Initial Problem

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

Preprocessing

Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₁ for location l1

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location l4

Problem after Preprocessing

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

MPRF for transition t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ < X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁+X₂ {O(n)}

MPRF for transition t₅: l4(X₀, X₁, X₂) → l1(X₀+X₁, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ of depth 1:

new bound:

2⋅X₁+X₂+1 {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₂+3⋅X₁+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₁+X₂ {O(n)}
t₄: 1 {O(1)}
t₅: 2⋅X₁+X₂+1 {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₂+3⋅X₁+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₁+X₂ {O(n)}
t₄: 1 {O(1)}
t₅: 2⋅X₁+X₂+1 {O(n)}
t₆: 1 {O(1)}

Sizebounds

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