NO

Problem 1: 

(VAR v_NonEmpty:S X:S Y:S Z:S)
(RULES
add(0,X:S) -> X:S
add(s(X:S),Y:S) -> s(add(X:S,Y:S))
and(ffalse,Y:S) -> ffalse
and(ttrue,X:S) -> X:S
first(0,X:S) -> nil
first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S))
from(X:S) -> cons(X:S,from(s(X:S)))
if(ffalse,X:S,Y:S) -> Y:S
if(ttrue,X:S,Y:S) -> X:S
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ADD(s(X:S),Y:S) -> ADD(X:S,Y:S)
 FIRST(s(X:S),cons(Y:S,Z:S)) -> FIRST(X:S,Z:S)
 FROM(X:S) -> FROM(s(X:S))
-> Rules:
 add(0,X:S) -> X:S
 add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 and(ffalse,Y:S) -> ffalse
 and(ttrue,X:S) -> X:S
 first(0,X:S) -> nil
 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S))
 from(X:S) -> cons(X:S,from(s(X:S)))
 if(ffalse,X:S,Y:S) -> Y:S
 if(ttrue,X:S,Y:S) -> X:S

Problem 1: 

Infinite Processor:
-> Pairs:
 ADD(s(X:S),Y:S) -> ADD(X:S,Y:S)
 FIRST(s(X:S),cons(Y:S,Z:S)) -> FIRST(X:S,Z:S)
 FROM(X:S) -> FROM(s(X:S))
-> Rules:
 add(0,X:S) -> X:S
 add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 and(ffalse,Y:S) -> ffalse
 and(ttrue,X:S) -> X:S
 first(0,X:S) -> nil
 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S))
 from(X:S) -> cons(X:S,from(s(X:S)))
 if(ffalse,X:S,Y:S) -> Y:S
 if(ttrue,X:S,Y:S) -> X:S
-> Pairs in cycle:
 FROM(X:S) -> FROM(s(X:S))

The problem is infinite.