Initial Problem

Start: f1
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F, G, H
Locations: f0, f1, f2
Transitions:
t₁: f0(X₀, X₁, X₂, X₃, X₄) → f0(1+3⋅X₀, X₁, F, H, G) :|: 1 ≤ F ∧ 1+2⋅G ≤ F ∧ 1+2⋅G ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ F ∧ F ≤ X₀
t₂: f0(X₀, X₁, X₂, X₃, X₄) → f0(1+3⋅X₀, X₁, F, H, G) :|: 1 ≤ F ∧ 1+F ≤ 2⋅G ∧ 1+2⋅G ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ F ∧ F ≤ X₀
t₃: f0(X₀, X₁, X₂, X₃, X₄) → f0(1+3⋅X₀, X₁, F, H, G) :|: 1 ≤ F ∧ 1+2⋅G ≤ F ∧ 1+X₀ ≤ 2⋅G ∧ 1 ≤ X₀ ∧ X₀ ≤ F ∧ F ≤ X₀
t₄: f0(X₀, X₁, X₂, X₃, X₄) → f0(1+3⋅X₀, X₁, F, H, G) :|: 1 ≤ F ∧ 1+F ≤ 2⋅G ∧ 1+X₀ ≤ 2⋅G ∧ 1 ≤ X₀ ∧ X₀ ≤ F ∧ F ≤ X₀
t₅: f0(X₀, X₁, X₂, X₃, X₄) → f0(F, X₁, X₂, H, F) :|: 1 ≤ 2⋅F ∧ 1 ≤ G ∧ X₀ ≤ 2⋅F ∧ 2⋅F ≤ X₀
t₀: f0(X₀, X₁, X₂, X₃, X₄) → f2(X₀, F, X₂, X₃, X₄) :|: X₀ ≤ 0
t₆: f1(X₀, X₁, X₂, X₃, X₄) → f0(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Cut unsatisfiable transition [t₂: f0→f0; t₃: f0→f0]

Eliminate variables [H; X₁; X₂; X₃; X₄] that do not contribute to the problem

Found invariant X₀ ≤ 0 for location f2

Problem after Preprocessing

Start: f1
Program_Vars: X₀
Temp_Vars: F, G
Locations: f0, f1, f2
Transitions:
t₂₃: f0(X₀) → f0(1+3⋅X₀) :|: 1 ≤ F ∧ 1+2⋅G ≤ F ∧ 1+2⋅G ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ F ∧ F ≤ X₀
t₂₄: f0(X₀) → f0(1+3⋅X₀) :|: 1 ≤ F ∧ 1+F ≤ 2⋅G ∧ 1+X₀ ≤ 2⋅G ∧ 1 ≤ X₀ ∧ X₀ ≤ F ∧ F ≤ X₀
t₂₅: f0(X₀) → f0(F) :|: 1 ≤ 2⋅F ∧ 1 ≤ G ∧ X₀ ≤ 2⋅F ∧ 2⋅F ≤ X₀
t₂₆: f0(X₀) → f2(X₀) :|: X₀ ≤ 0
t₂₇: f1(X₀) → f0(X₀)

Found invariant 4 ≤ X₀ for location f0_v2

Found invariant 2 ≤ X₀ for location f0_v3

Found invariant 1 ≤ X₀ for location f0_v1

Found invariant X₀ ≤ 0 for location f2

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: inf {Infinity}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: inf {Infinity}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}

Sizebounds

t₂₆, X₀: X₀ {O(n)}
t₂₇, X₀: X₀ {O(n)}