MAYBE

Problem:
 from(X) -> cons(X,n__from(s(X)))
 sel(0(),cons(X,XS)) -> X
 sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
 minus(X,0()) -> 0()
 minus(s(X),s(Y)) -> minus(X,Y)
 quot(0(),s(Y)) -> 0()
 quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
 zWquot(XS,nil()) -> nil()
 zWquot(nil(),XS) -> nil()
 zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
 from(X) -> n__from(X)
 zWquot(X1,X2) -> n__zWquot(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   sel#(s(N),cons(X,XS)) -> activate#(XS)
   sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
   minus#(s(X),s(Y)) -> minus#(X,Y)
   quot#(s(X),s(Y)) -> minus#(X,Y)
   quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y))
   zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS)
   zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS)
   zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y)
   activate#(n__from(X)) -> from#(X)
   activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2)
  TRS:
   from(X) -> cons(X,n__from(s(X)))
   sel(0(),cons(X,XS)) -> X
   sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
   minus(X,0()) -> 0()
   minus(s(X),s(Y)) -> minus(X,Y)
   quot(0(),s(Y)) -> 0()
   quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
   zWquot(XS,nil()) -> nil()
   zWquot(nil(),XS) -> nil()
   zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
   from(X) -> n__from(X)
   zWquot(X1,X2) -> n__zWquot(X1,X2)
   activate(n__from(X)) -> from(X)
   activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
   activate(X) -> X
  Usable Rule Processor:
   DPs:
    sel#(s(N),cons(X,XS)) -> activate#(XS)
    sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
    minus#(s(X),s(Y)) -> minus#(X,Y)
    quot#(s(X),s(Y)) -> minus#(X,Y)
    quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y))
    zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS)
    zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS)
    zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y)
    activate#(n__from(X)) -> from#(X)
    activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2)
   TRS:
    f18(x,y) -> x
    f18(x,y) -> y
    activate(n__from(X)) -> from(X)
    activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
    activate(X) -> X
    from(X) -> cons(X,n__from(s(X)))
    from(X) -> n__from(X)
    zWquot(XS,nil()) -> nil()
    zWquot(nil(),XS) -> nil()
    zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
    zWquot(X1,X2) -> n__zWquot(X1,X2)
    quot(0(),s(Y)) -> 0()
    quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
    minus(X,0()) -> 0()
    minus(s(X),s(Y)) -> minus(X,Y)
   ADG Processor:
    DPs:
     sel#(s(N),cons(X,XS)) -> activate#(XS)
     sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
     minus#(s(X),s(Y)) -> minus#(X,Y)
     quot#(s(X),s(Y)) -> minus#(X,Y)
     quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y))
     zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS)
     zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS)
     zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y)
     activate#(n__from(X)) -> from#(X)
     activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2)
    TRS:
     f18(x,y) -> x
     f18(x,y) -> y
     activate(n__from(X)) -> from(X)
     activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
     activate(X) -> X
     from(X) -> cons(X,n__from(s(X)))
     from(X) -> n__from(X)
     zWquot(XS,nil()) -> nil()
     zWquot(nil(),XS) -> nil()
     zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
     zWquot(X1,X2) -> n__zWquot(X1,X2)
     quot(0(),s(Y)) -> 0()
     quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
     minus(X,0()) -> 0()
     minus(s(X),s(Y)) -> minus(X,Y)
    graph:
     zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y) ->
     quot#(s(X),s(Y)) -> minus#(X,Y)
     zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y) ->
     quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y))
     zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS) ->
     activate#(n__from(X)) -> from#(X)
     zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS) ->
     activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2)
     zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS) ->
     activate#(n__from(X)) -> from#(X)
     zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS) ->
     activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2)
     quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) ->
     quot#(s(X),s(Y)) -> minus#(X,Y)
     quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) ->
     quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y))
     quot#(s(X),s(Y)) -> minus#(X,Y) ->
     minus#(s(X),s(Y)) -> minus#(X,Y)
     minus#(s(X),s(Y)) -> minus#(X,Y) ->
     minus#(s(X),s(Y)) -> minus#(X,Y)
     activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2) ->
     zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS)
     activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2) ->
     zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS)
     activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2) ->
     zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y)
     sel#(s(N),cons(X,XS)) -> activate#(XS) ->
     activate#(n__from(X)) -> from#(X)
     sel#(s(N),cons(X,XS)) -> activate#(XS) ->
     activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2)
     sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS)) ->
     sel#(s(N),cons(X,XS)) -> activate#(XS)
     sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS)) -> sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
    Restore Modifier:
     DPs:
      sel#(s(N),cons(X,XS)) -> activate#(XS)
      sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
      minus#(s(X),s(Y)) -> minus#(X,Y)
      quot#(s(X),s(Y)) -> minus#(X,Y)
      quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y))
      zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS)
      zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS)
      zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y)
      activate#(n__from(X)) -> from#(X)
      activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2)
     TRS:
      from(X) -> cons(X,n__from(s(X)))
      sel(0(),cons(X,XS)) -> X
      sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
      minus(X,0()) -> 0()
      minus(s(X),s(Y)) -> minus(X,Y)
      quot(0(),s(Y)) -> 0()
      quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
      zWquot(XS,nil()) -> nil()
      zWquot(nil(),XS) -> nil()
      zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
      from(X) -> n__from(X)
      zWquot(X1,X2) -> n__zWquot(X1,X2)
      activate(n__from(X)) -> from(X)
      activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
      activate(X) -> X
     SCC Processor:
      #sccs: 4
      #rules: 6
      #arcs: 17/100
      DPs:
       sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
      TRS:
       from(X) -> cons(X,n__from(s(X)))
       sel(0(),cons(X,XS)) -> X
       sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
       minus(X,0()) -> 0()
       minus(s(X),s(Y)) -> minus(X,Y)
       quot(0(),s(Y)) -> 0()
       quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
       zWquot(XS,nil()) -> nil()
       zWquot(nil(),XS) -> nil()
       zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
       from(X) -> n__from(X)
       zWquot(X1,X2) -> n__zWquot(X1,X2)
       activate(n__from(X)) -> from(X)
       activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
       activate(X) -> X
      Open
      
      DPs:
       zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS)
       activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2)
       zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS)
      TRS:
       from(X) -> cons(X,n__from(s(X)))
       sel(0(),cons(X,XS)) -> X
       sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
       minus(X,0()) -> 0()
       minus(s(X),s(Y)) -> minus(X,Y)
       quot(0(),s(Y)) -> 0()
       quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
       zWquot(XS,nil()) -> nil()
       zWquot(nil(),XS) -> nil()
       zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
       from(X) -> n__from(X)
       zWquot(X1,X2) -> n__zWquot(X1,X2)
       activate(n__from(X)) -> from(X)
       activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
       activate(X) -> X
      Open
      
      DPs:
       quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y))
      TRS:
       from(X) -> cons(X,n__from(s(X)))
       sel(0(),cons(X,XS)) -> X
       sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
       minus(X,0()) -> 0()
       minus(s(X),s(Y)) -> minus(X,Y)
       quot(0(),s(Y)) -> 0()
       quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
       zWquot(XS,nil()) -> nil()
       zWquot(nil(),XS) -> nil()
       zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
       from(X) -> n__from(X)
       zWquot(X1,X2) -> n__zWquot(X1,X2)
       activate(n__from(X)) -> from(X)
       activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
       activate(X) -> X
      Open
      
      DPs:
       minus#(s(X),s(Y)) -> minus#(X,Y)
      TRS:
       from(X) -> cons(X,n__from(s(X)))
       sel(0(),cons(X,XS)) -> X
       sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
       minus(X,0()) -> 0()
       minus(s(X),s(Y)) -> minus(X,Y)
       quot(0(),s(Y)) -> 0()
       quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
       zWquot(XS,nil()) -> nil()
       zWquot(nil(),XS) -> nil()
       zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
       from(X) -> n__from(X)
       zWquot(X1,X2) -> n__zWquot(X1,X2)
       activate(n__from(X)) -> from(X)
       activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
       activate(X) -> X
      Open