YES

Problem:
 terms(N) -> cons(recip(sqr(N)))
 sqr(0()) -> 0()
 sqr(s(X)) -> s(add(sqr(X),dbl(X)))
 dbl(0()) -> 0()
 dbl(s(X)) -> s(s(dbl(X)))
 add(0(),X) -> X
 add(s(X),Y) -> s(add(X,Y))
 first(0(),X) -> nil()
 first(s(X),cons(Y)) -> cons(Y)
 half(0()) -> 0()
 half(s(0())) -> 0()
 half(s(s(X))) -> s(half(X))
 half(dbl(X)) -> X

Proof:
 DP Processor:
  DPs:
   terms#(N) -> sqr#(N)
   sqr#(s(X)) -> dbl#(X)
   sqr#(s(X)) -> sqr#(X)
   sqr#(s(X)) -> add#(sqr(X),dbl(X))
   dbl#(s(X)) -> dbl#(X)
   add#(s(X),Y) -> add#(X,Y)
   half#(s(s(X))) -> half#(X)
  TRS:
   terms(N) -> cons(recip(sqr(N)))
   sqr(0()) -> 0()
   sqr(s(X)) -> s(add(sqr(X),dbl(X)))
   dbl(0()) -> 0()
   dbl(s(X)) -> s(s(dbl(X)))
   add(0(),X) -> X
   add(s(X),Y) -> s(add(X,Y))
   first(0(),X) -> nil()
   first(s(X),cons(Y)) -> cons(Y)
   half(0()) -> 0()
   half(s(0())) -> 0()
   half(s(s(X))) -> s(half(X))
   half(dbl(X)) -> X
  TDG Processor:
   DPs:
    terms#(N) -> sqr#(N)
    sqr#(s(X)) -> dbl#(X)
    sqr#(s(X)) -> sqr#(X)
    sqr#(s(X)) -> add#(sqr(X),dbl(X))
    dbl#(s(X)) -> dbl#(X)
    add#(s(X),Y) -> add#(X,Y)
    half#(s(s(X))) -> half#(X)
   TRS:
    terms(N) -> cons(recip(sqr(N)))
    sqr(0()) -> 0()
    sqr(s(X)) -> s(add(sqr(X),dbl(X)))
    dbl(0()) -> 0()
    dbl(s(X)) -> s(s(dbl(X)))
    add(0(),X) -> X
    add(s(X),Y) -> s(add(X,Y))
    first(0(),X) -> nil()
    first(s(X),cons(Y)) -> cons(Y)
    half(0()) -> 0()
    half(s(0())) -> 0()
    half(s(s(X))) -> s(half(X))
    half(dbl(X)) -> X
   graph:
    half#(s(s(X))) -> half#(X) -> half#(s(s(X))) -> half#(X)
    add#(s(X),Y) -> add#(X,Y) -> add#(s(X),Y) -> add#(X,Y)
    dbl#(s(X)) -> dbl#(X) -> dbl#(s(X)) -> dbl#(X)
    sqr#(s(X)) -> add#(sqr(X),dbl(X)) -> add#(s(X),Y) -> add#(X,Y)
    sqr#(s(X)) -> dbl#(X) -> dbl#(s(X)) -> dbl#(X)
    sqr#(s(X)) -> sqr#(X) -> sqr#(s(X)) -> add#(sqr(X),dbl(X))
    sqr#(s(X)) -> sqr#(X) -> sqr#(s(X)) -> sqr#(X)
    sqr#(s(X)) -> sqr#(X) -> sqr#(s(X)) -> dbl#(X)
    terms#(N) -> sqr#(N) -> sqr#(s(X)) -> add#(sqr(X),dbl(X))
    terms#(N) -> sqr#(N) -> sqr#(s(X)) -> sqr#(X)
    terms#(N) -> sqr#(N) -> sqr#(s(X)) -> dbl#(X)
   SCC Processor:
    #sccs: 4
    #rules: 4
    #arcs: 11/49
    DPs:
     sqr#(s(X)) -> sqr#(X)
    TRS:
     terms(N) -> cons(recip(sqr(N)))
     sqr(0()) -> 0()
     sqr(s(X)) -> s(add(sqr(X),dbl(X)))
     dbl(0()) -> 0()
     dbl(s(X)) -> s(s(dbl(X)))
     add(0(),X) -> X
     add(s(X),Y) -> s(add(X,Y))
     first(0(),X) -> nil()
     first(s(X),cons(Y)) -> cons(Y)
     half(0()) -> 0()
     half(s(0())) -> 0()
     half(s(s(X))) -> s(half(X))
     half(dbl(X)) -> X
    LPO Processor:
     argument filtering:
      pi(terms) = [0]
      pi(sqr) = [0]
      pi(recip) = 0
      pi(cons) = 0
      pi(0) = []
      pi(s) = [0]
      pi(dbl) = [0]
      pi(add) = [0,1]
      pi(first) = [0,1]
      pi(nil) = []
      pi(half) = 0
      pi(sqr#) = 0
     precedence:
      0 > terms > sqr > dbl > add > sqr# ~ half ~ nil ~ first ~ s ~ cons ~ recip
     problem:
      DPs:
       
      TRS:
       terms(N) -> cons(recip(sqr(N)))
       sqr(0()) -> 0()
       sqr(s(X)) -> s(add(sqr(X),dbl(X)))
       dbl(0()) -> 0()
       dbl(s(X)) -> s(s(dbl(X)))
       add(0(),X) -> X
       add(s(X),Y) -> s(add(X,Y))
       first(0(),X) -> nil()
       first(s(X),cons(Y)) -> cons(Y)
       half(0()) -> 0()
       half(s(0())) -> 0()
       half(s(s(X))) -> s(half(X))
       half(dbl(X)) -> X
     Qed
    
    DPs:
     dbl#(s(X)) -> dbl#(X)
    TRS:
     terms(N) -> cons(recip(sqr(N)))
     sqr(0()) -> 0()
     sqr(s(X)) -> s(add(sqr(X),dbl(X)))
     dbl(0()) -> 0()
     dbl(s(X)) -> s(s(dbl(X)))
     add(0(),X) -> X
     add(s(X),Y) -> s(add(X,Y))
     first(0(),X) -> nil()
     first(s(X),cons(Y)) -> cons(Y)
     half(0()) -> 0()
     half(s(0())) -> 0()
     half(s(s(X))) -> s(half(X))
     half(dbl(X)) -> X
    LPO Processor:
     argument filtering:
      pi(terms) = [0]
      pi(sqr) = [0]
      pi(recip) = 0
      pi(cons) = 0
      pi(0) = []
      pi(s) = [0]
      pi(dbl) = [0]
      pi(add) = [0,1]
      pi(first) = [0,1]
      pi(nil) = []
      pi(half) = 0
      pi(dbl#) = 0
     precedence:
      0 > terms > sqr > dbl > add > dbl# ~ half ~ nil ~ first ~ s ~ cons ~ recip
     problem:
      DPs:
       
      TRS:
       terms(N) -> cons(recip(sqr(N)))
       sqr(0()) -> 0()
       sqr(s(X)) -> s(add(sqr(X),dbl(X)))
       dbl(0()) -> 0()
       dbl(s(X)) -> s(s(dbl(X)))
       add(0(),X) -> X
       add(s(X),Y) -> s(add(X,Y))
       first(0(),X) -> nil()
       first(s(X),cons(Y)) -> cons(Y)
       half(0()) -> 0()
       half(s(0())) -> 0()
       half(s(s(X))) -> s(half(X))
       half(dbl(X)) -> X
     Qed
    
    DPs:
     add#(s(X),Y) -> add#(X,Y)
    TRS:
     terms(N) -> cons(recip(sqr(N)))
     sqr(0()) -> 0()
     sqr(s(X)) -> s(add(sqr(X),dbl(X)))
     dbl(0()) -> 0()
     dbl(s(X)) -> s(s(dbl(X)))
     add(0(),X) -> X
     add(s(X),Y) -> s(add(X,Y))
     first(0(),X) -> nil()
     first(s(X),cons(Y)) -> cons(Y)
     half(0()) -> 0()
     half(s(0())) -> 0()
     half(s(s(X))) -> s(half(X))
     half(dbl(X)) -> X
    LPO Processor:
     argument filtering:
      pi(terms) = [0]
      pi(sqr) = [0]
      pi(recip) = 0
      pi(cons) = 0
      pi(0) = []
      pi(s) = [0]
      pi(dbl) = [0]
      pi(add) = [0,1]
      pi(first) = [1]
      pi(nil) = []
      pi(half) = 0
      pi(add#) = 0
     precedence:
      terms > sqr > first ~ add ~ dbl > add# ~ half ~ nil ~ s ~ 0 ~ cons ~ recip
     problem:
      DPs:
       
      TRS:
       terms(N) -> cons(recip(sqr(N)))
       sqr(0()) -> 0()
       sqr(s(X)) -> s(add(sqr(X),dbl(X)))
       dbl(0()) -> 0()
       dbl(s(X)) -> s(s(dbl(X)))
       add(0(),X) -> X
       add(s(X),Y) -> s(add(X,Y))
       first(0(),X) -> nil()
       first(s(X),cons(Y)) -> cons(Y)
       half(0()) -> 0()
       half(s(0())) -> 0()
       half(s(s(X))) -> s(half(X))
       half(dbl(X)) -> X
     Qed
   
   DPs:
    half#(s(s(X))) -> half#(X)
   TRS:
    terms(N) -> cons(recip(sqr(N)))
    sqr(0()) -> 0()
    sqr(s(X)) -> s(add(sqr(X),dbl(X)))
    dbl(0()) -> 0()
    dbl(s(X)) -> s(s(dbl(X)))
    add(0(),X) -> X
    add(s(X),Y) -> s(add(X,Y))
    first(0(),X) -> nil()
    first(s(X),cons(Y)) -> cons(Y)
    half(0()) -> 0()
    half(s(0())) -> 0()
    half(s(s(X))) -> s(half(X))
    half(dbl(X)) -> X
   LPO Processor:
    argument filtering:
     pi(terms) = [0]
     pi(sqr) = [0]
     pi(recip) = 0
     pi(cons) = 0
     pi(0) = []
     pi(s) = [0]
     pi(dbl) = [0]
     pi(add) = [0,1]
     pi(first) = [1]
     pi(nil) = []
     pi(half) = [0]
     pi(half#) = [0]
    precedence:
     terms > sqr > half ~ first ~ add ~ dbl > half# ~ nil ~ s ~ 0 ~ cons ~ recip
    problem:
     DPs:
      
     TRS:
      terms(N) -> cons(recip(sqr(N)))
      sqr(0()) -> 0()
      sqr(s(X)) -> s(add(sqr(X),dbl(X)))
      dbl(0()) -> 0()
      dbl(s(X)) -> s(s(dbl(X)))
      add(0(),X) -> X
      add(s(X),Y) -> s(add(X,Y))
      first(0(),X) -> nil()
      first(s(X),cons(Y)) -> cons(Y)
      half(0()) -> 0()
      half(s(0())) -> 0()
      half(s(s(X))) -> s(half(X))
      half(dbl(X)) -> X
    Qed