Initial Problem

Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f1
Transitions:
t₀: f0(X₀, X₁) → f1(X₀, X₁) :|: 1 ≤ X₀
t₁: f1(X₀, X₁) → f1(1+X₀, X₁-X₀) :|: 1 ≤ X₁

Preprocessing

Found invariant 1 ≤ X₀ for location f1

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f1
Transitions:
t₀: f0(X₀, X₁) → f1(X₀, X₁) :|: 1 ≤ X₀
t₁: f1(X₀, X₁) → f1(1+X₀, X₁-X₀) :|: 1 ≤ X₁ ∧ 1 ≤ X₀

MPRF for transition t₁: f1(X₀, X₁) → f1(1+X₀, X₁-X₀) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

• f1: [X₁]

All Bounds

Timebounds

Overall timebound:X₁+1 {O(n)}
t₀: 1 {O(1)}
t₁: X₁ {O(n)}

Costbounds

Overall costbound: X₁+1 {O(n)}
t₀: 1 {O(1)}
t₁: X₁ {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₀+X₁ {O(n)}
t₁, X₁: 2⋅X₀+2⋅X₁ {O(n)}