Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 100 ∧ X₁ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 100 < X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ < X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₃, X₄, X₅, X₃, X₄, X₅, X₆)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₁, X₀+1, X₂-1, X₃, X₄, X₅, X₆)
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
Eliminate variables {X₆} that do not contribute to the problem
Found invariant X₂ ≤ X₅ for location l5
Found invariant X₂ ≤ X₅ for location l1
Found invariant X₂ ≤ X₅ for location l4
Found invariant X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 100 for location l3
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₄: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₅: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 100 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₅
t₁₆: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 100 < X₀ ∧ X₂ ≤ X₅
t₁₇: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ < X₁ ∧ X₂ ≤ X₅
t₁₈: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅)
t₁₉: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₁, X₀+1, X₂-1, X₃, X₄, X₅) :|: X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 100
t₂₀: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₅
new bound:
X₃+X₄+X₅+101 {O(n)}
MPRF:
l3 [X₅+100-X₀-X₁ ]
l1 [X₅+101-X₀-X₁ ]
new bound:
X₃+X₄+X₅+101 {O(n)}
MPRF:
l3 [X₅+101-X₀-X₁ ]
l1 [X₅+101-X₀-X₁ ]
Overall timebound:2⋅X₃+2⋅X₄+2⋅X₅+207 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: X₃+X₄+X₅+101 {O(n)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: X₃+X₄+X₅+101 {O(n)}
t₂₀: 1 {O(1)}
Overall costbound: 2⋅X₃+2⋅X₄+2⋅X₅+207 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: X₃+X₄+X₅+101 {O(n)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: X₃+X₄+X₅+101 {O(n)}
t₂₀: 1 {O(1)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₄, X₅: X₅ {O(n)}
t₁₅, X₀: 2⋅X₃+2⋅X₄+X₅+101 {O(n)}
t₁₅, X₁: 2⋅X₃+2⋅X₄+X₅+101 {O(n)}
t₁₅, X₂: 2⋅X₅+X₃+X₄+101 {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₅, X₅: X₅ {O(n)}
t₁₆, X₀: 2⋅X₄+3⋅X₃+X₅+101 {O(n)}
t₁₆, X₁: 2⋅X₃+3⋅X₄+X₅+101 {O(n)}
t₁₆, X₂: 3⋅X₅+X₃+X₄+101 {O(n)}
t₁₆, X₃: 2⋅X₃ {O(n)}
t₁₆, X₄: 2⋅X₄ {O(n)}
t₁₆, X₅: 2⋅X₅ {O(n)}
t₁₇, X₀: 2⋅X₄+3⋅X₃+X₅+101 {O(n)}
t₁₇, X₁: 2⋅X₃+3⋅X₄+X₅+101 {O(n)}
t₁₇, X₂: 3⋅X₅+X₃+X₄+101 {O(n)}
t₁₇, X₃: 2⋅X₃ {O(n)}
t₁₇, X₄: 2⋅X₄ {O(n)}
t₁₇, X₅: 2⋅X₅ {O(n)}
t₁₈, X₀: X₃ {O(n)}
t₁₈, X₁: X₄ {O(n)}
t₁₈, X₂: X₅ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₈, X₅: X₅ {O(n)}
t₁₉, X₀: 2⋅X₃+2⋅X₄+X₅+101 {O(n)}
t₁₉, X₁: 2⋅X₃+2⋅X₄+X₅+101 {O(n)}
t₁₉, X₂: 2⋅X₅+X₃+X₄+101 {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₁₉, X₅: X₅ {O(n)}
t₂₀, X₀: 2⋅X₅+4⋅X₄+6⋅X₃+202 {O(n)}
t₂₀, X₁: 2⋅X₅+4⋅X₃+6⋅X₄+202 {O(n)}
t₂₀, X₂: 2⋅X₃+2⋅X₄+6⋅X₅+202 {O(n)}
t₂₀, X₃: 4⋅X₃ {O(n)}
t₂₀, X₄: 4⋅X₄ {O(n)}
t₂₀, X₅: 4⋅X₅ {O(n)}