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") "Nancy"))
(constraint (= (f "Andrew Cencici") "Andrew"))
(constraint (= (f "Jan Kotas") "Jan"))
(constraint (= (f "Mariya Sergienko") "Mariya"))
(constraint (= (f "Launa Withers") "Launa"))
(constraint (= (f "Lakenya Edison") "Lakenya"))
(constraint (= (f "Brendan Hage") "Brendan"))
(constraint (= (f "Bradford Lango") "Bradford"))
(constraint (= (f "Rudolf Akiyama") "Rudolf"))
(constraint (= (f "Lara Constable") "Lara"))
(constraint (= (f "Madelaine Ghoston") "Madelaine"))
(constraint (= (f "Salley Hornak") "Salley"))
(constraint (= (f "Micha Junkin") "Micha"))
(constraint (= (f "Teddy Bobo") "Teddy"))
(constraint (= (f "Coralee Scalia") "Coralee"))
(constraint (= (f "Jeff Quashie") "Jeff"))
(constraint (= (f "Vena Babiarz") "Vena"))
(constraint (= (f "Karrie Lain") "Karrie"))
(constraint (= (f "Tobias Dermody") "Tobias"))
(constraint (= (f "Celsa Hopkins") "Celsa"))
(constraint (= (f "Kimberley Halpern") "Kimberley"))
(constraint (= (f "Phillip Rowden") "Phillip"))
(constraint (= (f "Elias Neil") "Elias"))
(constraint (= (f "Lashanda Cortes") "Lashanda"))
(constraint (= (f "Mackenzie Spell") "Mackenzie"))
(constraint (= (f "Kathlyn Eccleston") "Kathlyn"))
(constraint (= (f "Georgina Brescia") "Georgina"))
(constraint (= (f "Beata Miah") "Beata"))
(constraint (= (f "Desiree Seamons") "Desiree"))
(constraint (= (f "Jeanice Soderstrom") "Jeanice"))
(constraint (= (f "Mariel Jurgens") "Mariel"))
(constraint (= (f "Alida Bogle") "Alida"))
(constraint (= (f "Jacqualine Olague") "Jacqualine"))
(constraint (= (f "Joaquin Clasen") "Joaquin"))
(constraint (= (f "Samuel Richert") "Samuel"))
(constraint (= (f "Malissa Marcus") "Malissa"))
(constraint (= (f "Alaina Partida") "Alaina"))
(constraint (= (f "Trinidad Mulloy") "Trinidad"))
(constraint (= (f "Carlene Garrard") "Carlene"))
(constraint (= (f "Melodi Chism") "Melodi"))
(constraint (= (f "Bess Chilcott") "Bess"))
(constraint (= (f "Chong Aylward") "Chong"))
(constraint (= (f "Jani Ramthun") "Jani"))
(constraint (= (f "Jacquiline Heintz") "Jacquiline"))
(constraint (= (f "Hayley Marquess") "Hayley"))
(constraint (= (f "Andria Spagnoli") "Andria"))
(constraint (= (f "Irwin Covelli") "Irwin"))
(constraint (= (f "Gertude Montiel") "Gertude"))
(constraint (= (f "Stefany Reily") "Stefany"))
(constraint (= (f "Rae Mcgaughey") "Rae"))
(constraint (= (f "Cruz Latimore") "Cruz"))
(constraint (= (f "Maryann Casler") "Maryann"))
(constraint (= (f "Annalisa Gregori") "Annalisa"))
(constraint (= (f "Jenee Pannell") "Jenee"))

(check-synth)
Solution:
(define-fun f ((name String)) String (str.substr name 0 (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") "Nancy"))
(constraint (= (f "Andrew Cencici") "Andrew"))
(constraint (= (f "Jan Kotas") "Jan"))
(constraint (= (f "Mariya Sergienko") "Mariya"))

(check-synth)
Solution:
(define-fun f ((name String)) String (str.substr name 0 (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") "Nancy"))
(constraint (= (f "Andrew Cencici") "Andrew"))
(constraint (= (f "Jan Kotas") "Jan"))
(constraint (= (f "Mariya Sergienko") "Mariya"))

(check-synth)
Solution:
(define-fun f ((name String)) String (str.substr name 0 (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") "Nancy"))
(constraint (= (f "Andrew Cencici") "Andrew"))
(constraint (= (f "Jan Kotas") "Jan"))
(constraint (= (f "Mariya Sergienko") "Mariya"))

(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 ")"