┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "CGV1990"
┌ Info: 
└   KWARGS = (with_states = true, strategy = (:normalforms, 2))
┌ Info: 
└   GLOBAL_ID = Symbol("(:normalforms, 2)_with_states")
[ Info: Summary of the model:
[ Info: State variables: q1, q3, q35, q36, q7
[ Info: Parameters: k5, k3, S, V36, k4, k6, R, k7, V3
[ Info: Inputs: u
[ 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 10.942989066 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 10.942989066
[ Info: Computing Wronskians
┌ Info: Computed in 12.295003664 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 12.295003664
[ Info: Dimensions of the Wronskians [264]
┌ Info: Ranks of the Wronskians computed in 0.042740719 seconds
│   :rank_time = :rank_time
└   rank_times = 0.042740719

⌜ # Computing specializations..  	 Time: 0:00:10[K
✓ # Computing specializations..  	 Time: 0:00:11[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 2 for den.
└ Points used: 24.
[ Info: Groebner basis computed in 13.918781432 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 4.623245169 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 3 for den.
│ Maximal number of interpolated terms are: 3 for num. and 2 for den.
└ Points used: 72.
[ Info: Groebner basis computed in 0.546275158 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.037809324 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 25 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 8 fractions 8 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 5.89979207 seconds. Result: true
[ Info: Out of 414 initial generators there are 8 indepdendent
[ Info: The ranking of the new set of generators is 914
[ 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 2 for den.
└ Points used: 24.
[ Info: Groebner basis computed in 0.679152311 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.057602318 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: 3 for num. and 2 for den.
│ Maximal number of interpolated terms are: 2 for num. and 2 for den.
└ Points used: 28.
[ Info: Groebner basis computed in 0.071987304 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.057355518 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 32 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (14 in total): Nemo.QQMPolyRingElem[k5, k3, S, V36, k4, k6, R, k7, V3, q1, q3, q35, q36, q7]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 23
┌ Info: Final cleaning and simplification of generators. 
└ Out of 34 fractions 25 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.081649169 seconds. Result: true
[ Info: Out of 18 initial generators there are 14 indepdendent
[ Info: The ranking of the new set of generators is 2985
[ Info: The search for identifiable functions concluded in 71.73171464 seconds
[ Info: Processing CGV1990
┌ 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 0.08917936 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 0.08917936
[ Info: Computing Wronskians
┌ Info: Computed in 0.355716519 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 0.355716519
[ Info: Dimensions of the Wronskians [264]
┌ Info: Ranks of the Wronskians computed in 0.009651604 seconds
│   :rank_time = :rank_time
└   rank_times = 0.009651604
[ 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 2 for den.
└ Points used: 24.
[ Info: Groebner basis computed in 0.128192422 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.077685568 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 3 for den.
│ Maximal number of interpolated terms are: 3 for num. and 2 for den.
└ Points used: 72.
[ Info: Groebner basis computed in 0.481487581 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.036790246 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 25 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 8 fractions 8 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.199449451 seconds. Result: true
[ Info: Out of 414 initial generators there are 8 indepdendent
[ Info: The ranking of the new set of generators is 914
[ 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 2 for den.
└ Points used: 24.
[ Info: Groebner basis computed in 0.126159587 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.011291663 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: 3 for num. and 2 for den.
│ Maximal number of interpolated terms are: 2 for num. and 2 for den.
└ Points used: 28.
[ Info: Groebner basis computed in 0.099340501 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.013249408 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 32 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (14 in total): Nemo.QQMPolyRingElem[k5, k3, S, V36, k4, k6, R, k7, V3, q1, q3, q35, q36, q7]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 23
┌ Info: Final cleaning and simplification of generators. 
└ Out of 34 fractions 25 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.066164433 seconds. Result: true
[ Info: Out of 18 initial generators there are 14 indepdendent
[ Info: The ranking of the new set of generators is 2985
[ Info: The search for identifiable functions concluded in 2.25166845 seconds
┌ Info: Result is
│   result =
│    14-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     q7
│     q3
│     q1
│     k7
│     ⋮
│     (V36^2 + 1//25*V3^2)//(V36*V3)
│     (-S*V3 + 25*V36*R)//(q36 - q35)
└     (-k5*V36 + 1//5*k5*V3)//(q36*V3 - q35*V3)
