Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂
Temp_Vars: A1, B1, X, Y, Z
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₁₂: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l1(X₀, X₁, X₂, X₃, X₄, 0, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, 0)
t₁₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l1(X₀+1, X₁, 1, X₃, X₄, X₅, X₆, Y, X, Z, A1, X₃, Y, Y, Y, Y, X₁₇, X₁₇, 1, 1, 1, 0, X₂₂) :|: Y ≤ 0 ∧ X₀+1 ≤ X₁
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l2(X₀, X₁, B1, X₃, X₄, X₅, X₆, Y, X, Z, A1, X₃, Y, Y, Y, Y, X₁₇, 0, B1, B1, B1, 0, X₂₂) :|: X₀+1 ≤ X₁ ∧ Y ≤ 0 ∧ 2 ≤ B1
t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l2(X₀, X₁, B1, X₃, X₄, X₅, X₆, Y, X, Z, A1, X₃, Y, Y, Y, Y, X₁₇, 0, B1, B1, B1, 0, X₂₂) :|: X₀+1 ≤ X₁ ∧ Y ≤ 0 ∧ B1 ≤ 0
t₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₁ ≤ X₀
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, Y, X, Z, A1, X₃, Y, Y, Y, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 1 ≤ Y ∧ X₀+1 ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 3 ≤ X₂
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₂ ≤ 1
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l3(X₀, X₁, 2, X₃+1, X₄, X₅, X₇, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X₂ ≤ 2 ∧ 2 ≤ X₂
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l4(X₀, X₁, X₂, 0, X, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: X ≤ 0
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l4(X₀, X₁, X₂, 0, X, 0, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) :|: 1 ≤ X
t₃: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂)
t₄: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂)
Cut unreachable locations [l5; l6] from the program graph
Eliminate variables {A1,Z,X₃,X₄,X₅,X₆,X₇,X₈,X₉,X₁₀,X₁₁,X₁₂,X₁₃,X₁₄,X₁₅,X₁₆,X₁₇,X₁₈,X₁₉,X₂₀,X₂₁,X₂₂} that do not contribute to the problem
Found invariant 1+X₀ ≤ X₁ for location l2
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: B1, X, Y
Locations: l0, l1, l2, l3, l4
Transitions:
t₂₉: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₃₄: l1(X₀, X₁, X₂) → l1(X₀+1, X₁, 1) :|: Y ≤ 0 ∧ X₀+1 ≤ X₁
t₃₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, B1) :|: X₀+1 ≤ X₁ ∧ Y ≤ 0 ∧ 2 ≤ B1
t₃₃: l1(X₀, X₁, X₂) → l2(X₀, X₁, B1) :|: X₀+1 ≤ X₁ ∧ Y ≤ 0 ∧ B1 ≤ 0
t₃₀: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ ≤ X₀
t₃₁: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ Y ∧ X₀+1 ≤ X₁
t₃₅: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 3 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₃₆: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ 1 ∧ 1+X₀ ≤ X₁
t₃₇: l2(X₀, X₁, X₂) → l3(X₀, X₁, 2) :|: X₂ ≤ 2 ∧ 2 ≤ X₂ ∧ 1+X₀ ≤ X₁
t₃₈: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X ≤ 0
t₃₉: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 1 ≤ X
t₄₀: l4(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
Found invariant 1+X₀ ≤ X₁ for location l2
Found invariant X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ for location n_l1___1
Found invariant 1+X₀ ≤ X₁ for location l2
Found invariant X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ for location n_l1___1
Termination: true
Formula:
relevant size-bounds w.r.t. t₉₈:
X₀: X₀+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₉₈: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+12 {O(n)}
new bound:
4⋅X₀+4⋅X₁+12 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: B1, X, Y
Locations: l0, l1, l2, l3, l4, n_l1___1
Transitions:
t₂₉: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₃₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, B1) :|: X₀+1 ≤ X₁ ∧ Y ≤ 0 ∧ 2 ≤ B1
t₃₃: l1(X₀, X₁, X₂) → l2(X₀, X₁, B1) :|: X₀+1 ≤ X₁ ∧ Y ≤ 0 ∧ B1 ≤ 0
t₃₀: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ ≤ X₀
t₃₁: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ Y ∧ X₀+1 ≤ X₁
t₉₈: l1(X₀, X₁, X₂) → n_l1___1(X₀+1, X₁, 1) :|: 1+X₀ ≤ X₁
t₃₅: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 3 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁
t₃₆: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ 1 ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁
t₃₇: l2(X₀, X₁, X₂) → l3(X₀, X₁, 2) :|: X₂ ≤ 2 ∧ 2 ≤ X₂ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁
t₃₈: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X ≤ 0
t₃₉: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 1 ≤ X
t₄₀: l4(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
t₁₀₄: n_l1___1(X₀, X₁, X₂) → l2(X₀, X₁, B1) :|: X₀+1 ≤ X₁ ∧ Y ≤ 0 ∧ 2 ≤ B1 ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁
t₁₀₅: n_l1___1(X₀, X₁, X₂) → l2(X₀, X₁, B1) :|: X₀+1 ≤ X₁ ∧ Y ≤ 0 ∧ B1 ≤ 0 ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁
t₁₀₆: n_l1___1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁
t₁₀₇: n_l1___1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 ≤ Y ∧ X₀+1 ≤ X₁ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁
t₉₇: n_l1___1(X₀, X₁, X₂) → n_l1___1(X₀+1, X₁, 1) :|: X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁
Found invariant 1+X₀ ≤ X₁ for location l2
Found invariant X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ for location n_l1___1
Overall timebound:inf {Infinity}
t₂₉: 1 {O(1)}
t₃₀: 1 {O(1)}
t₃₁: 1 {O(1)}
t₃₂: 1 {O(1)}
t₃₃: 1 {O(1)}
t₉₈: 1 {O(1)}
t₃₅: 1 {O(1)}
t₃₆: 1 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: inf {Infinity}
t₉₇: 4⋅X₀+4⋅X₁+12 {O(n)}
t₁₀₄: 1 {O(1)}
t₁₀₅: 1 {O(1)}
t₁₀₆: 1 {O(1)}
t₁₀₇: 1 {O(1)}
Overall costbound: inf {Infinity}
t₂₉: 1 {O(1)}
t₃₀: 1 {O(1)}
t₃₁: 1 {O(1)}
t₃₂: 1 {O(1)}
t₃₃: 1 {O(1)}
t₉₈: 1 {O(1)}
t₃₅: 1 {O(1)}
t₃₆: 1 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: inf {Infinity}
t₉₇: 4⋅X₀+4⋅X₁+12 {O(n)}
t₁₀₄: 1 {O(1)}
t₁₀₅: 1 {O(1)}
t₁₀₆: 1 {O(1)}
t₁₀₇: 1 {O(1)}
t₂₉, X₀: X₀ {O(n)}
t₂₉, X₁: X₁ {O(n)}
t₂₉, X₂: X₂ {O(n)}
t₃₀, X₀: X₀ {O(n)}
t₃₀, X₁: X₁ {O(n)}
t₃₀, X₂: X₂ {O(n)}
t₃₁, X₀: X₀ {O(n)}
t₃₁, X₁: X₁ {O(n)}
t₃₁, X₂: X₂ {O(n)}
t₃₂, X₀: X₀ {O(n)}
t₃₂, X₁: X₁ {O(n)}
t₃₃, X₀: X₀ {O(n)}
t₃₃, X₁: X₁ {O(n)}
t₉₈, X₀: X₀+1 {O(n)}
t₉₈, X₁: X₁ {O(n)}
t₉₈, X₂: 1 {O(1)}
t₃₅, X₀: 4⋅X₁+7⋅X₀+14 {O(n)}
t₃₅, X₁: 3⋅X₁ {O(n)}
t₃₆, X₀: 4⋅X₁+7⋅X₀+14 {O(n)}
t₃₆, X₁: 3⋅X₁ {O(n)}
t₃₇, X₀: 4⋅X₁+7⋅X₀+14 {O(n)}
t₃₇, X₁: 3⋅X₁ {O(n)}
t₃₇, X₂: 2 {O(1)}
t₃₈, X₀: 20⋅X₁+35⋅X₀+70 {O(n)}
t₃₈, X₁: 15⋅X₁ {O(n)}
t₃₉, X₀: 20⋅X₁+35⋅X₀+70 {O(n)}
t₃₉, X₁: 15⋅X₁ {O(n)}
t₄₀, X₀: 40⋅X₁+70⋅X₀+140 {O(n)}
t₄₀, X₁: 30⋅X₁ {O(n)}
t₉₇, X₀: 4⋅X₁+5⋅X₀+13 {O(n)}
t₉₇, X₁: X₁ {O(n)}
t₉₇, X₂: 1 {O(1)}
t₁₀₄, X₀: 4⋅X₁+6⋅X₀+14 {O(n)}
t₁₀₄, X₁: 2⋅X₁ {O(n)}
t₁₀₅, X₀: 4⋅X₁+6⋅X₀+14 {O(n)}
t₁₀₅, X₁: 2⋅X₁ {O(n)}
t₁₀₆, X₀: 4⋅X₁+6⋅X₀+14 {O(n)}
t₁₀₆, X₁: 2⋅X₁ {O(n)}
t₁₀₆, X₂: 1 {O(1)}
t₁₀₇, X₀: 4⋅X₁+6⋅X₀+14 {O(n)}
t₁₀₇, X₁: 2⋅X₁ {O(n)}
t₁₀₇, X₂: 1 {O(1)}