤ X₀
t₂: l3(X₀, X₁, X₂, X₃) → l1(1, X₁, X₂, X₃) :|: E ≤ 9 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₃: l4(X₀, X₁, X₂, X₃) → l1(2, X₁, X₂, 2) :|: X₀ ≤ 9

Preprocessing

Cut unreachable locations [l3; l4] from the program graph

Eliminate variables {E,X₁,X₂,X₃} 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:
t₈: l0(X₀) → l1(0)
t₉: l1(X₀) → l1(1+X₀) :|: X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₁₀: l1(X₀) → l2(X₀) :|: 10 ≤ X₀ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀

MPRF for transition t₉: l1(X₀) → l1(1+X₀) :|: X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

10 {O(1)}

All Bounds

Timebounds

Overall timebound:12 {O(1)}
t₈: 1 {O(1)}
t₉: 10 {O(1)}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: 12 {O(1)}
t₈: 1 {O(1)}
t₉: 10 {O(1)}
t₁₀: 1 {O(1)}

Sizebounds

t₈, X₀: 0 {O(1)}
t₉, X₀: 10 {O(1)}
t₁₀, X₀: 10 {O(1)}