Initial Problem

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

Preprocessing

Found invariant X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location l5

Found invariant X₀ ≤ X₁ for location l1

Found invariant X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location l4

Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

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

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

new bound:

X₁+1 {O(n)}

MPRF:

l3 [X₀ ]
l1 [X₀+1 ]

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

new bound:

X₁+1 {O(n)}

MPRF:

l3 [X₀+1 ]
l1 [X₀+1 ]

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₂, X₀: X₁+1 {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: 2⋅X₁+1 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₄, X₀: X₁+1 {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: 2⋅X₁+1 {O(n)}
t₅, X₁: 2⋅X₁ {O(n)}