┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "Bruno2016"
┌ Info: 
└   KWARGS = (with_states = true, strategy = (:normalforms, 2))
┌ Info: 
└   GLOBAL_ID = Symbol("(:normalforms, 2)_with_states")
[ Info: Summary of the model:
[ Info: State variables: beta, cry, zea, beta10, OHbeta10, betaio, OHbetaio
[ Info: Parameters: kbeta10, kcrybeta, kbeta, kzea, kcryOH, kOHbeta10
[ Info: Inputs: 
[ 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 9.610506675 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 9.610506675
[ Info: Computing Wronskians
┌ Info: Computed in 7.223549181 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 7.223549181
[ Info: Dimensions of the Wronskians [4, 2]
┌ Info: Ranks of the Wronskians computed in 0.020978805 seconds
│   :rank_time = :rank_time
└   rank_times = 0.020978805

⌜ # Computing specializations..  	 Time: 0:00:06[K
✓ # Computing specializations..  	 Time: 0:00:07[K

⌜ # Computing specializations..  	 Time: 0:00:03[K
✓ # Computing specializations..  	 Time: 0:00:03[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 0 for den.
│ Maximal number of interpolated terms are: 2 for num. and 1 for den.
└ Points used: 12.
[ Info: Groebner basis computed in 8.729083553 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 2.926038222 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 5 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 3 fractions 3 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 3.20873488 seconds. Result: true
[ Info: Out of 4 initial generators there are 3 indepdendent
[ Info: The ranking of the new set of generators is 7
[ 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 0 for den.
│ Maximal number of interpolated terms are: 2 for num. and 1 for den.
└ Points used: 16.
[ Info: Groebner basis computed in 3.384758619 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.94038478 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 8 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (13 in total): Nemo.QQMPolyRingElem[kbeta10, kcrybeta, kbeta, kzea, kcryOH, kOHbeta10, beta, cry, zea, beta10, OHbeta10, betaio, OHbetaio]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 7
┌ Info: Final cleaning and simplification of generators. 
└ Out of 17 fractions 11 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 1.412474979 seconds. Result: true
[ Info: Out of 8 initial generators there are 6 indepdendent
[ Info: The ranking of the new set of generators is 24
[ Info: The search for identifiable functions concluded in 51.209787808 seconds
[ Info: Processing Bruno2016
┌ 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 0.015725168 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 0.015725168
[ Info: Computing Wronskians
┌ Info: Computed in 0.067369396 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 0.067369396
[ Info: Dimensions of the Wronskians [4, 2]
┌ Info: Ranks of the Wronskians computed in 1.8333e-5 seconds
│   :rank_time = :rank_time
└   rank_times = 1.8333e-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: 1 for num. and 0 for den.
│ Maximal number of interpolated terms are: 2 for num. and 1 for den.
└ Points used: 12.
[ Info: Groebner basis computed in 0.003890404 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.000788904 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 5 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 3 fractions 3 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.000711814 seconds. Result: true
[ Info: Out of 4 initial generators there are 3 indepdendent
[ Info: The ranking of the new set of generators is 7
[ 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 0 for den.
│ Maximal number of interpolated terms are: 2 for num. and 1 for den.
└ Points used: 16.
[ Info: Groebner basis computed in 0.006925947 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.001391106 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 8 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (13 in total): Nemo.QQMPolyRingElem[kbeta10, kcrybeta, kbeta, kzea, kcryOH, kOHbeta10, beta, cry, zea, beta10, OHbeta10, betaio, OHbetaio]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 7
┌ Info: Final cleaning and simplification of generators. 
└ Out of 17 fractions 11 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.001643429 seconds. Result: true
[ Info: Out of 8 initial generators there are 6 indepdendent
[ Info: The ranking of the new set of generators is 24
[ Info: The search for identifiable functions concluded in 0.190761424 seconds
┌ Info: Result is
│   result =
│    6-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     beta10
│     beta
│     kbeta
│     kbeta10
│     cry*kcryOH
└     kcrybeta + kcryOH
