Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ < 40
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 40 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ 0 ≤ X₃
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀+2, X₁, X₂, X₃) :|: X₃ < 0
t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀+2, X₁, X₂, X₃) :|: 0 < X₃
t₇: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
Eliminate variables {X₁,X₂} that do not contribute to the problem
Found invariant 40 ≤ X₀ for location l5
Found invariant 0 ≤ X₀ for location l1
Found invariant 40 ≤ X₀ for location l4
Found invariant X₀ ≤ 39 ∧ 0 ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₆: l0(X₀, X₃) → l2(X₀, X₃)
t₁₇: l1(X₀, X₃) → l3(X₀, X₃) :|: X₀ < 40 ∧ 0 ≤ X₀
t₁₈: l1(X₀, X₃) → l4(X₀, X₃) :|: 40 ≤ X₀ ∧ 0 ≤ X₀
t₁₉: l2(X₀, X₃) → l1(0, X₃)
t₂₀: l3(X₀, X₃) → l1(X₀+1, X₃) :|: X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀
t₂₁: l3(X₀, X₃) → l1(X₀+2, X₃) :|: X₃ < 0 ∧ X₀ ≤ 39 ∧ 0 ≤ X₀
t₂₂: l3(X₀, X₃) → l1(X₀+2, X₃) :|: 0 < X₃ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀
t₂₃: l4(X₀, X₃) → l5(X₀, X₃) :|: 40 ≤ X₀
new bound:
40 {O(1)}
MPRF:
l3 [39-X₀ ]
l1 [40-X₀ ]
new bound:
40 {O(1)}
MPRF:
l3 [40-X₀ ]
l1 [40-X₀ ]
new bound:
40 {O(1)}
MPRF:
l3 [40-X₀ ]
l1 [40-X₀ ]
new bound:
40 {O(1)}
MPRF:
l3 [40-X₀ ]
l1 [40-X₀ ]
Overall timebound:164 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 40 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 40 {O(1)}
t₂₁: 40 {O(1)}
t₂₂: 40 {O(1)}
t₂₃: 1 {O(1)}
Overall costbound: 164 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 40 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 40 {O(1)}
t₂₁: 40 {O(1)}
t₂₂: 40 {O(1)}
t₂₃: 1 {O(1)}
t₁₆, X₀: X₀ {O(n)}
t₁₆, X₃: X₃ {O(n)}
t₁₇, X₀: 39 {O(1)}
t₁₇, X₃: X₃ {O(n)}
t₁₈, X₀: 122 {O(1)}
t₁₈, X₃: 2⋅X₃ {O(n)}
t₁₉, X₀: 0 {O(1)}
t₁₉, X₃: X₃ {O(n)}
t₂₀, X₀: 40 {O(1)}
t₂₀, X₃: 0 {O(1)}
t₂₁, X₀: 41 {O(1)}
t₂₁, X₃: X₃ {O(n)}
t₂₂, X₀: 41 {O(1)}
t₂₂, X₃: X₃ {O(n)}
t₂₃, X₀: 122 {O(1)}
t₂₃, X₃: 2⋅X₃ {O(n)}