YES

Problem 1: 

(VAR v_NonEmpty:S N:S X:S Y:S)
(RULES
add(0,X:S) -> X:S
add(s,Y:S) -> s
dbl(0) -> 0
dbl(s) -> s
first(0,X:S) -> nil
first(s,cons(Y:S)) -> cons(Y:S)
sqr(0) -> 0
sqr(s) -> s
terms(N:S) -> cons(recip(sqr(N:S)))
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 TERMS(N:S) -> SQR(N:S)
-> Rules:
 add(0,X:S) -> X:S
 add(s,Y:S) -> s
 dbl(0) -> 0
 dbl(s) -> s
 first(0,X:S) -> nil
 first(s,cons(Y:S)) -> cons(Y:S)
 sqr(0) -> 0
 sqr(s) -> s
 terms(N:S) -> cons(recip(sqr(N:S)))

Problem 1: 

SCC Processor:
-> Pairs:
 TERMS(N:S) -> SQR(N:S)
-> Rules:
 add(0,X:S) -> X:S
 add(s,Y:S) -> s
 dbl(0) -> 0
 dbl(s) -> s
 first(0,X:S) -> nil
 first(s,cons(Y:S)) -> cons(Y:S)
 sqr(0) -> 0
 sqr(s) -> s
 terms(N:S) -> cons(recip(sqr(N:S)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.