Initial Problem

Start: start
Program_Vars: X₀, X₁
Temp_Vars:
Locations: eval, start
Transitions:
t₀: eval(X₀, X₁) → eval(X₀, X₀) :|: X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ X₀ ≤ 0
t₁: eval(X₀, X₁) → eval(X₀, X₀) :|: 0 ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁
t₂: eval(X₀, X₁) → eval(X₀, 0) :|: X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁
t₃: eval(X₀, X₁) → eval(X₀, X₁-1) :|: 0 ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀
t₄: 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, X₀) :|: X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ X₀ ≤ 0
t₁: eval(X₀, X₁) → eval(X₀, X₀) :|: 0 ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁
t₂: eval(X₀, X₁) → eval(X₀, 0) :|: X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁
t₃: eval(X₀, X₁) → eval(X₀, X₁-1) :|: 0 ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀
t₄: start(X₀, X₁) → eval(X₀, X₁)

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₀: eval(X₀, X₁) → eval(X₀, X₀) :|: X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ X₀ ≤ 0

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁: eval(X₀, X₁) → eval(X₀, X₀) :|: 0 ≤ 1+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁

MPRF for transition t₂: eval(X₀, X₁) → eval(X₀, 0) :|: X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁ {O(n)}

• eval: [X₁]

MPRF for transition t₃: eval(X₀, X₁) → eval(X₀, X₁-1) :|: 0 ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

• eval: [X₁]

All Bounds

Timebounds

Overall timebound:2⋅X₁+3 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁ {O(n)}
t₃: X₁ {O(n)}
t₄: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₁+3 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁ {O(n)}
t₃: X₁ {O(n)}
t₄: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₀ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₀ {O(n)}
t₂, X₀: 4⋅X₀ {O(n)}
t₂, X₁: 0 {O(1)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: X₀+X₁ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}