NO

Problem 1: 

(VAR v_NonEmpty:S x:S y:S z:S)
(RULES
cons(x:S,cons(y:S,z:S)) -> big
inf(x:S) -> cons(x:S,inf(s(x:S)))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 INF(x:S) -> CONS(x:S,inf(s(x:S)))
 INF(x:S) -> INF(s(x:S))
-> Rules:
 cons(x:S,cons(y:S,z:S)) -> big
 inf(x:S) -> cons(x:S,inf(s(x:S)))

Problem 1: 

Infinite Processor:
-> Pairs:
 INF(x:S) -> CONS(x:S,inf(s(x:S)))
 INF(x:S) -> INF(s(x:S))
-> Rules:
 cons(x:S,cons(y:S,z:S)) -> big
 inf(x:S) -> cons(x:S,inf(s(x:S)))
-> Pairs in cycle:
 INF(x:S) -> INF(s(x:S))

The problem is infinite.