Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₀, X₂, 0) :|: X₀ < 256
t₅: l3(X₀, X₁, X₂, X₃) → l6(X₀, 256, X₂, 0) :|: 256 ≤ X₀
t₁₀: l4(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₉: l5(X₀, X₁, X₂, X₃) → l1(X₀-X₁, X₁, X₂, X₃)
t₇: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₃ < X₁
t₈: l7(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃+1)
Preprocessing
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6
Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l7
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5
Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l8
Found invariant X₀ ≤ X₂ for location l1
Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ X₀ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₀, X₂, 0) :|: X₀ < 256 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₅: l3(X₀, X₁, X₂, X₃) → l6(X₀, 256, X₂, 0) :|: 256 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₁₀: l4(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₂ ∧ X₀ ≤ 0
t₉: l5(X₀, X₁, X₂, X₃) → l1(X₀-X₁, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₃ < X₁ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈: l7(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃+1) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
MPRF for transition t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ X₀ ≤ X₂ of depth 1:
new bound:
X₂ {O(n)}
MPRF for transition t₄: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₀, X₂, 0) :|: X₀ < 256 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF for transition t₅: l3(X₀, X₁, X₂, X₃) → l6(X₀, 256, X₂, 0) :|: 256 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂+255 {O(n)}
MPRF for transition t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₃ < X₁ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂+1 {O(n)}
MPRF for transition t₇: l6(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF for transition t₈: l7(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃+1) :|: 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF for transition t₉: l5(X₀, X₁, X₂, X₃) → l1(X₀-X₁, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
All Bounds
Timebounds
Overall timebound:7⋅X₂+260 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂ {O(n)}
t₃: 1 {O(1)}
t₄: X₂ {O(n)}
t₅: X₂+255 {O(n)}
t₆: X₂+1 {O(n)}
t₇: X₂ {O(n)}
t₈: X₂ {O(n)}
t₉: X₂ {O(n)}
t₁₀: 1 {O(1)}
Costbounds
Overall costbound: 7⋅X₂+260 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂ {O(n)}
t₃: 1 {O(1)}
t₄: X₂ {O(n)}
t₅: X₂+255 {O(n)}
t₆: X₂+1 {O(n)}
t₇: X₂ {O(n)}
t₈: X₂ {O(n)}
t₉: X₂ {O(n)}
t₁₀: 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: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₂+255 {O(n)}
t₂, X₁: X₁+511 {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₂+X₃ {O(n)}
t₃, X₀: 2⋅X₂+255 {O(n)}
t₃, X₁: X₁+511 {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: X₂+X₃ {O(n)}
t₄, X₀: 255 {O(1)}
t₄, X₁: 255 {O(1)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: 0 {O(1)}
t₅, X₀: X₂+255 {O(n)}
t₅, X₁: 256 {O(1)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: 0 {O(1)}
t₆, X₀: X₂+255 {O(n)}
t₆, X₁: 511 {O(1)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₂ {O(n)}
t₇, X₀: X₂+255 {O(n)}
t₇, X₁: 511 {O(1)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₂ {O(n)}
t₈, X₀: X₂+255 {O(n)}
t₈, X₁: 511 {O(1)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₂ {O(n)}
t₉, X₀: X₂+255 {O(n)}
t₉, X₁: 511 {O(1)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₂ {O(n)}
t₁₀, X₀: 2⋅X₂+255 {O(n)}
t₁₀, X₁: X₁+511 {O(n)}
t₁₀, X₂: 2⋅X₂ {O(n)}
t₁₀, X₃: X₂+X₃ {O(n)}