YES

Problem 1: 

(VAR v_NonEmpty:S X:S X1:S Y:S Z:S)
(RULES
2nd(cons(X:S,X1:S)) -> 2nd(cons1(X:S,activate(X1:S)))
2nd(cons1(X:S,cons(Y:S,Z:S))) -> Y:S
activate(n__from(X:S)) -> from(activate(X:S))
activate(n__s(X:S)) -> s(activate(X:S))
activate(X:S) -> X:S
from(X:S) -> cons(X:S,n__from(n__s(X:S)))
from(X:S) -> n__from(X:S)
s(X:S) -> n__s(X:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 2ND(cons(X:S,X1:S)) -> 2ND(cons1(X:S,activate(X1:S)))
 2ND(cons(X:S,X1:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__from(X:S)) -> FROM(activate(X:S))
 ACTIVATE(n__s(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__s(X:S)) -> S(activate(X:S))
-> Rules:
 2nd(cons(X:S,X1:S)) -> 2nd(cons1(X:S,activate(X1:S)))
 2nd(cons1(X:S,cons(Y:S,Z:S))) -> Y:S
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 s(X:S) -> n__s(X:S)

Problem 1: 

SCC Processor:
-> Pairs:
 2ND(cons(X:S,X1:S)) -> 2ND(cons1(X:S,activate(X1:S)))
 2ND(cons(X:S,X1:S)) -> ACTIVATE(X1:S)
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__from(X:S)) -> FROM(activate(X:S))
 ACTIVATE(n__s(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__s(X:S)) -> S(activate(X:S))
-> Rules:
 2nd(cons(X:S,X1:S)) -> 2nd(cons1(X:S,activate(X1:S)))
 2nd(cons1(X:S,cons(Y:S,Z:S))) -> Y:S
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 s(X:S) -> n__s(X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__s(X:S)) -> ACTIVATE(X:S)
->->-> Rules:
 2nd(cons(X:S,X1:S)) -> 2nd(cons1(X:S,activate(X1:S)))
 2nd(cons1(X:S,cons(Y:S,Z:S))) -> Y:S
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 s(X:S) -> n__s(X:S)

Problem 1: 

Subterm Processor:
-> Pairs:
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__s(X:S)) -> ACTIVATE(X:S)
-> Rules:
 2nd(cons(X:S,X1:S)) -> 2nd(cons1(X:S,activate(X1:S)))
 2nd(cons1(X:S,cons(Y:S,Z:S))) -> Y:S
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 s(X:S) -> n__s(X:S)
->Projection:
 pi(ACTIVATE) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 2nd(cons(X:S,X1:S)) -> 2nd(cons1(X:S,activate(X1:S)))
 2nd(cons1(X:S,cons(Y:S,Z:S))) -> Y:S
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 s(X:S) -> n__s(X:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.