Initial Problem

Start: start
Program_Vars: X₀
Temp_Vars: B
Locations: a, start
Transitions:
t₃: a(X₀) → a(B) :|: 1 ≤ B ∧ X₀ ≤ 2⋅B ∧ 2⋅B ≤ X₀
t₄: a(X₀) → a(B) :|: X₀ ≤ 1+2⋅B ∧ 1 ≤ 2⋅B ∧ 1+2⋅B ≤ X₀
t₀: start(X₀) → a(X₀) :|: 1 ≤ X₀
t₁: start(X₀) → a(X₀) :|: 2 ≤ X₀
t₂: start(X₀) → a(X₀) :|: 4 ≤ X₀

Preprocessing

Found invariant 1 ≤ X₀ for location a

Problem after Preprocessing

Start: start
Program_Vars: X₀
Temp_Vars: B
Locations: a, start
Transitions:
t₃: a(X₀) → a(B) :|: 1 ≤ B ∧ X₀ ≤ 2⋅B ∧ 2⋅B ≤ X₀ ∧ 1 ≤ X₀
t₄: a(X₀) → a(B) :|: X₀ ≤ 1+2⋅B ∧ 1 ≤ 2⋅B ∧ 1+2⋅B ≤ X₀ ∧ 1 ≤ X₀
t₀: start(X₀) → a(X₀) :|: 1 ≤ X₀
t₁: start(X₀) → a(X₀) :|: 2 ≤ X₀
t₂: start(X₀) → a(X₀) :|: 4 ≤ X₀

MPRF for transition t₃: a(X₀) → a(B) :|: 1 ≤ B ∧ X₀ ≤ 2⋅B ∧ 2⋅B ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

6⋅X₀ {O(n)}

• a: [2⋅X₀]

MPRF for transition t₄: a(X₀) → a(B) :|: X₀ ≤ 1+2⋅B ∧ 1 ≤ 2⋅B ∧ 1+2⋅B ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

6⋅X₀ {O(n)}

• a: [2⋅X₀]

All Bounds

Timebounds

Overall timebound:12⋅X₀+3 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 6⋅X₀ {O(n)}
t₄: 6⋅X₀ {O(n)}

Costbounds

Overall costbound: 12⋅X₀+3 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 6⋅X₀ {O(n)}
t₄: 6⋅X₀ {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₁, X₀: X₀ {O(n)}
t₂, X₀: X₀ {O(n)}
t₃, X₀: 3⋅X₀ {O(n)}
t₄, X₀: 3⋅X₀ {O(n)}