NO

Problem 1: 

(VAR v_NonEmpty:S f:S n:S x:S xs:S)
(RULES
app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
app(app(map,f:S),nil) -> nil
app(app(f:S,0),n:S) -> app(app(hd,app(app(map,f:S),app(app(cons,0),nil))),n:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(map,f:S),xs:S)
 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(cons,app(f:S,x:S))
 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S)
 APP(app(f:S,0),n:S) -> APP(app(cons,0),nil)
 APP(app(f:S,0),n:S) -> APP(app(hd,app(app(map,f:S),app(app(cons,0),nil))),n:S)
 APP(app(f:S,0),n:S) -> APP(app(map,f:S),app(app(cons,0),nil))
 APP(app(f:S,0),n:S) -> APP(hd,app(app(map,f:S),app(app(cons,0),nil)))
-> Rules:
 app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
 app(app(map,f:S),nil) -> nil
 app(app(f:S,0),n:S) -> app(app(hd,app(app(map,f:S),app(app(cons,0),nil))),n:S)

Problem 1: 

Infinite Processor:
-> Pairs:
 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(map,f:S),xs:S)
 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(cons,app(f:S,x:S))
 APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S)
 APP(app(f:S,0),n:S) -> APP(app(cons,0),nil)
 APP(app(f:S,0),n:S) -> APP(app(hd,app(app(map,f:S),app(app(cons,0),nil))),n:S)
 APP(app(f:S,0),n:S) -> APP(app(map,f:S),app(app(cons,0),nil))
 APP(app(f:S,0),n:S) -> APP(hd,app(app(map,f:S),app(app(cons,0),nil)))
-> Rules:
 app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
 app(app(map,f:S),nil) -> nil
 app(app(f:S,0),n:S) -> app(app(hd,app(app(map,f:S),app(app(cons,0),nil))),n:S)
-> Pairs in cycle:
 APP(app(f:S,0),n:S) -> APP(app(cons,0),nil)

The problem is infinite.