Analysing control-flow refined program

knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₇₄: evalEx1bb4in(X₀, X₁, X₂, X₃) → evalEx1bb5in(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₃

knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₇₅: evalEx1bb4in(X₀, X₁, X₂, X₃) → evalEx1bb1in_v1(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₃

knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₇₆: evalEx1bb1in_v1(X₀, X₁, X₂, X₃) → evalEx1bb4in_v1(X₀, X₁, 1+X₂, X₃) :|: X₂ ≤ 1+X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₁ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃

knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₇₇: evalEx1bb1in_v1(X₀, X₁, X₂, X₃) → evalEx1bb4in_v2(X₀, X₁, X₂, X₃-1) :|: 1 ≤ E ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₁ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃

knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₇₈: evalEx1bb1in_v1(X₀, X₁, X₂, X₃) → evalEx1bb4in_v2(X₀, X₁, X₂, X₃-1) :|: 1+E ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₁ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃

All Bounds

Timebounds

Overall timebound:2⋅X₀⋅X₀+8⋅X₀+6 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀ {O(n)}
t₃: 1 {O(1)}
t₄: X₀ {O(n)}
t₅: X₀⋅X₀+X₀ {O(n^2)}
t₆: X₀ {O(n)}
t₇: X₀+1 {O(n)}
t₉: X₀+1 {O(n)}
t₁₄: X₀⋅X₀+X₀ {O(n^2)}
t₁₅: X₀ {O(n)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀⋅X₀+8⋅X₀+6 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀ {O(n)}
t₃: 1 {O(1)}
t₄: X₀ {O(n)}
t₅: X₀⋅X₀+X₀ {O(n^2)}
t₆: X₀ {O(n)}
t₇: X₀+1 {O(n)}
t₉: X₀+1 {O(n)}
t₁₄: X₀⋅X₀+X₀ {O(n^2)}
t₁₅: X₀ {O(n)}
t₁₆: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: 0 {O(1)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₀ {O(n)}
t₂, X₂: 3⋅X₀⋅X₀+7⋅X₀+X₂+4 {O(n^2)}
t₂, X₃: 4⋅X₀+X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: 2⋅X₀ {O(n)}
t₃, X₂: 3⋅X₀⋅X₀+7⋅X₀+X₂+4 {O(n^2)}
t₃, X₃: 4⋅X₀+X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₀ {O(n)}
t₄, X₂: X₀+1 {O(n)}
t₄, X₃: X₀ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₀ {O(n)}
t₅, X₂: X₀⋅X₀+2⋅X₀+1 {O(n^2)}
t₅, X₃: X₀ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₀ {O(n)}
t₆, X₂: 3⋅X₀⋅X₀+7⋅X₀+4 {O(n^2)}
t₆, X₃: 4⋅X₀ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₀ {O(n)}
t₇, X₂: X₀⋅X₀+2⋅X₀+1 {O(n^2)}
t₇, X₃: X₀ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₀ {O(n)}
t₉, X₂: X₀⋅X₀+2⋅X₀+1 {O(n^2)}
t₉, X₃: X₀ {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₀ {O(n)}
t₁₄, X₂: X₀⋅X₀+2⋅X₀+1 {O(n^2)}
t₁₄, X₃: X₀ {O(n)}
t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: X₀ {O(n)}
t₁₅, X₂: 3⋅X₀⋅X₀+7⋅X₀+4 {O(n^2)}
t₁₅, X₃: 4⋅X₀ {O(n)}
t₁₆, X₀: X₀ {O(n)}
t₁₆, X₁: 2⋅X₀ {O(n)}
t₁₆, X₂: 3⋅X₀⋅X₀+7⋅X₀+X₂+4 {O(n^2)}
t₁₆, X₃: 4⋅X₀+X₃ {O(n)}