Initial Problem

Start: f1
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f1, f2, f3
Transitions:
t₀: f1(X₀, X₁) → f2(X₀, X₁) :|: 1 ≤ X₀ ∧ 1+X₀+X₁ ≤ 0
t₁: f2(X₀, X₁) → f2(X₀-X₁, X₁) :|: 0 ≤ X₀
t₂: f2(X₀, X₁) → f3(X₀, X₁) :|: 1+X₀ ≤ 0

Preprocessing

Found invariant 1 ≤ 0 for location f3

Found invariant 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location f2

Cut unsatisfiable transition [t₂: f2→f3]

Cut unreachable locations [f3] from the program graph

Problem after Preprocessing

Start: f1
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f1, f2
Transitions:
t₀: f1(X₀, X₁) → f2(X₀, X₁) :|: 1 ≤ X₀ ∧ 1+X₀+X₁ ≤ 0
t₁: f2(X₀, X₁) → f2(X₀-X₁, X₁) :|: 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀

Found invariant 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location f2

Found invariant 2+X₁ ≤ 0 ∧ 5+X₁ ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location f2_v1

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}