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(2⋅X₀, X₁+1) :|: 1 ≤ X₀ ∧ X₀ ≤ X₁+1

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(2⋅X₀, X₁+1) :|: 1 ≤ X₀ ∧ X₀ ≤ X₁+1

Analysing control-flow refined program

Found invariant 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___1

MPRF for transition t₁₅: n_l1___1(X₀, X₁) → n_l1___1(2⋅X₀, X₁+1) :|: 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₀ ≤ 2⋅X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₀+X₁+3 {O(n)}

MPRF:

n_l1___1 [X₁+2-X₀ ]

CFR: Improvement to new bound with the following program:

new bound:

2⋅X₀+X₁+3 {O(n)}

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(2⋅X₀, X₁+1) :|: 1 ≤ X₀ ∧ X₀ ≤ 1+X₁
t₁₅: n_l1___1(X₀, X₁) → n_l1___1(2⋅X₀, X₁+1) :|: 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₀ ≤ 2⋅X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀

All Bounds

Timebounds

Overall timebound:2⋅X₀+X₁+5 {O(n)}
t₀: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₅: 2⋅X₀+X₁+3 {O(n)}

Costbounds

Overall costbound: 2⋅X₀+X₁+5 {O(n)}
t₀: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₅: 2⋅X₀+X₁+3 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁₆, X₀: 2⋅X₀ {O(n)}
t₁₆, X₁: X₁+1 {O(n)}
t₁₅, X₀: 2⋅2^(2⋅X₀+X₁+3)⋅X₀ {O(EXP)}
t₁₅, X₁: 2⋅X₀+2⋅X₁+4 {O(n)}