┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "SLIQR"
┌ Info: 
└   KWARGS = (with_states = true, strategy = (:normalforms, 2))
┌ Info: 
└   GLOBAL_ID = Symbol("(:normalforms, 2)_with_states")
[ Info: Summary of the model:
[ Info: State variables: S, L, In, Q
[ Info: Parameters: b, e, Ninv, s, g, a
[ Info: Inputs: u
[ Info: Outputs: y
[ 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 10.604983194 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 10.604983194
[ Info: Computing Wronskians
┌ Info: Computed in 11.515244479 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 11.515244479
[ Info: Dimensions of the Wronskians [32]
┌ Info: Ranks of the Wronskians computed in 0.032716748 seconds
│   :rank_time = :rank_time
└   rank_times = 0.032716748

⌜ # Computing specializations..  	 Time: 0:00:10[K
✓ # Computing specializations..  	 Time: 0:00:11[K

⌜ # Computing specializations..  	 Time: 0:00:04[K
✓ # Computing specializations..  	 Time: 0:00:04[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: 2 for num. and 2 for den.
│ Maximal number of interpolated terms are: 2 for num. and 3 for den.
└ Points used: 48.
[ Info: Groebner basis computed in 13.415749534 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 4.791811864 seconds. Result: false
┌ Info: Computing parametric Groebner basis up to degrees (4, 4)
│ 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: 4 for num. and 2 for den.
│ Maximal number of interpolated terms are: 6 for num. and 3 for den.
└ Points used: 128.
[ Info: Groebner basis computed in 0.073206759 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.003813141 seconds. Result: false
┌ Info: Computing parametric Groebner basis up to degrees (8, 8)
│ 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: 7 for num. and 6 for den.
│ Maximal number of interpolated terms are: 14 for num. and 11 for den.
└ Points used: 480.
[ Info: Groebner basis computed in 0.375822487 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.004795277 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 14 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 6 fractions 6 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 5.903449456 seconds. Result: true
[ Info: Out of 40 initial generators there are 6 indepdendent
[ Info: The ranking of the new set of generators is 17563
[ 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: 5 for num. and 1 for den.
└ Points used: 96.
[ Info: Groebner basis computed in 5.456496618 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 1.52680689 seconds. Result: false
┌ Info: Computing parametric Groebner basis up to degrees (4, 4)
│ 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: 4 for num. and 4 for den.
│ Maximal number of interpolated terms are: 9 for num. and 5 for den.
└ Points used: 320.
[ Info: Groebner basis computed in 0.34618291 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.008604568 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 21 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (10 in total): Nemo.QQMPolyRingElem[b, e, Ninv, s, g, a, S, L, In, Q]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 22
┌ Info: Final cleaning and simplification of generators. 
└ Out of 23 fractions 18 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 1.556930696 seconds. Result: true
[ Info: Out of 15 initial generators there are 10 indepdendent
[ Info: The ranking of the new set of generators is 335
[ Info: The search for identifiable functions concluded in 77.149576238 seconds
[ Info: Processing SLIQR
┌ 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 0.012710968 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 0.012710968
[ Info: Computing Wronskians
┌ Info: Computed in 0.017732936 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 0.017732936
[ Info: Dimensions of the Wronskians [32]
┌ Info: Ranks of the Wronskians computed in 8.2428e-5 seconds
│   :rank_time = :rank_time
└   rank_times = 8.2428e-5
[ 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: 2 for num. and 3 for den.
└ Points used: 48.
[ Info: Groebner basis computed in 0.030119024 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.003140538 seconds. Result: false
┌ Info: Computing parametric Groebner basis up to degrees (4, 4)
│ 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: 4 for num. and 2 for den.
│ Maximal number of interpolated terms are: 6 for num. and 3 for den.
└ Points used: 128.
[ Info: Groebner basis computed in 0.141316562 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.003241907 seconds. Result: false
┌ Info: Computing parametric Groebner basis up to degrees (8, 8)
│ 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: 7 for num. and 6 for den.
│ Maximal number of interpolated terms are: 14 for num. and 11 for den.
└ Points used: 480.
[ Info: Groebner basis computed in 0.370236937 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.004917861 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 14 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 6 fractions 6 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.011369638 seconds. Result: true
[ Info: Out of 40 initial generators there are 6 indepdendent
[ Info: The ranking of the new set of generators is 17563
[ 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: 5 for num. and 1 for den.
└ Points used: 96.
[ Info: Groebner basis computed in 0.123303956 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.005221797 seconds. Result: false
┌ Info: Computing parametric Groebner basis up to degrees (4, 4)
│ 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: 4 for num. and 4 for den.
│ Maximal number of interpolated terms are: 9 for num. and 5 for den.
└ Points used: 320.
[ Info: Groebner basis computed in 0.304654909 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.008035454 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 21 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (10 in total): Nemo.QQMPolyRingElem[b, e, Ninv, s, g, a, S, L, In, Q]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 22
┌ Info: Final cleaning and simplification of generators. 
└ Out of 23 fractions 18 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.069377428 seconds. Result: true
[ Info: Out of 15 initial generators there are 10 indepdendent
[ Info: The ranking of the new set of generators is 335
[ Info: The search for identifiable functions concluded in 1.416013942 seconds
┌ Info: Result is
│   result =
│    10-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     In
│     s
│     Ninv
│     b
│     ⋮
│     In*a + Q*a + a*L
│     e*s*g - s*g + g*a
└     (e*S - S)//(e*Q)
