Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: E+1 ≤ 0
t₃: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 1 ≤ E
t₄: l1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₂
t₆: l2(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₁
t₇: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁+1, X₂, X₃)
t₁₀: l4(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁+1, X₂, X₃)
t₁₁: l5(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₈: l6(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₃
t₉: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀
t₁: l7(X₀, X₁, X₂, X₃) → l1(0, 0, X₂, X₃)

Preprocessing

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l2

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l6

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

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l8

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l1

Found invariant 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l4

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: E+1 ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 1 ≤ E ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₅: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₆: l2(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₇: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁+1, X₂, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₀: l4(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁+1, X₂, X₃) :|: 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₁: l5(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₈: l6(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₉: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁: l7(X₀, X₁, X₂, X₃) → l1(0, 0, X₂, X₃)

MPRF for transition t₅: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF for transition t₇: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁+1, X₂, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF for transition t₈: l6(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF for transition t₁₀: l4(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁+1, X₂, X₃) :|: 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

knowledge_propagation leads to new time bound X₂+X₃+1 {O(n)} for transition t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: E+1 ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀

knowledge_propagation leads to new time bound X₂+X₃+1 {O(n)} for transition t₃: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 1 ≤ E ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀

knowledge_propagation leads to new time bound 2⋅X₂+2⋅X₃+2 {O(n)} for transition t₆: l2(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀

All Bounds

Timebounds

Overall timebound:6⋅X₂+6⋅X₃+9 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂+X₃+1 {O(n)}
t₃: X₂+X₃+1 {O(n)}
t₄: 1 {O(1)}
t₅: X₂ {O(n)}
t₆: 2⋅X₂+2⋅X₃+2 {O(n)}
t₇: X₂ {O(n)}
t₈: X₃ {O(n)}
t₉: 1 {O(1)}
t₁₀: X₃ {O(n)}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: 6⋅X₂+6⋅X₃+9 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂+X₃+1 {O(n)}
t₃: X₂+X₃+1 {O(n)}
t₄: 1 {O(1)}
t₅: X₂ {O(n)}
t₆: 2⋅X₂+2⋅X₃+2 {O(n)}
t₇: X₂ {O(n)}
t₈: X₃ {O(n)}
t₉: 1 {O(1)}
t₁₀: X₃ {O(n)}
t₁₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: 0 {O(1)}
t₁, X₁: 0 {O(1)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₂+X₃ {O(n)}
t₂, X₁: X₂+X₃ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₂+X₃ {O(n)}
t₃, X₁: X₂+X₃ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: 2⋅X₂+2⋅X₃ {O(n)}
t₄, X₁: 2⋅X₂+2⋅X₃ {O(n)}
t₄, X₂: 3⋅X₂ {O(n)}
t₄, X₃: 3⋅X₃ {O(n)}
t₅, X₀: X₂+X₃ {O(n)}
t₅, X₁: X₂+X₃ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₂+X₃ {O(n)}
t₆, X₁: X₂+X₃ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₂+X₃ {O(n)}
t₇, X₁: X₂+X₃ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₂+X₃ {O(n)}
t₈, X₁: X₂+X₃ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₉, X₀: X₂+X₃ {O(n)}
t₉, X₁: X₂+X₃ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}
t₁₀, X₀: X₂+X₃ {O(n)}
t₁₀, X₁: X₂+X₃ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₁, X₀: 3⋅X₂+3⋅X₃ {O(n)}
t₁₁, X₁: 3⋅X₂+3⋅X₃ {O(n)}
t₁₁, X₂: 4⋅X₂ {O(n)}
t₁₁, X₃: 4⋅X₃ {O(n)}