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) :|: X₁ < X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁+1, X₂, X₃)
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)

Preprocessing

Found invariant X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l5

Found invariant X₃ ≤ X₁ ∧ X₀ ≤ X₂ for location l1

Found invariant X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l4

Found invariant 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ 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) :|: X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁+1, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁

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

new bound:

X₂+X₃ {O(n)}

MPRF for transition t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁+1, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₂+X₃ {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₂+2⋅X₃+4 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂+X₃ {O(n)}
t₃: 1 {O(1)}
t₄: X₂+X₃ {O(n)}
t₅: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₂+2⋅X₃+4 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂+X₃ {O(n)}
t₃: 1 {O(1)}
t₄: X₂+X₃ {O(n)}
t₅: 1 {O(1)}

Sizebounds

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