Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(1, X₂, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀, E, X₂, E) :|: X₀+2 ≤ X₁ ∧ X₂+1 ≤ (E)²
t₂: l1(X₀, X₁, X₂, X₃) → l1(E, X₁, X₂, E) :|: X₀+2 ≤ X₁ ∧ (E)² ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀+1

Preprocessing

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

Found invariant X₁ ≤ 1+X₀ for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: E
Locations: l0, l1, l2
Transitions:
t₉: l0(X₀, X₁, X₂) → l1(1, X₂, X₂)
t₁₀: l1(X₀, X₁, X₂) → l1(X₀, E, X₂) :|: X₀+2 ≤ X₁ ∧ X₂+1 ≤ (E)²
t₁₁: l1(X₀, X₁, X₂) → l1(E, X₁, X₂) :|: X₀+2 ≤ X₁ ∧ (E)² ≤ X₂
t₁₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁ ≤ X₀+1

Analysing control-flow refined program

Found invariant X₁ ≤ 1+X₀ for location l2

Found invariant X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location l1

Found invariant 3 ≤ X₂ 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: 1 {O(1)}

Costbounds

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

Sizebounds

t₉, X₀: 1 {O(1)}
t₉, X₁: X₂ {O(n)}
t₉, X₂: X₂ {O(n)}
t₁₀, X₂: 2⋅X₂ {O(n)}
t₁₁, X₂: 2⋅X₂ {O(n)}
t₁₂, X₂: 5⋅X₂ {O(n)}