Initial Problem

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

Preprocessing

Problem after Preprocessing

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

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁: eval(X₀, X₁) → eval(X₁, X₁) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ X₀

MPRF for transition t₀: eval(X₀, X₁) → eval(X₀-1, X₁) :|: 1 ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₀ {O(n)}

• eval: [X₀]

All Bounds

Timebounds

Overall timebound:X₀+2 {O(n)}
t₀: X₀ {O(n)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}

Costbounds

Overall costbound: X₀+2 {O(n)}
t₀: X₀ {O(n)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}

Sizebounds

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