Initial Problem

Start: f3
Program_Vars: X₀, X₁, X₂
Temp_Vars: D, E
Locations: f2, f3, f300
Transitions:
t₁: f2(X₀, X₁, X₂) → f2(E-1, X₁, X₂) :|: 1+X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ D ≤ 0
t₂: f2(X₀, X₁, X₂) → f2(E-1, X₁, X₂) :|: 1+X₀ ≤ 0 ∧ D ≤ 0 ∧ X₁ ≤ 0
t₃: f2(X₀, X₁, X₂) → f2(1+E, X₁, X₂) :|: 1+X₀ ≤ 0 ∧ 2 ≤ D
t₄: f2(X₀, X₁, X₂) → f2(E-1, X₁, X₂) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2+D ≤ 0
t₅: f2(X₀, X₁, X₂) → f2(E-1, X₁, X₂) :|: 1 ≤ X₀ ∧ 2+D ≤ 0 ∧ X₁ ≤ 0
t₆: f2(X₀, X₁, X₂) → f2(1+E, X₁, X₂) :|: 1 ≤ X₀ ∧ 0 ≤ D
t₇: f2(X₀, X₁, X₂) → f300(0, X₁, E) :|: 1+X₀ ≤ 0
t₈: f2(X₀, X₁, X₂) → f300(0, X₁, E) :|: 1 ≤ X₀
t₉: f2(X₀, X₁, X₂) → f300(X₀, X₁, E) :|: 0 ≤ X₀ ∧ X₀ ≤ 0
t₀: f3(X₀, X₁, X₂) → f2(X₀, X₁, X₂)

Preprocessing

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

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location f300

Problem after Preprocessing

Start: f3
Program_Vars: X₀, X₁
Temp_Vars: D, E
Locations: f2, f3, f300
Transitions:
t₁₉: f2(X₀, X₁) → f2(E-1, X₁) :|: 1+X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ D ≤ 0
t₂₀: f2(X₀, X₁) → f2(E-1, X₁) :|: 1+X₀ ≤ 0 ∧ D ≤ 0 ∧ X₁ ≤ 0
t₂₁: f2(X₀, X₁) → f2(1+E, X₁) :|: 1+X₀ ≤ 0 ∧ 2 ≤ D
t₂₂: f2(X₀, X₁) → f2(E-1, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2+D ≤ 0
t₂₃: f2(X₀, X₁) → f2(E-1, X₁) :|: 1 ≤ X₀ ∧ 2+D ≤ 0 ∧ X₁ ≤ 0
t₂₄: f2(X₀, X₁) → f2(1+E, X₁) :|: 1 ≤ X₀ ∧ 0 ≤ D
t₂₅: f2(X₀, X₁) → f300(0, X₁) :|: 1+X₀ ≤ 0
t₂₆: f2(X₀, X₁) → f300(0, X₁) :|: 1 ≤ X₀
t₂₇: f2(X₀, X₁) → f300(X₀, X₁) :|: 0 ≤ X₀ ∧ X₀ ≤ 0
t₂₈: f3(X₀, X₁) → f2(X₀, X₁)

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location f300

Found invariant X₁ ≤ 0 for location f2_v1

Found invariant 1 ≤ X₁ for location f2_v2

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₉: inf {Infinity}
t₂₀: inf {Infinity}
t₂₁: inf {Infinity}
t₂₂: inf {Infinity}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₉: inf {Infinity}
t₂₀: inf {Infinity}
t₂₁: inf {Infinity}
t₂₂: inf {Infinity}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}

Sizebounds

t₁₉, X₁: X₁ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₃, X₁: X₁ {O(n)}
t₂₄, X₁: X₁ {O(n)}
t₂₅, X₀: 0 {O(1)}
t₂₅, X₁: 7⋅X₁ {O(n)}
t₂₆, X₀: 0 {O(1)}
t₂₆, X₁: 7⋅X₁ {O(n)}
t₂₇, X₀: 0 {O(1)}
t₂₇, X₁: 7⋅X₁ {O(n)}
t₂₈, X₀: X₀ {O(n)}
t₂₈, X₁: X₁ {O(n)}