Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀+X₁, X₁+X₂, X₂-1, X₃) :|: 1 ≤ X₀
t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃-1) :|: X₀ ≤ 0
t₃: l2(X₀, X₁, X₂, X₃) → l1(X₃, X₃, X₃, X₃) :|: 1 ≤ X₃

Preprocessing

Found invariant X₀ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀+X₁, X₁+X₂, X₂-1, X₃) :|: 1 ≤ X₀
t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃-1) :|: X₀ ≤ 0
t₃: l2(X₀, X₁, X₂, X₃) → l1(X₃, X₃, X₃, X₃) :|: 1 ≤ X₃ ∧ X₀ ≤ 0

MPRF for transition t₃: l2(X₀, X₁, X₂, X₃) → l1(X₃, X₃, X₃, X₃) :|: 1 ≤ X₃ ∧ X₀ ≤ 0 of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

l2 [X₃ ]
l1 [X₃-1 ]

Found invariant 1 ≤ 0 for location l2

Found invariant 1 ≤ 0 for location l1

Found invariant X₀ ≤ 0 for location l2

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃-1) :|: X₀ ≤ 0 of depth 1:

new bound:

X₃+2 {O(n)}

MPRF:

l1 [1 ]
l2 [0 ]

Time-Bound by TWN-Loops:

TWN-Loops: t₁ 108⋅X₃⋅X₃+12⋅X₀+12⋅X₁+207⋅X₃+6⋅X₂+111 {O(n^2)}

relevant size-bounds w.r.t. t₃:
X₀: 3⋅X₃+2 {O(n)}
X₁: 3⋅X₃+2 {O(n)}
X₂: 3⋅X₃+2 {O(n)}
Runtime-bound of t₃: X₃+1 {O(n)}
Results in: 108⋅X₃⋅X₃+207⋅X₃+99 {O(n^2)}

relevant size-bounds w.r.t. t₀:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
X₂: X₂ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 12⋅X₀+12⋅X₁+6⋅X₂+12 {O(n)}

108⋅X₃⋅X₃+12⋅X₀+12⋅X₁+207⋅X₃+6⋅X₂+111 {O(n^2)}

Analysing control-flow refined program

Cut unsatisfiable transition t₆₀: n_l1___1→l2

Found invariant X₀ ≤ 0 for location l2

Found invariant X₃ ≤ 1+X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___1

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃-1) :|: X₀ ≤ 0

knowledge_propagation leads to new time bound X₃+2 {O(n)} for transition t₅₆: l1(X₀, X₁, X₂, X₃) → n_l1___1(X₀+X₁, X₁+X₂, X₂-1, X₃) :|: 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₀+X₂ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₃+2 {O(n)} for transition t₅₇: l1(X₀, X₁, X₂, X₃) → n_l1___2(X₀+X₁, X₁+X₂, X₂-1, X₃) :|: 1 ≤ X₀

knowledge_propagation leads to new time bound X₃+2 {O(n)} for transition t₅₄: n_l1___1(X₀, X₁, X₂, X₃) → n_l1___2(X₀+X₁, X₁+X₂, X₂-1, X₃) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₀+X₂ ∧ 1 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀

MPRF for transition t₆₁: n_l1___2(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃-1) :|: X₀ ≤ 0 of depth 1:

new bound:

X₃+2 {O(n)}

MPRF:

l1 [1 ]
n_l1___1 [1 ]
n_l1___2 [1 ]
l2 [0 ]

Found invariant X₀ ≤ 0 for location l2

Found invariant 1 ≤ X₃ ∧ 2+X₂ ≤ X₃ for location n_l1___2

Found invariant X₃ ≤ 1+X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___1

Found invariant X₀ ≤ 0 for location l2

Found invariant X₃ ≤ 1+X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___1

Time-Bound by TWN-Loops:

TWN-Loops: t₅₅ 1008⋅X₃⋅X₃+192⋅X₁⋅X₃+72⋅X₀⋅X₃+72⋅X₂⋅X₃+144⋅X₀+144⋅X₂+2816⋅X₃+384⋅X₁+1600 {O(n^2)}

TWN-Loops:

entry: t₅₄: n_l1___1(X₀, X₁, X₂, X₃) → n_l1___2(X₀+X₁, X₁+X₂, X₂-1, X₃) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₀+X₂ ∧ 1 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀
results in twn-loop: twn: (X₀,X₁,X₂,X₃) -> (X₀+X₁,X₁+X₂,X₂-1,X₃) :|: X₁ ≤ X₀+X₂ ∧ 1 ≤ X₀
entry: t₅₇: l1(X₀, X₁, X₂, X₃) → n_l1___2(X₀+X₁, X₁+X₂, X₂-1, X₃) :|: 1 ≤ X₀
results in twn-loop: twn: (X₀,X₁,X₂,X₃) -> (X₀+X₁,X₁+X₂,X₂-1,X₃) :|: X₁ ≤ X₀+X₂ ∧ 1 ≤ X₀
order: [X₂; X₁; X₀; X₃]
closed-form:
X₂: X₂ + [[n != 0]] * -1 * n^1
X₁: X₁ + [[n != 0]] * X₂ * n^1 + [[n != 0, n != 1]] * -1/2 * n^2 + [[n != 0, n != 1]] * 1/2 * n^1
X₀: X₀ + [[n != 0]] * X₁ * n^1 + [[n != 0, n != 1]] * 1/2⋅X₂ * n^2 + [[n != 0, n != 1]] * -1/2⋅X₂ * n^1 + [[n != 0, n != 1, n != 2]] * -1/6 * n^3 + [[n != 0, n != 1, n != 2]] * 1/2 * n^2 + [[n != 0, n != 1, n != 2]] * -1/3 * n^1
X₃: X₃

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ 0 < 3⋅X₂+6 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 9⋅X₂+11 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0
∨ 1 < 0 ∧ 6⋅X₁ < 6⋅X₀+6⋅X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11 ∧ 6⋅X₁ ≤ 6⋅X₀+6⋅X₂ ∧ 6⋅X₀+6⋅X₂ ≤ 6⋅X₁
∨ 0 < 3⋅X₂+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 0 < 3⋅X₂+3 ∧ 0 < 3⋅X₂+6 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 3⋅X₂+3 ∧ 9⋅X₂+11 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0
∨ 0 < 3⋅X₂+3 ∧ 6⋅X₁ < 6⋅X₀+6⋅X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11
∨ 0 < 3⋅X₂+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11 ∧ 6⋅X₁ ≤ 6⋅X₀+6⋅X₂ ∧ 6⋅X₀+6⋅X₂ ≤ 6⋅X₁
∨ 3⋅X₂+2 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 1 < 0
∨ 3⋅X₂+2 < 6⋅X₁ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 0 < 3⋅X₂+6 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 3⋅X₂+2 < 6⋅X₁ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 9⋅X₂+11 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0
∨ 3⋅X₂+2 < 6⋅X₁ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 6⋅X₁ < 6⋅X₀+6⋅X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11
∨ 3⋅X₂+2 < 6⋅X₁ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11 ∧ 6⋅X₁ ≤ 6⋅X₀+6⋅X₂ ∧ 6⋅X₀+6⋅X₂ ≤ 6⋅X₁
∨ 6 < 6⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 1 < 0
∨ 6 < 6⋅X₀ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 0 < 3⋅X₂+6 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 6 < 6⋅X₀ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 9⋅X₂+11 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0
∨ 6 < 6⋅X₀ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 6⋅X₁ < 6⋅X₀+6⋅X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11
∨ 6 < 6⋅X₀ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11 ∧ 6⋅X₁ ≤ 6⋅X₀+6⋅X₂ ∧ 6⋅X₀+6⋅X₂ ≤ 6⋅X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 6 ≤ 6⋅X₀ ∧ 6⋅X₀ ≤ 6 ∧ 1 < 0
∨ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 6 ≤ 6⋅X₀ ∧ 6⋅X₀ ≤ 6 ∧ 0 < 3⋅X₂+6 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 6 ≤ 6⋅X₀ ∧ 6⋅X₀ ≤ 6 ∧ 9⋅X₂+11 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0
∨ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 6 ≤ 6⋅X₀ ∧ 6⋅X₀ ≤ 6 ∧ 6⋅X₁ < 6⋅X₀+6⋅X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11
∨ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 6 ≤ 6⋅X₀ ∧ 6⋅X₀ ≤ 6 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11 ∧ 6⋅X₁ ≤ 6⋅X₀+6⋅X₂ ∧ 6⋅X₀+6⋅X₂ ≤ 6⋅X₁

Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: 3+6⋅X₀+6⋅X₁+3⋅X₂
M: 0
N: 3
Bound: 12⋅X₀+12⋅X₁+6⋅X₂+10 {O(n)}
Stabilization-Threshold for: X₁ ≤ X₀+X₂
alphas_abs: 6+6⋅X₀+6⋅X₁+9⋅X₂
M: 0
N: 3
Bound: 12⋅X₀+12⋅X₁+18⋅X₂+16 {O(n)}

relevant size-bounds w.r.t. t₅₄:
X₀: 12⋅X₃+2⋅X₀+2⋅X₁+8 {O(n)}
X₁: 12⋅X₃+4⋅X₁+8 {O(n)}
X₂: 3⋅X₃+X₂+3 {O(n)}
Runtime-bound of t₅₄: X₃+2 {O(n)}
Results in: 144⋅X₁⋅X₃+24⋅X₂⋅X₃+48⋅X₀⋅X₃+648⋅X₃⋅X₃+1780⋅X₃+288⋅X₁+48⋅X₂+96⋅X₀+968 {O(n^2)}

order: [X₂; X₁; X₀]
closed-form:
X₂: X₂ + [[n != 0]] * -1 * n^1
X₁: X₁ + [[n != 0]] * X₂ * n^1 + [[n != 0, n != 1]] * -1/2 * n^2 + [[n != 0, n != 1]] * 1/2 * n^1
X₀: X₀ + [[n != 0]] * X₁ * n^1 + [[n != 0, n != 1]] * 1/2⋅X₂ * n^2 + [[n != 0, n != 1]] * -1/2⋅X₂ * n^1 + [[n != 0, n != 1, n != 2]] * -1/6 * n^3 + [[n != 0, n != 1, n != 2]] * 1/2 * n^2 + [[n != 0, n != 1, n != 2]] * -1/3 * n^1

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ 0 < 3⋅X₂+6 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 9⋅X₂+11 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0
∨ 1 < 0 ∧ 6⋅X₁ < 6⋅X₀+6⋅X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11 ∧ 6⋅X₁ ≤ 6⋅X₀+6⋅X₂ ∧ 6⋅X₀+6⋅X₂ ≤ 6⋅X₁
∨ 0 < 3⋅X₂+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 0 < 3⋅X₂+3 ∧ 0 < 3⋅X₂+6 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 3⋅X₂+3 ∧ 9⋅X₂+11 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0
∨ 0 < 3⋅X₂+3 ∧ 6⋅X₁ < 6⋅X₀+6⋅X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11
∨ 0 < 3⋅X₂+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11 ∧ 6⋅X₁ ≤ 6⋅X₀+6⋅X₂ ∧ 6⋅X₀+6⋅X₂ ≤ 6⋅X₁
∨ 3⋅X₂+2 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 1 < 0
∨ 3⋅X₂+2 < 6⋅X₁ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 0 < 3⋅X₂+6 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 3⋅X₂+2 < 6⋅X₁ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 9⋅X₂+11 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0
∨ 3⋅X₂+2 < 6⋅X₁ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 6⋅X₁ < 6⋅X₀+6⋅X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11
∨ 3⋅X₂+2 < 6⋅X₁ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11 ∧ 6⋅X₁ ≤ 6⋅X₀+6⋅X₂ ∧ 6⋅X₀+6⋅X₂ ≤ 6⋅X₁
∨ 6 < 6⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 1 < 0
∨ 6 < 6⋅X₀ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 0 < 3⋅X₂+6 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 6 < 6⋅X₀ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 9⋅X₂+11 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0
∨ 6 < 6⋅X₀ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 6⋅X₁ < 6⋅X₀+6⋅X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11
∨ 6 < 6⋅X₀ ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11 ∧ 6⋅X₁ ≤ 6⋅X₀+6⋅X₂ ∧ 6⋅X₀+6⋅X₂ ≤ 6⋅X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 6 ≤ 6⋅X₀ ∧ 6⋅X₀ ≤ 6 ∧ 1 < 0
∨ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 6 ≤ 6⋅X₀ ∧ 6⋅X₀ ≤ 6 ∧ 0 < 3⋅X₂+6 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 6 ≤ 6⋅X₀ ∧ 6⋅X₀ ≤ 6 ∧ 9⋅X₂+11 < 6⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0
∨ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 6 ≤ 6⋅X₀ ∧ 6⋅X₀ ≤ 6 ∧ 6⋅X₁ < 6⋅X₀+6⋅X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11
∨ 0 ≤ 3⋅X₂+3 ∧ 3⋅X₂+3 ≤ 0 ∧ 3⋅X₂+2 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 3⋅X₂+2 ∧ 6 ≤ 6⋅X₀ ∧ 6⋅X₀ ≤ 6 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₂+6 ∧ 3⋅X₂+6 ≤ 0 ∧ 9⋅X₂+11 ≤ 6⋅X₁ ∧ 6⋅X₁ ≤ 9⋅X₂+11 ∧ 6⋅X₁ ≤ 6⋅X₀+6⋅X₂ ∧ 6⋅X₀+6⋅X₂ ≤ 6⋅X₁

Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: 3+6⋅X₀+6⋅X₁+3⋅X₂
M: 0
N: 3
Bound: 12⋅X₀+12⋅X₁+6⋅X₂+10 {O(n)}
Stabilization-Threshold for: X₁ ≤ X₀+X₂
alphas_abs: 6+6⋅X₀+6⋅X₁+9⋅X₂
M: 0
N: 3
Bound: 12⋅X₀+12⋅X₁+18⋅X₂+16 {O(n)}

relevant size-bounds w.r.t. t₅₇:
X₀: 6⋅X₃+X₀+X₁+4 {O(n)}
X₁: 6⋅X₃+X₁+X₂+4 {O(n)}
X₂: 3⋅X₃+X₂+4 {O(n)}
Runtime-bound of t₅₇: X₃+2 {O(n)}
Results in: 24⋅X₀⋅X₃+360⋅X₃⋅X₃+48⋅X₁⋅X₃+48⋅X₂⋅X₃+1036⋅X₃+48⋅X₀+96⋅X₁+96⋅X₂+632 {O(n^2)}

1008⋅X₃⋅X₃+192⋅X₁⋅X₃+72⋅X₀⋅X₃+72⋅X₂⋅X₃+144⋅X₀+144⋅X₂+2816⋅X₃+384⋅X₁+1600 {O(n^2)}

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:108⋅X₃⋅X₃+12⋅X₀+12⋅X₁+209⋅X₃+6⋅X₂+115 {O(n^2)}
t₀: 1 {O(1)}
t₁: 108⋅X₃⋅X₃+12⋅X₀+12⋅X₁+207⋅X₃+6⋅X₂+111 {O(n^2)}
t₂: X₃+2 {O(n)}
t₃: X₃+1 {O(n)}

Costbounds

Overall costbound: 108⋅X₃⋅X₃+12⋅X₀+12⋅X₁+209⋅X₃+6⋅X₂+115 {O(n^2)}
t₀: 1 {O(1)}
t₁: 108⋅X₃⋅X₃+12⋅X₀+12⋅X₁+207⋅X₃+6⋅X₂+111 {O(n^2)}
t₂: X₃+2 {O(n)}
t₃: X₃+1 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: 1259712⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+233280⋅X₂⋅X₃⋅X₃⋅X₃⋅X₃+419904⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃+419904⋅X₁⋅X₃⋅X₃⋅X₃⋅X₃+7313328⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+14256⋅X₂⋅X₂⋅X₃⋅X₃+1625184⋅X₀⋅X₃⋅X₃⋅X₃+1625184⋅X₁⋅X₃⋅X₃⋅X₃+18105444⋅X₃⋅X₃⋅X₃⋅X₃+46656⋅X₀⋅X₀⋅X₃⋅X₃+46656⋅X₁⋅X₁⋅X₃⋅X₃+51840⋅X₀⋅X₂⋅X₃⋅X₃+51840⋅X₁⋅X₂⋅X₃⋅X₃+902016⋅X₂⋅X₃⋅X₃⋅X₃+93312⋅X₀⋅X₁⋅X₃⋅X₃+100224⋅X₀⋅X₂⋅X₃+100224⋅X₁⋅X₂⋅X₃+1359612⋅X₂⋅X₃⋅X₃+1584⋅X₀⋅X₂⋅X₂+1584⋅X₁⋅X₂⋅X₂+1728⋅X₀⋅X₀⋅X₀+1728⋅X₁⋅X₁⋅X₁+180576⋅X₀⋅X₁⋅X₃+24430005⋅X₃⋅X₃⋅X₃+2451060⋅X₀⋅X₃⋅X₃+2451276⋅X₁⋅X₃⋅X₃+27540⋅X₂⋅X₂⋅X₃+288⋅X₂⋅X₂⋅X₂+2880⋅X₀⋅X₀⋅X₂+2880⋅X₁⋅X₁⋅X₂+5184⋅X₀⋅X₀⋅X₁+5184⋅X₀⋅X₁⋅X₁+5760⋅X₀⋅X₁⋅X₂+90288⋅X₀⋅X₀⋅X₃+90288⋅X₁⋅X₁⋅X₃+14892⋅X₂⋅X₂+1700352⋅X₀⋅X₃+1700766⋅X₁⋅X₃+18942525⋅X₃⋅X₃+48816⋅X₀⋅X₀+48840⋅X₁⋅X₁+54192⋅X₀⋅X₂+54204⋅X₁⋅X₂+942912⋅X₂⋅X₃+97656⋅X₀⋅X₁+254936⋅X₂+459697⋅X₀+459920⋅X₁+8005695⋅X₃+1443010 {O(n^6)}
t₁, X₁: 11664⋅X₃⋅X₃⋅X₃⋅X₃+1512⋅X₂⋅X₃⋅X₃+2592⋅X₀⋅X₃⋅X₃+2592⋅X₁⋅X₃⋅X₃+45360⋅X₃⋅X₃⋅X₃+144⋅X₀⋅X₀+144⋅X₁⋅X₁+168⋅X₀⋅X₂+168⋅X₁⋅X₂+288⋅X₀⋅X₁+2934⋅X₂⋅X₃+48⋅X₂⋅X₂+5040⋅X₀⋅X₃+5040⋅X₁⋅X₃+68607⋅X₃⋅X₃+1586⋅X₂+2724⋅X₀+2725⋅X₁+47664⋅X₃+12882 {O(n^4)}
t₁, X₂: 108⋅X₃⋅X₃+12⋅X₀+12⋅X₁+210⋅X₃+7⋅X₂+113 {O(n^2)}
t₁, X₃: 3⋅X₃+2 {O(n)}
t₂, X₀: 1259712⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+233280⋅X₂⋅X₃⋅X₃⋅X₃⋅X₃+419904⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃+419904⋅X₁⋅X₃⋅X₃⋅X₃⋅X₃+7313328⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+14256⋅X₂⋅X₂⋅X₃⋅X₃+1625184⋅X₀⋅X₃⋅X₃⋅X₃+1625184⋅X₁⋅X₃⋅X₃⋅X₃+18105444⋅X₃⋅X₃⋅X₃⋅X₃+46656⋅X₀⋅X₀⋅X₃⋅X₃+46656⋅X₁⋅X₁⋅X₃⋅X₃+51840⋅X₀⋅X₂⋅X₃⋅X₃+51840⋅X₁⋅X₂⋅X₃⋅X₃+902016⋅X₂⋅X₃⋅X₃⋅X₃+93312⋅X₀⋅X₁⋅X₃⋅X₃+100224⋅X₀⋅X₂⋅X₃+100224⋅X₁⋅X₂⋅X₃+1359612⋅X₂⋅X₃⋅X₃+1584⋅X₀⋅X₂⋅X₂+1584⋅X₁⋅X₂⋅X₂+1728⋅X₀⋅X₀⋅X₀+1728⋅X₁⋅X₁⋅X₁+180576⋅X₀⋅X₁⋅X₃+24430005⋅X₃⋅X₃⋅X₃+2451060⋅X₀⋅X₃⋅X₃+2451276⋅X₁⋅X₃⋅X₃+27540⋅X₂⋅X₂⋅X₃+288⋅X₂⋅X₂⋅X₂+2880⋅X₀⋅X₀⋅X₂+2880⋅X₁⋅X₁⋅X₂+5184⋅X₀⋅X₀⋅X₁+5184⋅X₀⋅X₁⋅X₁+5760⋅X₀⋅X₁⋅X₂+90288⋅X₀⋅X₀⋅X₃+90288⋅X₁⋅X₁⋅X₃+14892⋅X₂⋅X₂+1700352⋅X₀⋅X₃+1700766⋅X₁⋅X₃+18942525⋅X₃⋅X₃+48816⋅X₀⋅X₀+48840⋅X₁⋅X₁+54192⋅X₀⋅X₂+54204⋅X₁⋅X₂+942912⋅X₂⋅X₃+97656⋅X₀⋅X₁+254936⋅X₂+459698⋅X₀+459920⋅X₁+8005695⋅X₃+1443010 {O(n^6)}
t₂, X₁: 11664⋅X₃⋅X₃⋅X₃⋅X₃+1512⋅X₂⋅X₃⋅X₃+2592⋅X₀⋅X₃⋅X₃+2592⋅X₁⋅X₃⋅X₃+45360⋅X₃⋅X₃⋅X₃+144⋅X₀⋅X₀+144⋅X₁⋅X₁+168⋅X₀⋅X₂+168⋅X₁⋅X₂+288⋅X₀⋅X₁+2934⋅X₂⋅X₃+48⋅X₂⋅X₂+5040⋅X₀⋅X₃+5040⋅X₁⋅X₃+68607⋅X₃⋅X₃+1586⋅X₂+2724⋅X₀+2726⋅X₁+47664⋅X₃+12882 {O(n^4)}
t₂, X₂: 108⋅X₃⋅X₃+12⋅X₀+12⋅X₁+210⋅X₃+8⋅X₂+113 {O(n^2)}
t₂, X₃: 3⋅X₃+2 {O(n)}
t₃, X₀: 3⋅X₃+2 {O(n)}
t₃, X₁: 3⋅X₃+2 {O(n)}
t₃, X₂: 3⋅X₃+2 {O(n)}
t₃, X₃: 3⋅X₃+2 {O(n)}