┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "Transfection_4State"
┌ Info: 
└   KWARGS = (with_states = true, strategy = (:normalforms, 2))
┌ Info: 
└   GLOBAL_ID = Symbol("(:normalforms, 2)_with_states")
[ Info: Summary of the model:
[ Info: State variables: mRNA, GFP, enz, mRNAenz
[ Info: Parameters: b, kTL, d2, d1, d3
[ 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 10.635337734 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 10.635337734
[ Info: Computing Wronskians
┌ Info: Computed in 11.647648369 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 11.647648369
[ Info: Dimensions of the Wronskians [18]
┌ Info: Ranks of the Wronskians computed in 0.032839175 seconds
│   :rank_time = :rank_time
└   rank_times = 0.032839175

⌜ # 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 1 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 8.
[ Info: Groebner basis computed in 13.092070216 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 4.623747114 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 6 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 4 fractions 4 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 5.693170009 seconds. Result: true
[ Info: Out of 27 initial generators there are 4 indepdendent
[ Info: The ranking of the new set of generators is 37
[ 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 1 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 10.
[ Info: Groebner basis computed in 5.242148339 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 1.55917241 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 10 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (9 in total): Nemo.QQMPolyRingElem[b, kTL, d2, d1, d3, mRNA, GFP, enz, mRNAenz]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 16
┌ Info: Final cleaning and simplification of generators. 
└ Out of 18 fractions 11 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 2.360029937 seconds. Result: true
[ Info: Out of 9 initial generators there are 8 indepdendent
[ Info: The ranking of the new set of generators is 46
[ Info: The search for identifiable functions concluded in 76.605015119 seconds
[ Info: Processing Transfection_4State
┌ 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 0.011571088 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 0.011571088
[ Info: Computing Wronskians
┌ Info: Computed in 0.010277658 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 0.010277658
[ Info: Dimensions of the Wronskians [18]
┌ Info: Ranks of the Wronskians computed in 3.6363e-5 seconds
│   :rank_time = :rank_time
└   rank_times = 3.6363e-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 1 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 8.
[ Info: Groebner basis computed in 0.008043477 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.001950477 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 6 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 4 fractions 4 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.002092256 seconds. Result: true
[ Info: Out of 27 initial generators there are 4 indepdendent
[ Info: The ranking of the new set of generators is 37
[ 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 1 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 10.
[ Info: Groebner basis computed in 0.061431241 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.002508368 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 10 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (9 in total): Nemo.QQMPolyRingElem[b, kTL, d2, d1, d3, mRNA, GFP, enz, mRNAenz]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 16
┌ Info: Final cleaning and simplification of generators. 
└ Out of 18 fractions 11 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.003604613 seconds. Result: true
[ Info: Out of 9 initial generators there are 8 indepdendent
[ Info: The ranking of the new set of generators is 46
[ Info: The search for identifiable functions concluded in 0.234337092 seconds
┌ Info: Result is
│   result =
│    8-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     GFP
│     d3
│     d1
│     b
│     d2*mRNAenz
│     enz*d2
│     d2*mRNA
└     kTL*mRNAenz
