Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₄: l1(X₀, X₁) → l2(X₀, X₁) :|: 3 ≤ X₀ ∧ X₁ ≤ 9
t₅: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ ≤ 2
t₆: l1(X₀, X₁) → l3(X₀, X₁) :|: 10 ≤ X₁
t₇: l2(X₀, X₁) → l1(X₀, X₁+1)
t₈: l3(X₀, X₁) → l4(X₀+1, X₁)
t₂: l4(X₀, X₁) → l1(X₀, 0) :|: X₀ ≤ 4
t₃: l4(X₀, X₁) → l5(X₀, X₁) :|: 5 ≤ X₀
t₉: l5(X₀, X₁) → l7(X₀, X₁)
t₁: l6(X₀, X₁) → l4(X₀, X₁)
Preprocessing
Found invariant X₁ ≤ 9 ∧ X₁ ≤ 6+X₀ ∧ X₀+X₁ ≤ 13 ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 ∧ 3 ≤ X₀ for location l2
Found invariant 5 ≤ X₀ for location l7
Found invariant 5 ≤ X₀ for location l5
Found invariant 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 for location l1
Found invariant 0 ≤ X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 4 for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₄: l1(X₀, X₁) → l2(X₀, X₁) :|: 3 ≤ X₀ ∧ X₁ ≤ 9 ∧ 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4
t₅: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ ≤ 2 ∧ 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4
t₆: l1(X₀, X₁) → l3(X₀, X₁) :|: 10 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4
t₇: l2(X₀, X₁) → l1(X₀, X₁+1) :|: X₁ ≤ 9 ∧ X₁ ≤ 6+X₀ ∧ X₀+X₁ ≤ 13 ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 ∧ 3 ≤ X₀
t₈: l3(X₀, X₁) → l4(X₀+1, X₁) :|: 0 ≤ X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 4
t₂: l4(X₀, X₁) → l1(X₀, 0) :|: X₀ ≤ 4
t₃: l4(X₀, X₁) → l5(X₀, X₁) :|: 5 ≤ X₀
t₉: l5(X₀, X₁) → l7(X₀, X₁) :|: 5 ≤ X₀
t₁: l6(X₀, X₁) → l4(X₀, X₁)
MPRF for transition t₅: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ ≤ 2 ∧ 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 of depth 1:
new bound:
X₀+3 {O(n)}
MPRF:
l2 [3-X₀ ]
l3 [2-X₀ ]
l4 [3-X₀ ]
l1 [3-X₀ ]
MPRF for transition t₆: l1(X₀, X₁) → l3(X₀, X₁) :|: 10 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 of depth 1:
new bound:
X₀+5 {O(n)}
MPRF:
l2 [5-X₀ ]
l3 [4-X₀ ]
l4 [5-X₀ ]
l1 [5-X₀ ]
MPRF for transition t₈: l3(X₀, X₁) → l4(X₀+1, X₁) :|: 0 ≤ X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 4 of depth 1:
new bound:
X₀+5 {O(n)}
MPRF:
l2 [5-X₀ ]
l3 [5-X₀ ]
l4 [5-X₀ ]
l1 [5-X₀ ]
MPRF for transition t₂: l4(X₀, X₁) → l1(X₀, 0) :|: X₀ ≤ 4 of depth 1:
new bound:
X₀+5 {O(n)}
MPRF:
l2 [4-X₀ ]
l3 [4-X₀ ]
l4 [5-X₀ ]
l1 [4-X₀ ]
MPRF for transition t₄: l1(X₀, X₁) → l2(X₀, X₁) :|: 3 ≤ X₀ ∧ X₁ ≤ 9 ∧ 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 of depth 1:
new bound:
10⋅X₀+50 {O(n)}
MPRF:
l2 [9-X₁ ]
l1 [10-X₁ ]
l3 [-X₁ ]
l4 [-X₁ ]
MPRF for transition t₇: l2(X₀, X₁) → l1(X₀, X₁+1) :|: 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⋅X₀+50 {O(n)}
MPRF:
l2 [10-X₁ ]
l1 [10-X₁ ]
l3 [-X₁ ]
l4 [-X₁ ]
All Bounds
Timebounds
Overall timebound:24⋅X₀+122 {O(n)}
t₀: 1 {O(1)}
t₄: 10⋅X₀+50 {O(n)}
t₅: X₀+3 {O(n)}
t₆: X₀+5 {O(n)}
t₇: 10⋅X₀+50 {O(n)}
t₈: X₀+5 {O(n)}
t₂: X₀+5 {O(n)}
t₃: 1 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}
Costbounds
Overall costbound: 24⋅X₀+122 {O(n)}
t₀: 1 {O(1)}
t₄: 10⋅X₀+50 {O(n)}
t₅: X₀+3 {O(n)}
t₆: X₀+5 {O(n)}
t₇: 10⋅X₀+50 {O(n)}
t₈: X₀+5 {O(n)}
t₂: X₀+5 {O(n)}
t₃: 1 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₄, X₀: 4 {O(1)}
t₄, X₁: 9 {O(1)}
t₅, X₀: 2⋅X₀+9 {O(n)}
t₅, X₁: 0 {O(1)}
t₆, X₀: 4 {O(1)}
t₆, X₁: 10 {O(1)}
t₇, X₀: 4 {O(1)}
t₇, X₁: 10 {O(1)}
t₈, X₀: 2⋅X₀+9 {O(n)}
t₈, X₁: 10 {O(1)}
t₂, X₀: 2⋅X₀+9 {O(n)}
t₂, X₁: 0 {O(1)}
t₃, X₀: 3⋅X₀+9 {O(n)}
t₃, X₁: X₁+10 {O(n)}
t₉, X₀: 3⋅X₀+9 {O(n)}
t₉, X₁: X₁+10 {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}