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 ]
MPRF for transition t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀+X₁, X₁+X₂, X₂-1, X₃) :|: 1 ≤ X₀ of depth 3:
new bound:
243⋅X₃⋅X₃+27⋅X₀+27⋅X₁+27⋅X₂+460⋅X₃+272 {O(n^2)}
MPRF:
l1 [X₂+1 ; X₁+1 ; X₀ ]
l2 [X₂ ; X₁ ; X₀ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₆₁: 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 t₅₇: 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 t₅₈: 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 t₅₅: 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 t₆₂: 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: t₅₆ 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: t₅₅: 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: t₅₈: 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. t₅₅:
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 t₅₅: 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. t₅₈:
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 t₅₈: 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:243⋅X₃⋅X₃+27⋅X₀+27⋅X₁+27⋅X₂+462⋅X₃+276 {O(n^2)}
t₀: 1 {O(1)}
t₁: 243⋅X₃⋅X₃+27⋅X₀+27⋅X₁+27⋅X₂+460⋅X₃+272 {O(n^2)}
t₂: X₃+2 {O(n)}
t₃: X₃+1 {O(n)}
Costbounds
Overall costbound: 243⋅X₃⋅X₃+27⋅X₀+27⋅X₁+27⋅X₂+462⋅X₃+276 {O(n^2)}
t₀: 1 {O(1)}
t₁: 243⋅X₃⋅X₃+27⋅X₀+27⋅X₁+27⋅X₂+460⋅X₃+272 {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: 14348907⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+4782969⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃+4782969⋅X₁⋅X₃⋅X₃⋅X₃⋅X₃+4901067⋅X₂⋅X₃⋅X₃⋅X₃⋅X₃+81841914⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+1062882⋅X₀⋅X₁⋅X₃⋅X₃+1089126⋅X₀⋅X₂⋅X₃⋅X₃+1089126⋅X₁⋅X₂⋅X₃⋅X₃+18187092⋅X₀⋅X₃⋅X₃⋅X₃+18187092⋅X₁⋅X₃⋅X₃⋅X₃+18634212⋅X₂⋅X₃⋅X₃⋅X₃+204136038⋅X₃⋅X₃⋅X₃⋅X₃+531441⋅X₀⋅X₀⋅X₃⋅X₃+531441⋅X₁⋅X₁⋅X₃⋅X₃+557685⋅X₂⋅X₂⋅X₃⋅X₃+1010394⋅X₀⋅X₀⋅X₃+1010394⋅X₁⋅X₁⋅X₃+1060074⋅X₂⋅X₂⋅X₃+121014⋅X₀⋅X₁⋅X₂+19683⋅X₀⋅X₀⋅X₀+19683⋅X₁⋅X₁⋅X₁+2020788⋅X₀⋅X₁⋅X₃+2070468⋅X₀⋅X₂⋅X₃+2070468⋅X₁⋅X₂⋅X₃+21141⋅X₂⋅X₂⋅X₂+28074924⋅X₀⋅X₃⋅X₃+28075410⋅X₁⋅X₃⋅X₃+283169446⋅X₃⋅X₃⋅X₃+28763480⋅X₂⋅X₃⋅X₃+59049⋅X₀⋅X₀⋅X₁+59049⋅X₀⋅X₁⋅X₁+60507⋅X₀⋅X₀⋅X₂+60507⋅X₁⋅X₁⋅X₂+61965⋅X₀⋅X₂⋅X₂+61965⋅X₁⋅X₂⋅X₂+1198530⋅X₀⋅X₁+1227960⋅X₀⋅X₂+1228014⋅X₁⋅X₂+20507094⋅X₀⋅X₃+20508014⋅X₁⋅X₃+21009414⋅X₂⋅X₃+230175567⋅X₃⋅X₃+599238⋅X₀⋅X₀+599292⋅X₁⋅X₁+628722⋅X₂⋅X₂+104054155⋅X₃+6081184⋅X₀+6081729⋅X₁+6230241⋅X₂+20571098 {O(n^6)}
t₁, X₁: 59049⋅X₃⋅X₃⋅X₃⋅X₃+13122⋅X₀⋅X₃⋅X₃+13122⋅X₁⋅X₃⋅X₃+13608⋅X₂⋅X₃⋅X₃+225018⋅X₃⋅X₃⋅X₃+1458⋅X₀⋅X₁+1512⋅X₀⋅X₂+1512⋅X₁⋅X₂+25002⋅X₀⋅X₃+25002⋅X₁⋅X₃+25922⋅X₂⋅X₃+347767⋅X₃⋅X₃+729⋅X₀⋅X₀+729⋅X₁⋅X₁+783⋅X₂⋅X₂+14823⋅X₀+14824⋅X₁+15369⋅X₂+254181⋅X₃+75350 {O(n^4)}
t₁, X₂: 243⋅X₃⋅X₃+27⋅X₀+27⋅X₁+28⋅X₂+463⋅X₃+274 {O(n^2)}
t₁, X₃: 3⋅X₃+2 {O(n)}
t₂, X₀: 14348907⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+4782969⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃+4782969⋅X₁⋅X₃⋅X₃⋅X₃⋅X₃+4901067⋅X₂⋅X₃⋅X₃⋅X₃⋅X₃+81841914⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+1062882⋅X₀⋅X₁⋅X₃⋅X₃+1089126⋅X₀⋅X₂⋅X₃⋅X₃+1089126⋅X₁⋅X₂⋅X₃⋅X₃+18187092⋅X₀⋅X₃⋅X₃⋅X₃+18187092⋅X₁⋅X₃⋅X₃⋅X₃+18634212⋅X₂⋅X₃⋅X₃⋅X₃+204136038⋅X₃⋅X₃⋅X₃⋅X₃+531441⋅X₀⋅X₀⋅X₃⋅X₃+531441⋅X₁⋅X₁⋅X₃⋅X₃+557685⋅X₂⋅X₂⋅X₃⋅X₃+1010394⋅X₀⋅X₀⋅X₃+1010394⋅X₁⋅X₁⋅X₃+1060074⋅X₂⋅X₂⋅X₃+121014⋅X₀⋅X₁⋅X₂+19683⋅X₀⋅X₀⋅X₀+19683⋅X₁⋅X₁⋅X₁+2020788⋅X₀⋅X₁⋅X₃+2070468⋅X₀⋅X₂⋅X₃+2070468⋅X₁⋅X₂⋅X₃+21141⋅X₂⋅X₂⋅X₂+28074924⋅X₀⋅X₃⋅X₃+28075410⋅X₁⋅X₃⋅X₃+283169446⋅X₃⋅X₃⋅X₃+28763480⋅X₂⋅X₃⋅X₃+59049⋅X₀⋅X₀⋅X₁+59049⋅X₀⋅X₁⋅X₁+60507⋅X₀⋅X₀⋅X₂+60507⋅X₁⋅X₁⋅X₂+61965⋅X₀⋅X₂⋅X₂+61965⋅X₁⋅X₂⋅X₂+1198530⋅X₀⋅X₁+1227960⋅X₀⋅X₂+1228014⋅X₁⋅X₂+20507094⋅X₀⋅X₃+20508014⋅X₁⋅X₃+21009414⋅X₂⋅X₃+230175567⋅X₃⋅X₃+599238⋅X₀⋅X₀+599292⋅X₁⋅X₁+628722⋅X₂⋅X₂+104054155⋅X₃+6081185⋅X₀+6081729⋅X₁+6230241⋅X₂+20571098 {O(n^6)}
t₂, X₁: 59049⋅X₃⋅X₃⋅X₃⋅X₃+13122⋅X₀⋅X₃⋅X₃+13122⋅X₁⋅X₃⋅X₃+13608⋅X₂⋅X₃⋅X₃+225018⋅X₃⋅X₃⋅X₃+1458⋅X₀⋅X₁+1512⋅X₀⋅X₂+1512⋅X₁⋅X₂+25002⋅X₀⋅X₃+25002⋅X₁⋅X₃+25922⋅X₂⋅X₃+347767⋅X₃⋅X₃+729⋅X₀⋅X₀+729⋅X₁⋅X₁+783⋅X₂⋅X₂+14823⋅X₀+14825⋅X₁+15369⋅X₂+254181⋅X₃+75350 {O(n^4)}
t₂, X₂: 243⋅X₃⋅X₃+27⋅X₀+27⋅X₁+29⋅X₂+463⋅X₃+274 {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)}