Initial Problem

Start: start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: eval, start
Transitions:
t₀: eval(X₀, X₁, X₂, X₃, X₄) → eval(X₀, 1+X₁, X₂, X₃, 1+X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₂
t₁: eval(X₀, X₁, X₂, X₃, X₄) → eval(X₀, X₁, X₂, 1+X₃, 1+X₄) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₂
t₂: eval(X₀, X₁, X₂, X₃, X₄) → eval(X₀, X₁, X₂, 1+X₃, 1+X₄) :|: 1+X₃ ≤ X₂ ∧ X₀ ≤ X₁
t₃: eval(X₀, X₁, X₂, X₃, X₄) → eval(X₀, 1+X₁, X₂, X₃, 1+X₄) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃
t₄: start(X₀, X₁, X₂, X₃, X₄) → eval(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Eliminate variables [X₄] that do not contribute to the problem

Problem after Preprocessing

Start: start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval, start
Transitions:
t₉: eval(X₀, X₁, X₂, X₃) → eval(X₀, 1+X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₂
t₁₀: eval(X₀, X₁, X₂, X₃) → eval(X₀, X₁, X₂, 1+X₃) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₂
t₁₁: eval(X₀, X₁, X₂, X₃) → eval(X₀, X₁, X₂, 1+X₃) :|: 1+X₃ ≤ X₂ ∧ X₀ ≤ X₁
t₁₂: eval(X₀, X₁, X₂, X₃) → eval(X₀, 1+X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃
t₁₃: start(X₀, X₁, X₂, X₃) → eval(X₀, X₁, X₂, X₃)

MPRF for transition t₉: eval(X₀, X₁, X₂, X₃) → eval(X₀, 1+X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₂ of depth 1:

new bound:

X₀+X₁ {O(n)}

• eval: [X₀-X₁]

MPRF for transition t₁₀: eval(X₀, X₁, X₂, X₃) → eval(X₀, X₁, X₂, 1+X₃) :|: 1+X₁ ≤ X₀ ∧ 1+X₃ ≤ X₂ of depth 1:

new bound:

X₂+X₃ {O(n)}

• eval: [X₂-X₃]

MPRF for transition t₁₁: eval(X₀, X₁, X₂, X₃) → eval(X₀, X₁, X₂, 1+X₃) :|: 1+X₃ ≤ X₂ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₂+X₃ {O(n)}

• eval: [X₂-X₃]

MPRF for transition t₁₂: eval(X₀, X₁, X₂, X₃) → eval(X₀, 1+X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₂ ≤ X₃ of depth 1:

new bound:

X₀+X₁ {O(n)}

• eval: [X₀-X₁]

All Bounds

Timebounds

Overall timebound:2⋅X₀+2⋅X₁+2⋅X₂+2⋅X₃+1 {O(n)}
t₉: X₀+X₁ {O(n)}
t₁₀: X₂+X₃ {O(n)}
t₁₁: X₂+X₃ {O(n)}
t₁₂: X₀+X₁ {O(n)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀+2⋅X₁+2⋅X₂+2⋅X₃+1 {O(n)}
t₉: X₀+X₁ {O(n)}
t₁₀: X₂+X₃ {O(n)}
t₁₁: X₂+X₃ {O(n)}
t₁₂: X₀+X₁ {O(n)}
t₁₃: 1 {O(1)}

Sizebounds

t₉, X₀: X₀ {O(n)}
t₉, X₁: 2⋅X₁+X₀ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: 2⋅X₃+X₂ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: 2⋅X₁+X₀ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: 2⋅X₃+X₂ {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: 3⋅X₁+X₀ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: 2⋅X₂+4⋅X₃ {O(n)}
t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: 2⋅X₀+4⋅X₁ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: 3⋅X₃+X₂ {O(n)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₃ {O(n)}