NO

Problem 1: 

(VAR v_NonEmpty:S X:S Y:S Z:S)
(RULES
fcons(X:S,Z:S) -> cons(X:S,Z:S)
first(0,Z:S) -> nil
first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S))
first1(0,Z:S) -> nil1
first1(s(X:S),cons(Y:S,Z:S)) -> cons1(quote(Y:S),first1(X:S,Z:S))
from(X:S) -> cons(X:S,from(s(X:S)))
quote(sel(X:S,Z:S)) -> sel1(X:S,Z:S)
quote(0) -> 01
quote(s(X:S)) -> s1(quote(X:S))
quote1(first(X:S,Z:S)) -> first1(X:S,Z:S)
quote1(cons(X:S,Z:S)) -> cons1(quote(X:S),quote1(Z:S))
quote1(nil) -> nil1
sel(0,cons(X:S,Z:S)) -> X:S
sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z:S)
sel1(0,cons(X:S,Z:S)) -> quote(X:S)
sel1(s(X:S),cons(Y:S,Z:S)) -> sel1(X:S,Z:S)
unquote(01) -> 0
unquote(s1(X:S)) -> s(unquote(X:S))
unquote1(cons1(X:S,Z:S)) -> fcons(unquote(X:S),unquote1(Z:S))
unquote1(nil1) -> nil
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 FIRST(s(X:S),cons(Y:S,Z:S)) -> FIRST(X:S,Z:S)
 FIRST1(s(X:S),cons(Y:S,Z:S)) -> FIRST1(X:S,Z:S)
 FIRST1(s(X:S),cons(Y:S,Z:S)) -> QUOTE(Y:S)
 FROM(X:S) -> FROM(s(X:S))
 QUOTE(sel(X:S,Z:S)) -> SEL1(X:S,Z:S)
 QUOTE(s(X:S)) -> QUOTE(X:S)
 QUOTE1(first(X:S,Z:S)) -> FIRST1(X:S,Z:S)
 QUOTE1(cons(X:S,Z:S)) -> QUOTE(X:S)
 QUOTE1(cons(X:S,Z:S)) -> QUOTE1(Z:S)
 SEL(s(X:S),cons(Y:S,Z:S)) -> SEL(X:S,Z:S)
 SEL1(0,cons(X:S,Z:S)) -> QUOTE(X:S)
 SEL1(s(X:S),cons(Y:S,Z:S)) -> SEL1(X:S,Z:S)
 UNQUOTE(s1(X:S)) -> UNQUOTE(X:S)
 UNQUOTE1(cons1(X:S,Z:S)) -> FCONS(unquote(X:S),unquote1(Z:S))
 UNQUOTE1(cons1(X:S,Z:S)) -> UNQUOTE(X:S)
 UNQUOTE1(cons1(X:S,Z:S)) -> UNQUOTE1(Z:S)
-> Rules:
 fcons(X:S,Z:S) -> cons(X:S,Z:S)
 first(0,Z:S) -> nil
 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S))
 first1(0,Z:S) -> nil1
 first1(s(X:S),cons(Y:S,Z:S)) -> cons1(quote(Y:S),first1(X:S,Z:S))
 from(X:S) -> cons(X:S,from(s(X:S)))
 quote(sel(X:S,Z:S)) -> sel1(X:S,Z:S)
 quote(0) -> 01
 quote(s(X:S)) -> s1(quote(X:S))
 quote1(first(X:S,Z:S)) -> first1(X:S,Z:S)
 quote1(cons(X:S,Z:S)) -> cons1(quote(X:S),quote1(Z:S))
 quote1(nil) -> nil1
 sel(0,cons(X:S,Z:S)) -> X:S
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z:S)
 sel1(0,cons(X:S,Z:S)) -> quote(X:S)
 sel1(s(X:S),cons(Y:S,Z:S)) -> sel1(X:S,Z:S)
 unquote(01) -> 0
 unquote(s1(X:S)) -> s(unquote(X:S))
 unquote1(cons1(X:S,Z:S)) -> fcons(unquote(X:S),unquote1(Z:S))
 unquote1(nil1) -> nil

Problem 1: 

Infinite Processor:
-> Pairs:
 FIRST(s(X:S),cons(Y:S,Z:S)) -> FIRST(X:S,Z:S)
 FIRST1(s(X:S),cons(Y:S,Z:S)) -> FIRST1(X:S,Z:S)
 FIRST1(s(X:S),cons(Y:S,Z:S)) -> QUOTE(Y:S)
 FROM(X:S) -> FROM(s(X:S))
 QUOTE(sel(X:S,Z:S)) -> SEL1(X:S,Z:S)
 QUOTE(s(X:S)) -> QUOTE(X:S)
 QUOTE1(first(X:S,Z:S)) -> FIRST1(X:S,Z:S)
 QUOTE1(cons(X:S,Z:S)) -> QUOTE(X:S)
 QUOTE1(cons(X:S,Z:S)) -> QUOTE1(Z:S)
 SEL(s(X:S),cons(Y:S,Z:S)) -> SEL(X:S,Z:S)
 SEL1(0,cons(X:S,Z:S)) -> QUOTE(X:S)
 SEL1(s(X:S),cons(Y:S,Z:S)) -> SEL1(X:S,Z:S)
 UNQUOTE(s1(X:S)) -> UNQUOTE(X:S)
 UNQUOTE1(cons1(X:S,Z:S)) -> FCONS(unquote(X:S),unquote1(Z:S))
 UNQUOTE1(cons1(X:S,Z:S)) -> UNQUOTE(X:S)
 UNQUOTE1(cons1(X:S,Z:S)) -> UNQUOTE1(Z:S)
-> Rules:
 fcons(X:S,Z:S) -> cons(X:S,Z:S)
 first(0,Z:S) -> nil
 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S))
 first1(0,Z:S) -> nil1
 first1(s(X:S),cons(Y:S,Z:S)) -> cons1(quote(Y:S),first1(X:S,Z:S))
 from(X:S) -> cons(X:S,from(s(X:S)))
 quote(sel(X:S,Z:S)) -> sel1(X:S,Z:S)
 quote(0) -> 01
 quote(s(X:S)) -> s1(quote(X:S))
 quote1(first(X:S,Z:S)) -> first1(X:S,Z:S)
 quote1(cons(X:S,Z:S)) -> cons1(quote(X:S),quote1(Z:S))
 quote1(nil) -> nil1
 sel(0,cons(X:S,Z:S)) -> X:S
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,Z:S)
 sel1(0,cons(X:S,Z:S)) -> quote(X:S)
 sel1(s(X:S),cons(Y:S,Z:S)) -> sel1(X:S,Z:S)
 unquote(01) -> 0
 unquote(s1(X:S)) -> s(unquote(X:S))
 unquote1(cons1(X:S,Z:S)) -> fcons(unquote(X:S),unquote1(Z:S))
 unquote1(nil1) -> nil
-> Pairs in cycle:
 FROM(X:S) -> FROM(s(X:S))

The problem is infinite.