MAYBE

Problem:
 app(nil(),YS) -> YS
 app(cons(X,XS),YS) -> cons(X,n__app(activate(XS),YS))
 from(X) -> cons(X,n__from(s(X)))
 zWadr(nil(),YS) -> nil()
 zWadr(XS,nil()) -> nil()
 zWadr(cons(X,XS),cons(Y,YS)) -> cons(app(Y,cons(X,n__nil())),n__zWadr(activate(XS),activate(YS)))
 prefix(L) -> cons(nil(),n__zWadr(L,prefix(L)))
 app(X1,X2) -> n__app(X1,X2)
 from(X) -> n__from(X)
 nil() -> n__nil()
 zWadr(X1,X2) -> n__zWadr(X1,X2)
 activate(n__app(X1,X2)) -> app(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__nil()) -> nil()
 activate(n__zWadr(X1,X2)) -> zWadr(X1,X2)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   app#(cons(X,XS),YS) -> activate#(XS)
   zWadr#(cons(X,XS),cons(Y,YS)) -> activate#(YS)
   zWadr#(cons(X,XS),cons(Y,YS)) -> activate#(XS)
   zWadr#(cons(X,XS),cons(Y,YS)) -> app#(Y,cons(X,n__nil()))
   prefix#(L) -> prefix#(L)
   prefix#(L) -> nil#()
   activate#(n__app(X1,X2)) -> app#(X1,X2)
   activate#(n__from(X)) -> from#(X)
   activate#(n__nil()) -> nil#()
   activate#(n__zWadr(X1,X2)) -> zWadr#(X1,X2)
  TRS:
   app(nil(),YS) -> YS
   app(cons(X,XS),YS) -> cons(X,n__app(activate(XS),YS))
   from(X) -> cons(X,n__from(s(X)))
   zWadr(nil(),YS) -> nil()
   zWadr(XS,nil()) -> nil()
   zWadr(cons(X,XS),cons(Y,YS)) ->
   cons(app(Y,cons(X,n__nil())),n__zWadr(activate(XS),activate(YS)))
   prefix(L) -> cons(nil(),n__zWadr(L,prefix(L)))
   app(X1,X2) -> n__app(X1,X2)
   from(X) -> n__from(X)
   nil() -> n__nil()
   zWadr(X1,X2) -> n__zWadr(X1,X2)
   activate(n__app(X1,X2)) -> app(X1,X2)
   activate(n__from(X)) -> from(X)
   activate(n__nil()) -> nil()
   activate(n__zWadr(X1,X2)) -> zWadr(X1,X2)
   activate(X) -> X
  EDG Processor:
   DPs:
    app#(cons(X,XS),YS) -> activate#(XS)
    zWadr#(cons(X,XS),cons(Y,YS)) -> activate#(YS)
    zWadr#(cons(X,XS),cons(Y,YS)) -> activate#(XS)
    zWadr#(cons(X,XS),cons(Y,YS)) -> app#(Y,cons(X,n__nil()))
    prefix#(L) -> prefix#(L)
    prefix#(L) -> nil#()
    activate#(n__app(X1,X2)) -> app#(X1,X2)
    activate#(n__from(X)) -> from#(X)
    activate#(n__nil()) -> nil#()
    activate#(n__zWadr(X1,X2)) -> zWadr#(X1,X2)
   TRS:
    app(nil(),YS) -> YS
    app(cons(X,XS),YS) -> cons(X,n__app(activate(XS),YS))
    from(X) -> cons(X,n__from(s(X)))
    zWadr(nil(),YS) -> nil()
    zWadr(XS,nil()) -> nil()
    zWadr(cons(X,XS),cons(Y,YS)) ->
    cons(app(Y,cons(X,n__nil())),n__zWadr(activate(XS),activate(YS)))
    prefix(L) -> cons(nil(),n__zWadr(L,prefix(L)))
    app(X1,X2) -> n__app(X1,X2)
    from(X) -> n__from(X)
    nil() -> n__nil()
    zWadr(X1,X2) -> n__zWadr(X1,X2)
    activate(n__app(X1,X2)) -> app(X1,X2)
    activate(n__from(X)) -> from(X)
    activate(n__nil()) -> nil()
    activate(n__zWadr(X1,X2)) -> zWadr(X1,X2)
    activate(X) -> X
   graph:
    prefix#(L) -> prefix#(L) -> prefix#(L) -> prefix#(L)
    prefix#(L) -> prefix#(L) -> prefix#(L) -> nil#()
    zWadr#(cons(X,XS),cons(Y,YS)) -> activate#(XS) ->
    activate#(n__app(X1,X2)) -> app#(X1,X2)
    zWadr#(cons(X,XS),cons(Y,YS)) -> activate#(XS) ->
    activate#(n__from(X)) -> from#(X)
    zWadr#(cons(X,XS),cons(Y,YS)) -> activate#(XS) ->
    activate#(n__nil()) -> nil#()
    zWadr#(cons(X,XS),cons(Y,YS)) -> activate#(XS) ->
    activate#(n__zWadr(X1,X2)) -> zWadr#(X1,X2)
    zWadr#(cons(X,XS),cons(Y,YS)) -> activate#(YS) ->
    activate#(n__app(X1,X2)) -> app#(X1,X2)
    zWadr#(cons(X,XS),cons(Y,YS)) -> activate#(YS) ->
    activate#(n__from(X)) -> from#(X)
    zWadr#(cons(X,XS),cons(Y,YS)) -> activate#(YS) ->
    activate#(n__nil()) -> nil#()
    zWadr#(cons(X,XS),cons(Y,YS)) -> activate#(YS) ->
    activate#(n__zWadr(X1,X2)) -> zWadr#(X1,X2)
    zWadr#(cons(X,XS),cons(Y,YS)) -> app#(Y,cons(X,n__nil())) ->
    app#(cons(X,XS),YS) -> activate#(XS)
    activate#(n__zWadr(X1,X2)) -> zWadr#(X1,X2) ->
    zWadr#(cons(X,XS),cons(Y,YS)) -> activate#(YS)
    activate#(n__zWadr(X1,X2)) -> zWadr#(X1,X2) ->
    zWadr#(cons(X,XS),cons(Y,YS)) -> activate#(XS)
    activate#(n__zWadr(X1,X2)) -> zWadr#(X1,X2) ->
    zWadr#(cons(X,XS),cons(Y,YS)) -> app#(Y,cons(X,n__nil()))
    activate#(n__app(X1,X2)) -> app#(X1,X2) ->
    app#(cons(X,XS),YS) -> activate#(XS)
    app#(cons(X,XS),YS) -> activate#(XS) ->
    activate#(n__app(X1,X2)) -> app#(X1,X2)
    app#(cons(X,XS),YS) -> activate#(XS) ->
    activate#(n__from(X)) -> from#(X)
    app#(cons(X,XS),YS) -> activate#(XS) ->
    activate#(n__nil()) -> nil#()
    app#(cons(X,XS),YS) -> activate#(XS) -> activate#(n__zWadr(X1,X2)) -> zWadr#(X1,X2)
   SCC Processor:
    #sccs: 2
    #rules: 7
    #arcs: 19/100
    DPs:
     zWadr#(cons(X,XS),cons(Y,YS)) -> activate#(XS)
     activate#(n__zWadr(X1,X2)) -> zWadr#(X1,X2)
     zWadr#(cons(X,XS),cons(Y,YS)) -> app#(Y,cons(X,n__nil()))
     app#(cons(X,XS),YS) -> activate#(XS)
     activate#(n__app(X1,X2)) -> app#(X1,X2)
     zWadr#(cons(X,XS),cons(Y,YS)) -> activate#(YS)
    TRS:
     app(nil(),YS) -> YS
     app(cons(X,XS),YS) -> cons(X,n__app(activate(XS),YS))
     from(X) -> cons(X,n__from(s(X)))
     zWadr(nil(),YS) -> nil()
     zWadr(XS,nil()) -> nil()
     zWadr(cons(X,XS),cons(Y,YS)) ->
     cons(app(Y,cons(X,n__nil())),n__zWadr(activate(XS),activate(YS)))
     prefix(L) -> cons(nil(),n__zWadr(L,prefix(L)))
     app(X1,X2) -> n__app(X1,X2)
     from(X) -> n__from(X)
     nil() -> n__nil()
     zWadr(X1,X2) -> n__zWadr(X1,X2)
     activate(n__app(X1,X2)) -> app(X1,X2)
     activate(n__from(X)) -> from(X)
     activate(n__nil()) -> nil()
     activate(n__zWadr(X1,X2)) -> zWadr(X1,X2)
     activate(X) -> X
    Open
    
    DPs:
     prefix#(L) -> prefix#(L)
    TRS:
     app(nil(),YS) -> YS
     app(cons(X,XS),YS) -> cons(X,n__app(activate(XS),YS))
     from(X) -> cons(X,n__from(s(X)))
     zWadr(nil(),YS) -> nil()
     zWadr(XS,nil()) -> nil()
     zWadr(cons(X,XS),cons(Y,YS)) ->
     cons(app(Y,cons(X,n__nil())),n__zWadr(activate(XS),activate(YS)))
     prefix(L) -> cons(nil(),n__zWadr(L,prefix(L)))
     app(X1,X2) -> n__app(X1,X2)
     from(X) -> n__from(X)
     nil() -> n__nil()
     zWadr(X1,X2) -> n__zWadr(X1,X2)
     activate(n__app(X1,X2)) -> app(X1,X2)
     activate(n__from(X)) -> from(X)
     activate(n__nil()) -> nil()
     activate(n__zWadr(X1,X2)) -> zWadr(X1,X2)
     activate(X) -> X
    Open