Initial Problem

Start: f300
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇
Temp_Vars: S, T, U, V, W, X, Y
Locations: f1, f2, f3, f300
Transitions:
t₁: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, 256, S, T, U, V, W, Y, X₁₄, X₁₅, X₁₆, X₁₇) :|: X₇ ≤ 256 ∧ 1 ≤ X ∧ 1+X₅ ≤ X₆ ∧ 256 ≤ X₇
t₂: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, S, T, U, V, W, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) :|: 1+X₅ ≤ X₆ ∧ X₇ ≤ 0
t₄: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, S, T, U, V, W, Y, X₇, X₇, X₇, X) :|: 1+X₅ ≤ X₆ ∧ 1 ≤ X₇ ∧ 257 ≤ X₇
t₅: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, S, T, U, V, W, Y, X₇, X₇, X₇, X) :|: X₇ ≤ 255 ∧ 1+X₅ ≤ X₆ ∧ 1 ≤ X₇
t₃: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, S, T, X₁₀, X₁₁, X₁₂, X₁₃, 0, 0, 0, X₁₇) :|: X₆ ≤ X₅
t₀: f300(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇) → f1(S, T, U, V, W, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇)

Preprocessing

Eliminate variables [S; T; U; V; W; Y; X₀; X₁; X₂; X₃; X₄; X₈; X₉; X₁₀; X₁₁; X₁₂; X₁₃; X₁₄; X₁₅; X₁₆; X₁₇] that do not contribute to the problem

Found invariant X₁ ≤ X₀ for location f3

Found invariant 1 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location f2

Problem after Preprocessing

Start: f300
Program_Vars: X₀, X₁, X₂
Temp_Vars: X
Locations: f1, f2, f3, f300
Transitions:
t₁₁: f1(X₀, X₁, X₂) → f1(X₀, X₁, 256) :|: X₂ ≤ 256 ∧ 1 ≤ X ∧ 1+X₀ ≤ X₁ ∧ 256 ≤ X₂
t₁₂: f1(X₀, X₁, X₂) → f1(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ X₂ ≤ 0
t₁₃: f1(X₀, X₁, X₂) → f2(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 257 ≤ X₂
t₁₄: f1(X₀, X₁, X₂) → f2(X₀, X₁, X₂) :|: X₂ ≤ 255 ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₂
t₁₅: f1(X₀, X₁, X₂) → f3(X₀, X₁, X₂) :|: X₁ ≤ X₀
t₁₆: f300(X₀, X₁, X₂) → f1(X₀, X₁, X₂)

Found invariant X₂ ≤ 256 ∧ 256 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location f1_v2

Found invariant X₂ ≤ 0 ∧ 1+X₀ ≤ X₁ for location f1_v1

Found invariant X₁ ≤ X₀ for location f3

Found invariant 1 ≤ X₂ ∧ 1+X₀ ≤ X₁ for location f2

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₁: inf {Infinity}
t₁₂: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₁: inf {Infinity}
t₁₂: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}

Sizebounds

t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: 256 {O(1)}
t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: 255 {O(1)}
t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₆, X₀: X₀ {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₆, X₂: X₂ {O(n)}