Initial Problem

Start: f300
Program_Vars: X₀, X₁, X₂
Temp_Vars: D, E
Locations: f1, f2, f300
Transitions:
t₂: f2(X₀, X₁, X₂) → f1(X₀-1, D, E) :|: X₀ ≤ 1 ∧ 1 ≤ D
t₃: f2(X₀, X₁, X₂) → f1(X₀-1, D, E) :|: X₀ ≤ 1 ∧ 1+D ≤ 0
t₅: f2(X₀, X₁, X₂) → f1(X₀, 0, D) :|: X₀ ≤ 0
t₀: f2(X₀, X₁, X₂) → f2(X₀-1, D, X₂) :|: 1 ≤ D ∧ 2 ≤ X₀
t₁: f2(X₀, X₁, X₂) → f2(X₀-1, D, X₂) :|: 1+D ≤ 0 ∧ 2 ≤ X₀
t₄: f2(X₀, X₁, X₂) → f2(X₀, 0, X₂) :|: 1 ≤ X₀
t₆: f300(X₀, X₁, X₂) → f2(X₀, X₁, X₂)

Preprocessing

Eliminate variables [E; X₁; X₂] that do not contribute to the problem

Found invariant X₀ ≤ 0 for location f1

Problem after Preprocessing

Start: f300
Program_Vars: X₀
Temp_Vars: D
Locations: f1, f2, f300
Transitions:
t₁₃: f2(X₀) → f1(X₀-1) :|: X₀ ≤ 1 ∧ 1 ≤ D
t₁₄: f2(X₀) → f1(X₀-1) :|: X₀ ≤ 1 ∧ 1+D ≤ 0
t₁₅: f2(X₀) → f1(X₀) :|: X₀ ≤ 0
t₁₆: f2(X₀) → f2(X₀-1) :|: 1 ≤ D ∧ 2 ≤ X₀
t₁₇: f2(X₀) → f2(X₀-1) :|: 1+D ≤ 0 ∧ 2 ≤ X₀
t₁₈: f2(X₀) → f2(X₀) :|: 1 ≤ X₀
t₁₉: f300(X₀) → f2(X₀)

MPRF for transition t₁₆: f2(X₀) → f2(X₀-1) :|: 1 ≤ D ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

• f2: [X₀]

MPRF for transition t₁₇: f2(X₀) → f2(X₀-1) :|: 1+D ≤ 0 ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

• f2: [X₀]

Found invariant X₀ ≤ 0 for location f1

Found invariant 1 ≤ X₀ for location f2_v1

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: X₀ {O(n)}
t₁₇: X₀ {O(n)}
t₁₈: inf {Infinity}
t₁₉: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: X₀ {O(n)}
t₁₇: X₀ {O(n)}
t₁₈: inf {Infinity}
t₁₉: 1 {O(1)}

Sizebounds

t₁₃, X₀: 4⋅X₀+4 {O(n)}
t₁₄, X₀: 4⋅X₀+4 {O(n)}
t₁₅, X₀: X₀ {O(n)}
t₁₆, X₀: X₀ {O(n)}
t₁₇, X₀: X₀ {O(n)}
t₁₈, X₀: X₀ {O(n)}
t₁₉, X₀: X₀ {O(n)}