Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₈: l10(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: 2 < X₁ ∧ X₃ ≤ 9
t₉: l10(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ ≤ 2
t₁₀: l10(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: 9 < X₃
t₁₅: l11(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃)
t₁₁: l12(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃+1)
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₂, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, 0) :|: X₁ < 5
t₇: l6(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: 5 ≤ X₁
t₁₄: l7(X₀, X₁, X₂, X₃) → l6(X₀, X₀, X₂, X₃)
t₁₂: l8(X₀, X₁, X₂, X₃) → l9(X₁+1, X₁, X₂, X₃)
t₁₃: l9(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
Preprocessing
Found invariant X₂ ≤ X₁ ∧ 5 ≤ X₁ for location l11
Found invariant X₂ ≤ X₁ for location l6
Found invariant X₃ ≤ 9 ∧ X₂+X₃ ≤ 13 ∧ X₃ ≤ 6+X₁ ∧ X₁+X₃ ≤ 13 ∧ 0 ≤ X₃ ∧ X₂ ≤ 4+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 4+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ X₁ ≤ 4 ∧ 3 ≤ X₁ for location l12
Found invariant 0 ≤ X₃ ∧ X₂ ≤ 2+X₃ ∧ X₁ ≤ 2+X₃ ∧ X₀ ≤ 3+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 9 ∧ X₁ ≤ 4 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 9 ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 5 for location l7
Found invariant X₂ ≤ X₁ ∧ 5 ≤ X₁ for location l13
Found invariant 0 ≤ X₃ ∧ X₂ ≤ 2+X₃ ∧ X₁ ≤ 2+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ X₁ ≤ 4 for location l8
Found invariant 0 ≤ X₃ ∧ X₂ ≤ 4+X₃ ∧ X₁ ≤ 4+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ X₁ ≤ 4 for location l10
Found invariant 0 ≤ X₃ ∧ X₂ ≤ 2+X₃ ∧ X₁ ≤ 2+X₃ ∧ X₀ ≤ 3+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 9 ∧ X₁ ≤ 4 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 9 ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 5 for location l9
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₈: l10(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: 2 < X₁ ∧ X₃ ≤ 9 ∧ 0 ≤ X₃ ∧ X₂ ≤ 4+X₃ ∧ X₁ ≤ 4+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ X₁ ≤ 4
t₉: l10(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ ≤ 2 ∧ 0 ≤ X₃ ∧ X₂ ≤ 4+X₃ ∧ X₁ ≤ 4+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ X₁ ≤ 4
t₁₀: l10(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: 9 < X₃ ∧ 0 ≤ X₃ ∧ X₂ ≤ 4+X₃ ∧ X₁ ≤ 4+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ X₁ ≤ 4
t₁₅: l11(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ 5 ≤ X₁
t₁₁: l12(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ 9 ∧ X₂+X₃ ≤ 13 ∧ X₃ ≤ 6+X₁ ∧ X₁+X₃ ≤ 13 ∧ 0 ≤ X₃ ∧ X₂ ≤ 4+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 4+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ X₁ ≤ 4 ∧ 3 ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₂, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, 0) :|: X₁ < 5 ∧ X₂ ≤ X₁
t₇: l6(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: 5 ≤ X₁ ∧ X₂ ≤ X₁
t₁₄: l7(X₀, X₁, X₂, X₃) → l6(X₀, X₀, X₂, X₃) :|: 0 ≤ X₃ ∧ X₂ ≤ 2+X₃ ∧ X₁ ≤ 2+X₃ ∧ X₀ ≤ 3+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 9 ∧ X₁ ≤ 4 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 9 ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 5
t₁₂: l8(X₀, X₁, X₂, X₃) → l9(X₁+1, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ X₂ ≤ 2+X₃ ∧ X₁ ≤ 2+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ X₁ ≤ 4
t₁₃: l9(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ X₂ ≤ 2+X₃ ∧ X₁ ≤ 2+X₃ ∧ X₀ ≤ 3+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 9 ∧ X₁ ≤ 4 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 9 ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 5
MPRF for transition t₉: l10(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ ≤ 2 ∧ 0 ≤ X₃ ∧ X₂ ≤ 4+X₃ ∧ X₁ ≤ 4+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ X₁ ≤ 4 of depth 1:
new bound:
X₂+3 {O(n)}
MPRF:
l12 [3-X₁ ]
l10 [3-X₁ ]
l6 [3-X₁ ]
l8 [2-X₁ ]
l9 [3-X₀ ]
l7 [3-X₀ ]
MPRF for transition t₁₀: l10(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: 9 < X₃ ∧ 0 ≤ X₃ ∧ X₂ ≤ 4+X₃ ∧ X₁ ≤ 4+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ X₁ ≤ 4 of depth 1:
new bound:
X₂+5 {O(n)}
MPRF:
l12 [5-X₁ ]
l10 [5-X₁ ]
l6 [5-X₁ ]
l8 [4-X₁ ]
l9 [5-X₀ ]
l7 [5-X₀ ]
MPRF for transition t₆: l6(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, 0) :|: X₁ < 5 ∧ X₂ ≤ X₁ of depth 1:
new bound:
X₂+5 {O(n)}
MPRF:
l12 [4-X₁ ]
l10 [4-X₁ ]
l6 [5-X₁ ]
l8 [4-X₁ ]
l9 [5-X₀ ]
l7 [5-X₀ ]
MPRF for transition t₁₄: l7(X₀, X₁, X₂, X₃) → l6(X₀, X₀, X₂, X₃) :|: 0 ≤ X₃ ∧ X₂ ≤ 2+X₃ ∧ X₁ ≤ 2+X₃ ∧ X₀ ≤ 3+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 9 ∧ X₁ ≤ 4 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 9 ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 5 of depth 1:
new bound:
X₂+5 {O(n)}
MPRF:
l12 [5-X₁ ]
l10 [5-X₁ ]
l6 [5-X₁ ]
l8 [5-X₁ ]
l9 [6-X₀ ]
l7 [6-X₀ ]
MPRF for transition t₁₂: l8(X₀, X₁, X₂, X₃) → l9(X₁+1, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ X₂ ≤ 2+X₃ ∧ X₁ ≤ 2+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ X₁ ≤ 4 of depth 1:
new bound:
X₂+5 {O(n)}
MPRF:
l12 [5-X₁ ]
l10 [5-X₁ ]
l6 [5-X₁ ]
l8 [5-X₁ ]
l9 [5-X₀ ]
l7 [5-X₀ ]
MPRF for transition t₁₃: l9(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ X₂ ≤ 2+X₃ ∧ X₁ ≤ 2+X₃ ∧ X₀ ≤ 3+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 9 ∧ X₁ ≤ 4 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 9 ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 5 of depth 1:
new bound:
X₂+5 {O(n)}
MPRF:
l12 [5-X₁ ]
l10 [5-X₁ ]
l6 [5-X₁ ]
l8 [5-X₁ ]
l9 [5-X₁ ]
l7 [4-X₁ ]
MPRF for transition t₈: l10(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: 2 < X₁ ∧ X₃ ≤ 9 ∧ 0 ≤ X₃ ∧ X₂ ≤ 4+X₃ ∧ X₁ ≤ 4+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ X₁ ≤ 4 of depth 1:
new bound:
10⋅X₂+60 {O(n)}
MPRF:
l12 [9-X₃ ]
l10 [10-X₃ ]
l7 [10 ]
l6 [10 ]
l8 [-X₃ ]
l9 [-X₃ ]
MPRF for transition t₁₁: l12(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ 9 ∧ X₂+X₃ ≤ 13 ∧ X₃ ≤ 6+X₁ ∧ X₁+X₃ ≤ 13 ∧ 0 ≤ X₃ ∧ X₂ ≤ 4+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 4+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ X₁ ≤ 4 ∧ 3 ≤ X₁ of depth 1:
new bound:
8⋅X₂⋅X₂+80⋅X₂+180 {O(n^2)}
MPRF:
l12 [4⋅X₁-X₃ ]
l10 [4⋅X₁-X₃ ]
l7 [4⋅X₀ ]
l6 [4⋅X₁ ]
l8 [4⋅X₁-X₃ ]
l9 [4⋅X₁-X₃ ]
knowledge_propagation leads to new time bound 10⋅X₂+60 {O(n)} for transition t₁₁: l12(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃+1) :|: X₃ ≤ 9 ∧ X₂+X₃ ≤ 13 ∧ X₃ ≤ 6+X₁ ∧ X₁+X₃ ≤ 13 ∧ 0 ≤ X₃ ∧ X₂ ≤ 4+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 4+X₃ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 8 ∧ X₁ ≤ 4 ∧ 3 ≤ X₁
All Bounds
Timebounds
Overall timebound:26⋅X₂+156 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₈: 10⋅X₂+60 {O(n)}
t₉: X₂+3 {O(n)}
t₁₀: X₂+5 {O(n)}
t₁₅: 1 {O(1)}
t₁₁: 10⋅X₂+60 {O(n)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: X₂+5 {O(n)}
t₇: 1 {O(1)}
t₁₄: X₂+5 {O(n)}
t₁₂: X₂+5 {O(n)}
t₁₃: X₂+5 {O(n)}
Costbounds
Overall costbound: 26⋅X₂+156 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₈: 10⋅X₂+60 {O(n)}
t₉: X₂+3 {O(n)}
t₁₀: X₂+5 {O(n)}
t₁₅: 1 {O(1)}
t₁₁: 10⋅X₂+60 {O(n)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: X₂+5 {O(n)}
t₇: 1 {O(1)}
t₁₄: X₂+5 {O(n)}
t₁₂: X₂+5 {O(n)}
t₁₃: X₂+5 {O(n)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₈, X₀: 2⋅X₂+X₀+9 {O(n)}
t₈, X₁: 4 {O(1)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: 9 {O(1)}
t₉, X₀: 2⋅X₂+X₀+9 {O(n)}
t₉, X₁: 2⋅X₂+9 {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: 0 {O(1)}
t₁₀, X₀: 2⋅X₂+X₀+9 {O(n)}
t₁₀, X₁: 4 {O(1)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: 10 {O(1)}
t₁₅, X₀: 2⋅X₂+X₀+9 {O(n)}
t₁₅, X₁: 3⋅X₂+9 {O(n)}
t₁₅, X₂: 2⋅X₂ {O(n)}
t₁₅, X₃: X₃+10 {O(n)}
t₁₁, X₀: 2⋅X₂+X₀+9 {O(n)}
t₁₁, X₁: 4 {O(1)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: 10 {O(1)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₂ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: 2⋅X₂+X₀+9 {O(n)}
t₆, X₁: 2⋅X₂+9 {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: 0 {O(1)}
t₇, X₀: 2⋅X₂+X₀+9 {O(n)}
t₇, X₁: 3⋅X₂+9 {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₇, X₃: X₃+10 {O(n)}
t₁₄, X₀: 2⋅X₂+9 {O(n)}
t₁₄, X₁: 2⋅X₂+9 {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: 10 {O(1)}
t₁₂, X₀: 2⋅X₂+9 {O(n)}
t₁₂, X₁: 2⋅X₂+13 {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: 10 {O(1)}
t₁₃, X₀: 2⋅X₂+9 {O(n)}
t₁₃, X₁: 2⋅X₂+13 {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: 10 {O(1)}