Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₇: l0(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₁, X₀) :|: 0 ≤ X₀ ∧ 0 ≤ X₁
t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁ ∧ X₃+1 ≤ X₀
t₆: l1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₁ ∧ X₃+1 ≤ X₀
t₃: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂-1, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₀
t₂: l2(X₀, X₁, X₂, X₃) → l6(X₀, X₁, 1, X₃-1) :|: 1 ≤ X₃ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, E, X₃-1) :|: X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₃
t₁: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀
t₀: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃
Preprocessing
Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2
Found invariant 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6
Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l7
Found invariant 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5
Found invariant 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l4
Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ 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
Transitions:
t₇: l0(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₁, X₀) :|: 0 ≤ X₀ ∧ 0 ≤ X₁
t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆: l1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂+1 ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂-1, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂: l2(X₀, X₁, X₂, X₃) → l6(X₀, X₁, 1, X₃-1) :|: 1 ≤ X₃ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, E, X₃-1) :|: X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₀: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
MPRF for transition t₁: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₃: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂-1, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF for transition t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, E, X₃-1) :|: X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF for transition t₅: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
All Bounds
Timebounds
Overall timebound:4⋅X₀+5 {O(n)}
t₀: 1 {O(1)}
t₁: X₀+1 {O(n)}
t₂: 1 {O(1)}
t₃: X₀ {O(n)}
t₄: X₀ {O(n)}
t₅: X₀ {O(n)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₀+5 {O(n)}
t₀: 1 {O(1)}
t₁: X₀+1 {O(n)}
t₂: 1 {O(1)}
t₃: X₀ {O(n)}
t₄: X₀ {O(n)}
t₅: X₀ {O(n)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
Sizebounds
t₀, X₀: 2⋅X₀ {O(n)}
t₀, X₁: 2⋅X₁ {O(n)}
t₀, X₃: 0 {O(1)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₃: X₀ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 1 {O(1)}
t₂, X₃: X₀ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₃: X₀ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₃: X₀ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₃: X₀ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₃: X₀ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₁ {O(n)}
t₇, X₃: X₀ {O(n)}