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 ((col1 String) (col2 String)) String
    ((Start String) (ntString String) (ntInt Int) (ntBool Bool))
    ((Start String (ntString))
    (ntString String (col1 col2 " " "," "USA" "PA" "CT" "CA" "MD" "NY" (str.++ ntString ntString) (str.replace ntString ntString ntString) (str.at ntString ntInt) (str.from_int ntInt) (ite ntBool ntString ntString) (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 col1 String)
(declare-var col2 String)
(constraint (= (f "University of Pennsylvania" "Phialdelphia, PA, USA") "University of Pennsylvania, Phialdelphia, PA, USA"))
(constraint (= (f "UCLA" "Los Angeles, CA") "UCLA, Los Angeles, CA, USA"))
(constraint (= (f "Cornell University" "Ithaca, New York, USA") "Cornell University, Ithaca, New York, USA"))
(constraint (= (f "Penn" "Philadelphia, PA, USA") "Penn, Philadelphia, PA, USA"))
(constraint (= (f "University of Maryland College Park" "College Park, MD") "University of Maryland College Park, College Park, MD, USA"))
(constraint (= (f "University of Michigan" "Ann Arbor, MI, USA") "University of Michigan, Ann Arbor, MI, USA"))

(check-synth)
Solution:
(define-fun f ((col1 String) (col2 String)) String (let ((_let_1 (str.++ " " (str.++ col2 (str.++ "," (str.++ " " "USA")))))) (let ((_let_2 (str.contains col1 " "))) (let ((_let_3 (str.++ " " col2))) (str.++ col1 (ite (str.contains col2 "USA") (str.++ "," (ite _let_2 _let_3 _let_3)) (str.++ "," (ite _let_2 _let_1 _let_1))))))))

Question:
(set-logic SLIA)

(synth-fun f ((col1 String) (col2 String)) String
    ((Start String) (ntString String) (ntInt Int) (ntBool Bool))
    ((Start String (ntString))
    (ntString String (col1 col2 "New York" " " "," "AK" "AZ" "AR" "CA" "CO" "CT" "DE" "FL" "GA" "HI" "ID" "IL" "IN" "IA" "KS" "KY" "LA" "ME" "MD" "MA" "MI" "MN" "MS" "MO" "MT" "NE" "NV" "NH" "NJ" "NM" "NY" "NC" "ND" "OH" "OK" "OR" "PA" "RI" "SC" "SD" "TN" "TX" "UT" "VT" "VA" "WA" "WV" "WI" "USA" (str.++ ntString ntString) (str.replace ntString ntString ntString) (str.at ntString ntInt) (str.from_int ntInt) (ite ntBool ntString ntString) (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 col1 String)
(declare-var col2 String)
(constraint (= (f "University of Pennsylvania" "Phialdelphia, PA, USA") "Phialdelphia, PA, USA"))
(constraint (= (f "UCLA" "Los Angeles, CA") "Los Angeles, CA, USA"))
(constraint (= (f "Cornell University" "Ithaca, New York, USA") "Ithaca, NY, USA"))
(constraint (= (f "Penn" "Philadelphia, PA, USA") "Philadelphia, PA, USA"))
(constraint (= (f "University of Maryland College Park" "College Park, MD") "College Park, MD, USA"))
(constraint (= (f "University of Michigan" "Ann Arbor, MI, USA") "Ann Arbor, MI, USA"))
(constraint (= (f "UC Berkeley" "Berkeley, CA") "Berkeley, CA, USA"))
(constraint (= (f "MIT" "Cambridge, MA") "Cambridge, MA, USA"))
(constraint (= (f "Rice University" "Houston, TX") "Houston, TX, USA"))
(constraint (= (f "Yale University" "New Haven, CT, USA") "New Haven, CT, USA"))
(constraint (= (f "Columbia University" "New York, NY, USA") "New York, NY, USA"))
(constraint (= (f "NYU" "New York, New York, USA") "New York, NY, USA"))
(constraint (= (f "UC Berkeley" "Berkeley, CA") "Berkeley, CA, USA"))
(constraint (= (f "UIUC" "Urbana, IL") "Urbana, IL, USA"))
(constraint (= (f "Temple University" "Philadelphia, PA") "Philadelphia, PA, USA"))
(constraint (= (f "Harvard University" "Cambridge, MA, USA") "Cambridge, MA, USA"))
(constraint (= (f "University of Connecticut" "Storrs, CT, USA") "Storrs, CT, USA"))
(constraint (= (f "Drexel University" "Philadelphia, PA") "Philadelphia, PA, USA"))
(constraint (= (f "New Haven University" "New Haven, CT, USA") "New Haven, CT, USA"))
(constraint (= (f "University of California, Santa Barbara" "Santa Barbara, CA, USA") "Santa Barbara, CA, USA"))

(check-synth)
Solution:
(define-fun f ((col1 String) (col2 String)) String (let ((_let_1 (str.replace col2 "New York" "NY"))) (let ((_let_2 (str.contains col2 "PA"))) (ite (str.contains col2 "USA") (ite (str.contains col1 " ") (ite _let_2 _let_1 (ite (str.contains col2 "CA") _let_1 (ite (str.contains col2 "New York") (ite (str.prefixof "New York" col2) col2 _let_1) _let_1))) (ite _let_2 _let_1 (str.++ (str.++ (str.++ (str.++ (str.++ (str.++ "New York" ",") " ") "NY") ",") " ") "USA"))) (str.++ (str.replace col2 "New York" "MT") (str.++ "," (str.++ " " "USA")))))))

Question:
(set-logic SLIA)

(synth-fun f ((col1 String) (col2 String)) String
    ((Start String) (ntString String) (ntInt Int) (ntBool Bool))
    ((Start String (ntString))
    (ntString String (col1 col2 "New York" " " "," "USA" "PA" "CT" "CA" "MD" "NY" (str.++ ntString ntString) (str.replace ntString ntString ntString) (str.at ntString ntInt) (ite ntBool ntString ntString) (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 col1 String)
(declare-var col2 String)
(constraint (= (f "University of Pennsylvania" "Phialdelphia, PA, USA") "Phialdelphia, PA, USA"))
(constraint (= (f "UCLA" "Los Angeles, CA") "Los Angeles, CA, USA"))
(constraint (= (f "Cornell University" "Ithaca, New York, USA") "Ithaca, NY, USA"))
(constraint (= (f "Penn" "Philadelphia, PA, USA") "Philadelphia, PA, USA"))
(constraint (= (f "University of Maryland College Park" "College Park, MD") "College Park, MD, USA"))
(constraint (= (f "University of Michigan" "Ann Arbor, MI, USA") "Ann Arbor, MI, USA"))
(constraint (= (f "Columbia University" "New York, NY, USA") "New York, NY, USA"))
(constraint (= (f "NYU" "New York, New York, USA") "New York, NY, USA"))

(check-synth)
Solution:
(define-fun f ((col1 String) (col2 String)) String (let ((_let_1 (str.++ col2 ","))) (ite (str.prefixof "New York" col2) (str.++ "New York" (str.++ "," (str.++ " " (str.++ "NY" (str.++ "," (str.++ " " "USA")))))) (ite (str.suffixof "USA" col2) (str.replace col2 "New York" "NY") (str.++ (str.++ (ite (str.suffixof "CA" col2) _let_1 _let_1) " ") "USA")))))

Question:
(set-logic SLIA)

(synth-fun f ((col1 String) (col2 String)) String
    ((Start String) (ntString String) (ntInt Int) (ntBool Bool))
    ((Start String (ntString))
    (ntString String (col1 col2 " " "," "USA" "PA" "CT" "CA" "MD" "NY" (str.++ ntString ntString) (str.replace ntString ntString ntString) (str.at ntString ntInt) (ite ntBool ntString ntString) (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 col1 String)
(declare-var col2 String)
(constraint (= (f "University of Pennsylvania" "Phialdelphia, PA, USA") "University of Pennsylvania, Phialdelphia, PA, USA"))
(constraint (= (f "UCLA" "Los Angeles, CA") "UCLA, Los Angeles, CA, USA"))
(constraint (= (f "Cornell University" "Ithaca, New York, USA") "Cornell University, Ithaca, New York, USA"))
(constraint (= (f "Penn" "Philadelphia, PA, USA") "Penn, Philadelphia, PA, USA"))
(constraint (= (f "University of Maryland College Park" "College Park, MD") "University of Maryland College Park, College Park, MD, USA"))
(constraint (= (f "University of Michigan" "Ann Arbor, MI, USA") "University of Michigan, Ann Arbor, MI, USA"))

(check-synth)
Solution:


Output grammar:
root ::= "(define-fun f ((col1 String) (col2 String)) String " Start ")"
Start ::= ntString
ntString ::= "col1" | "col2" | "\" \"" | "\",\"" | "\"USA\"" | "\"PA\"" | "\"CT\"" | "\"CA\"" | "\"MD\"" | "\"NY\"" | "(" "str.++" " " ntString " " ntString ")" | "(" "str.replace" " " ntString " " ntString " " ntString ")" | "(" "str.at" " " ntString " " ntInt ")" | "(" "ite" " " ntBool " " ntString " " ntString ")" | "(" "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 ")"