YES

Problem 1: 

(VAR v_NonEmpty:S X:S XS:S)
(RULES
activate(n__zeros) -> zeros
activate(X:S) -> X:S
tail(cons(X:S,XS:S)) -> activate(XS:S)
zeros -> cons(0,n__zeros)
zeros -> n__zeros
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACTIVATE(n__zeros) -> ZEROS
 TAIL(cons(X:S,XS:S)) -> ACTIVATE(XS:S)
-> Rules:
 activate(n__zeros) -> zeros
 activate(X:S) -> X:S
 tail(cons(X:S,XS:S)) -> activate(XS:S)
 zeros -> cons(0,n__zeros)
 zeros -> n__zeros

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__zeros) -> ZEROS
 TAIL(cons(X:S,XS:S)) -> ACTIVATE(XS:S)
-> Rules:
 activate(n__zeros) -> zeros
 activate(X:S) -> X:S
 tail(cons(X:S,XS:S)) -> activate(XS:S)
 zeros -> cons(0,n__zeros)
 zeros -> n__zeros
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.