┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "MAPK model (5 outputs)"
┌ Info: 
└   KWARGS = (with_states = true, strategy = (:normalforms, 2))
┌ Info: 
└   GLOBAL_ID = Symbol("(:normalforms, 2)_with_states")
[ Info: Summary of the model:
[ Info: State variables: KS00, KS01, KS10, FS01, FS10, FS11, K, F, S00, S01, S10, S11
[ Info: Parameters: c0001, a10, gamma1000, alpha10, b00, beta11, c0111, beta10, alpha11, beta01, alpha01, gamma1100, c0011, c0010, b10, gamma1101, a00, b01, c1011, a01, gamma1110, gamma0100
[ Info: Inputs: 
[ Info: Outputs: y1, y2, y3, y4, y5
[ 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 37.691227664 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 37.691227664
[ Info: Computing Wronskians
┌ Info: Computed in 13.604590091 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 13.604590091
[ Info: Dimensions of the Wronskians [60, 1, 44, 96, 149]
┌ Info: Ranks of the Wronskians computed in 0.035526511 seconds
│   :rank_time = :rank_time
└   rank_times = 0.035526511

⌜ # Computing specializations..  	 Time: 0:00:14[K
✓ # Computing specializations..  	 Time: 0:00:15[K

⌜ # Computing specializations..  	 Time: 0:00:00[K
⌝ # Computing specializations..  	 Time: 0:00:00[K
✓ # Computing specializations..  	 Time: 0:00:01[K

⌜ # Computing specializations.. 	 Time: 0:00:00[K
  Points:  3[K
[K[A
✓ # Computing specializations.. 	 Time: 0:00:00[K

⌜ # Computing specializations..  	 Time: 0:00:05[K
✓ # Computing specializations..  	 Time: 0:00:05[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 0 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 6.
[ Info: Groebner basis computed in 19.700519725 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 7.489208341 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 23 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 22 fractions 22 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 8.099902488 seconds. Result: true
[ Info: Out of 513 initial generators there are 22 indepdendent
[ Info: The ranking of the new set of generators is 253
[ 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 0 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 6.
[ Info: Groebner basis computed in 5.453141395 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 1.419844102 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 36 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (34 in total): Nemo.QQMPolyRingElem[c0001, a10, gamma1000, alpha10, b00, beta11, c0111, beta10, alpha11, beta01, alpha01, gamma1100, c0011, c0010, b10, gamma1101, a00, b01, c1011, a01, gamma1110, gamma0100, KS00, KS01, KS10, FS01, FS10, FS11, K, F, S00, S01, S10, S11]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 1
┌ Info: Final cleaning and simplification of generators. 
└ Out of 68 fractions 34 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 2.175047454 seconds. Result: true
[ Info: Out of 39 initial generators there are 34 indepdendent
[ Info: The ranking of the new set of generators is 595
[ Info: The search for identifiable functions concluded in 116.096369962 seconds
[ Info: Processing MAPK model (5 outputs)
┌ 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 34.139908 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 34.139908
[ Info: Computing Wronskians
┌ Info: Computed in 1.609072168 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 1.609072168
[ Info: Dimensions of the Wronskians [60, 1, 44, 96, 149]
┌ Info: Ranks of the Wronskians computed in 0.00315753 seconds
│   :rank_time = :rank_time
└   rank_times = 0.00315753

⌜ # Computing specializations..  	 Time: 0:00:04[K
✓ # Computing specializations..  	 Time: 0:00:04[K

⌜ # Computing specializations..  	 Time: 0:00:00[K
⌝ # Computing specializations..  	 Time: 0:00:00[K
✓ # Computing specializations..  	 Time: 0:00:00[K

⌜ # Computing specializations.. 	 Time: 0:00:00[K
  Points:  4[K
[K[A
✓ # 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: 1 for num. and 0 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 6.
[ Info: Groebner basis computed in 5.747760262 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 3.769523434 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 23 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 22 fractions 22 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 1.791770695 seconds. Result: true
[ Info: Out of 513 initial generators there are 22 indepdendent
[ Info: The ranking of the new set of generators is 253
[ 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 0 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 6.
[ Info: Groebner basis computed in 0.106490439 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.021802897 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 36 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (34 in total): Nemo.QQMPolyRingElem[c0001, a10, gamma1000, alpha10, b00, beta11, c0111, beta10, alpha11, beta01, alpha01, gamma1100, c0011, c0010, b10, gamma1101, a00, b01, c1011, a01, gamma1110, gamma0100, KS00, KS01, KS10, FS01, FS10, FS11, K, F, S00, S01, S10, S11]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 1
┌ Info: Final cleaning and simplification of generators. 
└ Out of 68 fractions 34 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.032749226 seconds. Result: true
[ Info: Out of 39 initial generators there are 34 indepdendent
[ Info: The ranking of the new set of generators is 595
[ Info: The search for identifiable functions concluded in 48.447142427 seconds
┌ Info: Result is
│   result =
│    34-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     S11
│     S10
│     S01
│     S00
│     ⋮
│     gamma1000
│     a10
└     c0001
