YES

Problem:
 from(X) -> cons(X,n__from(s(X)))
 2ndspos(0(),Z) -> rnil()
 2ndspos(s(N),cons(X,n__cons(Y,Z))) -> rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
 2ndsneg(0(),Z) -> rnil()
 2ndsneg(s(N),cons(X,n__cons(Y,Z))) -> rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
 pi(X) -> 2ndspos(X,from(0()))
 plus(0(),Y) -> Y
 plus(s(X),Y) -> s(plus(X,Y))
 times(0(),Y) -> 0()
 times(s(X),Y) -> plus(Y,times(X,Y))
 square(X) -> times(X,X)
 from(X) -> n__from(X)
 cons(X1,X2) -> n__cons(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__cons(X1,X2)) -> cons(X1,X2)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   from#(X) -> cons#(X,n__from(s(X)))
   2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z)
   2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> 2ndsneg#(N,activate(Z))
   2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y)
   2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z)
   2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> 2ndspos#(N,activate(Z))
   2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y)
   pi#(X) -> from#(0())
   pi#(X) -> 2ndspos#(X,from(0()))
   plus#(s(X),Y) -> plus#(X,Y)
   times#(s(X),Y) -> times#(X,Y)
   times#(s(X),Y) -> plus#(Y,times(X,Y))
   square#(X) -> times#(X,X)
   activate#(n__from(X)) -> from#(X)
   activate#(n__cons(X1,X2)) -> cons#(X1,X2)
  TRS:
   from(X) -> cons(X,n__from(s(X)))
   2ndspos(0(),Z) -> rnil()
   2ndspos(s(N),cons(X,n__cons(Y,Z))) -> rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
   2ndsneg(0(),Z) -> rnil()
   2ndsneg(s(N),cons(X,n__cons(Y,Z))) -> rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
   pi(X) -> 2ndspos(X,from(0()))
   plus(0(),Y) -> Y
   plus(s(X),Y) -> s(plus(X,Y))
   times(0(),Y) -> 0()
   times(s(X),Y) -> plus(Y,times(X,Y))
   square(X) -> times(X,X)
   from(X) -> n__from(X)
   cons(X1,X2) -> n__cons(X1,X2)
   activate(n__from(X)) -> from(X)
   activate(n__cons(X1,X2)) -> cons(X1,X2)
   activate(X) -> X
  TDG Processor:
   DPs:
    from#(X) -> cons#(X,n__from(s(X)))
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z)
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> 2ndsneg#(N,activate(Z))
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y)
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z)
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> 2ndspos#(N,activate(Z))
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y)
    pi#(X) -> from#(0())
    pi#(X) -> 2ndspos#(X,from(0()))
    plus#(s(X),Y) -> plus#(X,Y)
    times#(s(X),Y) -> times#(X,Y)
    times#(s(X),Y) -> plus#(Y,times(X,Y))
    square#(X) -> times#(X,X)
    activate#(n__from(X)) -> from#(X)
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
   TRS:
    from(X) -> cons(X,n__from(s(X)))
    2ndspos(0(),Z) -> rnil()
    2ndspos(s(N),cons(X,n__cons(Y,Z))) -> rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
    2ndsneg(0(),Z) -> rnil()
    2ndsneg(s(N),cons(X,n__cons(Y,Z))) -> rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
    pi(X) -> 2ndspos(X,from(0()))
    plus(0(),Y) -> Y
    plus(s(X),Y) -> s(plus(X,Y))
    times(0(),Y) -> 0()
    times(s(X),Y) -> plus(Y,times(X,Y))
    square(X) -> times(X,X)
    from(X) -> n__from(X)
    cons(X1,X2) -> n__cons(X1,X2)
    activate(n__from(X)) -> from(X)
    activate(n__cons(X1,X2)) -> cons(X1,X2)
    activate(X) -> X
   graph:
    square#(X) -> times#(X,X) -> times#(s(X),Y) -> plus#(Y,times(X,Y))
    square#(X) -> times#(X,X) -> times#(s(X),Y) -> times#(X,Y)
    times#(s(X),Y) -> times#(X,Y) ->
    times#(s(X),Y) -> plus#(Y,times(X,Y))
    times#(s(X),Y) -> times#(X,Y) ->
    times#(s(X),Y) -> times#(X,Y)
    times#(s(X),Y) -> plus#(Y,times(X,Y)) -> plus#(s(X),Y) -> plus#(X,Y)
    plus#(s(X),Y) -> plus#(X,Y) -> plus#(s(X),Y) -> plus#(X,Y)
    pi#(X) -> 2ndspos#(X,from(0())) ->
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y)
    pi#(X) -> 2ndspos#(X,from(0())) ->
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> 2ndsneg#(N,activate(Z))
    pi#(X) -> 2ndspos#(X,from(0())) ->
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z)
    pi#(X) -> from#(0()) ->
    from#(X) -> cons#(X,n__from(s(X)))
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
    activate#(n__from(X)) -> from#(X)
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
    activate#(n__from(X)) -> from#(X)
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> 2ndspos#(N,activate(Z)) ->
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y)
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> 2ndspos#(N,activate(Z)) ->
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> 2ndsneg#(N,activate(Z))
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> 2ndspos#(N,activate(Z)) ->
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z)
    activate#(n__from(X)) -> from#(X) ->
    from#(X) -> cons#(X,n__from(s(X)))
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> 2ndsneg#(N,activate(Z)) ->
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y)
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> 2ndsneg#(N,activate(Z)) ->
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> 2ndspos#(N,activate(Z))
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> 2ndsneg#(N,activate(Z)) ->
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z)
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
    activate#(n__from(X)) -> from#(X)
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) -> activate#(n__from(X)) -> from#(X)
   CDG Processor:
    DPs:
     from#(X) -> cons#(X,n__from(s(X)))
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z)
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> 2ndsneg#(N,activate(Z))
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y)
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z)
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> 2ndspos#(N,activate(Z))
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y)
     pi#(X) -> from#(0())
     pi#(X) -> 2ndspos#(X,from(0()))
     plus#(s(X),Y) -> plus#(X,Y)
     times#(s(X),Y) -> times#(X,Y)
     times#(s(X),Y) -> plus#(Y,times(X,Y))
     square#(X) -> times#(X,X)
     activate#(n__from(X)) -> from#(X)
     activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    TRS:
     from(X) -> cons(X,n__from(s(X)))
     2ndspos(0(),Z) -> rnil()
     2ndspos(s(N),cons(X,n__cons(Y,Z))) -> rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
     2ndsneg(0(),Z) -> rnil()
     2ndsneg(s(N),cons(X,n__cons(Y,Z))) -> rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
     pi(X) -> 2ndspos(X,from(0()))
     plus(0(),Y) -> Y
     plus(s(X),Y) -> s(plus(X,Y))
     times(0(),Y) -> 0()
     times(s(X),Y) -> plus(Y,times(X,Y))
     square(X) -> times(X,X)
     from(X) -> n__from(X)
     cons(X1,X2) -> n__cons(X1,X2)
     activate(n__from(X)) -> from(X)
     activate(n__cons(X1,X2)) -> cons(X1,X2)
     activate(X) -> X
    graph:
     square#(X) -> times#(X,X) -> times#(s(X),Y) -> times#(X,Y)
     square#(X) -> times#(X,X) ->
     times#(s(X),Y) -> plus#(Y,times(X,Y))
     times#(s(X),Y) -> times#(X,Y) -> times#(s(X),Y) -> times#(X,Y)
     times#(s(X),Y) -> times#(X,Y) ->
     times#(s(X),Y) -> plus#(Y,times(X,Y))
     times#(s(X),Y) -> plus#(Y,times(X,Y)) ->
     plus#(s(X),Y) -> plus#(X,Y)
     plus#(s(X),Y) -> plus#(X,Y) -> plus#(s(X),Y) -> plus#(X,Y)
     pi#(X) -> from#(0()) ->
     from#(X) -> cons#(X,n__from(s(X)))
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
     activate#(n__from(X)) -> from#(X)
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
     activate#(n__cons(X1,X2)) -> cons#(X1,X2)
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
     activate#(n__from(X)) -> from#(X)
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
     activate#(n__cons(X1,X2)) -> cons#(X1,X2)
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> 2ndspos#(N,activate(Z)) ->
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z)
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> 2ndspos#(N,activate(Z)) ->
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> 2ndsneg#(N,activate(Z))
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> 2ndspos#(N,activate(Z)) ->
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y)
     activate#(n__from(X)) -> from#(X) ->
     from#(X) -> cons#(X,n__from(s(X)))
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> 2ndsneg#(N,activate(Z)) ->
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z)
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> 2ndsneg#(N,activate(Z)) ->
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> 2ndspos#(N,activate(Z))
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> 2ndsneg#(N,activate(Z)) ->
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y)
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
     activate#(n__from(X)) -> from#(X)
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
     activate#(n__cons(X1,X2)) -> cons#(X1,X2)
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
     activate#(n__from(X)) -> from#(X)
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
     activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    SCC Processor:
     #sccs: 3
     #rules: 4
     #arcs: 22/225
     DPs:
      2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> 2ndspos#(N,activate(Z))
      2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> 2ndsneg#(N,activate(Z))
     TRS:
      from(X) -> cons(X,n__from(s(X)))
      2ndspos(0(),Z) -> rnil()
      2ndspos(s(N),cons(X,n__cons(Y,Z))) -> rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
      2ndsneg(0(),Z) -> rnil()
      2ndsneg(s(N),cons(X,n__cons(Y,Z))) -> rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
      pi(X) -> 2ndspos(X,from(0()))
      plus(0(),Y) -> Y
      plus(s(X),Y) -> s(plus(X,Y))
      times(0(),Y) -> 0()
      times(s(X),Y) -> plus(Y,times(X,Y))
      square(X) -> times(X,X)
      from(X) -> n__from(X)
      cons(X1,X2) -> n__cons(X1,X2)
      activate(n__from(X)) -> from(X)
      activate(n__cons(X1,X2)) -> cons(X1,X2)
      activate(X) -> X
     KBO Processor:
      argument filtering:
       pi(from) = [0]
       pi(s) = 0
       pi(n__from) = 0
       pi(cons) = [1]
       pi(0) = []
       pi(2ndspos) = []
       pi(rnil) = []
       pi(n__cons) = [1]
       pi(activate) = [0]
       pi(posrecip) = []
       pi(2ndsneg) = [0]
       pi(rcons) = []
       pi(negrecip) = 0
       pi(pi) = [0]
       pi(plus) = 1
       pi(times) = []
       pi(square) = []
       pi(2ndspos#) = [0,1]
       pi(2ndsneg#) = [0,1]
      weight function:
       w0 = 1
       w(2ndsneg#) = w(square) = w(times) = w(rcons) = w(2ndsneg) = w(
       posrecip) = w(activate) = w(n__cons) = w(rnil) = w(2ndspos) = w(
       0) = w(cons) = w(from) = 1
       w(2ndspos#) = w(plus) = w(pi) = w(negrecip) = w(n__from) = w(s) = 0
      precedence:
       square ~ pi ~ posrecip > activate > times ~ from > 2ndspos# ~ 
       2ndspos ~ cons > 2ndsneg# ~ plus ~ negrecip ~ rcons ~ 2ndsneg ~ 
       n__cons ~ rnil ~ 0 ~ n__from ~ s
      problem:
       DPs:
        
       TRS:
        from(X) -> cons(X,n__from(s(X)))
        2ndspos(0(),Z) -> rnil()
        2ndspos(s(N),cons(X,n__cons(Y,Z))) -> rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
        2ndsneg(0(),Z) -> rnil()
        2ndsneg(s(N),cons(X,n__cons(Y,Z))) -> rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
        pi(X) -> 2ndspos(X,from(0()))
        plus(0(),Y) -> Y
        plus(s(X),Y) -> s(plus(X,Y))
        times(0(),Y) -> 0()
        times(s(X),Y) -> plus(Y,times(X,Y))
        square(X) -> times(X,X)
        from(X) -> n__from(X)
        cons(X1,X2) -> n__cons(X1,X2)
        activate(n__from(X)) -> from(X)
        activate(n__cons(X1,X2)) -> cons(X1,X2)
        activate(X) -> X
      Qed
     
     DPs:
      times#(s(X),Y) -> times#(X,Y)
     TRS:
      from(X) -> cons(X,n__from(s(X)))
      2ndspos(0(),Z) -> rnil()
      2ndspos(s(N),cons(X,n__cons(Y,Z))) -> rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
      2ndsneg(0(),Z) -> rnil()
      2ndsneg(s(N),cons(X,n__cons(Y,Z))) -> rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
      pi(X) -> 2ndspos(X,from(0()))
      plus(0(),Y) -> Y
      plus(s(X),Y) -> s(plus(X,Y))
      times(0(),Y) -> 0()
      times(s(X),Y) -> plus(Y,times(X,Y))
      square(X) -> times(X,X)
      from(X) -> n__from(X)
      cons(X1,X2) -> n__cons(X1,X2)
      activate(n__from(X)) -> from(X)
      activate(n__cons(X1,X2)) -> cons(X1,X2)
      activate(X) -> X
     LPO Processor:
      argument filtering:
       pi(from) = 0
       pi(s) = [0]
       pi(n__from) = 0
       pi(cons) = 0
       pi(0) = []
       pi(2ndspos) = []
       pi(rnil) = []
       pi(n__cons) = 0
       pi(activate) = 0
       pi(posrecip) = []
       pi(2ndsneg) = []
       pi(rcons) = 0
       pi(negrecip) = []
       pi(pi) = []
       pi(plus) = [0,1]
       pi(times) = [0,1]
       pi(square) = [0]
       pi(times#) = 0
      precedence:
       square > times > plus ~ pi > 2ndsneg ~ 2ndspos > times# ~ negrecip ~ 
       rcons ~ posrecip ~ activate ~ n__cons ~ rnil ~ 0 ~ cons ~ n__from ~ 
       s ~ from
      problem:
       DPs:
        
       TRS:
        from(X) -> cons(X,n__from(s(X)))
        2ndspos(0(),Z) -> rnil()
        2ndspos(s(N),cons(X,n__cons(Y,Z))) -> rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
        2ndsneg(0(),Z) -> rnil()
        2ndsneg(s(N),cons(X,n__cons(Y,Z))) -> rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
        pi(X) -> 2ndspos(X,from(0()))
        plus(0(),Y) -> Y
        plus(s(X),Y) -> s(plus(X,Y))
        times(0(),Y) -> 0()
        times(s(X),Y) -> plus(Y,times(X,Y))
        square(X) -> times(X,X)
        from(X) -> n__from(X)
        cons(X1,X2) -> n__cons(X1,X2)
        activate(n__from(X)) -> from(X)
        activate(n__cons(X1,X2)) -> cons(X1,X2)
        activate(X) -> X
      Qed
     
     DPs:
      plus#(s(X),Y) -> plus#(X,Y)
     TRS:
      from(X) -> cons(X,n__from(s(X)))
      2ndspos(0(),Z) -> rnil()
      2ndspos(s(N),cons(X,n__cons(Y,Z))) -> rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
      2ndsneg(0(),Z) -> rnil()
      2ndsneg(s(N),cons(X,n__cons(Y,Z))) -> rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
      pi(X) -> 2ndspos(X,from(0()))
      plus(0(),Y) -> Y
      plus(s(X),Y) -> s(plus(X,Y))
      times(0(),Y) -> 0()
      times(s(X),Y) -> plus(Y,times(X,Y))
      square(X) -> times(X,X)
      from(X) -> n__from(X)
      cons(X1,X2) -> n__cons(X1,X2)
      activate(n__from(X)) -> from(X)
      activate(n__cons(X1,X2)) -> cons(X1,X2)
      activate(X) -> X
     LPO Processor:
      argument filtering:
       pi(from) = 0
       pi(s) = [0]
       pi(n__from) = 0
       pi(cons) = 0
       pi(0) = []
       pi(2ndspos) = []
       pi(rnil) = []
       pi(n__cons) = 0
       pi(activate) = 0
       pi(posrecip) = []
       pi(2ndsneg) = []
       pi(rcons) = 0
       pi(negrecip) = []
       pi(pi) = []
       pi(plus) = [0,1]
       pi(times) = [0,1]
       pi(square) = [0]
       pi(plus#) = 0
      precedence:
       square > times > plus ~ pi > 2ndsneg ~ 2ndspos > plus# ~ negrecip ~ 
       rcons ~ posrecip ~ activate ~ n__cons ~ rnil ~ 0 ~ cons ~ n__from ~ 
       s ~ from
      problem:
       DPs:
        
       TRS:
        from(X) -> cons(X,n__from(s(X)))
        2ndspos(0(),Z) -> rnil()
        2ndspos(s(N),cons(X,n__cons(Y,Z))) -> rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
        2ndsneg(0(),Z) -> rnil()
        2ndsneg(s(N),cons(X,n__cons(Y,Z))) -> rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
        pi(X) -> 2ndspos(X,from(0()))
        plus(0(),Y) -> Y
        plus(s(X),Y) -> s(plus(X,Y))
        times(0(),Y) -> 0()
        times(s(X),Y) -> plus(Y,times(X,Y))
        square(X) -> times(X,X)
        from(X) -> n__from(X)
        cons(X1,X2) -> n__cons(X1,X2)
        activate(n__from(X)) -> from(X)
        activate(n__cons(X1,X2)) -> cons(X1,X2)
        activate(X) -> X
      Qed