Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀+X₁, X₁+X₂, X₂) :|: 1 ≤ X₀

Preprocessing

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀+X₁, X₁+X₂, X₂) :|: 1 ≤ X₀

Solv. Size Bound: t₁: l1→l1 for X₀

cycle: [t₁: l1→l1]
loop: (1 ≤ X₀,(X₀,X₁,X₂) -> (X₀+X₁,X₁+X₂,X₂)
overappr. closed-form: X₂⋅n⋅n+X₁⋅n+X₂⋅n+X₀ {O(n^3)}
runtime bound: inf {Infinity}

Solv. Size Bound - Lifting for t₁: l1→l1 and X₀: inf {Infinity}

Solv. Size Bound: t₁: l1→l1 for X₁

cycle: [t₁: l1→l1]
loop: (1 ≤ X₀,(X₁,X₂) -> (X₁+X₂,X₂)
overappr. closed-form: X₂⋅n+X₁ {O(n^2)}
runtime bound: inf {Infinity}

Solv. Size Bound - Lifting for t₁: l1→l1 and X₁: inf {Infinity}

Solv. Size Bound - Lifting for t₁: l1→l1 and X₀: inf {Infinity}

Solv. Size Bound - Lifting for t₁: l1→l1 and X₁: inf {Infinity}

Analysing control-flow refined program

Solv. Size Bound: t₂₈: n_l1___1→n_l1___1 for X₀

cycle: [t₂₈: n_l1___1→n_l1___1]
loop: (1+X₁ ≤ X₀+X₂ ∧ 1 ≤ X₀,(X₀,X₁,X₂) -> (X₀+X₁,X₁+X₂,X₂)
overappr. closed-form: X₂⋅n⋅n+X₁⋅n+X₂⋅n+X₀ {O(n^3)}
runtime bound: inf {Infinity}

Solv. Size Bound - Lifting for t₂₈: n_l1___1→n_l1___1 and X₀: inf {Infinity}

Solv. Size Bound: t₂₈: n_l1___1→n_l1___1 for X₁

cycle: [t₂₈: n_l1___1→n_l1___1]
loop: (1+X₁ ≤ X₀+X₂ ∧ 1 ≤ X₀,(X₁,X₂) -> (X₁+X₂,X₂)
overappr. closed-form: X₂⋅n+X₁ {O(n^2)}
runtime bound: inf {Infinity}

Solv. Size Bound - Lifting for t₂₈: n_l1___1→n_l1___1 and X₁: inf {Infinity}

Solv. Size Bound - Lifting for t₂₈: n_l1___1→n_l1___1 and X₀: inf {Infinity}

Solv. Size Bound - Lifting for t₂₈: n_l1___1→n_l1___1 and X₁: 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: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₂: X₂ {O(n)}