Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁)
t₁: l1(X₀, X₁) → l1(X₀, X₁+1-2⋅X₀) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁)
t₁: l1(X₀, X₁) → l1(X₀, X₁+1-2⋅X₀) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁

Analysing control-flow refined program

Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₀ for location n_l1___1

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₅: n_l1___1(X₀, X₁) → n_l1___1(X₀, X₁+1-2⋅X₀) :|: X₁ ≤ X₀ ∧ 2 ≤ 3⋅X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₀

CFR: Improvement to new bound with the following program:

new bound:

1 {O(1)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, n_l1___1
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁)
t₁₆: l1(X₀, X₁) → n_l1___1(X₀, X₁+1-2⋅X₀) :|: 1 ≤ X₀+X₁ ∧ X₁ ≤ X₀
t₁₅: n_l1___1(X₀, X₁) → n_l1___1(X₀, X₁+1-2⋅X₀) :|: X₁ ≤ X₀ ∧ 2 ≤ 3⋅X₀+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₀

All Bounds

Timebounds

Overall timebound:3 {O(1)}
t₀: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₅: 1 {O(1)}

Costbounds

Overall costbound: 3 {O(1)}
t₀: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₅: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁₆, X₀: X₀ {O(n)}
t₁₆, X₁: 3⋅X₀ {O(n)}
t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: 3⋅X₀ {O(n)}