Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₃: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂-1) :|: X₁+1 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ X₁
t₀: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₁+1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂

Preprocessing

Found invariant X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₃: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂-1) :|: X₁+1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀
t₀: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₁+1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₀: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₁+1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂

MPRF for transition t₁: l1(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂-1) :|: X₁+1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₁+X₂+1 {O(n)}

MPRF:

l2 [X₂+1-X₁ ]
l1 [X₂+1-X₁ ]

MPRF for transition t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

MPRF:

l2 [X₀-X₁ ]
l1 [1 ]

All Bounds

Timebounds

Overall timebound:2⋅X₁+X₀+X₂+3 {O(n)}
t₃: 1 {O(1)}
t₁: X₁+X₂+1 {O(n)}
t₂: X₀+X₁ {O(n)}
t₀: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₁+X₀+X₂+3 {O(n)}
t₃: 1 {O(1)}
t₁: X₁+X₂+1 {O(n)}
t₂: X₀+X₁ {O(n)}
t₀: 1 {O(1)}

Sizebounds

t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₁, X₀: X₀+X₁+X₂+1 {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: 2⋅X₂+X₁+1 {O(n)}
t₂, X₀: X₀+X₁+X₂+1 {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 2⋅X₂+X₁+1 {O(n)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}