Initial Problem

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

Preprocessing

Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5

Found invariant X₀ ≤ X₁ for location l1

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

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3

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) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 0 < X₀ ∧ X₀ ≤ X₁
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ X₀ ≤ X₁
t₁: l2(X₀, X₁, X₂) → l1(X₁, X₁, X₂)
t₄: l3(X₀, X₁, X₂) → l1(X₀-X₂-1, X₁, X₂) :|: 0 < X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₅: l3(X₀, X₁, X₂) → l1(X₀+X₂-1, X₁, X₂) :|: X₂ ≤ 0 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₆: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₀ ≤ 0

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

new bound:

X₁ {O(n)}

MPRF:

l3 [X₀-1 ]
l1 [X₀ ]

MPRF for transition t₄: l3(X₀, X₁, X₂) → l1(X₀-X₂-1, X₁, X₂) :|: 0 < X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l3 [X₀ ]
l1 [X₀ ]

MPRF for transition t₅: l3(X₀, X₁, X₂) → l1(X₀+X₂-1, X₁, X₂) :|: X₂ ≤ 0 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l3 [X₀ ]
l1 [X₀ ]

All Bounds

Timebounds

Overall timebound:3⋅X₁+4 {O(n)}
t₀: 1 {O(1)}
t₂: X₁ {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₁ {O(n)}
t₅: X₁ {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 3⋅X₁+4 {O(n)}
t₀: 1 {O(1)}
t₂: X₁ {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₁ {O(n)}
t₅: X₁ {O(n)}
t₆: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₂, X₀: 2⋅X₂+X₁ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₃, X₀: 3⋅X₁+4⋅X₂ {O(n)}
t₃, X₁: 3⋅X₁ {O(n)}
t₃, X₂: 3⋅X₂ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₄, X₀: 2⋅X₂+X₁ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₅, X₀: 2⋅X₂+X₁ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₆, X₀: 3⋅X₁+4⋅X₂ {O(n)}
t₆, X₁: 3⋅X₁ {O(n)}
t₆, X₂: 3⋅X₂ {O(n)}