Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: l0, l1, l2
Transitions:
t₂: l0(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₀
t₃: l0(X₀, X₁) → l2(X₀, C) :|: X₀ ≤ 0
t₀: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₀
t₁: l1(X₀, X₁) → l2(X₀, C) :|: X₀ ≤ 0

Preprocessing

Eliminate variables {C,X₁} that do not contribute to the problem

Found invariant X₀ ≤ 0 for location l2

Found invariant 0 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₈: l0(X₀) → l1(X₀-1) :|: 1 ≤ X₀
t₉: l0(X₀) → l2(X₀) :|: X₀ ≤ 0
t₁₀: l1(X₀) → l1(X₀-1) :|: 1 ≤ X₀ ∧ 0 ≤ X₀
t₁₁: l1(X₀) → l2(X₀) :|: X₀ ≤ 0 ∧ 0 ≤ X₀

MPRF for transition t₁₀: l1(X₀) → l1(X₀-1) :|: 1 ≤ X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l1 [X₀+1 ]

All Bounds

Timebounds

Overall timebound:X₀+4 {O(n)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: X₀+1 {O(n)}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: X₀+4 {O(n)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: X₀+1 {O(n)}
t₁₁: 1 {O(1)}

Sizebounds

t₈, X₀: X₀ {O(n)}
t₉, X₀: X₀ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₁, X₀: 0 {O(1)}