MAYBE

Problem:
 from(X) -> cons(X,n__from(n__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)
 s(X) -> n__s(X)
 cons(X1,X2) -> n__cons(X1,X2)
 activate(n__from(X)) -> from(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   from#(X) -> cons#(X,n__from(n__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)
   plus#(s(X),Y) -> s#(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)) -> activate#(X)
   activate#(n__from(X)) -> from#(activate(X))
   activate#(n__s(X)) -> activate#(X)
   activate#(n__s(X)) -> s#(activate(X))
   activate#(n__cons(X1,X2)) -> activate#(X1)
   activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
  TRS:
   from(X) -> cons(X,n__from(n__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)
   s(X) -> n__s(X)
   cons(X1,X2) -> n__cons(X1,X2)
   activate(n__from(X)) -> from(activate(X))
   activate(n__s(X)) -> s(activate(X))
   activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
   activate(X) -> X
  TDG Processor:
   DPs:
    from#(X) -> cons#(X,n__from(n__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)
    plus#(s(X),Y) -> s#(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)) -> activate#(X)
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__s(X)) -> activate#(X)
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__cons(X1,X2)) -> activate#(X1)
    activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
   TRS:
    from(X) -> cons(X,n__from(n__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)
    s(X) -> n__s(X)
    cons(X1,X2) -> n__cons(X1,X2)
    activate(n__from(X)) -> from(activate(X))
    activate(n__s(X)) -> s(activate(X))
    activate(n__cons(X1,X2)) -> cons(activate(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) -> s#(plus(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) -> s#(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(n__s(X)))
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
    activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
    activate#(n__cons(X1,X2)) -> activate#(X1)
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
    activate#(n__s(X)) -> s#(activate(X))
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
    activate#(n__s(X)) -> activate#(X)
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
    activate#(n__from(X)) -> from#(activate(X))
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
    activate#(n__from(X)) -> activate#(X)
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
    activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
    activate#(n__cons(X1,X2)) -> activate#(X1)
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
    activate#(n__s(X)) -> s#(activate(X))
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
    activate#(n__s(X)) -> activate#(X)
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
    activate#(n__from(X)) -> from#(activate(X))
    2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
    activate#(n__from(X)) -> activate#(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__cons(X1,X2)) -> activate#(X1) ->
    activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
    activate#(n__cons(X1,X2)) -> activate#(X1) ->
    activate#(n__cons(X1,X2)) -> activate#(X1)
    activate#(n__cons(X1,X2)) -> activate#(X1) ->
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__cons(X1,X2)) -> activate#(X1) ->
    activate#(n__s(X)) -> activate#(X)
    activate#(n__cons(X1,X2)) -> activate#(X1) ->
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__cons(X1,X2)) -> activate#(X1) ->
    activate#(n__from(X)) -> activate#(X)
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__cons(X1,X2)) -> activate#(X1)
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__s(X)) -> activate#(X)
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__from(X)) -> activate#(X)
    activate#(n__from(X)) -> from#(activate(X)) ->
    from#(X) -> cons#(X,n__from(n__s(X)))
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__cons(X1,X2)) -> activate#(X1)
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__s(X)) -> activate#(X)
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__from(X)) -> activate#(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#(activate(X1),X2)
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
    activate#(n__cons(X1,X2)) -> activate#(X1)
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
    activate#(n__s(X)) -> s#(activate(X))
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
    activate#(n__s(X)) -> activate#(X)
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
    activate#(n__from(X)) -> from#(activate(X))
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
    activate#(n__from(X)) -> activate#(X)
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
    activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
    activate#(n__cons(X1,X2)) -> activate#(X1)
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
    activate#(n__s(X)) -> s#(activate(X))
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
    activate#(n__s(X)) -> activate#(X)
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
    activate#(n__from(X)) -> from#(activate(X))
    2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) -> activate#(n__from(X)) -> activate#(X)
   CDG Processor:
    DPs:
     from#(X) -> cons#(X,n__from(n__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)
     plus#(s(X),Y) -> s#(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)) -> activate#(X)
     activate#(n__from(X)) -> from#(activate(X))
     activate#(n__s(X)) -> activate#(X)
     activate#(n__s(X)) -> s#(activate(X))
     activate#(n__cons(X1,X2)) -> activate#(X1)
     activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
    TRS:
     from(X) -> cons(X,n__from(n__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)
     s(X) -> n__s(X)
     cons(X1,X2) -> n__cons(X1,X2)
     activate(n__from(X)) -> from(activate(X))
     activate(n__s(X)) -> s(activate(X))
     activate(n__cons(X1,X2)) -> cons(activate(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)
     times#(s(X),Y) -> plus#(Y,times(X,Y)) ->
     plus#(s(X),Y) -> s#(plus(X,Y))
     plus#(s(X),Y) -> plus#(X,Y) -> plus#(s(X),Y) -> plus#(X,Y)
     plus#(s(X),Y) -> plus#(X,Y) -> plus#(s(X),Y) -> s#(plus(X,Y))
     pi#(X) -> from#(0()) ->
     from#(X) -> cons#(X,n__from(n__s(X)))
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
     activate#(n__from(X)) -> activate#(X)
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
     activate#(n__from(X)) -> from#(activate(X))
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
     activate#(n__s(X)) -> activate#(X)
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
     activate#(n__s(X)) -> s#(activate(X))
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
     activate#(n__cons(X1,X2)) -> activate#(X1)
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
     activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
     activate#(n__from(X)) -> activate#(X)
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
     activate#(n__from(X)) -> from#(activate(X))
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
     activate#(n__s(X)) -> activate#(X)
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
     activate#(n__s(X)) -> s#(activate(X))
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
     activate#(n__cons(X1,X2)) -> activate#(X1)
     2ndsneg#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
     activate#(n__cons(X1,X2)) -> cons#(activate(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__cons(X1,X2)) -> activate#(X1) ->
     activate#(n__from(X)) -> activate#(X)
     activate#(n__cons(X1,X2)) -> activate#(X1) ->
     activate#(n__from(X)) -> from#(activate(X))
     activate#(n__cons(X1,X2)) -> activate#(X1) ->
     activate#(n__s(X)) -> activate#(X)
     activate#(n__cons(X1,X2)) -> activate#(X1) ->
     activate#(n__s(X)) -> s#(activate(X))
     activate#(n__cons(X1,X2)) -> activate#(X1) ->
     activate#(n__cons(X1,X2)) -> activate#(X1)
     activate#(n__cons(X1,X2)) -> activate#(X1) ->
     activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
     activate#(n__from(X)) -> activate#(X) ->
     activate#(n__from(X)) -> activate#(X)
     activate#(n__from(X)) -> activate#(X) ->
     activate#(n__from(X)) -> from#(activate(X))
     activate#(n__from(X)) -> activate#(X) ->
     activate#(n__s(X)) -> activate#(X)
     activate#(n__from(X)) -> activate#(X) ->
     activate#(n__s(X)) -> s#(activate(X))
     activate#(n__from(X)) -> activate#(X) ->
     activate#(n__cons(X1,X2)) -> activate#(X1)
     activate#(n__from(X)) -> activate#(X) ->
     activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
     activate#(n__from(X)) -> from#(activate(X)) ->
     from#(X) -> cons#(X,n__from(n__s(X)))
     activate#(n__s(X)) -> activate#(X) ->
     activate#(n__from(X)) -> activate#(X)
     activate#(n__s(X)) -> activate#(X) ->
     activate#(n__from(X)) -> from#(activate(X))
     activate#(n__s(X)) -> activate#(X) ->
     activate#(n__s(X)) -> activate#(X)
     activate#(n__s(X)) -> activate#(X) ->
     activate#(n__s(X)) -> s#(activate(X))
     activate#(n__s(X)) -> activate#(X) ->
     activate#(n__cons(X1,X2)) -> activate#(X1)
     activate#(n__s(X)) -> activate#(X) ->
     activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
     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)) -> activate#(X)
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
     activate#(n__from(X)) -> from#(activate(X))
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
     activate#(n__s(X)) -> activate#(X)
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
     activate#(n__s(X)) -> s#(activate(X))
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
     activate#(n__cons(X1,X2)) -> activate#(X1)
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Z) ->
     activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
     activate#(n__from(X)) -> activate#(X)
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
     activate#(n__from(X)) -> from#(activate(X))
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
     activate#(n__s(X)) -> activate#(X)
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
     activate#(n__s(X)) -> s#(activate(X))
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
     activate#(n__cons(X1,X2)) -> activate#(X1)
     2ndspos#(s(N),cons(X,n__cons(Y,Z))) -> activate#(Y) ->
     activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2)
    SCC Processor:
     #sccs: 4
     #rules: 7
     #arcs: 58/400
     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(n__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)
      s(X) -> n__s(X)
      cons(X1,X2) -> n__cons(X1,X2)
      activate(n__from(X)) -> from(activate(X))
      activate(n__s(X)) -> s(activate(X))
      activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
      activate(X) -> X
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [2ndsneg#](x0, x1) = x1 + 3,
       
       [2ndspos#](x0, x1) = 2x1 + 6,
       
       [square](x0) = 4x0 + 2,
       
       [times](x0, x1) = 0,
       
       [plus](x0, x1) = x1,
       
       [pi](x0) = 2x0 + 7,
       
       [negrecip](x0) = 2x0,
       
       [rcons](x0, x1) = 0,
       
       [2ndsneg](x0, x1) = 2x1 + 4,
       
       [posrecip](x0) = 4,
       
       [activate](x0) = 3x0 + 2,
       
       [n__cons](x0, x1) = 2x1 + 2,
       
       [s](x0) = 0,
       
       [rnil] = 0,
       
       [2ndspos](x0, x1) = 3x1 + 1,
       
       [0] = 0,
       
       [cons](x0, x1) = 3x1 + 2,
       
       [n__from](x0) = 0,
       
       [n__s](x0) = 0,
       
       [from](x0) = 2
      orientation:
       2ndsneg#(s(N),cons(X,n__cons(Y,Z))) = 6Z + 11 >= 6Z + 10 = 2ndspos#(N,activate(Z))
       
       2ndspos#(s(N),cons(X,n__cons(Y,Z))) = 12Z + 22 >= 3Z + 5 = 2ndsneg#(N,activate(Z))
       
       from(X) = 2 >= 2 = cons(X,n__from(n__s(X)))
       
       2ndspos(0(),Z) = 3Z + 1 >= 0 = rnil()
       
       2ndspos(s(N),cons(X,n__cons(Y,Z))) = 18Z + 25 >= 0 = rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
       
       2ndsneg(0(),Z) = 2Z + 4 >= 0 = rnil()
       
       2ndsneg(s(N),cons(X,n__cons(Y,Z))) = 12Z + 20 >= 0 = rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
       
       pi(X) = 2X + 7 >= 7 = 2ndspos(X,from(0()))
       
       plus(0(),Y) = Y >= Y = Y
       
       plus(s(X),Y) = Y >= 0 = s(plus(X,Y))
       
       times(0(),Y) = 0 >= 0 = 0()
       
       times(s(X),Y) = 0 >= 0 = plus(Y,times(X,Y))
       
       square(X) = 4X + 2 >= 0 = times(X,X)
       
       from(X) = 2 >= 0 = n__from(X)
       
       s(X) = 0 >= 0 = n__s(X)
       
       cons(X1,X2) = 3X2 + 2 >= 2X2 + 2 = n__cons(X1,X2)
       
       activate(n__from(X)) = 2 >= 2 = from(activate(X))
       
       activate(n__s(X)) = 2 >= 0 = s(activate(X))
       
       activate(n__cons(X1,X2)) = 6X2 + 8 >= 3X2 + 2 = cons(activate(X1),X2)
       
       activate(X) = 3X + 2 >= X = X
      problem:
       DPs:
        
       TRS:
        from(X) -> cons(X,n__from(n__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)
        s(X) -> n__s(X)
        cons(X1,X2) -> n__cons(X1,X2)
        activate(n__from(X)) -> from(activate(X))
        activate(n__s(X)) -> s(activate(X))
        activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
        activate(X) -> X
      Qed
     
     DPs:
      activate#(n__cons(X1,X2)) -> activate#(X1)
      activate#(n__s(X)) -> activate#(X)
      activate#(n__from(X)) -> activate#(X)
     TRS:
      from(X) -> cons(X,n__from(n__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)
      s(X) -> n__s(X)
      cons(X1,X2) -> n__cons(X1,X2)
      activate(n__from(X)) -> from(activate(X))
      activate(n__s(X)) -> s(activate(X))
      activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
      activate(X) -> X
     Open
     
     DPs:
      times#(s(X),Y) -> times#(X,Y)
     TRS:
      from(X) -> cons(X,n__from(n__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)
      s(X) -> n__s(X)
      cons(X1,X2) -> n__cons(X1,X2)
      activate(n__from(X)) -> from(activate(X))
      activate(n__s(X)) -> s(activate(X))
      activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
      activate(X) -> X
     LPO Processor:
      argument filtering:
       pi(from) = []
       pi(n__s) = [0]
       pi(n__from) = []
       pi(cons) = [1]
       pi(0) = []
       pi(2ndspos) = 0
       pi(rnil) = []
       pi(s) = [0]
       pi(n__cons) = 1
       pi(activate) = [0]
       pi(posrecip) = []
       pi(2ndsneg) = [0]
       pi(rcons) = 0
       pi(negrecip) = []
       pi(pi) = [0]
       pi(plus) = [0,1]
       pi(times) = [0,1]
       pi(square) = [0]
       pi(times#) = [0]
      precedence:
       square > times ~ activate > plus > s > 2ndsneg > 0 ~ from > times# ~ 
       pi ~ negrecip ~ rcons ~ posrecip ~ n__cons ~ rnil ~ 2ndspos ~ 
       cons ~ n__from ~ n__s
      problem:
       DPs:
        
       TRS:
        from(X) -> cons(X,n__from(n__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)
        s(X) -> n__s(X)
        cons(X1,X2) -> n__cons(X1,X2)
        activate(n__from(X)) -> from(activate(X))
        activate(n__s(X)) -> s(activate(X))
        activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
        activate(X) -> X
      Qed
     
     DPs:
      plus#(s(X),Y) -> plus#(X,Y)
     TRS:
      from(X) -> cons(X,n__from(n__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)
      s(X) -> n__s(X)
      cons(X1,X2) -> n__cons(X1,X2)
      activate(n__from(X)) -> from(activate(X))
      activate(n__s(X)) -> s(activate(X))
      activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
      activate(X) -> X
     LPO Processor:
      argument filtering:
       pi(from) = []
       pi(n__s) = [0]
       pi(n__from) = []
       pi(cons) = [1]
       pi(0) = []
       pi(2ndspos) = 0
       pi(rnil) = []
       pi(s) = [0]
       pi(n__cons) = 1
       pi(activate) = [0]
       pi(posrecip) = []
       pi(2ndsneg) = [0]
       pi(rcons) = 0
       pi(negrecip) = []
       pi(pi) = [0]
       pi(plus) = [0,1]
       pi(times) = [0,1]
       pi(square) = [0]
       pi(plus#) = [0]
      precedence:
       square > times ~ activate > plus > s > 2ndsneg > 0 ~ from > plus# ~ 
       pi ~ negrecip ~ rcons ~ posrecip ~ n__cons ~ rnil ~ 2ndspos ~ 
       cons ~ n__from ~ n__s
      problem:
       DPs:
        
       TRS:
        from(X) -> cons(X,n__from(n__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)
        s(X) -> n__s(X)
        cons(X1,X2) -> n__cons(X1,X2)
        activate(n__from(X)) -> from(activate(X))
        activate(n__s(X)) -> s(activate(X))
        activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
        activate(X) -> X
      Qed