┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "cLV1 (2o)"
┌ Info: 
└   KWARGS = (with_states = true, strategy = (:normalforms, 2))
┌ Info: 
└   GLOBAL_ID = Symbol("(:normalforms, 2)_with_states")
[ Info: Summary of the model:
[ Info: State variables: pi1, pi2, pi3
[ Info: Parameters: B21, A23, A33, B31, A21, A11, g3, g2, A31, A13, g1, B11, A32, A12, A22
[ Info: Inputs: u1
[ Info: Outputs: y1, y2
[ Info: Summary of the model:
[ Info: State variables: x1, x2
[ Info: Parameters: a, b, d, c
[ Info: Inputs: 
[ Info: Outputs: y
[ Info: Computing IO-equations
┌ Info: Computed in 15.0120548 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 15.0120548
[ Info: Computing Wronskians
┌ Info: Computed in 11.616729838 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 11.616729838
[ Info: Dimensions of the Wronskians [47, 6]
┌ Info: Ranks of the Wronskians computed in 0.031121541 seconds
│   :rank_time = :rank_time
└   rank_times = 0.031121541

⌜ # Computing specializations..  	 Time: 0:00:10[K
✓ # Computing specializations..  	 Time: 0:00:11[K
[ Info: Simplifying identifiable functions
┌ Info: Computing parametric Groebner basis up to degrees (2, 2)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 1 for num. and 1 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 8.
[ Info: Groebner basis computed in 13.881616504 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 4.431768692 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 16 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 14 fractions 14 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 4.905830479 seconds. Result: true
[ Info: Out of 101 initial generators there are 14 indepdendent
[ Info: The ranking of the new set of generators is 186
[ Info: Simplifying identifiable functions
┌ Info: Computing parametric Groebner basis up to degrees (2, 2)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 2 for num. and 2 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 12.
[ Info: Groebner basis computed in 0.538455204 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.006605278 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 19 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (18 in total): Nemo.QQMPolyRingElem[B21, A23, A33, B31, A21, A11, g3, g2, A31, A13, g1, B11, A32, A12, A22, pi1, pi2, pi3]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 46
┌ Info: Final cleaning and simplification of generators. 
└ Out of 34 fractions 18 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.009696428 seconds. Result: true
[ Info: Out of 24 initial generators there are 17 indepdendent
[ Info: The ranking of the new set of generators is 159
[ Info: The search for identifiable functions concluded in 72.200436989 seconds
[ Info: Processing cLV1 (2o)
┌ Info: Averaging over 1 runs.
│ Using keyword arguments:
│ NamedTuple{(:with_states, :strategy), Tuple{Bool, Tuple{Symbol, Int64}}}
│ (with_states = true, strategy = (:normalforms, 2))
└ ID: (:normalforms, 2)_with_states
[ Info: Computing IO-equations
┌ Info: Computed in 0.029025411 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 0.029025411
[ Info: Computing Wronskians
┌ Info: Computed in 0.03495418 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 0.03495418
[ Info: Dimensions of the Wronskians [47, 6]
┌ Info: Ranks of the Wronskians computed in 0.00016301 seconds
│   :rank_time = :rank_time
└   rank_times = 0.00016301
[ Info: Simplifying identifiable functions
┌ Info: Computing parametric Groebner basis up to degrees (2, 2)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 1 for num. and 1 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 8.
[ Info: Groebner basis computed in 0.107284733 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.009882524 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 16 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 14 fractions 14 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.015763968 seconds. Result: true
[ Info: Out of 101 initial generators there are 14 indepdendent
[ Info: The ranking of the new set of generators is 186
[ Info: Simplifying identifiable functions
┌ Info: Computing parametric Groebner basis up to degrees (2, 2)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 2 for num. and 2 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 12.
[ Info: Groebner basis computed in 0.026941371 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.028049886 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 19 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (18 in total): Nemo.QQMPolyRingElem[B21, A23, A33, B31, A21, A11, g3, g2, A31, A13, g1, B11, A32, A12, A22, pi1, pi2, pi3]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 46
┌ Info: Final cleaning and simplification of generators. 
└ Out of 34 fractions 18 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.009838584 seconds. Result: true
[ Info: Out of 24 initial generators there are 17 indepdendent
[ Info: The ranking of the new set of generators is 159
[ Info: The search for identifiable functions concluded in 0.801695608 seconds
┌ Info: Result is
│   result =
│    17-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     pi2
│     pi1
│     A22
│     A12
│     ⋮
│     A13*pi3
│     A33*pi3
└     A23*pi3
