┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "Pivastatin"
┌ 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
[ Info: Parameters: r3, k3, r1, k4, k2, T0, k, k1
[ 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 12.316450154 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 12.316450154
[ Info: Computing Wronskians
┌ Info: Computed in 11.701115498 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 11.701115498
[ Info: Dimensions of the Wronskians [245]
┌ Info: Ranks of the Wronskians computed in 0.041298622 seconds
│   :rank_time = :rank_time
└   rank_times = 0.041298622

⌜ # 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 1 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 10.
[ Info: Groebner basis computed in 14.382425245 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 5.941543532 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 10.040724884 seconds. Result: true
[ Info: Out of 251 initial generators there are 7 indepdendent
[ Info: The ranking of the new set of generators is 57
[ 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 0.592684529 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.004298389 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[r3, k3, r1, k4, k2, T0, k, k1, x1, x2, x3]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 25
┌ Info: Final cleaning and simplification of generators. 
└ Out of 23 fractions 14 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.005988171 seconds. Result: true
[ Info: Out of 11 initial generators there are 10 indepdendent
[ Info: The ranking of the new set of generators is 70
[ Info: The search for identifiable functions concluded in 76.861169443 seconds
[ Info: Processing Pivastatin
┌ 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 0.840514132 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 0.840514132
[ Info: Computing Wronskians
┌ Info: Computed in 0.212165193 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 0.212165193
[ Info: Dimensions of the Wronskians [245]
┌ Info: Ranks of the Wronskians computed in 0.008642421 seconds
│   :rank_time = :rank_time
└   rank_times = 0.008642421

⌜ # Computing specializations..  	 Time: 0:00:00[K
✓ # 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: 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 1.129757446 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 1.200975881 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 4.22799311 seconds. Result: true
[ Info: Out of 251 initial generators there are 7 indepdendent
[ Info: The ranking of the new set of generators is 57
[ 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 0.019982032 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.004355044 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[r3, k3, r1, k4, k2, T0, k, k1, x1, x2, x3]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 25
┌ Info: Final cleaning and simplification of generators. 
└ Out of 23 fractions 14 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.146231243 seconds. Result: true
[ Info: Out of 11 initial generators there are 10 indepdendent
[ Info: The ranking of the new set of generators is 70
[ Info: The search for identifiable functions concluded in 8.441090823 seconds
┌ Info: Result is
│   result =
│    10-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     k2
│     k4
│     r1
│     k3
│     ⋮
│     k1*x1
│     k*x3
└     T0*k1
