You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs.

Question:
(set-logic SLIA)

(synth-fun f ((name String)) String
    ((Start String) (ntString String) (ntInt Int) (ntBool Bool))
    ((Start String (ntString))
    (ntString String (name " " "." (str.++ ntString ntString) (str.replace ntString ntString ntString) (str.at ntString ntInt) (str.from_int ntInt) (str.substr ntString ntInt ntInt)))
    (ntInt Int (0 1 2 (+ ntInt ntInt) (- ntInt ntInt) (str.len ntString) (str.to_int ntString) (str.indexof ntString ntString ntInt)))
    (ntBool Bool (true false (str.prefixof ntString ntString) (str.suffixof ntString ntString) (str.contains ntString ntString)))))

(declare-var name String)
(constraint (= (f "Nancy FreeHafer") "N.F."))
(constraint (= (f "Andrew Cencici") "A.C."))
(constraint (= (f "Jan Kotas") "J.K."))
(constraint (= (f "Mariya Sergienko") "M.S."))
(constraint (= (f "Launa Withers") "L.W."))
(constraint (= (f "Lakenya Edison") "L.E."))
(constraint (= (f "Brendan Hage") "B.H."))
(constraint (= (f "Bradford Lango") "B.L."))
(constraint (= (f "Rudolf Akiyama") "R.A."))
(constraint (= (f "Lara Constable") "L.C."))
(constraint (= (f "Madelaine Ghoston") "M.G."))
(constraint (= (f "Salley Hornak") "S.H."))
(constraint (= (f "Micha Junkin") "M.J."))
(constraint (= (f "Teddy Bobo") "T.B."))
(constraint (= (f "Coralee Scalia") "C.S."))
(constraint (= (f "Jeff Quashie") "J.Q."))
(constraint (= (f "Vena Babiarz") "V.B."))
(constraint (= (f "Karrie Lain") "K.L."))
(constraint (= (f "Tobias Dermody") "T.D."))
(constraint (= (f "Celsa Hopkins") "C.H."))
(constraint (= (f "Kimberley Halpern") "K.H."))
(constraint (= (f "Phillip Rowden") "P.R."))
(constraint (= (f "Elias Neil") "E.N."))
(constraint (= (f "Lashanda Cortes") "L.C."))
(constraint (= (f "Mackenzie Spell") "M.S."))
(constraint (= (f "Kathlyn Eccleston") "K.E."))
(constraint (= (f "Georgina Brescia") "G.B."))
(constraint (= (f "Beata Miah") "B.M."))
(constraint (= (f "Desiree Seamons") "D.S."))
(constraint (= (f "Jeanice Soderstrom") "J.S."))
(constraint (= (f "Mariel Jurgens") "M.J."))
(constraint (= (f "Alida Bogle") "A.B."))
(constraint (= (f "Jacqualine Olague") "J.O."))
(constraint (= (f "Joaquin Clasen") "J.C."))
(constraint (= (f "Samuel Richert") "S.R."))
(constraint (= (f "Malissa Marcus") "M.M."))
(constraint (= (f "Alaina Partida") "A.P."))
(constraint (= (f "Trinidad Mulloy") "T.M."))
(constraint (= (f "Carlene Garrard") "C.G."))
(constraint (= (f "Melodi Chism") "M.C."))
(constraint (= (f "Bess Chilcott") "B.C."))
(constraint (= (f "Chong Aylward") "C.A."))
(constraint (= (f "Jani Ramthun") "J.R."))
(constraint (= (f "Jacquiline Heintz") "J.H."))
(constraint (= (f "Hayley Marquess") "H.M."))
(constraint (= (f "Andria Spagnoli") "A.S."))
(constraint (= (f "Irwin Covelli") "I.C."))
(constraint (= (f "Gertude Montiel") "G.M."))
(constraint (= (f "Stefany Reily") "S.R."))
(constraint (= (f "Rae Mcgaughey") "R.M."))
(constraint (= (f "Cruz Latimore") "C.L."))
(constraint (= (f "Maryann Casler") "M.C."))
(constraint (= (f "Annalisa Gregori") "A.G."))
(constraint (= (f "Jenee Pannell") "J.P."))

(check-synth)
Solution:
(define-fun f ((name String)) String (str.++ (str.at name 0) (str.++ "." (str.++ (str.at name (+ 1 (str.indexof name " " 0))) "."))))

Question:
(set-logic SLIA)

(synth-fun f ((name String)) String
    ((Start String) (ntString String) (ntInt Int) (ntBool Bool))
    ((Start String (ntString))
    (ntString String (name " " "." (str.++ ntString ntString) (str.replace ntString ntString ntString) (str.at ntString ntInt) (str.from_int ntInt) (str.substr ntString ntInt ntInt)))
    (ntInt Int (0 1 2 (+ ntInt ntInt) (- ntInt ntInt) (str.len ntString) (str.to_int ntString) (str.indexof ntString ntString ntInt)))
    (ntBool Bool (true false (str.prefixof ntString ntString) (str.suffixof ntString ntString) (str.contains ntString ntString)))))

(declare-var name String)
(constraint (= (f "Nancy FreeHafer") "N.F."))
(constraint (= (f "Andrew Cencici") "A.C."))
(constraint (= (f "Jan Kotas") "J.K."))
(constraint (= (f "Mariya Sergienko") "M.S."))
(constraint (= (f "Launa Withers") "L.W."))
(constraint (= (f "Launa Withers") "L.W."))
(constraint (= (f "Launa Withers") "L.W."))
(constraint (= (f "Lakenya Edison") "L.E."))
(constraint (= (f "Lakenya Edison") "L.E."))
(constraint (= (f "Lakenya Edison") "L.E."))
(constraint (= (f "Brendan Hage") "B.H."))
(constraint (= (f "Brendan Hage") "B.H."))
(constraint (= (f "Brendan Hage") "B.H."))
(constraint (= (f "Bradford Lango") "B.L."))
(constraint (= (f "Bradford Lango") "B.L."))
(constraint (= (f "Bradford Lango") "B.L."))
(constraint (= (f "Rudolf Akiyama") "R.A."))
(constraint (= (f "Rudolf Akiyama") "R.A."))
(constraint (= (f "Rudolf Akiyama") "R.A."))
(constraint (= (f "Lara Constable") "L.C."))
(constraint (= (f "Lara Constable") "L.C."))
(constraint (= (f "Lara Constable") "L.C."))
(constraint (= (f "Madelaine Ghoston") "M.G."))
(constraint (= (f "Madelaine Ghoston") "M.G."))
(constraint (= (f "Madelaine Ghoston") "M.G."))
(constraint (= (f "Salley Hornak") "S.H."))
(constraint (= (f "Salley Hornak") "S.H."))
(constraint (= (f "Salley Hornak") "S.H."))
(constraint (= (f "Micha Junkin") "M.J."))
(constraint (= (f "Micha Junkin") "M.J."))
(constraint (= (f "Micha Junkin") "M.J."))
(constraint (= (f "Teddy Bobo") "T.B."))
(constraint (= (f "Teddy Bobo") "T.B."))
(constraint (= (f "Teddy Bobo") "T.B."))
(constraint (= (f "Coralee Scalia") "C.S."))
(constraint (= (f "Coralee Scalia") "C.S."))
(constraint (= (f "Coralee Scalia") "C.S."))
(constraint (= (f "Jeff Quashie") "J.Q."))
(constraint (= (f "Jeff Quashie") "J.Q."))
(constraint (= (f "Jeff Quashie") "J.Q."))
(constraint (= (f "Vena Babiarz") "V.B."))
(constraint (= (f "Vena Babiarz") "V.B."))
(constraint (= (f "Vena Babiarz") "V.B."))
(constraint (= (f "Karrie Lain") "K.L."))
(constraint (= (f "Karrie Lain") "K.L."))
(constraint (= (f "Karrie Lain") "K.L."))
(constraint (= (f "Tobias Dermody") "T.D."))
(constraint (= (f "Tobias Dermody") "T.D."))
(constraint (= (f "Tobias Dermody") "T.D."))
(constraint (= (f "Celsa Hopkins") "C.H."))
(constraint (= (f "Celsa Hopkins") "C.H."))
(constraint (= (f "Celsa Hopkins") "C.H."))
(constraint (= (f "Kimberley Halpern") "K.H."))
(constraint (= (f "Kimberley Halpern") "K.H."))
(constraint (= (f "Kimberley Halpern") "K.H."))
(constraint (= (f "Phillip Rowden") "P.R."))
(constraint (= (f "Phillip Rowden") "P.R."))
(constraint (= (f "Phillip Rowden") "P.R."))
(constraint (= (f "Elias Neil") "E.N."))
(constraint (= (f "Elias Neil") "E.N."))
(constraint (= (f "Elias Neil") "E.N."))
(constraint (= (f "Lashanda Cortes") "L.C."))
(constraint (= (f "Lashanda Cortes") "L.C."))
(constraint (= (f "Lashanda Cortes") "L.C."))
(constraint (= (f "Mackenzie Spell") "M.S."))
(constraint (= (f "Mackenzie Spell") "M.S."))
(constraint (= (f "Mackenzie Spell") "M.S."))
(constraint (= (f "Kathlyn Eccleston") "K.E."))
(constraint (= (f "Kathlyn Eccleston") "K.E."))
(constraint (= (f "Kathlyn Eccleston") "K.E."))
(constraint (= (f "Georgina Brescia") "G.B."))
(constraint (= (f "Georgina Brescia") "G.B."))
(constraint (= (f "Georgina Brescia") "G.B."))
(constraint (= (f "Beata Miah") "B.M."))
(constraint (= (f "Beata Miah") "B.M."))
(constraint (= (f "Beata Miah") "B.M."))
(constraint (= (f "Desiree Seamons") "D.S."))
(constraint (= (f "Desiree Seamons") "D.S."))
(constraint (= (f "Desiree Seamons") "D.S."))
(constraint (= (f "Jeanice Soderstrom") "J.S."))
(constraint (= (f "Jeanice Soderstrom") "J.S."))
(constraint (= (f "Jeanice Soderstrom") "J.S."))
(constraint (= (f "Mariel Jurgens") "M.J."))
(constraint (= (f "Mariel Jurgens") "M.J."))
(constraint (= (f "Mariel Jurgens") "M.J."))
(constraint (= (f "Alida Bogle") "A.B."))
(constraint (= (f "Alida Bogle") "A.B."))
(constraint (= (f "Alida Bogle") "A.B."))
(constraint (= (f "Jacqualine Olague") "J.O."))
(constraint (= (f "Jacqualine Olague") "J.O."))
(constraint (= (f "Jacqualine Olague") "J.O."))
(constraint (= (f "Joaquin Clasen") "J.C."))
(constraint (= (f "Joaquin Clasen") "J.C."))
(constraint (= (f "Joaquin Clasen") "J.C."))
(constraint (= (f "Samuel Richert") "S.R."))
(constraint (= (f "Samuel Richert") "S.R."))
(constraint (= (f "Samuel Richert") "S.R."))
(constraint (= (f "Malissa Marcus") "M.M."))
(constraint (= (f "Malissa Marcus") "M.M."))
(constraint (= (f "Malissa Marcus") "M.M."))
(constraint (= (f "Alaina Partida") "A.P."))
(constraint (= (f "Alaina Partida") "A.P."))
(constraint (= (f "Alaina Partida") "A.P."))
(constraint (= (f "Trinidad Mulloy") "T.M."))
(constraint (= (f "Trinidad Mulloy") "T.M."))
(constraint (= (f "Trinidad Mulloy") "T.M."))
(constraint (= (f "Carlene Garrard") "C.G."))
(constraint (= (f "Carlene Garrard") "C.G."))
(constraint (= (f "Carlene Garrard") "C.G."))
(constraint (= (f "Melodi Chism") "M.C."))
(constraint (= (f "Melodi Chism") "M.C."))
(constraint (= (f "Melodi Chism") "M.C."))
(constraint (= (f "Bess Chilcott") "B.C."))
(constraint (= (f "Bess Chilcott") "B.C."))
(constraint (= (f "Bess Chilcott") "B.C."))
(constraint (= (f "Chong Aylward") "C.A."))
(constraint (= (f "Chong Aylward") "C.A."))
(constraint (= (f "Chong Aylward") "C.A."))
(constraint (= (f "Jani Ramthun") "J.R."))
(constraint (= (f "Jani Ramthun") "J.R."))
(constraint (= (f "Jani Ramthun") "J.R."))
(constraint (= (f "Jacquiline Heintz") "J.H."))
(constraint (= (f "Jacquiline Heintz") "J.H."))
(constraint (= (f "Jacquiline Heintz") "J.H."))
(constraint (= (f "Hayley Marquess") "H.M."))
(constraint (= (f "Hayley Marquess") "H.M."))
(constraint (= (f "Hayley Marquess") "H.M."))
(constraint (= (f "Andria Spagnoli") "A.S."))
(constraint (= (f "Andria Spagnoli") "A.S."))
(constraint (= (f "Andria Spagnoli") "A.S."))
(constraint (= (f "Irwin Covelli") "I.C."))
(constraint (= (f "Irwin Covelli") "I.C."))
(constraint (= (f "Irwin Covelli") "I.C."))
(constraint (= (f "Gertude Montiel") "G.M."))
(constraint (= (f "Gertude Montiel") "G.M."))
(constraint (= (f "Gertude Montiel") "G.M."))
(constraint (= (f "Stefany Reily") "S.R."))
(constraint (= (f "Stefany Reily") "S.R."))
(constraint (= (f "Stefany Reily") "S.R."))
(constraint (= (f "Rae Mcgaughey") "R.M."))
(constraint (= (f "Rae Mcgaughey") "R.M."))
(constraint (= (f "Rae Mcgaughey") "R.M."))
(constraint (= (f "Cruz Latimore") "C.L."))
(constraint (= (f "Cruz Latimore") "C.L."))
(constraint (= (f "Cruz Latimore") "C.L."))
(constraint (= (f "Maryann Casler") "M.C."))
(constraint (= (f "Maryann Casler") "M.C."))
(constraint (= (f "Maryann Casler") "M.C."))
(constraint (= (f "Annalisa Gregori") "A.G."))
(constraint (= (f "Annalisa Gregori") "A.G."))
(constraint (= (f "Annalisa Gregori") "A.G."))
(constraint (= (f "Jenee Pannell") "J.P."))
(constraint (= (f "Jenee Pannell") "J.P."))
(constraint (= (f "Jenee Pannell") "J.P."))
(constraint (= (f "Launa Withers") "L.W."))
(constraint (= (f "Lakenya Edison") "L.E."))
(constraint (= (f "Brendan Hage") "B.H."))
(constraint (= (f "Bradford Lango") "B.L."))
(constraint (= (f "Rudolf Akiyama") "R.A."))
(constraint (= (f "Lara Constable") "L.C."))
(constraint (= (f "Madelaine Ghoston") "M.G."))
(constraint (= (f "Salley Hornak") "S.H."))
(constraint (= (f "Micha Junkin") "M.J."))
(constraint (= (f "Teddy Bobo") "T.B."))
(constraint (= (f "Coralee Scalia") "C.S."))
(constraint (= (f "Jeff Quashie") "J.Q."))
(constraint (= (f "Vena Babiarz") "V.B."))
(constraint (= (f "Karrie Lain") "K.L."))
(constraint (= (f "Tobias Dermody") "T.D."))
(constraint (= (f "Celsa Hopkins") "C.H."))
(constraint (= (f "Kimberley Halpern") "K.H."))
(constraint (= (f "Phillip Rowden") "P.R."))
(constraint (= (f "Elias Neil") "E.N."))
(constraint (= (f "Lashanda Cortes") "L.C."))
(constraint (= (f "Mackenzie Spell") "M.S."))
(constraint (= (f "Kathlyn Eccleston") "K.E."))
(constraint (= (f "Georgina Brescia") "G.B."))
(constraint (= (f "Beata Miah") "B.M."))
(constraint (= (f "Desiree Seamons") "D.S."))
(constraint (= (f "Jeanice Soderstrom") "J.S."))
(constraint (= (f "Mariel Jurgens") "M.J."))
(constraint (= (f "Alida Bogle") "A.B."))
(constraint (= (f "Jacqualine Olague") "J.O."))
(constraint (= (f "Joaquin Clasen") "J.C."))
(constraint (= (f "Samuel Richert") "S.R."))
(constraint (= (f "Malissa Marcus") "M.M."))
(constraint (= (f "Alaina Partida") "A.P."))
(constraint (= (f "Trinidad Mulloy") "T.M."))
(constraint (= (f "Carlene Garrard") "C.G."))
(constraint (= (f "Melodi Chism") "M.C."))
(constraint (= (f "Bess Chilcott") "B.C."))
(constraint (= (f "Chong Aylward") "C.A."))
(constraint (= (f "Jani Ramthun") "J.R."))
(constraint (= (f "Jacquiline Heintz") "J.H."))
(constraint (= (f "Hayley Marquess") "H.M."))
(constraint (= (f "Andria Spagnoli") "A.S."))
(constraint (= (f "Irwin Covelli") "I.C."))
(constraint (= (f "Gertude Montiel") "G.M."))
(constraint (= (f "Stefany Reily") "S.R."))
(constraint (= (f "Rae Mcgaughey") "R.M."))
(constraint (= (f "Cruz Latimore") "C.L."))
(constraint (= (f "Maryann Casler") "M.C."))
(constraint (= (f "Annalisa Gregori") "A.G."))
(constraint (= (f "Jenee Pannell") "J.P."))

(check-synth)
Solution:
(define-fun f ((name String)) String (str.++ (str.at name 0) (str.++ "." (str.++ (str.at name (+ 1 (str.indexof name " " 0))) "."))))

Question:
(set-logic SLIA)

(synth-fun f ((name String)) String
    ((Start String) (ntString String) (ntInt Int) (ntBool Bool))
    ((Start String (ntString))
    (ntString String (name " " "." (str.++ ntString ntString) (str.replace ntString ntString ntString) (str.at ntString ntInt) (str.from_int ntInt) (str.substr ntString ntInt ntInt)))
    (ntInt Int (0 1 2 (+ ntInt ntInt) (- ntInt ntInt) (str.len ntString) (str.to_int ntString) (str.indexof ntString ntString ntInt)))
    (ntBool Bool (true false (str.prefixof ntString ntString) (str.suffixof ntString ntString) (str.contains ntString ntString)))))

(declare-var name String)
(constraint (= (f "Nancy FreeHafer") "N.F."))
(constraint (= (f "Andrew Cencici") "A.C."))
(constraint (= (f "Jan Kotas") "J.K."))
(constraint (= (f "Mariya Sergienko") "M.S."))

(check-synth)
Solution:
(define-fun f ((name String)) String (str.++ (str.at name 0) (str.++ "." (str.++ (str.at name (+ 1 (str.indexof name " " 0))) "."))))

Question:
(set-logic SLIA)

(synth-fun f ((name String)) String
    ((Start String) (ntString String) (ntInt Int) (ntBool Bool))
    ((Start String (ntString))
    (ntString String (name " " "." (str.++ ntString ntString) (str.replace ntString ntString ntString) (str.at ntString ntInt) (str.substr ntString ntInt ntInt)))
    (ntInt Int (0 1 2 (+ ntInt ntInt) (- ntInt ntInt) (str.len ntString) (str.indexof ntString ntString ntInt)))
    (ntBool Bool (true false (str.prefixof ntString ntString) (str.suffixof ntString ntString)))))

(declare-var name String)
(constraint (= (f "Nancy FreeHafer") "N.F."))
(constraint (= (f "Andrew Cencici") "A.C."))
(constraint (= (f "Jan Kotas") "J.K."))
(constraint (= (f "Mariya Sergienko") "M.S."))

(check-synth)
Solution:


Output grammar:
root ::= "(define-fun f ((name String)) String " Start ")"
Start ::= ntString
ntString ::= "name" | "\" \"" | "\".\"" | "(" "str.++" " " ntString " " ntString ")" | "(" "str.replace" " " ntString " " ntString " " ntString ")" | "(" "str.at" " " ntString " " ntInt ")" | "(" "str.substr" " " ntString " " ntInt " " ntInt ")"
ntInt ::= "0" | "1" | "2" | "(" "+" " " ntInt " " ntInt ")" | "(" "-" " " ntInt " " ntInt ")" | "(" "str.len" " " ntString ")" | "(" "str.indexof" " " ntString " " ntString " " ntInt ")"
ntBool ::= "true" | "false" | "(" "str.prefixof" " " ntString " " ntString ")" | "(" "str.suffixof" " " ntString " " ntString ")"