Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ < 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₆, 73, 74, X₃, X₄, X₅, X₆)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀-X₁, X₂+1, X₁+1, X₃, X₄, X₅, X₆)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

Preprocessing

Eliminate variables {X₃,X₄,X₅} that do not contribute to the problem

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 74 ≤ X₂ ∧ 147 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 75+X₀ ≤ X₂ ∧ 73 ≤ X₁ ∧ 74+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location l5

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 74 ≤ X₂ ∧ 147 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 73 ≤ X₁ for location l1

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 74 ≤ X₂ ∧ 147 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 75+X₀ ≤ X₂ ∧ 73 ≤ X₁ ∧ 74+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location l4

Found invariant 0 ≤ X₃ ∧ 74 ≤ X₂+X₃ ∧ 73 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 74 ≤ X₂ ∧ 147 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 74 ≤ X₀+X₂ ∧ 73 ≤ X₁ ∧ 73 ≤ X₀+X₁ ∧ 0 ≤ 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:
t₁₁: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₁₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 74 ≤ X₂ ∧ 147 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 73 ≤ X₁
t₁₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 74 ≤ X₂ ∧ 147 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 73 ≤ X₁
t₁₄: l2(X₀, X₁, X₂, X₃) → l1(X₃, 73, 74, X₃)
t₁₅: l3(X₀, X₁, X₂, X₃) → l1(X₀-X₁, X₂+1, X₁+1, X₃) :|: 0 ≤ X₃ ∧ 74 ≤ X₂+X₃ ∧ 73 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 74 ≤ X₂ ∧ 147 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 74 ≤ X₀+X₂ ∧ 73 ≤ X₁ ∧ 73 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 74 ≤ X₂ ∧ 147 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 75+X₀ ≤ X₂ ∧ 73 ≤ X₁ ∧ 74+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0

MPRF for transition t₁₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 74 ≤ X₂ ∧ 147 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 73 ≤ X₁ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF for transition t₁₅: l3(X₀, X₁, X₂, X₃) → l1(X₀-X₁, X₂+1, X₁+1, X₃) :|: 0 ≤ X₃ ∧ 74 ≤ X₂+X₃ ∧ 73 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ 74 ≤ X₂ ∧ 147 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 74 ≤ X₀+X₂ ∧ 73 ≤ X₁ ∧ 73 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

2⋅X₃+1 {O(n)}

All Bounds

Timebounds

Overall timebound:3⋅X₃+6 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₃+1 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 2⋅X₃+1 {O(n)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 3⋅X₃+6 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₃+1 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 2⋅X₃+1 {O(n)}
t₁₆: 1 {O(1)}

Sizebounds

t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₂, X₀: 5⋅X₃+75 {O(n)}
t₁₂, X₁: 4⋅X₃+75 {O(n)}
t₁₂, X₂: 4⋅X₃+150 {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₃, X₀: 6⋅X₃+75 {O(n)}
t₁₃, X₁: 4⋅X₃+148 {O(n)}
t₁₃, X₂: 4⋅X₃+150 {O(n)}
t₁₃, X₃: 2⋅X₃ {O(n)}
t₁₄, X₀: X₃ {O(n)}
t₁₄, X₁: 73 {O(1)}
t₁₄, X₂: 74 {O(1)}
t₁₄, X₃: X₃ {O(n)}
t₁₅, X₀: 5⋅X₃+75 {O(n)}
t₁₅, X₁: 4⋅X₃+75 {O(n)}
t₁₅, X₂: 4⋅X₃+76 {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₆, X₀: 6⋅X₃+75 {O(n)}
t₁₆, X₁: 4⋅X₃+148 {O(n)}
t₁₆, X₂: 4⋅X₃+150 {O(n)}
t₁₆, X₃: 2⋅X₃ {O(n)}