┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "SIR 21"
┌ Info: 
└   KWARGS = (with_states = true, strategy = (:normalforms, 2))
┌ Info: 
└   GLOBAL_ID = Symbol("(:normalforms, 2)_with_states")
[ Info: Summary of the model:
[ Info: State variables: N, S, I, R, C, D
[ Info: Parameters: mu, q, r, pp, beta
[ Info: Inputs: 
[ Info: Outputs: y1, y2, y3
[ 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 14.351878197 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 14.351878197
[ Info: Computing Wronskians
┌ Info: Computed in 10.702412887 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 10.702412887
[ Info: Dimensions of the Wronskians [4, 4, 1]
┌ Info: Ranks of the Wronskians computed in 0.033219563 seconds
│   :rank_time = :rank_time
└   rank_times = 0.033219563

⌜ # Computing specializations..  	 Time: 0:00:09[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 1 for den.
└ Points used: 10.
[ Info: Groebner basis computed in 12.207048291 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 4.413272925 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 7 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 5 fractions 5 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 3.255084876 seconds. Result: true
[ Info: Out of 6 initial generators there are 5 indepdendent
[ Info: The ranking of the new set of generators is 16
[ 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 5.098887789 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 1.429165442 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[mu, q, r, pp, beta, N, S, I, R, C, D]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 11
┌ Info: Final cleaning and simplification of generators. 
└ Out of 20 fractions 10 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 2.275451604 seconds. Result: true
[ Info: Out of 12 initial generators there are 10 indepdendent
[ Info: The ranking of the new set of generators is 55
[ Info: The search for identifiable functions concluded in 74.457492858 seconds
[ Info: Processing SIR 21
┌ 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 0.033018859 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 0.033018859
[ Info: Computing Wronskians
┌ Info: Computed in 0.020808819 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 0.020808819
[ Info: Dimensions of the Wronskians [4, 4, 1]
┌ Info: Ranks of the Wronskians computed in 2.7172e-5 seconds
│   :rank_time = :rank_time
└   rank_times = 2.7172e-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 1 for den.
└ Points used: 10.
[ Info: Groebner basis computed in 0.008153599 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.001527324 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 7 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 5 fractions 5 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.001304269 seconds. Result: true
[ Info: Out of 6 initial generators there are 5 indepdendent
[ Info: The ranking of the new set of generators is 16
[ 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 0.011243637 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.002474475 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[mu, q, r, pp, beta, N, S, I, R, C, D]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 11
┌ Info: Final cleaning and simplification of generators. 
└ Out of 20 fractions 10 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.003069568 seconds. Result: true
[ Info: Out of 12 initial generators there are 10 indepdendent
[ Info: The ranking of the new set of generators is 55
[ Info: The search for identifiable functions concluded in 0.296440214 seconds
┌ Info: Result is
│   result =
│    10-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     D
│     C
│     I
│     S
│     ⋮
│     r
│     q
└     mu
