Initial Problem

Start: start0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: lbl32, start, start0, stop
Transitions:
t₃: lbl32(X₀, X₁, X₂, X₃) → lbl32(X₀, X₁, X₂, X₃-1) :|: 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₂: lbl32(X₀, X₁, X₂, X₃) → stop(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ 2 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₁: start(X₀, X₁, X₂, X₃) → lbl32(X₀, X₁, X₂, X₃-1) :|: 2 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₀: start(X₀, X₁, X₂, X₃) → stop(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1 ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₄: start0(X₀, X₁, X₂, X₃) → start(X₀, X₂, X₂, X₀)

Preprocessing

Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location start

Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location stop

Found invariant 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀ for location lbl32

Problem after Preprocessing

Start: start0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: lbl32, start, start0, stop
Transitions:
t₃: lbl32(X₀, X₁, X₂, X₃) → lbl32(X₀, X₁, X₂, X₃-1) :|: 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀ ∧ 3 ≤ X₀+X₃
t₂: lbl32(X₀, X₁, X₂, X₃) → stop(X₀, X₁, X₂, X₃) :|: X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ 2 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 3 ≤ X₀+X₃
t₁: start(X₀, X₁, X₂, X₃) → lbl32(X₀, X₁, X₂, X₃-1) :|: 2 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₀: start(X₀, X₁, X₂, X₃) → stop(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1 ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₄: start0(X₀, X₁, X₂, X₃) → start(X₀, X₂, X₂, X₀)

MPRF for transition t₃: lbl32(X₀, X₁, X₂, X₃) → lbl32(X₀, X₁, X₂, X₃-1) :|: 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀ ∧ 3 ≤ X₀+X₃ of depth 1:

new bound:

X₀ {O(n)}

• lbl32: [X₃]

All Bounds

Timebounds

Overall timebound:X₀+4 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₀ {O(n)}
t₄: 1 {O(1)}

Costbounds

Overall costbound: X₀+4 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₀ {O(n)}
t₄: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₂ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₀ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₂ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₀ {O(n)}
t₂, X₀: 2⋅X₀ {O(n)}
t₂, X₁: 2⋅X₂ {O(n)}
t₂, X₂: 2⋅X₂ {O(n)}
t₂, X₃: 1 {O(1)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₂ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₀ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₀ {O(n)}