NO

Problem:
 leq(0(),x) -> tt()
 leq(s(x),0()) -> ff()
 leq(s(x),s(y)) -> leq(x,y)
 split(nil()) -> app(nil(),nil())
 split(cons(x,nil())) -> app(cons(x,nil()),nil())
 split(cons(x,cons(y,xs))) -> split1(x,y,split(xs))
 split1(x,y,app(xs,ys)) -> app(cons(x,xs),cons(y,ys))
 merge([](),xs) -> xs
 merge(xs,[]()) -> xs
 merge(cons(x,xs),cons(y,ys)) -> ifmerge(leq(x,y),x,y,xs,ys)
 ifmerge(tt(),x,y,xs,ys) -> cons(x,merge(xs,cons(y,ys)))
 ifmerge(ff(),x,y,xs,ys) -> cons(y,merge(cons(x,xs),ys))
 mergesort(xs) -> mergesort1(split(xs))
 mergesort1(app(xs,ys)) -> merge(mergesort(xs),mergesort(ys))

Proof:
 Unfolding Processor:
  loop length: 3
  terms:
   mergesort(nil())
   mergesort1(split(nil()))
   mergesort1(app(nil(),nil()))
  context: merge(mergesort(nil()),[])
  substitution:
   
  Qed