Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, 0, X₂, X₃) :|: X₀ < 5
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 5 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ 2
t₆: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 9 < X₁
t₄: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 2 < X₀ ∧ X₁ ≤ 9
t₉: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₈: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃)
t₇: l6(X₀, X₁, X₂, X₃) → l3(X₀, X₁+1, X₂, X₃)
Preprocessing
Eliminate variables {X₃} that do not contribute to the problem
Found invariant X₂ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₁+X₂ ≤ 13 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 9 ∧ X₁ ≤ 6+X₀ ∧ X₀+X₁ ≤ 13 ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 ∧ 3 ≤ X₀ for location l6
Found invariant X₂ ≤ X₀ ∧ 5 ≤ X₀ for location l7
Found invariant X₂ ≤ 4 ∧ X₂ ≤ 2+X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ 0 ≤ X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 4 for location l5
Found invariant X₂ ≤ X₀ for location l1
Found invariant X₂ ≤ X₀ ∧ 5 ≤ X₀ for location l4
Found invariant X₂ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₂₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂₁: l1(X₀, X₁, X₂) → l3(X₀, 0, X₂) :|: X₀ < 5 ∧ X₂ ≤ X₀
t₂₂: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 5 ≤ X₀ ∧ X₂ ≤ X₀
t₂₃: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₂₅: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ 2 ∧ X₂ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4
t₂₆: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 9 < X₁ ∧ X₂ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4
t₂₄: l3(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 2 < X₀ ∧ X₁ ≤ 9 ∧ X₂ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4
t₂₇: l4(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ 5 ≤ X₀
t₂₈: l5(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₂ ≤ 4 ∧ X₂ ≤ 2+X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ 0 ≤ X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 4
t₂₉: l6(X₀, X₁, X₂) → l3(X₀, X₁+1, X₂) :|: X₂ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₁+X₂ ≤ 13 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 9 ∧ X₁ ≤ 6+X₀ ∧ X₀+X₁ ≤ 13 ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 ∧ 3 ≤ X₀
MPRF for transition t₂₁: l1(X₀, X₁, X₂) → l3(X₀, 0, X₂) :|: X₀ < 5 ∧ X₂ ≤ X₀ of depth 1:
new bound:
X₂+5 {O(n)}
MPRF:
l5 [4-X₀ ]
l1 [5-X₀ ]
l6 [4-X₀ ]
l3 [4-X₀ ]
MPRF for transition t₂₅: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ 2 ∧ X₂ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 of depth 1:
new bound:
X₂+5 {O(n)}
MPRF:
l5 [4-X₀ ]
l1 [5-X₀ ]
l6 [5-X₀ ]
l3 [5-X₀ ]
MPRF for transition t₂₆: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 9 < X₁ ∧ X₂ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 of depth 1:
new bound:
X₂+5 {O(n)}
MPRF:
l5 [4-X₀ ]
l1 [5-X₀ ]
l6 [5-X₀ ]
l3 [5-X₀ ]
MPRF for transition t₂₈: l5(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₂ ≤ 4 ∧ X₂ ≤ 2+X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ 0 ≤ X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 4 of depth 1:
new bound:
X₂+5 {O(n)}
MPRF:
l5 [5-X₀ ]
l1 [5-X₀ ]
l6 [5-X₀ ]
l3 [5-X₀ ]
MPRF for transition t₂₄: l3(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 2 < X₀ ∧ X₁ ≤ 9 ∧ X₂ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 of depth 1:
new bound:
10⋅X₂+60 {O(n)}
MPRF:
l1 [10 ]
l5 [-X₁ ]
l6 [9-X₁ ]
l3 [10-X₁ ]
MPRF for transition t₂₉: l6(X₀, X₁, X₂) → l3(X₀, X₁+1, X₂) :|: X₂ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₁+X₂ ≤ 13 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 9 ∧ X₁ ≤ 6+X₀ ∧ X₀+X₁ ≤ 13 ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 ∧ 3 ≤ X₀ of depth 1:
new bound:
10⋅X₂+60 {O(n)}
MPRF:
l1 [10 ]
l5 [-X₁ ]
l6 [10-X₁ ]
l3 [10-X₁ ]
All Bounds
Timebounds
Overall timebound:24⋅X₂+144 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: X₂+5 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 10⋅X₂+60 {O(n)}
t₂₅: X₂+5 {O(n)}
t₂₆: X₂+5 {O(n)}
t₂₇: 1 {O(1)}
t₂₈: X₂+5 {O(n)}
t₂₉: 10⋅X₂+60 {O(n)}
Costbounds
Overall costbound: 24⋅X₂+144 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: X₂+5 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 10⋅X₂+60 {O(n)}
t₂₅: X₂+5 {O(n)}
t₂₆: X₂+5 {O(n)}
t₂₇: 1 {O(1)}
t₂₈: X₂+5 {O(n)}
t₂₉: 10⋅X₂+60 {O(n)}
Sizebounds
t₂₀, X₀: X₀ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₁, X₀: 2⋅X₂+9 {O(n)}
t₂₁, X₁: 0 {O(1)}
t₂₁, X₂: X₂ {O(n)}
t₂₂, X₀: 3⋅X₂+9 {O(n)}
t₂₂, X₁: X₁+10 {O(n)}
t₂₂, X₂: 2⋅X₂ {O(n)}
t₂₃, X₀: X₂ {O(n)}
t₂₃, X₁: X₁ {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₄, X₀: 4 {O(1)}
t₂₄, X₁: 9 {O(1)}
t₂₄, X₂: X₂ {O(n)}
t₂₅, X₀: 2⋅X₂+9 {O(n)}
t₂₅, X₁: 0 {O(1)}
t₂₅, X₂: X₂ {O(n)}
t₂₆, X₀: 4 {O(1)}
t₂₆, X₁: 10 {O(1)}
t₂₆, X₂: X₂ {O(n)}
t₂₇, X₀: 3⋅X₂+9 {O(n)}
t₂₇, X₁: X₁+10 {O(n)}
t₂₇, X₂: 2⋅X₂ {O(n)}
t₂₈, X₀: 2⋅X₂+9 {O(n)}
t₂₈, X₁: 10 {O(1)}
t₂₈, X₂: X₂ {O(n)}
t₂₉, X₀: 4 {O(1)}
t₂₉, X₁: 10 {O(1)}
t₂₉, X₂: X₂ {O(n)}