Initial Problem

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

Preprocessing

Cut unsatisfiable transition [t₁: eval→eval; t₂: 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+X₁ ≤ X₀
t₃: eval(X₀, X₁) → eval(1+X₀, X₁) :|: 1+X₀ ≤ X₁ ∧ X₀ ≤ X₁
t₄: start(X₀, X₁) → eval(X₀, X₁)

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

new bound:

X₀+X₁ {O(n)}

• eval: [X₀-X₁]

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

new bound:

X₀+X₁+1 {O(n)}

• eval: [1+X₁-X₀]

All Bounds

Timebounds

Overall timebound:2⋅X₀+2⋅X₁+2 {O(n)}
t₀: X₀+X₁ {O(n)}
t₃: X₀+X₁+1 {O(n)}
t₄: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀+2⋅X₁+2 {O(n)}
t₀: X₀+X₁ {O(n)}
t₃: X₀+X₁+1 {O(n)}
t₄: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: 2⋅X₁+X₀ {O(n)}
t₃, X₀: 2⋅X₀+X₁+1 {O(n)}
t₃, X₁: X₁ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}