┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "Chemical reaction network"
┌ Info: 
└   KWARGS = (with_states = true, strategy = (:normalforms, 2))
┌ Info: 
└   GLOBAL_ID = Symbol("(:normalforms, 2)_with_states")
[ Info: Summary of the model:
[ Info: State variables: x1, x2, x3, x4, x5, x6
[ Info: Parameters: k5, k3, k4, k2, k6, k1
[ 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 15.296813832 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 15.296813832
[ Info: Computing Wronskians
┌ Info: Computed in 11.544654514 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 11.544654514
[ Info: Dimensions of the Wronskians [17, 29]
┌ Info: Ranks of the Wronskians computed in 0.032249287 seconds
│   :rank_time = :rank_time
└   rank_times = 0.032249287

⌜ # Computing specializations..  	 Time: 0:00:10[K
✓ # Computing specializations..  	 Time: 0:00:10[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: 1 for num. and 2 for den.
│ Maximal number of interpolated terms are: 1 for num. and 2 for den.
└ Points used: 20.
[ Info: Groebner basis computed in 13.332109944 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 4.481989849 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 8 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 5.050252958 seconds. Result: true
[ Info: Out of 72 initial generators there are 6 indepdendent
[ Info: The ranking of the new set of generators is 24
[ 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: 1 for num. and 1 for den.
└ Points used: 6.
[ Info: Groebner basis computed in 5.275083012 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 1.334984548 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 14 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (12 in total): Nemo.QQMPolyRingElem[k5, k3, k4, k2, k6, k1, x1, x2, x3, x4, x5, x6]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 1
┌ Info: Final cleaning and simplification of generators. 
└ Out of 24 fractions 12 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 1.743432691 seconds. Result: true
[ Info: Out of 14 initial generators there are 12 indepdendent
[ Info: The ranking of the new set of generators is 78
[ Info: The search for identifiable functions concluded in 77.031512789 seconds
[ Info: Processing Chemical reaction network
┌ 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 0.046767289 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 0.046767289
[ Info: Computing Wronskians
┌ Info: Computed in 0.111353702 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 0.111353702
[ Info: Dimensions of the Wronskians [17, 29]
┌ Info: Ranks of the Wronskians computed in 8.5272e-5 seconds
│   :rank_time = :rank_time
└   rank_times = 8.5272e-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 2 for den.
│ Maximal number of interpolated terms are: 1 for num. and 2 for den.
└ Points used: 20.
[ Info: Groebner basis computed in 0.023304045 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.003984662 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 8 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 0.006250057 seconds. Result: true
[ Info: Out of 72 initial generators there are 6 indepdendent
[ Info: The ranking of the new set of generators is 24
[ 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: 1 for num. and 1 for den.
└ Points used: 6.
[ Info: Groebner basis computed in 0.013790498 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.003964474 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 14 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (12 in total): Nemo.QQMPolyRingElem[k5, k3, k4, k2, k6, k1, x1, x2, x3, x4, x5, x6]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 1
┌ Info: Final cleaning and simplification of generators. 
└ Out of 24 fractions 12 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.004655636 seconds. Result: true
[ Info: Out of 14 initial generators there are 12 indepdendent
[ Info: The ranking of the new set of generators is 78
[ Info: The search for identifiable functions concluded in 0.360263048 seconds
┌ Info: Result is
│   result =
│    12-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     x6
│     x5
│     x4
│     x3
│     ⋮
│     k4
│     k3
└     k5
