┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "HighDimNonLin"
┌ 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, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20
[ Info: Parameters: p7, p20, p2, p18, p1, km, p9, p6, p15, p5, p14, p4, p13, p8, p10, vm, p17, p12, p3, p16, p11, p19
[ Info: Inputs: u
[ Info: Outputs: y1, y2, y3, y4, y5, y6, y7, y8, y9, y10, y11, y12, y13, y14, y15, y16, y17, y18, y19, y20
[ 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 24.203325531 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 24.203325531
[ Info: Computing Wronskians
┌ Info: Computed in 20.312308557 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 20.312308557
[ Info: Dimensions of the Wronskians [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3]
┌ Info: Ranks of the Wronskians computed in 0.037129498 seconds
│   :rank_time = :rank_time
└   rank_times = 0.037129498

⌜ # Computing specializations..  	 Time: 0:00:10[K
✓ # Computing specializations..  	 Time: 0:00:11[K

⌜ # Computing specializations..  	 Time: 0:00:03[K
✓ # Computing specializations..  	 Time: 0:00:03[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 13.929174953 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 4.315151755 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 24 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 4.612387769 seconds. Result: true
[ Info: Out of 43 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 1 for den.
│ Maximal number of interpolated terms are: 1 for num. and 2 for den.
└ Points used: 16.
[ Info: Groebner basis computed in 4.183566194 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 1.335249295 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 44 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (42 in total): Nemo.QQMPolyRingElem[p7, p20, p2, p18, p1, km, p9, p6, p15, p5, p14, p4, p13, p8, p10, vm, p17, p12, p3, p16, p11, p19, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 1
┌ Info: Final cleaning and simplification of generators. 
└ Out of 84 fractions 43 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 2.354380297 seconds. Result: true
[ Info: Out of 62 initial generators there are 42 indepdendent
[ Info: The ranking of the new set of generators is 903
[ Info: The search for identifiable functions concluded in 96.998092491 seconds
[ Info: Processing HighDimNonLin
┌ 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 10.841822154 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 10.841822154
[ Info: Computing Wronskians
┌ Info: Computed in 7.791635766 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 7.791635766
[ Info: Dimensions of the Wronskians [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3]
┌ Info: Ranks of the Wronskians computed in 6.3691e-5 seconds
│   :rank_time = :rank_time
└   rank_times = 6.3691e-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 0.023190463 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.004264671 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 24 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 0.004835494 seconds. Result: true
[ Info: Out of 43 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 1 for den.
│ Maximal number of interpolated terms are: 1 for num. and 2 for den.
└ Points used: 16.
[ Info: Groebner basis computed in 0.09135088 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.009462482 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 44 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (42 in total): Nemo.QQMPolyRingElem[p7, p20, p2, p18, p1, km, p9, p6, p15, p5, p14, p4, p13, p8, p10, vm, p17, p12, p3, p16, p11, p19, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 1
┌ Info: Final cleaning and simplification of generators. 
└ Out of 84 fractions 43 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.039790751 seconds. Result: true
[ Info: Out of 62 initial generators there are 42 indepdendent
[ Info: The ranking of the new set of generators is 903
[ Info: The search for identifiable functions concluded in 20.54945336 seconds
┌ Info: Result is
│   result =
│    42-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     x20
│     x19
│     x18
│     x17
│     ⋮
│     p2
│     p20
└     p7
