Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₁
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₂, X₃, X₄, X₅)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₁-1, X₀, X₂, X₃, X₄, X₅)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅)
Eliminate variables {X₂,X₅} that do not contribute to the problem
Found invariant X₁ ≤ 0 for location l5
Found invariant X₁ ≤ 0 for location l4
Found invariant 1 ≤ X₁ for location l3
Start: l0
Program_Vars: X₀, X₁, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₂: l0(X₀, X₁, X₃, X₄) → l2(X₀, X₁, X₃, X₄)
t₁₃: l1(X₀, X₁, X₃, X₄) → l3(X₀, X₁, X₃, X₄) :|: 0 < X₁
t₁₄: l1(X₀, X₁, X₃, X₄) → l4(X₀, X₁, X₃, X₄) :|: X₁ ≤ 0
t₁₅: l2(X₀, X₁, X₃, X₄) → l1(X₃, X₄, X₃, X₄)
t₁₆: l3(X₀, X₁, X₃, X₄) → l1(X₁-1, X₀, X₃, X₄) :|: 1 ≤ X₁
t₁₇: l4(X₀, X₁, X₃, X₄) → l5(X₀, X₁, X₃, X₄) :|: X₁ ≤ 0
Found invariant X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ for location n_l3___3
Found invariant 1 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₀ for location n_l1___2
Found invariant X₁ ≤ X₄ ∧ X₁ ≤ 0 for location l5
Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location l1
Found invariant X₁ ≤ X₄ ∧ X₁ ≤ 0 for location l4
Found invariant 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l3___1
new bound:
X₃+X₄ {O(n)}
MPRF:
n_l3___1 [X₀+X₁-1 ]
n_l1___2 [X₀+X₁ ]
new bound:
X₃+X₄ {O(n)}
MPRF:
n_l3___1 [X₀+X₁ ]
n_l1___2 [X₀+X₁ ]
new bound:
2⋅X₃+2⋅X₄ {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l4, l5, n_l1___2, n_l3___1, n_l3___3
Transitions:
t₁₂: l0(X₀, X₁, X₃, X₄) → l2(X₀, X₁, X₃, X₄)
t₁₄: l1(X₀, X₁, X₃, X₄) → l4(X₀, X₁, X₃, X₄) :|: X₁ ≤ 0 ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₆₇: l1(X₀, X₁, X₃, X₄) → n_l3___3(X₀, X₁, X₃, X₄) :|: X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 < X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁₅: l2(X₀, X₁, X₃, X₄) → l1(X₃, X₄, X₃, X₄)
t₁₇: l4(X₀, X₁, X₃, X₄) → l5(X₀, X₁, X₃, X₄) :|: X₁ ≤ 0 ∧ X₁ ≤ X₄ ∧ X₁ ≤ 0
t₇₃: n_l1___2(X₀, X₁, X₃, X₄) → l4(X₀, X₁, X₃, X₄) :|: X₁ ≤ 0 ∧ 1 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₀
t₆₆: n_l1___2(X₀, X₁, X₃, X₄) → n_l3___1(X₀, X₁, X₃, X₄) :|: 0 ≤ X₀ ∧ 0 < X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 0 ≤ X₀
t₆₈: n_l3___1(X₀, X₁, X₃, X₄) → n_l1___2(X₁-1, X₀, X₃, X₄) :|: 0 < X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₆₉: n_l3___3(X₀, X₁, X₃, X₄) → n_l1___2(X₁-1, X₀, X₃, X₄) :|: 0 < X₄ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁
Overall timebound:2⋅X₃+2⋅X₄+7 {O(n)}
t₁₂: 1 {O(1)}
t₁₄: 1 {O(1)}
t₆₇: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₇: 1 {O(1)}
t₆₆: X₃+X₄ {O(n)}
t₇₃: 1 {O(1)}
t₆₈: X₃+X₄ {O(n)}
t₆₉: 1 {O(1)}
Overall costbound: 2⋅X₃+2⋅X₄+7 {O(n)}
t₁₂: 1 {O(1)}
t₁₄: 1 {O(1)}
t₆₇: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₇: 1 {O(1)}
t₆₆: X₃+X₄ {O(n)}
t₇₃: 1 {O(1)}
t₆₈: X₃+X₄ {O(n)}
t₆₉: 1 {O(1)}
t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₄, X₀: X₃ {O(n)}
t₁₄, X₁: X₄ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₆₇, X₀: X₃ {O(n)}
t₆₇, X₁: X₄ {O(n)}
t₆₇, X₃: X₃ {O(n)}
t₆₇, X₄: X₄ {O(n)}
t₁₅, X₀: X₃ {O(n)}
t₁₅, X₁: X₄ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₇, X₀: 2⋅X₃+X₄ {O(n)}
t₁₇, X₁: 2⋅X₄+X₃ {O(n)}
t₁₇, X₃: 3⋅X₃ {O(n)}
t₁₇, X₄: 3⋅X₄ {O(n)}
t₆₆, X₀: X₃+X₄ {O(n)}
t₆₆, X₁: X₃+X₄ {O(n)}
t₆₆, X₃: X₃ {O(n)}
t₆₆, X₄: X₄ {O(n)}
t₇₃, X₀: 2⋅X₄+X₃ {O(n)}
t₇₃, X₁: 2⋅X₃+X₄ {O(n)}
t₇₃, X₃: 2⋅X₃ {O(n)}
t₇₃, X₄: 2⋅X₄ {O(n)}
t₆₈, X₀: X₃+X₄ {O(n)}
t₆₈, X₁: X₃+X₄ {O(n)}
t₆₈, X₃: X₃ {O(n)}
t₆₈, X₄: X₄ {O(n)}
t₆₉, X₀: X₄ {O(n)}
t₆₉, X₁: X₃ {O(n)}
t₆₉, X₃: X₃ {O(n)}
t₆₉, X₄: X₄ {O(n)}