Initial Problem

Start: start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval, start
Transitions:
t₀: eval(X₀, X₁, X₂) → eval(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₀
t₁: eval(X₀, X₁, X₂) → eval(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂
t₂: eval(X₀, X₁, X₂) → eval(X₀, X₁, X₂-1) :|: 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₁
t₃: eval(X₀, X₁, X₂) → eval(X₀, X₁, X₂-1) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ X₁
t₄: eval(X₀, X₁, X₂) → eval(X₀, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁
t₅: eval(X₀, X₁, X₂) → eval(X₀, X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁
t₆: start(X₀, X₁, X₂) → eval(X₀, X₁, X₂)

Preprocessing

Cut unsatisfiable transition [t₂: eval→eval; t₄: eval→eval; t₅: eval→eval]

Problem after Preprocessing

Start: start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval, start
Transitions:
t₀: eval(X₀, X₁, X₂) → eval(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₀
t₁: eval(X₀, X₁, X₂) → eval(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂
t₃: eval(X₀, X₁, X₂) → eval(X₀, X₁, X₂-1) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ X₁
t₆: start(X₀, X₁, X₂) → eval(X₀, X₁, X₂)

MPRF for transition t₀: eval(X₀, X₁, X₂) → eval(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₀ of depth 1:

new bound:

X₀+X₁ {O(n)}

• eval: [X₀-X₁]

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

new bound:

X₀+X₁ {O(n)}

• eval: [X₀-X₁]

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

new bound:

X₁+X₂ {O(n)}

• eval: [X₂-X₁]

All Bounds

Timebounds

Overall timebound:2⋅X₀+3⋅X₁+X₂+1 {O(n)}
t₀: X₀+X₁ {O(n)}
t₁: X₀+X₁ {O(n)}
t₃: X₁+X₂ {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀+3⋅X₁+X₂+1 {O(n)}
t₀: X₀+X₁ {O(n)}
t₁: X₀+X₁ {O(n)}
t₃: X₁+X₂ {O(n)}
t₆: 1 {O(1)}

Sizebounds

t₀, X₀: 2⋅X₁+3⋅X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 2⋅X₁+3⋅X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₃, X₀: 4⋅X₁+7⋅X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: 4⋅X₂+X₁ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}