Initial Problem

Start: start
Program_Vars: X₀, X₁
Temp_Vars:
Locations: eval, start
Transitions:
t₀: eval(X₀, X₁) → eval(X₀-1, X₁) :|: 1 ≤ X₀
t₁: eval(X₀, X₁) → eval(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₂: eval(X₀, X₁) → eval(X₀, X₁-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ 0
t₃: eval(X₀, X₁) → eval(X₀, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
t₄: eval(X₀, X₁) → eval(X₀, X₁) :|: 1 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₁ ≤ 0
t₅: eval(X₀, X₁) → eval(X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ X₁ ≤ 0
t₆: start(X₀, X₁) → eval(X₀, X₁)

Preprocessing

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

Problem after Preprocessing

Start: start
Program_Vars: X₀, X₁
Temp_Vars:
Locations: eval, start
Transitions:
t₀: eval(X₀, X₁) → eval(X₀-1, X₁) :|: 1 ≤ X₀
t₁: eval(X₀, X₁) → eval(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₃: eval(X₀, X₁) → eval(X₀, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
t₆: start(X₀, X₁) → eval(X₀, X₁)

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

new bound:

X₀ {O(n)}

• eval: [X₀]

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

new bound:

X₀ {O(n)}

• eval: [X₀]

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

new bound:

X₁ {O(n)}

• eval: [X₁]

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₃, X₀: 3⋅X₀ {O(n)}
t₃, X₁: 3⋅X₁ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}