Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, 0, 0) :|: 1 ≤ X₁
t₃: l2(X₀, X₁, X₂, X₃) → l1(X₀+X₃, X₁-1, X₂, X₃) :|: X₁ ≤ X₂
t₂: l2(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂+1, X₃+X₂) :|: X₂+1 ≤ X₁

Preprocessing

Eliminate variables {X₀,X₃} that do not contribute to the problem

Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₉: l0(X₁, X₂) → l1(X₁, X₂)
t₁₀: l1(X₁, X₂) → l2(X₁, 0) :|: 1 ≤ X₁
t₁₂: l2(X₁, X₂) → l1(X₁-1, X₂) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₁: l2(X₁, X₂) → l2(X₁, X₂+1) :|: X₂+1 ≤ X₁ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁

Analysing control-flow refined program

Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location n_l2___2

Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location n_l2___3

Found invariant X₂ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ for location n_l1___1

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₉: 1 {O(1)}
t₁₀: inf {Infinity}
t₁₁: inf {Infinity}
t₁₂: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₉: 1 {O(1)}
t₁₀: inf {Infinity}
t₁₁: inf {Infinity}
t₁₂: inf {Infinity}

Sizebounds

t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: 0 {O(1)}
t₁₁, X₁: X₁ {O(n)}
t₁₂, X₁: X₁ {O(n)}