Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(D, 0, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂) :|: X₁ ≤ 9
t₄: l1(X₀, X₁, X₂) → l2(X₀, X₁, 0) :|: 10 ≤ X₁
t₂: l2(X₀, X₁, X₂) → l2(X₀, X₁, X₂+1) :|: X₂ ≤ 9
t₃: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 10 ≤ X₂
Eliminate variables {D,X₀} that do not contribute to the problem
Found invariant X₂ ≤ 10 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 20 ∧ 0 ≤ X₂ ∧ 10 ≤ X₁+X₂ ∧ X₁ ≤ 10+X₂ ∧ X₁ ≤ 10 ∧ 10 ≤ X₁ for location l2
Found invariant X₁ ≤ 10 ∧ 0 ≤ X₁ for location l1
Found invariant X₂ ≤ 10 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 20 ∧ 10 ≤ X₂ ∧ 20 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ 10 ∧ 10 ≤ X₁ for location l3
Start: l0
Program_Vars: X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₁₂: l0(X₁, X₂) → l1(0, X₂)
t₁₃: l1(X₁, X₂) → l1(X₁+1, X₂) :|: X₁ ≤ 9 ∧ X₁ ≤ 10 ∧ 0 ≤ X₁
t₁₄: l1(X₁, X₂) → l2(X₁, 0) :|: 10 ≤ X₁ ∧ X₁ ≤ 10 ∧ 0 ≤ X₁
t₁₅: l2(X₁, X₂) → l2(X₁, X₂+1) :|: X₂ ≤ 9 ∧ X₂ ≤ 10 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 20 ∧ 0 ≤ X₂ ∧ 10 ≤ X₁+X₂ ∧ X₁ ≤ 10+X₂ ∧ X₁ ≤ 10 ∧ 10 ≤ X₁
t₁₆: l2(X₁, X₂) → l3(X₁, X₂) :|: 10 ≤ X₂ ∧ X₂ ≤ 10 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 20 ∧ 0 ≤ X₂ ∧ 10 ≤ X₁+X₂ ∧ X₁ ≤ 10+X₂ ∧ X₁ ≤ 10 ∧ 10 ≤ X₁
new bound:
10 {O(1)}
MPRF:
l1 [10-X₁ ]
new bound:
11 {O(1)}
MPRF:
l2 [11-X₂ ]
Overall timebound:24 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 10 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 11 {O(1)}
t₁₆: 1 {O(1)}
Overall costbound: 24 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 10 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 11 {O(1)}
t₁₆: 1 {O(1)}
t₁₂, X₁: 0 {O(1)}
t₁₂, X₂: X₂ {O(n)}
t₁₃, X₁: 10 {O(1)}
t₁₃, X₂: X₂ {O(n)}
t₁₄, X₁: 10 {O(1)}
t₁₄, X₂: 0 {O(1)}
t₁₅, X₁: 10 {O(1)}
t₁₅, X₂: 10 {O(1)}
t₁₆, X₁: 10 {O(1)}
t₁₆, X₂: 10 {O(1)}