Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, 100, 1, X₃, X₄, X₅)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-X₁, X₁-X₂, -X₂, X₃, X₄, X₅)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

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

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ 99+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 101 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ 1+X₂ ∧ 98 ≤ X₁+X₂ ∧ X₁ ≤ 100+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 100 ∧ X₀+X₁ ≤ 99 ∧ 99 ≤ X₁ ∧ 100+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location l5

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ 99+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 101 ∧ 0 ≤ 1+X₂ ∧ 98 ≤ X₁+X₂ ∧ X₁ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ 98 ≤ X₁ for location l1

Found invariant X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ 99+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 101 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ 1+X₂ ∧ 98 ≤ X₁+X₂ ∧ X₁ ≤ 100+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 100 ∧ X₀+X₁ ≤ 99 ∧ 99 ≤ X₁ ∧ 100+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location l4

Found invariant 0 ≤ X₃ ∧ 0 ≤ 1+X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 99 ≤ X₁+X₃ ∧ X₁ ≤ 100+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ 99+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 101 ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ 1+X₂ ∧ 98 ≤ X₁+X₂ ∧ X₁ ≤ 100+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ 99 ≤ X₁ ∧ 99 ≤ 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:
t₁₂: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₁₃: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ 99+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 101 ∧ 0 ≤ 1+X₂ ∧ 98 ≤ X₁+X₂ ∧ X₁ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ 98 ≤ X₁
t₁₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ 99+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 101 ∧ 0 ≤ 1+X₂ ∧ 98 ≤ X₁+X₂ ∧ X₁ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ 98 ≤ X₁
t₁₅: l2(X₀, X₁, X₂, X₃) → l1(X₃, 100, 1, X₃)
t₁₆: l3(X₀, X₁, X₂, X₃) → l1(X₀-X₁, X₁-X₂, -X₂, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ 1+X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 99 ≤ X₁+X₃ ∧ X₁ ≤ 100+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ 99+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 101 ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ 1+X₂ ∧ 98 ≤ X₁+X₂ ∧ X₁ ≤ 100+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ 99 ≤ X₁ ∧ 99 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₇: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ 99+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 101 ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ 1+X₂ ∧ 98 ≤ X₁+X₂ ∧ X₁ ≤ 100+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 100 ∧ X₀+X₁ ≤ 99 ∧ 99 ≤ X₁ ∧ 100+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0

MPRF for transition t₁₃: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ 99+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 101 ∧ 0 ≤ 1+X₂ ∧ 98 ≤ X₁+X₂ ∧ X₁ ≤ 100+X₂ ∧ X₁ ≤ 100 ∧ 98 ≤ X₁ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

l3 [X₀-98 ]
l1 [X₀+1 ]

MPRF for transition t₁₆: l3(X₀, X₁, X₂, X₃) → l1(X₀-X₁, X₁-X₂, -X₂, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ 1+X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 99 ≤ X₁+X₃ ∧ X₁ ≤ 100+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ 99+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 101 ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ 1+X₂ ∧ 98 ≤ X₁+X₂ ∧ X₁ ≤ 100+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ 99 ≤ X₁ ∧ 99 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

l3 [X₀+1 ]
l1 [X₀+1 ]

All Bounds

Timebounds

Overall timebound:2⋅X₃+6 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: X₃+1 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: X₃+1 {O(n)}
t₁₇: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₃+6 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: X₃+1 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: X₃+1 {O(n)}
t₁₇: 1 {O(1)}

Sizebounds

t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₃, X₀: X₃+100 {O(n)}
t₁₃, X₁: 100 {O(1)}
t₁₃, X₂: 1 {O(1)}
t₁₃, X₃: X₃ {O(n)}
t₁₄, X₀: 2⋅X₃+100 {O(n)}
t₁₄, X₁: 100 {O(1)}
t₁₄, X₂: 1 {O(1)}
t₁₄, X₃: 2⋅X₃ {O(n)}
t₁₅, X₀: X₃ {O(n)}
t₁₅, X₁: 100 {O(1)}
t₁₅, X₂: 1 {O(1)}
t₁₅, X₃: X₃ {O(n)}
t₁₆, X₀: X₃+100 {O(n)}
t₁₆, X₁: 100 {O(1)}
t₁₆, X₂: 1 {O(1)}
t₁₆, X₃: X₃ {O(n)}
t₁₇, X₀: 2⋅X₃+100 {O(n)}
t₁₇, X₁: 100 {O(1)}
t₁₇, X₂: 1 {O(1)}
t₁₇, X₃: 2⋅X₃ {O(n)}