NO

Problem 1: 

(VAR v_NonEmpty:S L:S X:S X1:S X2:S XS:S Y:S YS:S)
(RULES
activate(n__app(X1:S,X2:S)) -> app(X1:S,X2:S)
activate(n__from(X:S)) -> from(X:S)
activate(n__nil) -> nil
activate(n__zWadr(X1:S,X2:S)) -> zWadr(X1:S,X2:S)
activate(X:S) -> X:S
app(nil,YS:S) -> YS:S
app(cons(X:S,XS:S),YS:S) -> cons(X:S,n__app(activate(XS:S),YS:S))
app(X1:S,X2:S) -> n__app(X1:S,X2:S)
from(X:S) -> cons(X:S,n__from(s(X:S)))
from(X:S) -> n__from(X:S)
nil -> n__nil
prefix(L:S) -> cons(nil,n__zWadr(L:S,prefix(L:S)))
zWadr(nil,YS:S) -> nil
zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(app(Y:S,cons(X:S,n__nil)),n__zWadr(activate(XS:S),activate(YS:S)))
zWadr(X1:S,X2:S) -> n__zWadr(X1:S,X2:S)
zWadr(XS:S,nil) -> nil
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACTIVATE(n__app(X1:S,X2:S)) -> APP(X1:S,X2:S)
 ACTIVATE(n__from(X:S)) -> FROM(X:S)
 ACTIVATE(n__nil) -> NIL
 ACTIVATE(n__zWadr(X1:S,X2:S)) -> ZWADR(X1:S,X2:S)
 APP(cons(X:S,XS:S),YS:S) -> ACTIVATE(XS:S)
 PREFIX(L:S) -> NIL
 PREFIX(L:S) -> PREFIX(L:S)
 ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> ACTIVATE(XS:S)
 ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> ACTIVATE(YS:S)
 ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> APP(Y:S,cons(X:S,n__nil))
-> Rules:
 activate(n__app(X1:S,X2:S)) -> app(X1:S,X2:S)
 activate(n__from(X:S)) -> from(X:S)
 activate(n__nil) -> nil
 activate(n__zWadr(X1:S,X2:S)) -> zWadr(X1:S,X2:S)
 activate(X:S) -> X:S
 app(nil,YS:S) -> YS:S
 app(cons(X:S,XS:S),YS:S) -> cons(X:S,n__app(activate(XS:S),YS:S))
 app(X1:S,X2:S) -> n__app(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 nil -> n__nil
 prefix(L:S) -> cons(nil,n__zWadr(L:S,prefix(L:S)))
 zWadr(nil,YS:S) -> nil
 zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(app(Y:S,cons(X:S,n__nil)),n__zWadr(activate(XS:S),activate(YS:S)))
 zWadr(X1:S,X2:S) -> n__zWadr(X1:S,X2:S)
 zWadr(XS:S,nil) -> nil

Problem 1: 

Infinite Processor:
-> Pairs:
 ACTIVATE(n__app(X1:S,X2:S)) -> APP(X1:S,X2:S)
 ACTIVATE(n__from(X:S)) -> FROM(X:S)
 ACTIVATE(n__nil) -> NIL
 ACTIVATE(n__zWadr(X1:S,X2:S)) -> ZWADR(X1:S,X2:S)
 APP(cons(X:S,XS:S),YS:S) -> ACTIVATE(XS:S)
 PREFIX(L:S) -> NIL
 PREFIX(L:S) -> PREFIX(L:S)
 ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> ACTIVATE(XS:S)
 ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> ACTIVATE(YS:S)
 ZWADR(cons(X:S,XS:S),cons(Y:S,YS:S)) -> APP(Y:S,cons(X:S,n__nil))
-> Rules:
 activate(n__app(X1:S,X2:S)) -> app(X1:S,X2:S)
 activate(n__from(X:S)) -> from(X:S)
 activate(n__nil) -> nil
 activate(n__zWadr(X1:S,X2:S)) -> zWadr(X1:S,X2:S)
 activate(X:S) -> X:S
 app(nil,YS:S) -> YS:S
 app(cons(X:S,XS:S),YS:S) -> cons(X:S,n__app(activate(XS:S),YS:S))
 app(X1:S,X2:S) -> n__app(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 nil -> n__nil
 prefix(L:S) -> cons(nil,n__zWadr(L:S,prefix(L:S)))
 zWadr(nil,YS:S) -> nil
 zWadr(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(app(Y:S,cons(X:S,n__nil)),n__zWadr(activate(XS:S),activate(YS:S)))
 zWadr(X1:S,X2:S) -> n__zWadr(X1:S,X2:S)
 zWadr(XS:S,nil) -> nil
-> Pairs in cycle:
 PREFIX(L:S) -> PREFIX(L:S)

The problem is infinite.