Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: f0, f15, f19, f6
Transitions:
t₀: f0(X₀, X₁, X₂, X₃) → f6(0, 0, X₂, X₃)
t₃: f15(X₀, X₁, X₂, X₃) → f19(1+X₂, X₁, X₂, 1) :|: X₀ ≤ 1+X₂ ∧ 1+X₂ ≤ X₀
t₄: f15(X₀, X₁, X₂, X₃) → f19(X₀, X₁, X₂, 0) :|: X₀ ≤ X₂
t₅: f15(X₀, X₁, X₂, X₃) → f19(X₀, X₁, X₂, 0) :|: 2+X₂ ≤ X₀
t₆: f6(X₀, X₁, X₂, X₃) → f15(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ X₁
t₇: f6(X₀, X₁, X₂, X₃) → f15(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ X₁
t₈: f6(X₀, X₁, X₂, X₃) → f19(X₀, X₁, X₀, 1) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁
t₁: f6(X₀, X₁, X₂, X₃) → f6(X₀, 1+X₁, X₂, X₃) :|: 1+X₁ ≤ X₂
t₂: f6(X₀, X₁, X₂, X₃) → f6(2+X₀, 1+X₁, X₂, X₃) :|: 1+X₁ ≤ X₂

Preprocessing

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

Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location f15

Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location f19

Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location f6

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: f0, f15, f19, f6
Transitions:
t₁₉: f0(X₀, X₁, X₂) → f6(0, 0, X₂)
t₂₀: f15(X₀, X₁, X₂) → f19(1+X₂, X₁, X₂) :|: X₀ ≤ 1+X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁
t₂₁: f15(X₀, X₁, X₂) → f19(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁
t₂₂: f15(X₀, X₁, X₂) → f19(X₀, X₁, X₂) :|: 2+X₂ ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₁
t₂₃: f6(X₀, X₁, X₂) → f15(X₀, X₁, X₂) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₄: f6(X₀, X₁, X₂) → f15(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₅: f6(X₀, X₁, X₂) → f19(X₀, X₁, X₀) :|: X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₆: f6(X₀, X₁, X₂) → f6(X₀, 1+X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₇: f6(X₀, X₁, X₂) → f6(2+X₀, 1+X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁

MPRF for transition t₂₆: f6(X₀, X₁, X₂) → f6(X₀, 1+X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂ {O(n)}

• f6: [X₂-X₁]

MPRF for transition t₂₇: f6(X₀, X₁, X₂) → f6(2+X₀, 1+X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂ {O(n)}

• f6: [X₂-X₁]

All Bounds

Timebounds

Overall timebound:2⋅X₂+7 {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: X₂ {O(n)}
t₂₇: X₂ {O(n)}

Costbounds

Overall costbound: 2⋅X₂+7 {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: X₂ {O(n)}
t₂₇: X₂ {O(n)}

Sizebounds

t₁₉, X₀: 0 {O(1)}
t₁₉, X₁: 0 {O(1)}
t₁₉, X₂: X₂ {O(n)}
t₂₀, X₀: 4⋅X₂ {O(n)}
t₂₀, X₁: 4⋅X₂ {O(n)}
t₂₀, X₂: 3⋅X₂ {O(n)}
t₂₁, X₀: 4⋅X₂ {O(n)}
t₂₁, X₁: 4⋅X₂ {O(n)}
t₂₁, X₂: 2⋅X₂ {O(n)}
t₂₂, X₀: 4⋅X₂ {O(n)}
t₂₂, X₁: 4⋅X₂ {O(n)}
t₂₂, X₂: 3⋅X₂ {O(n)}
t₂₃, X₀: 4⋅X₂ {O(n)}
t₂₃, X₁: 4⋅X₂ {O(n)}
t₂₃, X₂: 2⋅X₂ {O(n)}
t₂₄, X₀: 4⋅X₂ {O(n)}
t₂₄, X₁: 4⋅X₂ {O(n)}
t₂₄, X₂: 3⋅X₂ {O(n)}
t₂₅, X₀: 4⋅X₂ {O(n)}
t₂₅, X₁: 4⋅X₂ {O(n)}
t₂₅, X₂: 4⋅X₂ {O(n)}
t₂₆, X₀: 2⋅X₂ {O(n)}
t₂₆, X₁: 2⋅X₂ {O(n)}
t₂₆, X₂: X₂ {O(n)}
t₂₇, X₀: 2⋅X₂ {O(n)}
t₂₇, X₁: 2⋅X₂ {O(n)}
t₂₇, X₂: X₂ {O(n)}