┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "Crauste_SI"
┌ 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, E, S, M, P
[ Info: Parameters: rho_P, mu_EE, delta_NE, mu_LE, delta_EL, mu_N, mu_M, delta_LM, mu_PE, mu_PL, mu_LL, mu_P, rho_E
[ 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 15.436030351 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 15.436030351
[ Info: Computing Wronskians
┌ Info: Computed in 11.678134373 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 11.678134373
[ Info: Dimensions of the Wronskians [8, 14, 10]
┌ Info: Ranks of the Wronskians computed in 0.031052732 seconds
│   :rank_time = :rank_time
└   rank_times = 0.031052732

⌜ # Computing specializations..  	 Time: 0:00:10[K
✓ # Computing specializations..  	 Time: 0:00:11[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 13.67499854 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 4.393607898 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 14 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 12 fractions 12 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 4.886658669 seconds. Result: true
[ Info: Out of 30 initial generators there are 12 indepdendent
[ Info: The ranking of the new set of generators is 159
[ 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 5.169643386 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 1.510430891 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 19 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (18 in total): Nemo.QQMPolyRingElem[rho_P, mu_EE, delta_NE, mu_LE, delta_EL, mu_N, mu_M, delta_LM, mu_PE, mu_PL, mu_LL, mu_P, rho_E, N, E, S, M, P]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 46
┌ Info: Final cleaning and simplification of generators. 
└ Out of 34 fractions 19 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 1.44185509 seconds. Result: true
[ Info: Out of 20 initial generators there are 17 indepdendent
[ Info: The ranking of the new set of generators is 159
[ Info: The search for identifiable functions concluded in 80.211375898 seconds
[ Info: Processing Crauste_SI
┌ 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 0.016666137 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 0.016666137
[ Info: Computing Wronskians
┌ Info: Computed in 0.01349694 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 0.01349694
[ Info: Dimensions of the Wronskians [8, 14, 10]
┌ Info: Ranks of the Wronskians computed in 3.1534e-5 seconds
│   :rank_time = :rank_time
└   rank_times = 3.1534e-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 0.009594418 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.002649753 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 14 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 12 fractions 12 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.002309435 seconds. Result: true
[ Info: Out of 30 initial generators there are 12 indepdendent
[ Info: The ranking of the new set of generators is 159
[ 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 0.012026891 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.002556836 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 19 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (18 in total): Nemo.QQMPolyRingElem[rho_P, mu_EE, delta_NE, mu_LE, delta_EL, mu_N, mu_M, delta_LM, mu_PE, mu_PL, mu_LL, mu_P, rho_E, N, E, S, M, P]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 46
┌ Info: Final cleaning and simplification of generators. 
└ Out of 34 fractions 19 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.003585332 seconds. Result: true
[ Info: Out of 20 initial generators there are 17 indepdendent
[ Info: The ranking of the new set of generators is 159
[ Info: The search for identifiable functions concluded in 0.471749473 seconds
┌ Info: Result is
│   result =
│    17-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     M
│     S
│     E
│     N
│     ⋮
│     P*rho_E
│     delta_NE*P
└     rho_P*P
