Initial Problem

Start: f1
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: f1, f2, f300
Transitions:
t₁: f1(X₀, X₁, X₂, X₃) → f2(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₂
t₂: f1(X₀, X₁, X₂, X₃) → f300(X₀, X₁, X₂, E) :|: 1+X₀ ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₂
t₃: f1(X₀, X₁, X₂, X₃) → f300(X₀, X₁, X₂, E) :|: 1+X₂ ≤ X₁ ∧ X₀ ≤ X₁
t₄: f1(X₀, X₁, X₂, X₃) → f300(X₀, X₁, X₂, E) :|: 1+X₁ ≤ X₀
t₀: f2(X₀, X₁, X₂, X₃) → f2(1+X₀, 1+X₁, X₂-1, X₃)

Preprocessing

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

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location f2

Problem after Preprocessing

Start: f1
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: f1, f2, f300
Transitions:
t₇: f1(X₀, X₁, X₂) → f2(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₂
t₈: f1(X₀, X₁, X₂) → f300(X₀, X₁, X₂) :|: 1+X₀ ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₂
t₉: f1(X₀, X₁, X₂) → f300(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ X₀ ≤ X₁
t₁₀: f1(X₀, X₁, X₂) → f300(X₀, X₁, X₂) :|: 1+X₁ ≤ X₀
t₁₁: f2(X₀, X₁, X₂) → f2(1+X₀, 1+X₁, X₂-1) :|: X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location f2

Found invariant 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location f2_v1

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: inf {Infinity}

Sizebounds

t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₂ {O(n)}