Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₁, X₁, X₂, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃
t₈: l7(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₃ < X₀
t₉: l8(X₀, X₁, X₂, X₃) → l7(X₀+X₂, X₁, X₂, X₃)
t₁₀: l9(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃)

Preprocessing

Found invariant X₀ ≤ X₃ for location l8

Found invariant 1+X₃ ≤ X₀ for location l10

Found invariant 1+X₃ ≤ X₀ for location l9

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₁, X₁, X₂, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃
t₈: l7(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₃ < X₀
t₉: l8(X₀, X₁, X₂, X₃) → l7(X₀+X₂, X₁, X₂, X₃) :|: X₀ ≤ X₃
t₁₀: l9(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₀

Solv. Size Bound: t₇: l7→l8 for X₀

cycle: [t₇: l7→l8; t₉: l8→l7]
loop: (X₀ ≤ X₃,(X₀,X₂) -> (X₀+X₂,X₂)
overappr. closed-form: X₂⋅n+X₀ {O(n^2)}
runtime bound: inf {Infinity}

Solv. Size Bound - Lifting for t₇: l7→l8 and X₀: inf {Infinity}

Solv. Size Bound: t₉: l8→l7 for X₀

cycle: [t₉: l8→l7; t₇: l7→l8]
loop: (X₀+X₂ ≤ X₃,(X₀,X₂) -> (X₀+X₂,X₂)
overappr. closed-form: X₂⋅n+X₀ {O(n^2)}
runtime bound: inf {Infinity}

Solv. Size Bound - Lifting for t₉: l8→l7 and X₀: inf {Infinity}

Solv. Size Bound - Lifting for t₇: l7→l8 and X₀: inf {Infinity}

Solv. Size Bound - Lifting for t₉: l8→l7 and X₀: inf {Infinity}

Chain transitions t₉: l8→l7 and t₈: l7→l9 to t₇₅: l8→l9

Chain transitions t₆: l6→l7 and t₈: l7→l9 to t₇₆: l6→l9

Chain transitions t₆: l6→l7 and t₇: l7→l8 to t₇₇: l6→l8

Chain transitions t₉: l8→l7 and t₇: l7→l8 to t₇₈: l8→l8

Analysing control-flow refined program

Found invariant X₁ ≤ X₃ for location l8

Found invariant 1+X₃ ≤ X₀ for location l10

Solv. Size Bound: t₇₈: l8→l8 for X₀

cycle: [t₇₈: l8→l8]
loop: (X₀+X₂ ≤ X₃,(X₀,X₂) -> (X₀+X₂,X₂)
overappr. closed-form: X₂⋅n+X₀ {O(n^2)}
runtime bound: inf {Infinity}

Solv. Size Bound - Lifting for t₇₈: l8→l8 and X₀: inf {Infinity}

Solv. Size Bound - Lifting for t₇₈: l8→l8 and X₀: inf {Infinity}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₃ for location n_l8___1

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l8___3

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l7

Found invariant X₁ ≤ X₃ for location n_l7___2

Found invariant 1+X₃ ≤ X₀ ∧ X₁ ≤ X₀ for location l10

Found invariant 1+X₃ ≤ X₀ ∧ X₁ ≤ X₀ for location l9

Solv. Size Bound: t₁₄₁: n_l7___2→n_l8___1 for X₀

cycle: [t₁₄₁: n_l7___2→n_l8___1; t₁₄₃: n_l8___1→n_l7___2]
loop: (X₀ ≤ X₂+X₃ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₂+X₃,(X₀,X₂) -> (X₀+X₂,X₂)
overappr. closed-form: X₂⋅n+X₀ {O(n^2)}
runtime bound: inf {Infinity}

Solv. Size Bound - Lifting for t₁₄₁: n_l7___2→n_l8___1 and X₀: inf {Infinity}

Solv. Size Bound: t₁₄₃: n_l8___1→n_l7___2 for X₀

cycle: [t₁₄₃: n_l8___1→n_l7___2; t₁₄₁: n_l7___2→n_l8___1]
loop: (X₀ ≤ X₂+X₃ ∧ X₀ ≤ X₃ ∧ X₀+X₂ ≤ X₃,(X₀,X₂) -> (X₀+X₂,X₂)
overappr. closed-form: X₂⋅n+X₀ {O(n^2)}
runtime bound: inf {Infinity}

Solv. Size Bound - Lifting for t₁₄₃: n_l8___1→n_l7___2 and X₀: inf {Infinity}

Solv. Size Bound - Lifting for t₁₄₁: n_l7___2→n_l8___1 and X₀: inf {Infinity}

Solv. Size Bound - Lifting for t₁₄₃: n_l8___1→n_l7___2 and X₀: inf {Infinity}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: inf {Infinity}
t₈: 1 {O(1)}
t₉: inf {Infinity}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: inf {Infinity}
t₈: 1 {O(1)}
t₉: inf {Infinity}
t₁₀: 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: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₁ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: 2⋅X₂ {O(n)}
t₈, X₃: 2⋅X₃ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}
t₁₀, X₁: 2⋅X₁ {O(n)}
t₁₀, X₂: 2⋅X₂ {O(n)}
t₁₀, X₃: 2⋅X₃ {O(n)}