┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "Pharm"
┌ Info: 
└   KWARGS = (with_states = true, strategy = (:normalforms, 2))
┌ Info: 
└   GLOBAL_ID = Symbol("(:normalforms, 2)_with_states")
[ Info: Summary of the model:
[ Info: State variables: x0, x1, x2, x3
[ Info: Parameters: a2, ka, n, b2, kc, b1, a1
[ Info: Inputs: 
[ Info: Outputs: y1
[ 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 52.017493982 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 52.017493982
[ Info: Computing Wronskians
┌ Info: Computed in 54.575132169 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 54.575132169
[ Info: Dimensions of the Wronskians [2936]
┌ Info: Ranks of the Wronskians computed in 5.1028176 seconds
│   :rank_time = :rank_time
└   rank_times = 5.1028176

⌜ # Computing specializations..  	 Time: 0:00:13[K
✓ # Computing specializations..  	 Time: 0:00:13[K

⌜ # Computing specializations..  	 Time: 0:00:00[K
⌝ # Computing specializations..  	 Time: 0:00:00[K
⌟ # Computing specializations..  	 Time: 0:00:01[K
✓ # Computing specializations..  	 Time: 0:00:01[K

⌜ # Computing specializations.. 	 Time: 0:00:00[K
  Points:  2[K
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⌝ # Computing specializations.. 	 Time: 0:00:00[K
  Points:  5[K
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✓ # Computing specializations.. 	 Time: 0:00:01[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: 1 for num. and 1 for den.
└ Points used: 6.
[ Info: Groebner basis computed in 18.387190271 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 12.041660042 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 7 fractions 7 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 44.564095832 seconds. Result: true
[ Info: Out of 3535 initial generators there are 7 indepdendent
[ Info: The ranking of the new set of generators is 28
[ 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 0.875667186 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.29973503 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 12 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (11 in total): Nemo.QQMPolyRingElem[a2, ka, n, b2, kc, b1, a1, x0, x1, x2, x3]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 1
┌ Info: Final cleaning and simplification of generators. 
└ Out of 22 fractions 11 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.102167754 seconds. Result: true
[ Info: Out of 12 initial generators there are 11 indepdendent
[ Info: The ranking of the new set of generators is 66
[ Info: The search for identifiable functions concluded in 215.759236903 seconds
[ Info: Processing Pharm
┌ 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 42.81938822 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 42.81938822
[ Info: Computing Wronskians
┌ Info: Computed in 40.936970633 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 40.936970633
[ Info: Dimensions of the Wronskians [2936]
┌ Info: Ranks of the Wronskians computed in 4.619619488 seconds
│   :rank_time = :rank_time
└   rank_times = 4.619619488

⌜ # Computing specializations..  	 Time: 0:00:08[K
✓ # Computing specializations..  	 Time: 0:00:08[K

⌜ # Computing specializations..  	 Time: 0:00:00[K
⌝ # Computing specializations..  	 Time: 0:00:00[K
⌟ # Computing specializations..  	 Time: 0:00:01[K
✓ # Computing specializations..  	 Time: 0:00:01[K

⌜ # Computing specializations.. 	 Time: 0:00:00[K
  Points:  3[K
[K[A
⌝ # Computing specializations.. 	 Time: 0:00:00[K
  Points:  6[K
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✓ # Computing specializations.. 	 Time: 0:00:00[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: 1 for num. and 1 for den.
└ Points used: 6.
[ Info: Groebner basis computed in 12.328370353 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 7.737195748 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 7 fractions 7 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 35.593906608 seconds. Result: true
[ Info: Out of 3535 initial generators there are 7 indepdendent
[ Info: The ranking of the new set of generators is 28
[ 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 0.234994529 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.260686525 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 12 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (11 in total): Nemo.QQMPolyRingElem[a2, ka, n, b2, kc, b1, a1, x0, x1, x2, x3]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 1
┌ Info: Final cleaning and simplification of generators. 
└ Out of 22 fractions 11 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.081566736 seconds. Result: true
[ Info: Out of 12 initial generators there are 11 indepdendent
[ Info: The ranking of the new set of generators is 66
[ Info: The search for identifiable functions concluded in 152.25752809 seconds
┌ Info: Result is
│   result =
│    11-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     x3
│     x2
│     x1
│     x0
│     ⋮
│     n
│     ka
└     a2
