Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₂ ∧ X₀ ≤ X₁
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ < X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₃, X₁, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀+X₂, X₁, X₂, X₃)
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)

Preprocessing

Found invariant X₃ ≤ X₀ for location l5

Found invariant X₃ ≤ X₀ for location l1

Found invariant X₃ ≤ X₀ for location l4

Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₂ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₃ ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₃ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₃, X₁, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀+X₂, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₂ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₁+X₃+1 {O(n)}

MPRF:

l3 [X₁-X₀ ]
l1 [X₁+1-X₀ ]

MPRF for transition t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀+X₂, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₁+X₂+X₃ {O(n)}

MPRF:

l3 [X₁+1-X₀ ]
l1 [X₁+X₂-X₀ ]

All Bounds

Timebounds

Overall timebound:2⋅X₁+2⋅X₃+X₂+6 {O(n)}
t₀: 1 {O(1)}
t₂: X₁+X₃+1 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₅: X₁+X₂+X₃ {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₁+2⋅X₃+X₂+6 {O(n)}
t₀: 1 {O(1)}
t₂: X₁+X₃+1 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₅: X₁+X₂+X₃ {O(n)}
t₆: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₂, X₀: X₁⋅X₂+X₂⋅X₂+X₂⋅X₃+X₂+X₃ {O(n^2)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₃ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₁⋅X₂+X₂⋅X₂+X₂⋅X₃+2⋅X₃+X₂ {O(n^2)}
t₄, X₁: 2⋅X₁ {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₅, X₀: X₁⋅X₂+X₂⋅X₂+X₂⋅X₃+X₂+X₃ {O(n^2)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₁⋅X₂+X₂⋅X₂+X₂⋅X₃+3⋅X₃+X₂ {O(n^2)}
t₆, X₁: 3⋅X₁ {O(n)}
t₆, X₂: 3⋅X₂ {O(n)}
t₆, X₃: 3⋅X₃ {O(n)}