Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F
Locations: f0, f3, f6
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄) → f3(0, 0, X₂, X₃, X₄)
t₁: f3(X₀, X₁, X₂, X₃, X₄) → f3(X₀, X₁, X₂-1, F, X₄) :|: 1 ≤ F ∧ 1 ≤ X₂
t₂: f3(X₀, X₁, X₂, X₃, X₄) → f3(X₀, X₁, X₂-2, F, X₄) :|: 1 ≤ X₂ ∧ F ≤ 0
t₃: f3(X₀, X₁, X₂, X₃, X₄) → f6(X₀, X₁, X₂, X₃, F) :|: X₂ ≤ 0
t₄: f6(X₀, X₁, X₂, X₃, X₄) → f6(1, X₁, X₂, X₃, F) :|: 1 ≤ X₄
t₅: f6(X₀, X₁, X₂, X₃, X₄) → f6(0, X₁, X₂, X₃, F) :|: X₄ ≤ 0

Preprocessing

Eliminate variables [X₀; X₁; X₃] that do not contribute to the problem

Found invariant X₀ ≤ 0 for location f6

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars: F
Locations: f0, f3, f6
Transitions:
t₁₃: f0(X₀, X₁) → f3(X₀, X₁)
t₁₄: f3(X₀, X₁) → f3(X₀-1, X₁) :|: 1 ≤ F ∧ 1 ≤ X₀
t₁₅: f3(X₀, X₁) → f3(X₀-2, X₁) :|: 1 ≤ X₀ ∧ F ≤ 0
t₁₆: f3(X₀, X₁) → f6(X₀, F) :|: X₀ ≤ 0
t₁₇: f6(X₀, X₁) → f6(X₀, F) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
t₁₈: f6(X₀, X₁) → f6(X₀, F) :|: X₁ ≤ 0 ∧ X₀ ≤ 0

MPRF for transition t₁₄: f3(X₀, X₁) → f3(X₀-1, X₁) :|: 1 ≤ F ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

• f3: [X₀]

MPRF for transition t₁₅: f3(X₀, X₁) → f3(X₀-2, X₁) :|: 1 ≤ X₀ ∧ F ≤ 0 of depth 1:

new bound:

X₀ {O(n)}

• f3: [X₀]

Found invariant X₀ ≤ 0 for location f6_v1

Found invariant X₀ ≤ 0 for location f6

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₆, X₀: 3⋅X₀ {O(n)}
t₁₇, X₀: 3⋅X₀ {O(n)}
t₁₈, X₀: 3⋅X₀ {O(n)}