Initial Problem

Start: l0
Program_Vars: X₀
Temp_Vars: B
Locations: l0, l1
Transitions:
t₀: l0(X₀) → l1(X₀) :|: 1 ≤ X₀
t₁: l0(X₀) → l1(X₀) :|: 2 ≤ X₀
t₂: l0(X₀) → l1(X₀) :|: 4 ≤ X₀
t₃: l1(X₀) → l1(B) :|: 2 ≤ 2⋅B ∧ X₀ ≤ 2⋅B ∧ 2⋅B ≤ X₀
t₄: l1(X₀) → l1(B) :|: 1 ≤ 2⋅B ∧ X₀ ≤ 2⋅B+1 ∧ 2⋅B+1 ≤ X₀

Preprocessing

Found invariant 1 ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars: B
Locations: l0, l1
Transitions:
t₀: l0(X₀) → l1(X₀) :|: 1 ≤ X₀
t₁: l0(X₀) → l1(X₀) :|: 2 ≤ X₀
t₂: l0(X₀) → l1(X₀) :|: 4 ≤ X₀
t₃: l1(X₀) → l1(B) :|: 2 ≤ 2⋅B ∧ X₀ ≤ 2⋅B ∧ 2⋅B ≤ X₀ ∧ 1 ≤ X₀
t₄: l1(X₀) → l1(B) :|: 1 ≤ 2⋅B ∧ X₀ ≤ 2⋅B+1 ∧ 2⋅B+1 ≤ X₀ ∧ 1 ≤ X₀

MPRF for transition t₃: l1(X₀) → l1(B) :|: 2 ≤ 2⋅B ∧ X₀ ≤ 2⋅B ∧ 2⋅B ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

6⋅X₀ {O(n)}

MPRF for transition t₄: l1(X₀) → l1(B) :|: 1 ≤ 2⋅B ∧ X₀ ≤ 2⋅B+1 ∧ 2⋅B+1 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

6⋅X₀+3 {O(n)}

All Bounds

Timebounds

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

Costbounds

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