Initial Problem

Start: f3
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: f1, f2, f3, f300
Transitions:
t₀: f2(X₀, X₁, X₂) → f2(X₀, X₁-1, X₂) :|: X₀ ≤ 29
t₁: f2(X₀, X₁, X₂) → f300(X₀, X₁-1, X₂) :|: 30 ≤ X₀
t₄: f3(X₀, X₁, X₂) → f300(X₀, X₁, X₂)
t₃: f300(X₀, X₁, X₂) → f1(X₀, X₁, D) :|: 20 ≤ X₁
t₂: f300(X₀, X₁, X₂) → f2(X₀, X₁, X₂) :|: X₁ ≤ 19

Preprocessing

Eliminate variables [D; X₂] that do not contribute to the problem

Found invariant 20 ≤ X₁ for location f1

Found invariant X₁ ≤ 19 for location f2

Problem after Preprocessing

Start: f3
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f1, f2, f3, f300
Transitions:
t₉: f2(X₀, X₁) → f2(X₀, X₁-1) :|: X₀ ≤ 29 ∧ X₁ ≤ 19
t₁₀: f2(X₀, X₁) → f300(X₀, X₁-1) :|: 30 ≤ X₀ ∧ X₁ ≤ 19
t₁₁: f3(X₀, X₁) → f300(X₀, X₁)
t₁₂: f300(X₀, X₁) → f1(X₀, X₁) :|: 20 ≤ X₁
t₁₃: f300(X₀, X₁) → f2(X₀, X₁) :|: X₁ ≤ 19

Found invariant X₁ ≤ 18 ∧ 12+X₁ ≤ X₀ ∧ 30 ≤ X₀ for location f300_v1

Found invariant 20 ≤ X₁ for location f1

Found invariant X₁ ≤ 18 ∧ 12+X₁ ≤ X₀ ∧ 30 ≤ X₀ for location f2_v3

Found invariant X₁ ≤ 19 for location f2_v1

Found invariant X₁ ≤ 18 ∧ X₀+X₁ ≤ 47 ∧ X₀ ≤ 29 for location f2_v2

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₉: inf {Infinity}
t₁₀: inf {Infinity}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₉: inf {Infinity}
t₁₀: inf {Infinity}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: inf {Infinity}

Sizebounds

t₉, X₀: X₀ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₃, X₀: X₀ {O(n)}