Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₄: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀, X₀) :|: X₀ ≤ 0 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
t₁: l1(X₀, X₁) → l1(X₀, X₀) :|: 1 ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ X₀+1 ≤ X₁
t₂: l1(X₀, X₁) → l1(X₀, 0) :|: 1 ≤ X₀ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
t₃: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ X₁ ≤ X₀

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₄: l0(X₀, X₁) → l1(X₀, X₁)
t₀: l1(X₀, X₁) → l1(X₀, X₀) :|: X₀ ≤ 0 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
t₁: l1(X₀, X₁) → l1(X₀, X₀) :|: 1 ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ X₀+1 ≤ X₁
t₂: l1(X₀, X₁) → l1(X₀, 0) :|: 1 ≤ X₀ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁
t₃: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ X₁ ≤ X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₀: l1(X₀, X₁) → l1(X₀, X₀) :|: X₀ ≤ 0 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁: l1(X₀, X₁) → l1(X₀, X₀) :|: 1 ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ X₀+1 ≤ X₁

MPRF for transition t₂: l1(X₀, X₁) → l1(X₀, 0) :|: 1 ≤ X₀ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l1 [X₁ ]

MPRF for transition t₃: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l1 [X₁ ]

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
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)}