┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "SIWR original"
┌ Info: 
└   KWARGS = (with_states = true, strategy = (:normalforms, 2))
┌ Info: 
└   GLOBAL_ID = Symbol("(:normalforms, 2)_with_states")
[ Info: Summary of the model:
[ Info: State variables: S, I, W, R
[ Info: Parameters: bi, gam, mu, bw, k, xi, a
[ Info: Inputs: 
[ Info: Outputs: y
[ 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 8.10564193 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 8.10564193
[ Info: Computing Wronskians
┌ Info: Computed in 8.502304946 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 8.502304946
[ Info: Dimensions of the Wronskians [676]
┌ Info: Ranks of the Wronskians computed in 0.11006203 seconds
│   :rank_time = :rank_time
└   rank_times = 0.11006203

⌜ # Computing specializations..  	 Time: 0:00:07[K
✓ # Computing specializations..  	 Time: 0:00:07[K

⌜ # Computing specializations..  	 Time: 0:00:00[K
✓ # 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 9.591010066 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 5.376246417 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 8 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 7 fractions 7 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 12.131289871 seconds. Result: true
[ Info: Out of 770 initial generators there are 7 indepdendent
[ Info: The ranking of the new set of generators is 28
[ 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 0.639543479 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.006943916 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 13 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (11 in total): Nemo.QQMPolyRingElem[bi, gam, mu, bw, k, xi, a, S, I, W, R]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 1
┌ Info: Final cleaning and simplification of generators. 
└ Out of 22 fractions 11 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.007799909 seconds. Result: true
[ Info: Out of 12 initial generators there are 11 indepdendent
[ Info: The ranking of the new set of generators is 66
[ Info: The search for identifiable functions concluded in 60.212306651 seconds
[ Info: Processing SIWR original
┌ 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 0.920860111 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 0.920860111
[ Info: Computing Wronskians
┌ Info: Computed in 1.831905202 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 1.831905202
[ Info: Dimensions of the Wronskians [676]
┌ Info: Ranks of the Wronskians computed in 0.122624402 seconds
│   :rank_time = :rank_time
└   rank_times = 0.122624402

⌜ # 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
[ 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 1.696328522 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 1.36495185 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 8 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 7 fractions 7 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 6.311628865 seconds. Result: true
[ Info: Out of 770 initial generators there are 7 indepdendent
[ Info: The ranking of the new set of generators is 28
[ 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 0.024490053 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.042327699 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 13 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (11 in total): Nemo.QQMPolyRingElem[bi, gam, mu, bw, k, xi, a, S, I, W, R]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 1
┌ Info: Final cleaning and simplification of generators. 
└ Out of 22 fractions 11 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.014277095 seconds. Result: true
[ Info: Out of 12 initial generators there are 11 indepdendent
[ Info: The ranking of the new set of generators is 66
[ Info: The search for identifiable functions concluded in 13.723273508 seconds
┌ Info: Result is
│   result =
│    11-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     R
│     W
│     I
│     S
│     ⋮
│     mu
│     gam
└     bi
