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) → l3(X₀, X₁, X₂, X₃)
t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ < 0
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₃, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ < X₂
t₃: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ < X₁
t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀+X₁-X₂-1, X₁, X₂, X₃)

Preprocessing

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

Found invariant X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀ for location l4

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) → l3(X₀, X₁, X₂, X₃)
t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₇: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₃, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ X₂ ≤ X₁
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ < X₂
t₃: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ < X₁
t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀+X₁-X₂-1, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀

MPRF for transition t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF for transition t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀+X₁-X₂-1, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃+1 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₃+8 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: X₃+1 {O(n)}
t₅: 1 {O(1)}
t₆: X₃+1 {O(n)}
t₇: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₃+8 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: X₃+1 {O(n)}
t₅: 1 {O(1)}
t₆: X₃+1 {O(n)}
t₇: 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: X₃ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₃+1 {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: 2⋅X₃+1 {O(n)}
t₅, X₁: 2⋅X₁ {O(n)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}
t₆, X₀: X₃+1 {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: 2⋅X₀+2⋅X₃+1 {O(n)}
t₇, X₁: 4⋅X₁ {O(n)}
t₇, X₂: 4⋅X₂ {O(n)}
t₇, X₃: 4⋅X₃ {O(n)}