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)
t₈: l1(X₀, X₁) → l3(X₀, X₁-1)
t₉: l2(X₀, X₁) → l3(X₀, X₁-X₀)
t₄: l3(X₀, X₁) → l4(X₀, X₁) :|: 1 ≤ X₁
t₅: l3(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 0
t₆: l4(X₀, X₁) → l1(X₀, X₁) :|: X₁+1 ≤ X₀
t₇: l4(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ X₁
t₁₀: l5(X₀, X₁) → l7(X₀, X₁)
t₃: l6(X₀, X₁) → l3(X₀, X₁) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
t₁: l6(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ 0
t₂: l6(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ X₀
Preprocessing
Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2
Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l1
Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4
Found invariant 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ 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)
t₈: l1(X₀, X₁) → l3(X₀, X₁-1) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₉: l2(X₀, X₁) → l3(X₀, X₁-X₀) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄: l3(X₀, X₁) → l4(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₅: l3(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 0 ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆: l4(X₀, X₁) → l1(X₀, X₁) :|: X₁+1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇: l4(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀: l5(X₀, X₁) → l7(X₀, X₁)
t₃: l6(X₀, X₁) → l3(X₀, X₁) :|: 1 ≤ X₀ ∧ X₀+1 ≤ X₁
t₁: l6(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ 0
t₂: l6(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ X₀
MPRF for transition t₈: l1(X₀, X₁) → l3(X₀, X₁-1) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀+X₁+2 {O(n)}
MPRF:
l3 [X₀+X₁-2 ]
l1 [X₀+X₁-2 ]
l4 [X₀+X₁-2 ]
l2 [X₁-2 ]
MPRF for transition t₉: l2(X₀, X₁) → l3(X₀, X₁-X₀) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF:
l3 [X₁ ]
l1 [X₁ ]
l4 [X₁ ]
l2 [X₁+1-X₀ ]
MPRF for transition t₄: l3(X₀, X₁) → l4(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF:
l3 [X₁ ]
l1 [X₁-1 ]
l4 [X₁-1 ]
l2 [X₁-X₀ ]
MPRF for transition t₆: l4(X₀, X₁) → l1(X₀, X₁) :|: X₁+1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF:
l3 [X₁ ]
l1 [X₁-1 ]
l4 [X₁ ]
l2 [X₁-X₀ ]
MPRF for transition t₇: l4(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF:
l3 [X₁ ]
l1 [X₁ ]
l4 [X₁ ]
l2 [X₁-1 ]
All Bounds
Timebounds
Overall timebound:5⋅X₁+X₀+8 {O(n)}
t₀: 1 {O(1)}
t₈: X₀+X₁+2 {O(n)}
t₉: X₁ {O(n)}
t₄: X₁ {O(n)}
t₅: 1 {O(1)}
t₆: X₁ {O(n)}
t₇: X₁ {O(n)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
Costbounds
Overall costbound: 5⋅X₁+X₀+8 {O(n)}
t₀: 1 {O(1)}
t₈: X₀+X₁+2 {O(n)}
t₉: X₁ {O(n)}
t₄: X₁ {O(n)}
t₅: 1 {O(1)}
t₆: X₁ {O(n)}
t₇: X₁ {O(n)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: 2⋅X₀ {O(n)}
t₅, X₁: 2⋅X₁ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₁₀, X₀: 4⋅X₀ {O(n)}
t₁₀, X₁: 4⋅X₁ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}