Initial Problem

Start: f3
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: G
Locations: f0, f1, f3
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅) → f0(X₀-1, X₂, X₂-1, X₀, X₄, X₅) :|: 1 ≤ X₀
t₂: f0(X₀, X₁, X₂, X₃, X₄, X₅) → f0(5000, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₂ ∧ X₀ ≤ 0
t₁: f1(X₀, X₁, X₂, X₃, X₄, X₅) → f0(X₀-1, X₁, X₂-1, X₃, X₂, X₀) :|: 1 ≤ X₀ ∧ 1 ≤ X₂
t₃: f3(X₀, X₁, X₂, X₃, X₄, X₅) → f0(5000, X₁, G, X₃, X₄, X₅) :|: 1 ≤ G

Preprocessing

Cut unreachable locations [f1] from the program graph

Eliminate variables [X₁; X₃; X₄; X₅] that do not contribute to the problem

Found invariant 0 ≤ 4999+X₁ ∧ 0 ≤ 4999+X₀+X₁ ∧ X₀ ≤ 4999+X₁ ∧ X₀ ≤ 5000 ∧ 0 ≤ X₀ for location f0

Problem after Preprocessing

Start: f3
Program_Vars: X₀, X₁
Temp_Vars: G
Locations: f0, f3
Transitions:
t₈: f0(X₀, X₁) → f0(X₀-1, X₁-1) :|: 1 ≤ X₀ ∧ X₀ ≤ 5000 ∧ 0 ≤ 4999+X₀+X₁ ∧ X₀ ≤ 4999+X₁ ∧ 0 ≤ 4999+X₁ ∧ 0 ≤ X₀
t₉: f0(X₀, X₁) → f0(5000, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ X₀ ≤ 5000 ∧ 0 ≤ 4999+X₀+X₁ ∧ X₀ ≤ 4999+X₁ ∧ 0 ≤ 4999+X₁ ∧ 0 ≤ X₀
t₁₀: f3(X₀, X₁) → f0(5000, G) :|: 1 ≤ G

Cut unsatisfiable transition [t₂₁: f0→f0_v1]

Found invariant 0 ≤ 4999+X₁ ∧ 0 ≤ 4999+X₀+X₁ ∧ X₀ ≤ 4999+X₁ ∧ X₀ ≤ 4999 ∧ 0 ≤ X₀ for location f0_v2

Found invariant 1 ≤ X₁ ∧ 5001 ≤ X₀+X₁ ∧ X₀ ≤ 4999+X₁ ∧ X₀ ≤ 5000 ∧ 5000 ≤ X₀ for location f0

Found invariant 0 ≤ X₁ ∧ 4999 ≤ X₀+X₁ ∧ X₀ ≤ 4999+X₁ ∧ X₀ ≤ 4999 ∧ 4999 ≤ X₀ for location f0_v3

Found invariant 1 ≤ X₁ ∧ 5001 ≤ X₀+X₁ ∧ X₀ ≤ 4999+X₁ ∧ X₀ ≤ 5000 ∧ 5000 ≤ X₀ for location f0_v1

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

t₈, X₀: 10000 {O(1)}
t₉, X₀: 5000 {O(1)}
t₁₀, X₀: 5000 {O(1)}