Initial Problem

Start: f300
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: f1, f300, f5
Transitions:
t₃: f300(X₀, X₁) → f1(X₀, C) :|: X₀ ≤ 0
t₂: f300(X₀, X₁) → f5(X₀-1, X₁) :|: 1 ≤ X₀
t₁: f5(X₀, X₁) → f1(X₀, C) :|: X₀ ≤ 0
t₀: f5(X₀, X₁) → f5(X₀-1, X₁) :|: 1 ≤ X₀

Preprocessing

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

Found invariant X₀ ≤ 0 for location f1

Found invariant 0 ≤ X₀ for location f5

Problem after Preprocessing

Start: f300
Program_Vars: X₀
Temp_Vars:
Locations: f1, f300, f5
Transitions:
t₇: f300(X₀) → f1(X₀) :|: X₀ ≤ 0
t₈: f300(X₀) → f5(X₀-1) :|: 1 ≤ X₀
t₉: f5(X₀) → f1(X₀) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₀: f5(X₀) → f5(X₀-1) :|: 1 ≤ X₀ ∧ 0 ≤ X₀

MPRF for transition t₁₀: f5(X₀) → f5(X₀-1) :|: 1 ≤ X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

• f5: [1+X₀]

All Bounds

Timebounds

Overall timebound:X₀+4 {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: X₀+1 {O(n)}

Costbounds

Overall costbound: X₀+4 {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: X₀+1 {O(n)}

Sizebounds

t₇, X₀: X₀ {O(n)}
t₈, X₀: X₀ {O(n)}
t₉, X₀: 0 {O(1)}
t₁₀, X₀: X₀ {O(n)}