┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "p53"
┌ 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, x4
[ Info: Parameters: p7, p4, p13, p18, p8, p23, p1, p3, p10, p25, p16, p11, p22, p20, p17, p21, p9, p6, p12, p15, p24, p5, p14
[ Info: Inputs: u1
[ Info: Outputs: y1, y2, y3, y4
[ 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 14.163507411 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 14.163507411
[ Info: Computing Wronskians
┌ Info: Computed in 11.676616122 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 11.676616122
[ Info: Dimensions of the Wronskians [7, 14, 12, 12]
┌ Info: Ranks of the Wronskians computed in 0.032366773 seconds
│   :rank_time = :rank_time
└   rank_times = 0.032366773

⌜ # 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: 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 13.515394476 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 4.423137645 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 4 for den.
│ Maximal number of interpolated terms are: 1 for num. and 2 for den.
└ Points used: 40.
[ Info: Groebner basis computed in 0.059058224 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.006647068 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 23 fractions 23 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 5.12047205 seconds. Result: true
[ Info: Out of 41 initial generators there are 23 indepdendent
[ Info: The ranking of the new set of generators is 279
[ 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 0.599986894 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.0079001 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 0 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 12.
[ Info: Groebner basis computed in 0.102138121 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.007208837 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 28 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (27 in total): Nemo.QQMPolyRingElem[p7, p4, p13, p18, p8, p23, p1, p3, p10, p25, p16, p11, p22, p20, p17, p21, p9, p6, p12, p15, p24, p5, p14, x1, x2, x3, x4]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 27
┌ Info: Final cleaning and simplification of generators. 
└ Out of 53 fractions 27 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.026691814 seconds. Result: true
[ Info: Out of 37 initial generators there are 27 indepdendent
[ Info: The ranking of the new set of generators is 381
[ Info: The search for identifiable functions concluded in 71.957218067 seconds
[ Info: Processing p53
┌ 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 0.093909736 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 0.093909736
[ Info: Computing Wronskians
┌ Info: Computed in 0.035544173 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 0.035544173
[ Info: Dimensions of the Wronskians [7, 14, 12, 12]
┌ Info: Ranks of the Wronskians computed in 5.1382e-5 seconds
│   :rank_time = :rank_time
└   rank_times = 5.1382e-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 0 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 6.
[ Info: Groebner basis computed in 0.028096026 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.005100219 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 4 for den.
│ Maximal number of interpolated terms are: 1 for num. and 2 for den.
└ Points used: 40.
[ Info: Groebner basis computed in 0.057270238 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.054563503 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 23 fractions 23 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.011939676 seconds. Result: true
[ Info: Out of 41 initial generators there are 23 indepdendent
[ Info: The ranking of the new set of generators is 279
[ 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 0.040413155 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.007601385 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 0 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 12.
[ Info: Groebner basis computed in 0.082809262 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.006848878 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 28 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (27 in total): Nemo.QQMPolyRingElem[p7, p4, p13, p18, p8, p23, p1, p3, p10, p25, p16, p11, p22, p20, p17, p21, p9, p6, p12, p15, p24, p5, p14, x1, x2, x3, x4]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 27
┌ Info: Final cleaning and simplification of generators. 
└ Out of 53 fractions 27 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.038334575 seconds. Result: true
[ Info: Out of 37 initial generators there are 27 indepdendent
[ Info: The ranking of the new set of generators is 381
[ Info: The search for identifiable functions concluded in 1.210215725 seconds
┌ Info: Result is
│   result =
│    27-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     x4
│     x3
│     x2
│     x1
│     ⋮
│     p4
│     p7
└     p22^4
