┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "Fujita"
┌ Info: 
└   KWARGS = (with_states = true, strategy = (:normalforms, 2))
┌ Info: 
└   GLOBAL_ID = Symbol("(:normalforms, 2)_with_states")
[ Info: Summary of the model:
[ Info: State variables: EGFR, pEGFR, pEGFR_Akt, Akt, pAkt, S6, pAkt_S6, pS6, EGF_EGFR
[ Info: Parameters: a2, a3, reaction_1_k1, reaction_4_k1, reaction_9_k1, reaction_1_k2, reaction_7_k1, reaction_6_k1, a1, reaction_3_k1, reaction_5_k1, reaction_2_k1, EGFR_turnover, reaction_2_k2, reaction_5_k2, reaction_8_k1
[ Info: Inputs: pro_EGFR
[ Info: Outputs: y1, y2, y3
[ 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 15.50856847 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 15.50856847
[ Info: Computing Wronskians
┌ Info: Computed in 10.669908928 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 10.669908928
[ Info: Dimensions of the Wronskians [18, 9, 145]
┌ Info: Ranks of the Wronskians computed in 0.024702262 seconds
│   :rank_time = :rank_time
└   rank_times = 0.024702262

⌜ # Computing specializations..  	 Time: 0:00:07[K
✓ # Computing specializations..  	 Time: 0:00:07[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 1 for den.
│ Maximal number of interpolated terms are: 3 for num. and 1 for den.
└ Points used: 32.
[ Info: Groebner basis computed in 9.303760192 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 2.904246621 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 14 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 12 fractions 12 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 3.210362324 seconds. Result: true
[ Info: Out of 217 initial generators there are 12 indepdendent
[ Info: The ranking of the new set of generators is 368
[ 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 1 for den.
│ Maximal number of interpolated terms are: 3 for num. and 1 for den.
└ Points used: 40.
[ Info: Groebner basis computed in 3.42024615 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.964993129 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: 3 for num. and 1 for den.
│ Maximal number of interpolated terms are: 3 for num. and 1 for den.
└ Points used: 48.
[ Info: Groebner basis computed in 0.046632681 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.043357546 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 22 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (25 in total): Nemo.QQMPolyRingElem[a2, a3, reaction_1_k1, reaction_4_k1, reaction_9_k1, reaction_1_k2, reaction_7_k1, reaction_6_k1, a1, reaction_3_k1, reaction_5_k1, reaction_2_k1, EGFR_turnover, reaction_2_k2, reaction_5_k2, reaction_8_k1, EGFR, pEGFR, pEGFR_Akt, Akt, pAkt, S6, pAkt_S6, pS6, EGF_EGFR]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 65
┌ Info: Final cleaning and simplification of generators. 
└ Out of 71 fractions 56 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 1.590563364 seconds. Result: true
[ Info: Out of 23 initial generators there are 20 indepdendent
[ Info: The ranking of the new set of generators is 306
[ Info: The search for identifiable functions concluded in 64.752608206 seconds
[ Info: Processing Fujita
┌ 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 0.227420218 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 0.227420218
[ Info: Computing Wronskians
┌ Info: Computed in 0.363128791 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 0.363128791
[ Info: Dimensions of the Wronskians [18, 9, 145]
┌ Info: Ranks of the Wronskians computed in 0.001319005 seconds
│   :rank_time = :rank_time
└   rank_times = 0.001319005
[ 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: 3 for num. and 1 for den.
└ Points used: 32.
[ Info: Groebner basis computed in 0.105492451 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.01120313 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 14 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 12 fractions 12 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.023946581 seconds. Result: true
[ Info: Out of 217 initial generators there are 12 indepdendent
[ Info: The ranking of the new set of generators is 368
[ 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 1 for den.
│ Maximal number of interpolated terms are: 3 for num. and 1 for den.
└ Points used: 40.
[ Info: Groebner basis computed in 0.040949391 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.037549633 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: 3 for num. and 1 for den.
│ Maximal number of interpolated terms are: 3 for num. and 1 for den.
└ Points used: 48.
[ Info: Groebner basis computed in 0.046843372 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.003639314 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 22 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (25 in total): Nemo.QQMPolyRingElem[a2, a3, reaction_1_k1, reaction_4_k1, reaction_9_k1, reaction_1_k2, reaction_7_k1, reaction_6_k1, a1, reaction_3_k1, reaction_5_k1, reaction_2_k1, EGFR_turnover, reaction_2_k2, reaction_5_k2, reaction_8_k1, EGFR, pEGFR, pEGFR_Akt, Akt, pAkt, S6, pAkt_S6, pS6, EGF_EGFR]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 65
┌ Info: Final cleaning and simplification of generators. 
└ Out of 71 fractions 56 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.021729262 seconds. Result: true
[ Info: Out of 23 initial generators there are 20 indepdendent
[ Info: The ranking of the new set of generators is 306
[ Info: The search for identifiable functions concluded in 2.497022989 seconds
┌ Info: Result is
│   result =
│    20-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     reaction_8_k1
│     reaction_5_k2
│     reaction_2_k2
│     reaction_3_k1
│     ⋮
│     a2*pS6
│     reaction_9_k1*reaction_2_k1*EGF_EGFR
└     reaction_1_k1 - reaction_9_k1 - reaction_1_k2
