Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: f0, f2, f4, f5
Transitions:
t₁: f0(X₀, X₁, X₂) → f2(X₀, X₁, 1) :|: 1 ≤ X₀
t₃: f0(X₀, X₁, X₂) → f4(X₀, X₁, 0) :|: X₀ ≤ 0
t₂: f4(X₀, X₁, X₂) → f4(X₀, X₁-1, X₂) :|: 1 ≤ X₁
t₀: f4(X₀, X₁, X₂) → f5(X₀, X₁, 1) :|: X₀ ≤ 0 ∧ X₁ ≤ 0

Preprocessing

Eliminate variables [X₂] that do not contribute to the problem

Found invariant 1 ≤ X₀ for location f2

Found invariant X₀ ≤ 0 for location f4

Found invariant X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location f5

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f2, f4, f5
Transitions:
t₇: f0(X₀, X₁) → f2(X₀, X₁) :|: 1 ≤ X₀
t₈: f0(X₀, X₁) → f4(X₀, X₁) :|: X₀ ≤ 0
t₉: f4(X₀, X₁) → f4(X₀, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
t₁₀: f4(X₀, X₁) → f5(X₀, X₁) :|: X₀ ≤ 0 ∧ X₁ ≤ 0

MPRF for transition t₉: f4(X₀, X₁) → f4(X₀, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 of depth 1:

new bound:

X₁ {O(n)}

• f4: [X₁]

All Bounds

Timebounds

Overall timebound:X₁+3 {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₁ {O(n)}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: X₁+3 {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₁ {O(n)}
t₁₀: 1 {O(1)}

Sizebounds

t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₁₀, X₀: 2⋅X₀ {O(n)}
t₁₀, X₁: 2⋅X₁ {O(n)}