┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "SIRS forced"
┌ 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, r, x1, x2
[ Info: Parameters: nu, b1, b0, M, mu, g
[ Info: Inputs: 
[ Info: Outputs: y1, y2
[ 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 16.658412403 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 16.658412403
[ Info: Computing Wronskians
┌ Info: Computed in 18.45154327 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 18.45154327
[ Info: Dimensions of the Wronskians [830, 3]
┌ Info: Ranks of the Wronskians computed in 0.300729871 seconds
│   :rank_time = :rank_time
└   rank_times = 0.300729871

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

⌜ # Computing specializations..  	 Time: 0:00:00[K
✓ # 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: 2 for num. and 0 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 8.
[ Info: Groebner basis computed in 14.213579354 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 4.819117597 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 7 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 5 fractions 5 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 5.643041017 seconds. Result: true
[ Info: Out of 2586 initial generators there are 5 indepdendent
[ Info: The ranking of the new set of generators is 16
[ 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 2 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 12.
[ Info: Groebner basis computed in 5.686192354 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 1.513150959 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 15 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (11 in total): Nemo.QQMPolyRingElem[nu, b1, b0, M, mu, g, s, i, r, x1, x2]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 10
┌ Info: Final cleaning and simplification of generators. 
└ Out of 19 fractions 10 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 2.160465681 seconds. Result: true
[ Info: Out of 12 initial generators there are 10 indepdendent
[ Info: The ranking of the new set of generators is 88
[ Info: The search for identifiable functions concluded in 91.516983391 seconds
[ Info: Processing SIRS forced
┌ 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 0.680425068 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 0.680425068
[ Info: Computing Wronskians
┌ Info: Computed in 6.869759315 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 6.869759315
[ Info: Dimensions of the Wronskians [830, 3]
┌ Info: Ranks of the Wronskians computed in 0.260705481 seconds
│   :rank_time = :rank_time
└   rank_times = 0.260705481

⌜ # 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: 2 for num. and 0 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 8.
[ Info: Groebner basis computed in 0.877218309 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.527777511 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 7 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 5 fractions 5 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.683026495 seconds. Result: true
[ Info: Out of 2586 initial generators there are 5 indepdendent
[ Info: The ranking of the new set of generators is 16
[ 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 2 for den.
│ Maximal number of interpolated terms are: 1 for num. and 1 for den.
└ Points used: 12.
[ Info: Groebner basis computed in 0.039240526 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.006821147 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 15 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (11 in total): Nemo.QQMPolyRingElem[nu, b1, b0, M, mu, g, s, i, r, x1, x2]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 10
┌ Info: Final cleaning and simplification of generators. 
└ Out of 19 fractions 10 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.012642143 seconds. Result: true
[ Info: Out of 12 initial generators there are 10 indepdendent
[ Info: The ranking of the new set of generators is 88
[ Info: The search for identifiable functions concluded in 10.615889044 seconds
┌ Info: Result is
│   result =
│    10-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     r
│     i
│     s
│     g
│     ⋮
│     M^2
│     b1*x1
└     (M*x2)//x1
