Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: f0, f16, f6
Transitions:
t₀: f0(X₀, X₁, X₂, X₃) → f6(1, X₂, X₂, X₃)
t₃: f6(X₀, X₁, X₂, X₃) → f16(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1+X₀
t₁: f6(X₀, X₁, X₂, X₃) → f6(X₀, E, X₂, E) :|: 1+X₂ ≤ (E)² ∧ 2+X₀ ≤ X₁
t₂: f6(X₀, X₁, X₂, X₃) → f6(E, X₁, X₂, E) :|: 2+X₀ ≤ X₁ ∧ (E)² ≤ X₂

Preprocessing

Eliminate variables [X₃] that do not contribute to the problem

Found invariant X₁ ≤ 1+X₀ for location f16

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁, X₂
Temp_Vars: E
Locations: f0, f16, f6
Transitions:
t₈: f0(X₀, X₁, X₂) → f6(1, X₂, X₂)
t₉: f6(X₀, X₁, X₂) → f16(X₀, X₁, X₂) :|: X₁ ≤ 1+X₀
t₁₀: f6(X₀, X₁, X₂) → f6(X₀, E, X₂) :|: 1+X₂ ≤ (E)² ∧ 2+X₀ ≤ X₁
t₁₁: f6(X₀, X₁, X₂) → f6(E, X₁, X₂) :|: 2+X₀ ≤ X₁ ∧ (E)² ≤ X₂

Found invariant X₁ ≤ 1+X₀ for location f16

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: inf {Infinity}
t₁₁: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: inf {Infinity}
t₁₁: inf {Infinity}

Sizebounds

t₈, X₀: 1 {O(1)}
t₈, X₁: X₂ {O(n)}
t₈, X₂: X₂ {O(n)}
t₉, X₂: 3⋅X₂ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₁, X₂: X₂ {O(n)}