Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁) :|: X₀+X₁+1 ≤ 0 ∧ 1 ≤ X₀
t₁: l1(X₀, X₁) → l1(X₀-X₁, X₁) :|: 0 ≤ X₀
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀+1 ≤ 0

Preprocessing

Found invariant 1 ≤ 0 for location l2

Found invariant 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l1

Cut unsatisfiable transition t₂: l1→l2

Cut unreachable locations [l2] from the program graph

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁) → l1(X₀, X₁) :|: X₀+X₁+1 ≤ 0 ∧ 1 ≤ X₀
t₁: l1(X₀, X₁) → l1(X₀-X₁, X₁) :|: 0 ≤ X₀ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1 ≤ X₀

Solv. Size Bound: t₁: l1→l1 for X₀

cycle: [t₁: l1→l1]
loop: (0 ≤ X₀,(X₀,X₁) -> (X₀-X₁,X₁)
overappr. closed-form: X₁⋅n+X₀ {O(n^2)}
runtime bound: inf {Infinity}

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

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

Analysing control-flow refined program

Found invariant 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location l1

Found invariant 2+X₁ ≤ 0 ∧ 5+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location n_l1___1

Solv. Size Bound: t₃₂: n_l1___1→n_l1___1 for X₀

cycle: [t₃₂: n_l1___1→n_l1___1]
loop: (1 ≤ X₀+X₁,(X₀,X₁) -> (X₀-X₁,X₁)
overappr. closed-form: X₁⋅n+X₀ {O(n^2)}
runtime bound: inf {Infinity}

Solv. Size Bound - Lifting for t₃₂: n_l1___1→n_l1___1 and X₀: inf {Infinity}

Solv. Size Bound - Lifting for t₃₂: n_l1___1→n_l1___1 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: 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)}
t₁, X₁: X₁ {O(n)}