Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: f0, f1
Transitions:
t₀: f0(X₀, X₁, X₂) → f1(X₀, X₁, X₂)
t₁: f1(X₀, X₁, X₂) → f1(X₀+X₁, X₁-1, X₂) :|: 1 ≤ X₀
t₂: f1(X₀, X₁, X₂) → f1(X₀+X₂, X₁, X₂-1) :|: 1 ≤ X₀

Preprocessing

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: f0, f1
Transitions:
t₀: f0(X₀, X₁, X₂) → f1(X₀, X₁, X₂)
t₁: f1(X₀, X₁, X₂) → f1(X₀+X₁, X₁-1, X₂) :|: 1 ≤ X₀
t₂: f1(X₀, X₁, X₂) → f1(X₀+X₂, X₁, X₂-1) :|: 1 ≤ X₀

Found invariant 2+X₂ ≤ X₀ for location f1_v1

Found invariant 2+X₁ ≤ X₀ for location f1_v2

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}