Initial Problem

Start: f2
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: f1, f2, f300
Transitions:
t₂: f2(X₀, X₁, X₂) → f300(X₀, X₁, X₂)
t₁: f300(X₀, X₁, X₂) → f1(X₀, X₁, D) :|: X₁ ≤ X₀
t₀: f300(X₀, X₁, X₂) → f300(1+X₀, X₁, X₂) :|: 1+X₀ ≤ X₁

Preprocessing

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

Found invariant X₁ ≤ X₀ for location f1

Problem after Preprocessing

Start: f2
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f1, f2, f300
Transitions:
t₆: f2(X₀, X₁) → f300(X₀, X₁)
t₇: f300(X₀, X₁) → f1(X₀, X₁) :|: X₁ ≤ X₀
t₈: f300(X₀, X₁) → f300(1+X₀, X₁) :|: 1+X₀ ≤ X₁

MPRF for transition t₈: f300(X₀, X₁) → f300(1+X₀, X₁) :|: 1+X₀ ≤ X₁ of depth 1:

new bound:

X₀+X₁ {O(n)}

• f300: [X₁-X₀]

All Bounds

Timebounds

Overall timebound:X₀+X₁+2 {O(n)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: X₀+X₁ {O(n)}

Costbounds

Overall costbound: X₀+X₁+2 {O(n)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: X₀+X₁ {O(n)}

Sizebounds

t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₇, X₀: 3⋅X₀+X₁ {O(n)}
t₇, X₁: 2⋅X₁ {O(n)}
t₈, X₀: 2⋅X₀+X₁ {O(n)}
t₈, X₁: X₁ {O(n)}