Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: f0, f2, f3, f5
Transitions:
t₃: f0(X₀, X₁, X₂) → f2(0, X₁, X₂) :|: 1 ≤ X₂
t₄: f0(X₀, X₁, X₂) → f3(0, X₁, X₂) :|: X₂ ≤ 0
t₀: f2(X₀, X₁, X₂) → f2(1+X₀, X₁, X₂)
t₁: f3(X₀, X₁, X₂) → f3(X₀, X₁-1, X₂) :|: 1 ≤ X₁
t₅: f3(X₀, X₁, X₂) → f5(0, X₁, X₂) :|: X₁ ≤ 0
t₂: f5(X₀, X₁, X₂) → f5(X₀, X₁, 1)

Preprocessing

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

Found invariant X₁ ≤ 0 for location f3

Found invariant 1 ≤ X₁ for location f2

Found invariant X₁ ≤ 1 ∧ X₀+X₁ ≤ 1 ∧ X₀ ≤ 0 for location f5

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f2, f3, f5
Transitions:
t₁₃: f0(X₀, X₁) → f2(X₀, X₁) :|: 1 ≤ X₁
t₁₄: f0(X₀, X₁) → f3(X₀, X₁) :|: X₁ ≤ 0
t₁₅: f2(X₀, X₁) → f2(X₀, X₁) :|: 1 ≤ X₁
t₁₆: f3(X₀, X₁) → f3(X₀-1, X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 0
t₁₇: f3(X₀, X₁) → f5(X₀, X₁) :|: X₀ ≤ 0 ∧ X₁ ≤ 0
t₁₈: f5(X₀, X₁) → f5(X₀, 1) :|: X₀+X₁ ≤ 1 ∧ X₁ ≤ 1 ∧ X₀ ≤ 0

Found invariant X₁ ≤ 1 ∧ X₀+X₁ ≤ 1 ∧ X₀ ≤ 0 for location f5

Found invariant X₁ ≤ 0 for location f3

Found invariant 1 ≤ X₁ for location f2

Found invariant 1 ≤ X₁ for location f2_v1

MPRF for transition t₁₆: f3(X₀, X₁) → f3(X₀-1, X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 0 of depth 1:

new bound:

X₀ {O(n)}

• f3: [X₀]

Found invariant X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location f5

Found invariant X₁ ≤ 1 ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location f5_v1

Found invariant X₁ ≤ 0 for location f3

Found invariant 1 ≤ X₁ for location f2

All Bounds

Timebounds

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

Costbounds

Overall costbound: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₆: X₀ {O(n)}
t₁₇: 1 {O(1)}
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: X₀ {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₇, X₀: 2⋅X₀ {O(n)}
t₁₇, X₁: 2⋅X₁ {O(n)}
t₁₈, X₀: 2⋅X₀ {O(n)}
t₁₈, X₁: 1 {O(1)}