MAYBE

Problem:
 from(X) -> cons(X,from(s(X)))
 sel(0(),cons(X,XS)) -> X
 sel(s(N),cons(X,XS)) -> sel(N,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),zWquot(XS,YS))

Proof:
 DP Processor:
  DPs:
   from#(X) -> from#(s(X))
   sel#(s(N),cons(X,XS)) -> sel#(N,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)) -> zWquot#(XS,YS)
   zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y)
  TRS:
   from(X) -> cons(X,from(s(X)))
   sel(0(),cons(X,XS)) -> X
   sel(s(N),cons(X,XS)) -> sel(N,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),zWquot(XS,YS))
  Usable Rule Processor:
   DPs:
    from#(X) -> from#(s(X))
    sel#(s(N),cons(X,XS)) -> sel#(N,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)) -> zWquot#(XS,YS)
    zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y)
   TRS:
    f14(x,y) -> x
    f14(x,y) -> y
    minus(X,0()) -> 0()
    minus(s(X),s(Y)) -> minus(X,Y)
   EDG Processor:
    DPs:
     from#(X) -> from#(s(X))
     sel#(s(N),cons(X,XS)) -> sel#(N,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)) -> zWquot#(XS,YS)
     zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y)
    TRS:
     f14(x,y) -> x
     f14(x,y) -> y
     minus(X,0()) -> 0()
     minus(s(X),s(Y)) -> minus(X,Y)
    graph:
     zWquot#(cons(X,XS),cons(Y,YS)) -> zWquot#(XS,YS) ->
     zWquot#(cons(X,XS),cons(Y,YS)) -> zWquot#(XS,YS)
     zWquot#(cons(X,XS),cons(Y,YS)) -> zWquot#(XS,YS) ->
     zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y)
     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))
     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)
     sel#(s(N),cons(X,XS)) -> sel#(N,XS) ->
     sel#(s(N),cons(X,XS)) -> sel#(N,XS)
     from#(X) -> from#(s(X)) -> from#(X) -> from#(s(X))
    Restore Modifier:
     DPs:
      from#(X) -> from#(s(X))
      sel#(s(N),cons(X,XS)) -> sel#(N,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)) -> zWquot#(XS,YS)
      zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y)
     TRS:
      from(X) -> cons(X,from(s(X)))
      sel(0(),cons(X,XS)) -> X
      sel(s(N),cons(X,XS)) -> sel(N,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),zWquot(XS,YS))
     SCC Processor:
      #sccs: 5
      #rules: 5
      #arcs: 10/49
      DPs:
       from#(X) -> from#(s(X))
      TRS:
       from(X) -> cons(X,from(s(X)))
       sel(0(),cons(X,XS)) -> X
       sel(s(N),cons(X,XS)) -> sel(N,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),zWquot(XS,YS))
      Open
      
      DPs:
       sel#(s(N),cons(X,XS)) -> sel#(N,XS)
      TRS:
       from(X) -> cons(X,from(s(X)))
       sel(0(),cons(X,XS)) -> X
       sel(s(N),cons(X,XS)) -> sel(N,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),zWquot(XS,YS))
      Open
      
      DPs:
       zWquot#(cons(X,XS),cons(Y,YS)) -> zWquot#(XS,YS)
      TRS:
       from(X) -> cons(X,from(s(X)))
       sel(0(),cons(X,XS)) -> X
       sel(s(N),cons(X,XS)) -> sel(N,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),zWquot(XS,YS))
      Open
      
      DPs:
       quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y))
      TRS:
       from(X) -> cons(X,from(s(X)))
       sel(0(),cons(X,XS)) -> X
       sel(s(N),cons(X,XS)) -> sel(N,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),zWquot(XS,YS))
      Open
      
      DPs:
       minus#(s(X),s(Y)) -> minus#(X,Y)
      TRS:
       from(X) -> cons(X,from(s(X)))
       sel(0(),cons(X,XS)) -> X
       sel(s(N),cons(X,XS)) -> sel(N,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),zWquot(XS,YS))
      Open