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 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 for transition t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀+X₁, X₁+X₂, X₂-1, X₃) :|: 1 ≤ X₀ of depth 3:
new bound:
162⋅X₃⋅X₃+27⋅X₀+27⋅X₁+27⋅X₂+379⋅X₃+272 {O(n^2)}
Chain transitions t₂: l1→l2 and t₃: l2→l1 to t₃₄: l1→l1
Analysing control-flow refined program
Found invariant X₀ ≤ 0 for location l2
knowledge_propagation leads to new time bound 162⋅X₃⋅X₃+27⋅X₀+27⋅X₁+27⋅X₂+379⋅X₃+273 {O(n^2)} for transition t₃₄: l1(X₀, X₁, X₂, X₃) -{2}> l1(X₃-1, X₃-1, X₃-1, X₃-1) :|: X₀ ≤ 0 ∧ 2 ≤ X₃ ∧ X₀ ≤ 0
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Cut unsatisfiable transition t₆₆: 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 t₆₂: 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 t₆₃: 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 t₆₀: 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 t₆₇: n_l1___2(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃-1) :|: X₀ ≤ 0 of depth 1:
new bound:
2⋅X₃+4 {O(n)}
TWN: t₆₁: n_l1___2→n_l1___2
cycle: [t₆₁: n_l1___2→n_l1___2]
loop: (X₁ ≤ X₀+X₂ ∧ 1 ≤ X₀,(X₀,X₁,X₂) -> (X₀+X₁,X₁+X₂,X₂-1)
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: 6+6⋅X₀+6⋅X₁+3⋅X₂
M: 0
N: 3
Bound: 12⋅X₀+12⋅X₁+6⋅X₂+16 {O(n)}
Stabilization-Threshold for: X₁ ≤ X₀+X₂
alphas_abs: 11+6⋅X₀+6⋅X₁+9⋅X₂
M: 0
N: 3
Bound: 12⋅X₀+12⋅X₁+18⋅X₂+26 {O(n)}
loop: (X₁ ≤ X₀+X₂ ∧ 1 ≤ X₀,(X₀,X₁,X₂) -> (X₀+X₁,X₁+X₂,X₂-1)
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: 6+6⋅X₀+6⋅X₁+3⋅X₂
M: 0
N: 3
Bound: 12⋅X₀+12⋅X₁+6⋅X₂+16 {O(n)}
Stabilization-Threshold for: X₁ ≤ X₀+X₂
alphas_abs: 11+6⋅X₀+6⋅X₁+9⋅X₂
M: 0
N: 3
Bound: 12⋅X₀+12⋅X₁+18⋅X₂+26 {O(n)}
TWN - Lifting for t₆₁: n_l1___2→n_l1___2 of 24⋅X₀+24⋅X₁+24⋅X₂+44 {O(n)}
relevant size-bounds w.r.t. t₆₀:
X₀: 2⋅X₀+2⋅X₁+8⋅X₃+8 {O(n)}
X₁: 4⋅X₁+8⋅X₃+8 {O(n)}
X₂: 2⋅X₃+X₂+3 {O(n)}
Runtime-bound of t₆₀: X₃+2 {O(n)}
Results in: 144⋅X₁⋅X₃+24⋅X₂⋅X₃+432⋅X₃⋅X₃+48⋅X₀⋅X₃+1364⋅X₃+288⋅X₁+48⋅X₂+96⋅X₀+1000 {O(n^2)}
TWN - Lifting for t₆₁: n_l1___2→n_l1___2 of 24⋅X₀+24⋅X₁+24⋅X₂+44 {O(n)}
relevant size-bounds w.r.t. t₆₃:
X₀: 4⋅X₃+X₀+X₁+4 {O(n)}
X₁: 4⋅X₃+X₁+X₂+4 {O(n)}
X₂: 2⋅X₃+X₂+4 {O(n)}
Runtime-bound of t₆₃: X₃+2 {O(n)}
Results in: 24⋅X₀⋅X₃+240⋅X₃⋅X₃+48⋅X₁⋅X₃+48⋅X₂⋅X₃+48⋅X₀+812⋅X₃+96⋅X₁+96⋅X₂+664 {O(n^2)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:162⋅X₃⋅X₃+27⋅X₀+27⋅X₁+27⋅X₂+381⋅X₃+276 {O(n^2)}
t₀: 1 {O(1)}
t₁: 162⋅X₃⋅X₃+27⋅X₀+27⋅X₁+27⋅X₂+379⋅X₃+272 {O(n^2)}
t₂: X₃+2 {O(n)}
t₃: X₃+1 {O(n)}
Costbounds
Overall costbound: 162⋅X₃⋅X₃+27⋅X₀+27⋅X₁+27⋅X₂+381⋅X₃+276 {O(n^2)}
t₀: 1 {O(1)}
t₁: 162⋅X₃⋅X₃+27⋅X₀+27⋅X₁+27⋅X₂+379⋅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: 4251528⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+2125764⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃+2125764⋅X₁⋅X₃⋅X₃⋅X₃⋅X₃+2178252⋅X₂⋅X₃⋅X₃⋅X₃⋅X₃+29944404⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+10227060⋅X₂⋅X₃⋅X₃⋅X₃+354294⋅X₀⋅X₀⋅X₃⋅X₃+354294⋅X₁⋅X₁⋅X₃⋅X₃+371790⋅X₂⋅X₂⋅X₃⋅X₃+708588⋅X₀⋅X₁⋅X₃⋅X₃+726084⋅X₀⋅X₂⋅X₃⋅X₃+726084⋅X₁⋅X₂⋅X₃⋅X₃+91873278⋅X₃⋅X₃⋅X₃⋅X₃+9981468⋅X₀⋅X₃⋅X₃⋅X₃+9981468⋅X₁⋅X₃⋅X₃⋅X₃+121014⋅X₀⋅X₁⋅X₂+156307271⋅X₃⋅X₃⋅X₃+1663578⋅X₀⋅X₁⋅X₃+1704510⋅X₀⋅X₂⋅X₃+1704510⋅X₁⋅X₂⋅X₃+18907641⋅X₀⋅X₃⋅X₃+18907965⋅X₁⋅X₃⋅X₃+19371827⋅X₂⋅X₃⋅X₃+19683⋅X₀⋅X₀⋅X₀+19683⋅X₁⋅X₁⋅X₁+21141⋅X₂⋅X₂⋅X₂+59049⋅X₀⋅X₀⋅X₁+59049⋅X₀⋅X₁⋅X₁+60507⋅X₀⋅X₀⋅X₂+60507⋅X₁⋅X₁⋅X₂+61965⋅X₀⋅X₂⋅X₂+61965⋅X₁⋅X₂⋅X₂+831789⋅X₀⋅X₀⋅X₃+831789⋅X₁⋅X₁⋅X₃+872721⋅X₂⋅X₂⋅X₃+1198530⋅X₀⋅X₁+1227960⋅X₀⋅X₂+1228014⋅X₁⋅X₂+155389252⋅X₃⋅X₃+16882128⋅X₀⋅X₃+16882886⋅X₁⋅X₃+17295996⋅X₂⋅X₃+599238⋅X₀⋅X₀+599292⋅X₁⋅X₁+628722⋅X₂⋅X₂+6081184⋅X₀+6081729⋅X₁+6230241⋅X₂+85661001⋅X₃+20571098 {O(n^6)}
t₁, X₁: 26244⋅X₃⋅X₃⋅X₃⋅X₃+123444⋅X₃⋅X₃⋅X₃+8748⋅X₀⋅X₃⋅X₃+8748⋅X₁⋅X₃⋅X₃+9072⋅X₂⋅X₃⋅X₃+1458⋅X₀⋅X₁+1512⋅X₀⋅X₂+1512⋅X₁⋅X₂+20574⋅X₀⋅X₃+20574⋅X₁⋅X₃+21332⋅X₂⋅X₃+234095⋅X₃⋅X₃+729⋅X₀⋅X₀+729⋅X₁⋅X₁+783⋅X₂⋅X₂+14823⋅X₀+14824⋅X₁+15369⋅X₂+209165⋅X₃+75350 {O(n^4)}
t₁, X₂: 162⋅X₃⋅X₃+27⋅X₀+27⋅X₁+28⋅X₂+381⋅X₃+274 {O(n^2)}
t₁, X₃: 2⋅X₃+2 {O(n)}
t₂, X₀: 4251528⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+2125764⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃+2125764⋅X₁⋅X₃⋅X₃⋅X₃⋅X₃+2178252⋅X₂⋅X₃⋅X₃⋅X₃⋅X₃+29944404⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+10227060⋅X₂⋅X₃⋅X₃⋅X₃+354294⋅X₀⋅X₀⋅X₃⋅X₃+354294⋅X₁⋅X₁⋅X₃⋅X₃+371790⋅X₂⋅X₂⋅X₃⋅X₃+708588⋅X₀⋅X₁⋅X₃⋅X₃+726084⋅X₀⋅X₂⋅X₃⋅X₃+726084⋅X₁⋅X₂⋅X₃⋅X₃+91873278⋅X₃⋅X₃⋅X₃⋅X₃+9981468⋅X₀⋅X₃⋅X₃⋅X₃+9981468⋅X₁⋅X₃⋅X₃⋅X₃+121014⋅X₀⋅X₁⋅X₂+156307271⋅X₃⋅X₃⋅X₃+1663578⋅X₀⋅X₁⋅X₃+1704510⋅X₀⋅X₂⋅X₃+1704510⋅X₁⋅X₂⋅X₃+18907641⋅X₀⋅X₃⋅X₃+18907965⋅X₁⋅X₃⋅X₃+19371827⋅X₂⋅X₃⋅X₃+19683⋅X₀⋅X₀⋅X₀+19683⋅X₁⋅X₁⋅X₁+21141⋅X₂⋅X₂⋅X₂+59049⋅X₀⋅X₀⋅X₁+59049⋅X₀⋅X₁⋅X₁+60507⋅X₀⋅X₀⋅X₂+60507⋅X₁⋅X₁⋅X₂+61965⋅X₀⋅X₂⋅X₂+61965⋅X₁⋅X₂⋅X₂+831789⋅X₀⋅X₀⋅X₃+831789⋅X₁⋅X₁⋅X₃+872721⋅X₂⋅X₂⋅X₃+1198530⋅X₀⋅X₁+1227960⋅X₀⋅X₂+1228014⋅X₁⋅X₂+155389252⋅X₃⋅X₃+16882128⋅X₀⋅X₃+16882886⋅X₁⋅X₃+17295996⋅X₂⋅X₃+599238⋅X₀⋅X₀+599292⋅X₁⋅X₁+628722⋅X₂⋅X₂+6081185⋅X₀+6081729⋅X₁+6230241⋅X₂+85661001⋅X₃+20571098 {O(n^6)}
t₂, X₁: 26244⋅X₃⋅X₃⋅X₃⋅X₃+123444⋅X₃⋅X₃⋅X₃+8748⋅X₀⋅X₃⋅X₃+8748⋅X₁⋅X₃⋅X₃+9072⋅X₂⋅X₃⋅X₃+1458⋅X₀⋅X₁+1512⋅X₀⋅X₂+1512⋅X₁⋅X₂+20574⋅X₀⋅X₃+20574⋅X₁⋅X₃+21332⋅X₂⋅X₃+234095⋅X₃⋅X₃+729⋅X₀⋅X₀+729⋅X₁⋅X₁+783⋅X₂⋅X₂+14823⋅X₀+14825⋅X₁+15369⋅X₂+209165⋅X₃+75350 {O(n^4)}
t₂, X₂: 162⋅X₃⋅X₃+27⋅X₀+27⋅X₁+29⋅X₂+381⋅X₃+274 {O(n^2)}
t₂, X₃: 2⋅X₃+2 {O(n)}
t₃, X₀: 2⋅X₃+2 {O(n)}
t₃, X₁: 2⋅X₃+2 {O(n)}
t₃, X₂: 2⋅X₃+2 {O(n)}
t₃, X₃: 2⋅X₃+2 {O(n)}