Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁
Temp_Vars: M, N, O, P
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₅: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₅, X₃, X₃, X₃, X₅, X₅, X₀, X₁, X₈, X₉, X₁₀, X₁₁)
t₆: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₅, X₃, X₃, X₃, X₅, X₅, M, N, M, N, X₁₀, X₁₁)
t₉: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₀+1, X₁, X₃, X₃, X₅, X₅, X₀, X₁, X₈, X₉, X₁₀, X₁₁)
t₁₁: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₀, X₁+1, X₃, X₃, X₅, X₅, X₀, X₁, X₈, X₉, X₁₀, X₁₁)
t₁: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₂: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁)
t₇: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l3(O, P, X₃, M, X₅, N, X₀, X₁, M, N, O, P)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l2(X₀, X₁, X₃, X₃, X₅, X₅, X₀, X₁, X₈, X₉, X₁₀, X₁₁) :|: X₁+1 ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l2(X₀, X₁, X₃, X₃, X₅, X₅, X₀, X₁, X₈, X₉, X₁₀, X₁₁) :|: X₀+1 ≤ X₁
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l3(O, P, X₃, M, X₅, N, X₀, X₀, M, N, O, P) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁₀: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₀+1, X₁, X₃, X₃, X₅, X₅, X₀, X₁, X₈, X₉, X₁₀, X₁₁) :|: X₀+1 ≤ X₁
t₁₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁) → l1(X₀, X₁+1, X₃, X₃, X₅, X₅, X₀, X₁, X₈, X₉, X₁₀, X₁₁) :|: X₁ ≤ X₀

Preprocessing

Eliminate variables {X₂,X₄,X₆,X₇,X₈,X₉,X₁₀,X₁₁} that do not contribute to the problem

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₃, X₅
Temp_Vars: M, N, O, P
Locations: l0, l1, l2, l3
Transitions:
t₂₀: l0(X₀, X₁, X₃, X₅) → l1(X₀, X₁, X₃, X₅)
t₂₃: l0(X₀, X₁, X₃, X₅) → l1(X₅, X₃, X₃, X₅)
t₂₄: l0(X₀, X₁, X₃, X₅) → l1(X₅, X₃, X₃, X₅)
t₂₆: l0(X₀, X₁, X₃, X₅) → l1(X₀+1, X₁, X₃, X₅)
t₂₇: l0(X₀, X₁, X₃, X₅) → l1(X₀, X₁+1, X₃, X₅)
t₂₁: l0(X₀, X₁, X₃, X₅) → l2(X₀, X₁, X₃, X₅)
t₂₂: l0(X₀, X₁, X₃, X₅) → l3(X₀, X₁, X₃, X₅)
t₂₅: l0(X₀, X₁, X₃, X₅) → l3(O, P, M, N)
t₂₈: l1(X₀, X₁, X₃, X₅) → l2(X₀, X₁, X₃, X₅) :|: X₁+1 ≤ X₀
t₂₉: l1(X₀, X₁, X₃, X₅) → l2(X₀, X₁, X₃, X₅) :|: X₀+1 ≤ X₁
t₃₀: l1(X₀, X₁, X₃, X₅) → l3(O, P, M, N) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₃₁: l2(X₀, X₁, X₃, X₅) → l1(X₀+1, X₁, X₃, X₅) :|: X₀+1 ≤ X₁
t₃₂: l2(X₀, X₁, X₃, X₅) → l1(X₀, X₁+1, X₃, X₅) :|: X₁ ≤ X₀

Found invariant X₅ ≤ X₀ ∧ X₃ ≤ X₁ for location l2

Found invariant X₅ ≤ X₀ ∧ X₃ ≤ X₁ for location l1

Found invariant X₅ ≤ X₀ ∧ X₃ ≤ X₁ for location l2

Found invariant X₅ ≤ X₀ ∧ X₃ ≤ X₁ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₂₈ 16⋅X₀+16⋅X₁+8⋅X₃+8⋅X₅+44 {O(n)}

TWN-Loops:

entry: t₂₇: l0(X₀, X₁, X₃, X₅) → l1(X₀, X₁+1, X₃, X₅)
results in twn-loop: twn: (X₀,X₁,X₃,X₅) -> (X₀,X₁+1,X₃,X₅) :|: X₁+1 ≤ X₀ ∧ X₁ ≤ X₀
entry: t₂₆: l0(X₀, X₁, X₃, X₅) → l1(X₀+1, X₁, X₃, X₅)
results in twn-loop: twn: (X₀,X₁,X₃,X₅) -> (X₀,X₁+1,X₃,X₅) :|: X₁+1 ≤ X₀ ∧ X₁ ≤ X₀
entry: t₂₄: l0(X₀, X₁, X₃, X₅) → l1(X₅, X₃, X₃, X₅)
results in twn-loop: twn: (X₀,X₁,X₃,X₅) -> (X₀,X₁+1,X₃,X₅) :|: X₁+1 ≤ X₀ ∧ X₁ ≤ X₀
entry: t₂₃: l0(X₀, X₁, X₃, X₅) → l1(X₅, X₃, X₃, X₅)
results in twn-loop: twn: (X₀,X₁,X₃,X₅) -> (X₀,X₁+1,X₃,X₅) :|: X₁+1 ≤ X₀ ∧ X₁ ≤ X₀
entry: t₂₀: l0(X₀, X₁, X₃, X₅) → l1(X₀, X₁, X₃, X₅)
results in twn-loop: twn: (X₀,X₁,X₃,X₅) -> (X₀,X₁+1,X₃,X₅) :|: X₁+1 ≤ X₀ ∧ X₁ ≤ X₀
entry: t₂₁: l0(X₀, X₁, X₃, X₅) → l2(X₀, X₁, X₃, X₅)
results in twn-loop: twn: (X₀,X₁,X₃,X₅) -> (X₀,1+X₁,X₃,X₅) :|: X₁ ≤ X₀ ∧ 2+X₁ ≤ X₀
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₁ < X₀ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1

Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₁+1 ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₂₇:
X₀: X₀ {O(n)}
X₁: X₁+1 {O(n)}
Runtime-bound of t₂₇: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+10 {O(n)}

order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₁ < X₀ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1

Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₁+1 ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₂₆:
X₀: X₀+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₆: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+10 {O(n)}

order: [X₀; X₁; X₃; X₅]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1
X₃: X₃
X₅: X₅

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₁ < X₀ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1

Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₁+1 ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₂₄:
X₀: X₅ {O(n)}
X₁: X₃ {O(n)}
Runtime-bound of t₂₄: 1 {O(1)}
Results in: 4⋅X₃+4⋅X₅+6 {O(n)}

order: [X₀; X₁; X₃; X₅]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1
X₃: X₃
X₅: X₅

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₁ < X₀ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1

Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₁+1 ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₂₃:
X₀: X₅ {O(n)}
X₁: X₃ {O(n)}
Runtime-bound of t₂₃: 1 {O(1)}
Results in: 4⋅X₃+4⋅X₅+6 {O(n)}

order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₁ < X₀ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁+1 ≤ X₀ ∧ X₀ ≤ X₁+1

Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₁+1 ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₂₀:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₀: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+6 {O(n)}

order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 2+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ 1 < 0
∨ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁

Stabilization-Threshold for: 2+X₁ ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₂₁:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₁: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+6 {O(n)}

16⋅X₀+16⋅X₁+8⋅X₃+8⋅X₅+44 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₃₂ 16⋅X₀+16⋅X₁+8⋅X₃+8⋅X₅+44 {O(n)}

relevant size-bounds w.r.t. t₂₇:
X₀: X₀ {O(n)}
X₁: X₁+1 {O(n)}
Runtime-bound of t₂₇: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+10 {O(n)}

relevant size-bounds w.r.t. t₂₆:
X₀: X₀+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₆: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+10 {O(n)}

relevant size-bounds w.r.t. t₂₄:
X₀: X₅ {O(n)}
X₁: X₃ {O(n)}
Runtime-bound of t₂₄: 1 {O(1)}
Results in: 4⋅X₃+4⋅X₅+6 {O(n)}

relevant size-bounds w.r.t. t₂₃:
X₀: X₅ {O(n)}
X₁: X₃ {O(n)}
Runtime-bound of t₂₃: 1 {O(1)}
Results in: 4⋅X₃+4⋅X₅+6 {O(n)}

relevant size-bounds w.r.t. t₂₀:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₀: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+6 {O(n)}

relevant size-bounds w.r.t. t₂₁:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₁: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+6 {O(n)}

16⋅X₀+16⋅X₁+8⋅X₃+8⋅X₅+44 {O(n)}

Found invariant 1 ≤ 0 for location l2

Found invariant 1 ≤ 0 for location l1

Found invariant X₅ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ for location l2

Found invariant X₅ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ for location l1

Found invariant X₅ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ for location l2

Found invariant X₅ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ for location l1

Found invariant X₀ ≤ X₁ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₂₉ 1280⋅X₀⋅X₁+160⋅X₃⋅X₃+160⋅X₅⋅X₅+320⋅X₃⋅X₅+640⋅X₀⋅X₀+640⋅X₀⋅X₃+640⋅X₀⋅X₅+640⋅X₁⋅X₁+640⋅X₁⋅X₃+640⋅X₁⋅X₅+1668⋅X₃+1668⋅X₅+3338⋅X₀+3338⋅X₁+4346 {O(n^2)}

TWN-Loops:

entry: t₃₂: l2(X₀, X₁, X₃, X₅) → l1(X₀, X₁+1, X₃, X₅) :|: X₁ ≤ X₀
results in twn-loop: twn: (X₀,X₁,X₃,X₅) -> (X₀+1,X₁,X₃,X₅) :|: X₀+1 ≤ X₁ ∧ X₀+1 ≤ X₁
entry: t₂₇: l0(X₀, X₁, X₃, X₅) → l1(X₀, X₁+1, X₃, X₅)
results in twn-loop: twn: (X₀,X₁,X₃,X₅) -> (X₀+1,X₁,X₃,X₅) :|: X₀+1 ≤ X₁ ∧ X₀+1 ≤ X₁
entry: t₂₆: l0(X₀, X₁, X₃, X₅) → l1(X₀+1, X₁, X₃, X₅)
results in twn-loop: twn: (X₀,X₁,X₃,X₅) -> (X₀+1,X₁,X₃,X₅) :|: X₀+1 ≤ X₁ ∧ X₀+1 ≤ X₁
entry: t₂₄: l0(X₀, X₁, X₃, X₅) → l1(X₅, X₃, X₃, X₅)
results in twn-loop: twn: (X₀,X₁,X₃,X₅) -> (X₀+1,X₁,X₃,X₅) :|: X₀+1 ≤ X₁ ∧ X₀+1 ≤ X₁
entry: t₂₃: l0(X₀, X₁, X₃, X₅) → l1(X₅, X₃, X₃, X₅)
results in twn-loop: twn: (X₀,X₁,X₃,X₅) -> (X₀+1,X₁,X₃,X₅) :|: X₀+1 ≤ X₁ ∧ X₀+1 ≤ X₁
entry: t₂₀: l0(X₀, X₁, X₃, X₅) → l1(X₀, X₁, X₃, X₅)
results in twn-loop: twn: (X₀,X₁,X₃,X₅) -> (X₀+1,X₁,X₃,X₅) :|: X₀+1 ≤ X₁ ∧ X₀+1 ≤ X₁
entry: t₂₁: l0(X₀, X₁, X₃, X₅) → l2(X₀, X₁, X₃, X₅)
results in twn-loop: twn: (X₀,X₁,X₃,X₅) -> (1+X₀,X₁,X₃,X₅) :|: X₀+1 ≤ X₁ ∧ 2+X₀ ≤ X₁
order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁

Termination: true
Formula:

1 < 0
∨ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1

Stabilization-Threshold for: X₀+1 ≤ X₁
alphas_abs: X₀+1+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}

relevant size-bounds w.r.t. t₃₂:
X₀: 2⋅X₅+4⋅X₀+1 {O(n)}
X₁: 10⋅X₃+16⋅X₀+20⋅X₁+8⋅X₅+45 {O(n)}
Runtime-bound of t₃₂: 16⋅X₀+16⋅X₁+8⋅X₃+8⋅X₅+44 {O(n)}
Results in: 1280⋅X₀⋅X₁+160⋅X₃⋅X₃+160⋅X₅⋅X₅+320⋅X₃⋅X₅+640⋅X₀⋅X₀+640⋅X₀⋅X₃+640⋅X₀⋅X₅+640⋅X₁⋅X₁+640⋅X₁⋅X₃+640⋅X₁⋅X₅+1664⋅X₃+1664⋅X₅+3328⋅X₀+3328⋅X₁+4312 {O(n^2)}

order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁

Termination: true
Formula:

1 < 0
∨ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1

Stabilization-Threshold for: X₀+1 ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₂₇:
X₀: X₀ {O(n)}
X₁: X₁+1 {O(n)}
Runtime-bound of t₂₇: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+6 {O(n)}

order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁

Termination: true
Formula:

1 < 0
∨ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1

Stabilization-Threshold for: X₀+1 ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₂₆:
X₀: X₀+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₆: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+6 {O(n)}

order: [X₀; X₁; X₃; X₅]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁
X₃: X₃
X₅: X₅

Termination: true
Formula:

1 < 0
∨ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1

Stabilization-Threshold for: X₀+1 ≤ X₁
alphas_abs: X₀+1+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}

relevant size-bounds w.r.t. t₂₄:
X₀: X₅ {O(n)}
X₁: X₃ {O(n)}
Runtime-bound of t₂₄: 1 {O(1)}
Results in: 2⋅X₃+2⋅X₅+6 {O(n)}

order: [X₀; X₁; X₃; X₅]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁
X₃: X₃
X₅: X₅

Termination: true
Formula:

1 < 0
∨ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1

Stabilization-Threshold for: X₀+1 ≤ X₁
alphas_abs: X₀+1+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}

relevant size-bounds w.r.t. t₂₃:
X₀: X₅ {O(n)}
X₁: X₃ {O(n)}
Runtime-bound of t₂₃: 1 {O(1)}
Results in: 2⋅X₃+2⋅X₅+6 {O(n)}

order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁

Termination: true
Formula:

1 < 0
∨ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1

Stabilization-Threshold for: X₀+1 ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₂₀:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₀: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+4 {O(n)}

order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 2+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₀ < X₁ ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₀ ≤ X₁ ∧ X₁ ≤ 2+X₀ ∧ 1 < 0
∨ 2+X₀ ≤ X₁ ∧ X₁ ≤ 2+X₀ ∧ X₀+1 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₀ ≤ X₁ ∧ X₁ ≤ 2+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀+1 ≤ X₁ ∧ X₁ ≤ X₀+1

Stabilization-Threshold for: 2+X₀ ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₀+1 ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₂₁:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₁: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+6 {O(n)}

1280⋅X₀⋅X₁+160⋅X₃⋅X₃+160⋅X₅⋅X₅+320⋅X₃⋅X₅+640⋅X₀⋅X₀+640⋅X₀⋅X₃+640⋅X₀⋅X₅+640⋅X₁⋅X₁+640⋅X₁⋅X₃+640⋅X₁⋅X₅+1668⋅X₃+1668⋅X₅+3338⋅X₀+3338⋅X₁+4346 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₃₁ 1280⋅X₀⋅X₁+160⋅X₃⋅X₃+160⋅X₅⋅X₅+320⋅X₃⋅X₅+640⋅X₀⋅X₀+640⋅X₀⋅X₃+640⋅X₀⋅X₅+640⋅X₁⋅X₁+640⋅X₁⋅X₃+640⋅X₁⋅X₅+1668⋅X₃+1668⋅X₅+3338⋅X₀+3338⋅X₁+4346 {O(n^2)}

relevant size-bounds w.r.t. t₃₂:
X₀: 2⋅X₅+4⋅X₀+1 {O(n)}
X₁: 10⋅X₃+16⋅X₀+20⋅X₁+8⋅X₅+45 {O(n)}
Runtime-bound of t₃₂: 16⋅X₀+16⋅X₁+8⋅X₃+8⋅X₅+44 {O(n)}
Results in: 1280⋅X₀⋅X₁+160⋅X₃⋅X₃+160⋅X₅⋅X₅+320⋅X₃⋅X₅+640⋅X₀⋅X₀+640⋅X₀⋅X₃+640⋅X₀⋅X₅+640⋅X₁⋅X₁+640⋅X₁⋅X₃+640⋅X₁⋅X₅+1664⋅X₃+1664⋅X₅+3328⋅X₀+3328⋅X₁+4312 {O(n^2)}

relevant size-bounds w.r.t. t₂₇:
X₀: X₀ {O(n)}
X₁: X₁+1 {O(n)}
Runtime-bound of t₂₇: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+6 {O(n)}

relevant size-bounds w.r.t. t₂₆:
X₀: X₀+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₆: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+6 {O(n)}

relevant size-bounds w.r.t. t₂₄:
X₀: X₅ {O(n)}
X₁: X₃ {O(n)}
Runtime-bound of t₂₄: 1 {O(1)}
Results in: 2⋅X₃+2⋅X₅+6 {O(n)}

relevant size-bounds w.r.t. t₂₃:
X₀: X₅ {O(n)}
X₁: X₃ {O(n)}
Runtime-bound of t₂₃: 1 {O(1)}
Results in: 2⋅X₃+2⋅X₅+6 {O(n)}

relevant size-bounds w.r.t. t₂₀:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₀: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+4 {O(n)}

relevant size-bounds w.r.t. t₂₁:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₁: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+6 {O(n)}

1280⋅X₀⋅X₁+160⋅X₃⋅X₃+160⋅X₅⋅X₅+320⋅X₃⋅X₅+640⋅X₀⋅X₀+640⋅X₀⋅X₃+640⋅X₀⋅X₅+640⋅X₁⋅X₁+640⋅X₁⋅X₃+640⋅X₁⋅X₅+1668⋅X₃+1668⋅X₅+3338⋅X₀+3338⋅X₁+4346 {O(n^2)}

Analysing control-flow refined program

Cut unsatisfiable transition t₂₇₇: n_l1___4→n_l2___5

Found invariant X₁ ≤ 1+X₀ for location n_l1___6

Found invariant 1+X₀ ≤ X₁ for location n_l2___7

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___4

Found invariant X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ for location n_l2___5

Found invariant X₀ ≤ X₁ for location n_l1___3

Found invariant 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ for location n_l2___1

Found invariant X₅ ≤ X₀ ∧ 1+X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l2___2

Found invariant 1+X₁ ≤ X₀ for location n_l2___8

Found invariant X₁ ≤ 1+X₀ for location n_l1___6

Found invariant 2+X₅ ≤ X₃ ∧ 2+X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ for location n_l2___7

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___4

Found invariant X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ for location n_l2___5

Found invariant 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₁ for location n_l1___3

Found invariant 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ for location n_l2___1

Found invariant X₅ ≤ X₀ ∧ 1+X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l2___2

Found invariant 1+X₁ ≤ X₀ for location n_l2___8

Found invariant X₁ ≤ 1+X₀ for location n_l1___6

Found invariant 1+X₀ ≤ X₁ for location n_l2___7

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___4

Found invariant X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ for location n_l2___5

Found invariant X₀ ≤ X₁ for location n_l1___3

Found invariant 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ for location n_l2___1

Found invariant X₅ ≤ X₀ ∧ 1+X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l2___2

Found invariant 1+X₁ ≤ X₀ for location n_l2___8

Found invariant X₁ ≤ 1+X₀ for location n_l1___6

Found invariant 1+X₀ ≤ X₁ for location n_l2___7

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___4

Found invariant X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ for location n_l2___5

Found invariant X₀ ≤ X₁ for location n_l1___3

Found invariant 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ for location n_l2___1

Found invariant X₅ ≤ X₀ ∧ 1+X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l2___2

Found invariant 1+X₁ ≤ X₀ for location n_l2___8

Time-Bound by TWN-Loops:

TWN-Loops: t₂₇₆ 16⋅X₃+16⋅X₅+28⋅X₀+28⋅X₁+44 {O(n)}

TWN-Loops:

entry: t₂₈₀: n_l2___1(X₀, X₁, X₃, X₅) → n_l1___3(X₀+1, X₁, X₃, X₅) :|: 1+X₀ ≤ X₁ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁
results in twn-loop: twn:Inv: [X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁] , (X₀,X₁,X₃,X₅) -> (X₀+1,X₁,X₃,X₅) :|: X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁
entry: t₂₈₅: l2(X₀, X₁, X₃, X₅) → n_l1___3(X₀+1, X₁, X₃, X₅) :|: 1+X₀ ≤ X₁
results in twn-loop: twn:Inv: [X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁] , (X₀,X₁,X₃,X₅) -> (X₀+1,X₁,X₃,X₅) :|: X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁
entry: t₂₇₄: l1(X₀, X₁, X₃, X₅) → n_l2___7(X₀, X₁, X₃, X₅) :|: 1+X₀ ≤ X₁
results in twn-loop: twn:Inv: [1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁] , (X₀,X₁,X₃,X₅) -> (1+X₀,X₁,X₃,X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 2+X₀ ≤ X₁
order: [X₀; X₁; X₃; X₅]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁
X₃: X₃
X₅: X₅

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
∨ 1+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1+X₀ < X₁ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ 1 < 0
∨ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀

Stabilization-Threshold for: 1+X₀ ≤ X₁
alphas_abs: 1+X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}
Stabilization-Threshold for: X₀ ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₂₈₀:
X₀: 2⋅X₅+3⋅X₀+2 {O(n)}
X₁: 2⋅X₃+3⋅X₁+1 {O(n)}
Runtime-bound of t₂₈₀: 1 {O(1)}
Results in: 12⋅X₀+12⋅X₁+8⋅X₃+8⋅X₅+20 {O(n)}

order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
∨ 1+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1+X₀ < X₁ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ 1 < 0
∨ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀

Stabilization-Threshold for: 1+X₀ ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₀ ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₂₈₅:
X₀: X₀+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₈₅: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+10 {O(n)}

order: [X₀; X₁]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ 1+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀
∨ 2+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₀ < X₁ ∧ 1+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₀ ≤ X₁ ∧ X₁ ≤ 2+X₀ ∧ 1 < 0
∨ 2+X₀ ≤ X₁ ∧ X₁ ≤ 2+X₀ ∧ 1+X₀ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₀ ≤ X₁ ∧ X₁ ≤ 2+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀

Stabilization-Threshold for: 2+X₀ ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: 1+X₀ ≤ X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₂₇₄:
X₀: 2⋅X₅+3⋅X₀+1 {O(n)}
X₁: 2⋅X₃+3⋅X₁+1 {O(n)}
Runtime-bound of t₂₇₄: 1 {O(1)}
Results in: 12⋅X₀+12⋅X₁+8⋅X₃+8⋅X₅+14 {O(n)}

16⋅X₃+16⋅X₅+28⋅X₀+28⋅X₁+44 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₂₈₃ 16⋅X₃+16⋅X₅+28⋅X₀+28⋅X₁+44 {O(n)}

relevant size-bounds w.r.t. t₂₈₀:
X₀: 2⋅X₅+3⋅X₀+2 {O(n)}
X₁: 2⋅X₃+3⋅X₁+1 {O(n)}
Runtime-bound of t₂₈₀: 1 {O(1)}
Results in: 12⋅X₀+12⋅X₁+8⋅X₃+8⋅X₅+20 {O(n)}

relevant size-bounds w.r.t. t₂₈₅:
X₀: X₀+1 {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₈₅: 1 {O(1)}
Results in: 4⋅X₀+4⋅X₁+10 {O(n)}

relevant size-bounds w.r.t. t₂₇₄:
X₀: 2⋅X₅+3⋅X₀+1 {O(n)}
X₁: 2⋅X₃+3⋅X₁+1 {O(n)}
Runtime-bound of t₂₇₄: 1 {O(1)}
Results in: 12⋅X₀+12⋅X₁+8⋅X₃+8⋅X₅+14 {O(n)}

16⋅X₃+16⋅X₅+28⋅X₀+28⋅X₁+44 {O(n)}

Found invariant X₅ ≤ X₀ ∧ 1+X₃ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₀ for location n_l1___6

Found invariant 1+X₀ ≤ X₁ for location n_l2___7

Found invariant 1 ≤ 0 for location n_l1___4

Found invariant 1 ≤ 0 for location n_l2___5

Found invariant X₀ ≤ X₁ for location n_l1___3

Found invariant 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ for location n_l2___1

Found invariant X₅ ≤ X₀ ∧ 1+X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l2___2

Found invariant X₅ ≤ X₀ ∧ 2+X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location n_l2___8

Found invariant X₁ ≤ 1+X₀ for location n_l1___6

Found invariant 1+X₀ ≤ X₁ for location n_l2___7

Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___4

Found invariant X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ for location n_l2___5

Found invariant X₀ ≤ X₁ for location n_l1___3

Found invariant 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ for location n_l2___1

Found invariant X₅ ≤ X₀ ∧ 1+X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l2___2

Found invariant 1+X₁ ≤ X₀ for location n_l2___8

Found invariant X₁ ≤ X₀ for location n_l1___6

Found invariant 1+X₀ ≤ X₁ for location n_l2___7

Found invariant 1 ≤ 0 for location n_l1___4

Found invariant 1 ≤ 0 for location n_l2___5

Found invariant X₀ ≤ X₁ for location n_l1___3

Found invariant 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ for location n_l2___1

Found invariant X₅ ≤ X₀ ∧ 1+X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l2___2

Found invariant 1+X₁ ≤ X₀ for location n_l2___8

Time-Bound by TWN-Loops:

TWN-Loops: t₂₇₉ 24⋅X₃+24⋅X₅+42⋅X₀+42⋅X₁+66 {O(n)}

TWN-Loops:

entry: t₂₈₁: n_l2___2(X₀, X₁, X₃, X₅) → n_l1___6(X₀, X₁+1, X₃, X₅) :|: 1+X₁ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 1+X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀
results in twn-loop: twn:Inv: [X₁ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀] , (X₀,X₁,X₃,X₅) -> (X₀,X₁+1,X₃,X₅) :|: X₁ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀
entry: t₂₈₆: l2(X₀, X₁, X₃, X₅) → n_l1___6(X₀, X₁+1, X₃, X₅) :|: X₁ ≤ X₀
results in twn-loop: twn:Inv: [X₁ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀] , (X₀,X₁,X₃,X₅) -> (X₀,X₁+1,X₃,X₅) :|: X₁ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀
entry: t₂₇₅: l1(X₀, X₁, X₃, X₅) → n_l2___8(X₀, X₁, X₃, X₅) :|: 1+X₁ ≤ X₀
results in twn-loop: twn:Inv: [1+X₁ ≤ X₀ ∧ X₁ ≤ X₀] , (X₀,X₁,X₃,X₅) -> (X₀,1+X₁,X₃,X₅) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 2+X₁ ≤ X₀
order: [X₀; X₁; X₃; X₅]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1
X₃: X₃
X₅: X₅

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 1+X₁ < X₀ ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ 1 < 0 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₁ < X₀ ∧ 1 < 0 ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
∨ X₁ < X₀ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₁ < X₀ ∧ 1+X₁ < X₀ ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < X₀ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ X₁ < X₀ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < X₀ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0 ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₀ ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁

Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: 1+X₁ ≤ X₀
alphas_abs: 1+X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}
Stabilization-Threshold for: X₁ ≤ 1+X₀
alphas_abs: 1+X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}

relevant size-bounds w.r.t. t₂₈₁:
X₀: 2⋅X₅+3⋅X₀+1 {O(n)}
X₁: 2⋅X₃+3⋅X₁+2 {O(n)}
Runtime-bound of t₂₈₁: 1 {O(1)}
Results in: 12⋅X₃+12⋅X₅+18⋅X₀+18⋅X₁+30 {O(n)}

order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 1+X₁ < X₀ ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ 1 < 0 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₁ < X₀ ∧ 1 < 0 ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
∨ X₁ < X₀ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₁ < X₀ ∧ 1+X₁ < X₀ ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < X₀ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ X₁ < X₀ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ < X₀ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0 ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₀ ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 < 0
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₁ < 1+X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁

Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: 1+X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₁ ≤ 1+X₀
alphas_abs: 1+X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}

relevant size-bounds w.r.t. t₂₈₆:
X₀: X₀ {O(n)}
X₁: X₁+1 {O(n)}
Runtime-bound of t₂₈₆: 1 {O(1)}
Results in: 6⋅X₀+6⋅X₁+16 {O(n)}

order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ X₁ < X₀ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0
∨ 1 < 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ 2+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₁ < X₀ ∧ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₁ < X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ 2+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₁ < X₀ ∧ X₁ < X₀ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₁ < X₀ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ 2+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0
∨ 2+X₁ < X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₁ < X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ 1 < 0
∨ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ 1 < 0 ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ X₁ < X₀ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁
∨ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 < 0
∨ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2+X₁ ≤ X₀ ∧ X₀ ≤ 2+X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ 1+X₁

Stabilization-Threshold for: 2+X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}
Stabilization-Threshold for: 1+X₁ ≤ X₀
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₂₇₅:
X₀: 2⋅X₅+3⋅X₀+1 {O(n)}
X₁: 2⋅X₃+3⋅X₁+1 {O(n)}
Runtime-bound of t₂₇₅: 1 {O(1)}
Results in: 12⋅X₃+12⋅X₅+18⋅X₀+18⋅X₁+20 {O(n)}

24⋅X₃+24⋅X₅+42⋅X₀+42⋅X₁+66 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₂₈₄ 24⋅X₃+24⋅X₅+42⋅X₀+42⋅X₁+66 {O(n)}

relevant size-bounds w.r.t. t₂₈₁:
X₀: 2⋅X₅+3⋅X₀+1 {O(n)}
X₁: 2⋅X₃+3⋅X₁+2 {O(n)}
Runtime-bound of t₂₈₁: 1 {O(1)}
Results in: 12⋅X₃+12⋅X₅+18⋅X₀+18⋅X₁+30 {O(n)}

relevant size-bounds w.r.t. t₂₈₆:
X₀: X₀ {O(n)}
X₁: X₁+1 {O(n)}
Runtime-bound of t₂₈₆: 1 {O(1)}
Results in: 6⋅X₀+6⋅X₁+16 {O(n)}

relevant size-bounds w.r.t. t₂₇₅:
X₀: 2⋅X₅+3⋅X₀+1 {O(n)}
X₁: 2⋅X₃+3⋅X₁+1 {O(n)}
Runtime-bound of t₂₇₅: 1 {O(1)}
Results in: 12⋅X₃+12⋅X₅+18⋅X₀+18⋅X₁+20 {O(n)}

24⋅X₃+24⋅X₅+42⋅X₀+42⋅X₁+66 {O(n)}

CFR: Improvement to new bound with the following program:

new bound:

140⋅X₀+140⋅X₁+80⋅X₃+80⋅X₅+220 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₃, X₅
Temp_Vars: M, N, O, P
Locations: l0, l1, l2, l3, n_l1___3, n_l1___4, n_l1___6, n_l2___1, n_l2___2, n_l2___5, n_l2___7, n_l2___8
Transitions:
t₂₀: l0(X₀, X₁, X₃, X₅) → l1(X₀, X₁, X₃, X₅)
t₂₃: l0(X₀, X₁, X₃, X₅) → l1(X₅, X₃, X₃, X₅)
t₂₄: l0(X₀, X₁, X₃, X₅) → l1(X₅, X₃, X₃, X₅)
t₂₆: l0(X₀, X₁, X₃, X₅) → l1(X₀+1, X₁, X₃, X₅)
t₂₇: l0(X₀, X₁, X₃, X₅) → l1(X₀, X₁+1, X₃, X₅)
t₂₁: l0(X₀, X₁, X₃, X₅) → l2(X₀, X₁, X₃, X₅)
t₂₂: l0(X₀, X₁, X₃, X₅) → l3(X₀, X₁, X₃, X₅)
t₂₅: l0(X₀, X₁, X₃, X₅) → l3(O, P, M, N)
t₃₀: l1(X₀, X₁, X₃, X₅) → l3(O, P, M, N) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₂₇₂: l1(X₀, X₁, X₃, X₅) → n_l2___1(X₀, X₁, X₃, X₅) :|: X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁
t₂₇₃: l1(X₀, X₁, X₃, X₅) → n_l2___2(X₀, X₁, X₃, X₅) :|: X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1+X₁ ≤ X₀
t₂₇₄: l1(X₀, X₁, X₃, X₅) → n_l2___7(X₀, X₁, X₃, X₅) :|: 1+X₀ ≤ X₁
t₂₇₅: l1(X₀, X₁, X₃, X₅) → n_l2___8(X₀, X₁, X₃, X₅) :|: 1+X₁ ≤ X₀
t₂₈₅: l2(X₀, X₁, X₃, X₅) → n_l1___3(X₀+1, X₁, X₃, X₅) :|: 1+X₀ ≤ X₁
t₂₈₆: l2(X₀, X₁, X₃, X₅) → n_l1___6(X₀, X₁+1, X₃, X₅) :|: X₁ ≤ X₀
t₂₉₇: n_l1___3(X₀, X₁, X₃, X₅) → l3(O, P, M, N) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₂₇₆: n_l1___3(X₀, X₁, X₃, X₅) → n_l2___7(X₀, X₁, X₃, X₅) :|: X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ X₁
t₂₉₈: n_l1___4(X₀, X₁, X₃, X₅) → l3(O, P, M, N) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₂₉₉: n_l1___6(X₀, X₁, X₃, X₅) → l3(O, P, M, N) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ 1+X₀
t₂₇₈: n_l1___6(X₀, X₁, X₃, X₅) → n_l2___5(X₀, X₁, X₃, X₅) :|: X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀
t₂₇₉: n_l1___6(X₀, X₁, X₃, X₅) → n_l2___8(X₀, X₁, X₃, X₅) :|: X₁ ≤ 1+X₀ ∧ 1+X₁ ≤ X₀ ∧ X₁ ≤ 1+X₀
t₂₈₀: n_l2___1(X₀, X₁, X₃, X₅) → n_l1___3(X₀+1, X₁, X₃, X₅) :|: 1+X₀ ≤ X₁ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁
t₂₈₁: n_l2___2(X₀, X₁, X₃, X₅) → n_l1___6(X₀, X₁+1, X₃, X₅) :|: 1+X₁ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₀ ∧ 1+X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀
t₂₈₂: n_l2___5(X₀, X₁, X₃, X₅) → n_l1___4(X₀+1, X₁, X₃, X₅) :|: X₀+1 ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁
t₂₈₃: n_l2___7(X₀, X₁, X₃, X₅) → n_l1___3(X₀+1, X₁, X₃, X₅) :|: 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₁
t₂₈₄: n_l2___8(X₀, X₁, X₃, X₅) → n_l1___6(X₀, X₁+1, X₃, X₅) :|: 1+X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₀

All Bounds

Timebounds

Overall timebound:140⋅X₀+140⋅X₁+80⋅X₃+80⋅X₅+242 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₃₀: 1 {O(1)}
t₂₇₂: 1 {O(1)}
t₂₇₃: 1 {O(1)}
t₂₇₄: 1 {O(1)}
t₂₇₅: 1 {O(1)}
t₂₈₅: 1 {O(1)}
t₂₈₆: 1 {O(1)}
t₂₇₆: 16⋅X₃+16⋅X₅+28⋅X₀+28⋅X₁+44 {O(n)}
t₂₉₇: 1 {O(1)}
t₂₉₈: 1 {O(1)}
t₂₇₈: 1 {O(1)}
t₂₇₉: 24⋅X₃+24⋅X₅+42⋅X₀+42⋅X₁+66 {O(n)}
t₂₉₉: 1 {O(1)}
t₂₈₀: 1 {O(1)}
t₂₈₁: 1 {O(1)}
t₂₈₂: 1 {O(1)}
t₂₈₃: 16⋅X₃+16⋅X₅+28⋅X₀+28⋅X₁+44 {O(n)}
t₂₈₄: 24⋅X₃+24⋅X₅+42⋅X₀+42⋅X₁+66 {O(n)}

Costbounds

Overall costbound: 140⋅X₀+140⋅X₁+80⋅X₃+80⋅X₅+242 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₃₀: 1 {O(1)}
t₂₇₂: 1 {O(1)}
t₂₇₃: 1 {O(1)}
t₂₇₄: 1 {O(1)}
t₂₇₅: 1 {O(1)}
t₂₈₅: 1 {O(1)}
t₂₈₆: 1 {O(1)}
t₂₇₆: 16⋅X₃+16⋅X₅+28⋅X₀+28⋅X₁+44 {O(n)}
t₂₉₇: 1 {O(1)}
t₂₉₈: 1 {O(1)}
t₂₇₈: 1 {O(1)}
t₂₇₉: 24⋅X₃+24⋅X₅+42⋅X₀+42⋅X₁+66 {O(n)}
t₂₉₉: 1 {O(1)}
t₂₈₀: 1 {O(1)}
t₂₈₁: 1 {O(1)}
t₂₈₂: 1 {O(1)}
t₂₈₃: 16⋅X₃+16⋅X₅+28⋅X₀+28⋅X₁+44 {O(n)}
t₂₈₄: 24⋅X₃+24⋅X₅+42⋅X₀+42⋅X₁+66 {O(n)}

Sizebounds

t₂₀, X₀: X₀ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₀, X₅: X₅ {O(n)}
t₂₁, X₀: X₀ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₁, X₅: X₅ {O(n)}
t₂₂, X₀: X₀ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₂, X₅: X₅ {O(n)}
t₂₃, X₀: X₅ {O(n)}
t₂₃, X₁: X₃ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₃, X₅: X₅ {O(n)}
t₂₄, X₀: X₅ {O(n)}
t₂₄, X₁: X₃ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₄, X₅: X₅ {O(n)}
t₂₆, X₀: X₀+1 {O(n)}
t₂₆, X₁: X₁ {O(n)}
t₂₆, X₃: X₃ {O(n)}
t₂₆, X₅: X₅ {O(n)}
t₂₇, X₀: X₀ {O(n)}
t₂₇, X₁: X₁+1 {O(n)}
t₂₇, X₃: X₃ {O(n)}
t₂₇, X₅: X₅ {O(n)}
t₂₇₂, X₀: 2⋅X₅+3⋅X₀+1 {O(n)}
t₂₇₂, X₁: 2⋅X₃+3⋅X₁+1 {O(n)}
t₂₇₂, X₃: 5⋅X₃ {O(n)}
t₂₇₂, X₅: 5⋅X₅ {O(n)}
t₂₇₃, X₀: 2⋅X₅+3⋅X₀+1 {O(n)}
t₂₇₃, X₁: 2⋅X₃+3⋅X₁+1 {O(n)}
t₂₇₃, X₃: 5⋅X₃ {O(n)}
t₂₇₃, X₅: 5⋅X₅ {O(n)}
t₂₇₄, X₀: 2⋅X₅+3⋅X₀+1 {O(n)}
t₂₇₄, X₁: 2⋅X₃+3⋅X₁+1 {O(n)}
t₂₇₄, X₃: 5⋅X₃ {O(n)}
t₂₇₄, X₅: 5⋅X₅ {O(n)}
t₂₇₅, X₀: 2⋅X₅+3⋅X₀+1 {O(n)}
t₂₇₅, X₁: 2⋅X₃+3⋅X₁+1 {O(n)}
t₂₇₅, X₃: 5⋅X₃ {O(n)}
t₂₇₅, X₅: 5⋅X₅ {O(n)}
t₂₈₅, X₀: X₀+1 {O(n)}
t₂₈₅, X₁: X₁ {O(n)}
t₂₈₅, X₃: X₃ {O(n)}
t₂₈₅, X₅: X₅ {O(n)}
t₂₈₆, X₀: X₀ {O(n)}
t₂₈₆, X₁: X₁+1 {O(n)}
t₂₈₆, X₃: X₃ {O(n)}
t₂₈₆, X₅: X₅ {O(n)}
t₂₇₆, X₀: 16⋅X₃+20⋅X₅+28⋅X₁+35⋅X₀+48 {O(n)}
t₂₇₆, X₁: 4⋅X₃+7⋅X₁+2 {O(n)}
t₂₇₆, X₃: 11⋅X₃ {O(n)}
t₂₇₆, X₅: 11⋅X₅ {O(n)}
t₂₇₈, X₀: X₀ {O(n)}
t₂₇₈, X₁: X₁+1 {O(n)}
t₂₇₈, X₃: X₃ {O(n)}
t₂₇₈, X₅: X₅ {O(n)}
t₂₇₉, X₀: 4⋅X₅+7⋅X₀+2 {O(n)}
t₂₇₉, X₁: 24⋅X₅+28⋅X₃+42⋅X₀+49⋅X₁+70 {O(n)}
t₂₇₉, X₃: 11⋅X₃ {O(n)}
t₂₇₉, X₅: 11⋅X₅ {O(n)}
t₂₈₀, X₀: 2⋅X₅+3⋅X₀+2 {O(n)}
t₂₈₀, X₁: 2⋅X₃+3⋅X₁+1 {O(n)}
t₂₈₀, X₃: 5⋅X₃ {O(n)}
t₂₈₀, X₅: 5⋅X₅ {O(n)}
t₂₈₁, X₀: 2⋅X₅+3⋅X₀+1 {O(n)}
t₂₈₁, X₁: 2⋅X₃+3⋅X₁+2 {O(n)}
t₂₈₁, X₃: 5⋅X₃ {O(n)}
t₂₈₁, X₅: 5⋅X₅ {O(n)}
t₂₈₂, X₀: X₀+1 {O(n)}
t₂₈₂, X₁: X₁+1 {O(n)}
t₂₈₂, X₃: X₃ {O(n)}
t₂₈₂, X₅: X₅ {O(n)}
t₂₈₃, X₀: 16⋅X₃+20⋅X₅+28⋅X₁+35⋅X₀+48 {O(n)}
t₂₈₃, X₁: 4⋅X₃+7⋅X₁+2 {O(n)}
t₂₈₃, X₃: 11⋅X₃ {O(n)}
t₂₈₃, X₅: 11⋅X₅ {O(n)}
t₂₈₄, X₀: 4⋅X₅+7⋅X₀+2 {O(n)}
t₂₈₄, X₁: 24⋅X₅+28⋅X₃+42⋅X₀+49⋅X₁+70 {O(n)}
t₂₈₄, X₃: 11⋅X₃ {O(n)}
t₂₈₄, X₅: 11⋅X₅ {O(n)}