Initial Problem

Start: start
Program_Vars: X₀, X₁
Temp_Vars:
Locations: div, end, start
Transitions:
t₂: div(X₀, X₁) → div(X₀, X₁-X₀) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁
t₀: div(X₀, X₁) → end(X₀, X₁) :|: X₀ ≤ 0
t₁: div(X₀, X₁) → end(X₀, X₁) :|: X₁ ≤ X₀
t₃: start(X₀, X₁) → div(X₀, X₁)

Preprocessing

Problem after Preprocessing

Start: start
Program_Vars: X₀, X₁
Temp_Vars:
Locations: div, end, start
Transitions:
t₂: div(X₀, X₁) → div(X₀, X₁-X₀) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁
t₀: div(X₀, X₁) → end(X₀, X₁) :|: X₀ ≤ 0
t₁: div(X₀, X₁) → end(X₀, X₁) :|: X₁ ≤ X₀
t₃: start(X₀, X₁) → div(X₀, X₁)

MPRF for transition t₂: div(X₀, X₁) → div(X₀, X₁-X₀) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ of depth 1:

new bound:

X₀+X₁ {O(n)}

• div: [X₁-X₀]

All Bounds

Timebounds

Overall timebound:X₀+X₁+3 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁ {O(n)}
t₃: 1 {O(1)}

Costbounds

Overall costbound: X₀+X₁+3 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁ {O(n)}
t₃: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: 2⋅X₀ {O(n)}
t₁, X₁: 2⋅X₁ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}