YES

Problem:
 app(app(neq(),0()),0()) -> false()
 app(app(neq(),0()),app(s(),y)) -> true()
 app(app(neq(),app(s(),x)),0()) -> true()
 app(app(neq(),app(s(),x)),app(s(),y)) -> app(app(neq(),x),y)
 app(app(filter(),f),nil()) -> nil()
 app(app(filter(),f),app(app(cons(),y),ys)) ->
 app(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
 app(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
 app(app(cons(),y),app(app(filter(),f),ys))
 app(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app(app(filter(),f),ys)
 nonzero() -> app(filter(),app(neq(),0()))

Proof:
 DP Processor:
  DPs:
   app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
   app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
   app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
   app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
   app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
   app#(app(filter(),f),app(app(cons(),y),ys)) ->
   app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
   app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
   app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
   app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
   app#(app(cons(),y),app(app(filter(),f),ys))
   app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
   app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
   nonzero#() -> app#(neq(),0())
   nonzero#() -> app#(filter(),app(neq(),0()))
  TRS:
   app(app(neq(),0()),0()) -> false()
   app(app(neq(),0()),app(s(),y)) -> true()
   app(app(neq(),app(s(),x)),0()) -> true()
   app(app(neq(),app(s(),x)),app(s(),y)) -> app(app(neq(),x),y)
   app(app(filter(),f),nil()) -> nil()
   app(app(filter(),f),app(app(cons(),y),ys)) ->
   app(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
   app(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
   app(app(cons(),y),app(app(filter(),f),ys))
   app(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app(app(filter(),f),ys)
   nonzero() -> app(filter(),app(neq(),0()))
  TDG Processor:
   DPs:
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys))
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    nonzero#() -> app#(neq(),0())
    nonzero#() -> app#(filter(),app(neq(),0()))
   TRS:
    app(app(neq(),0()),0()) -> false()
    app(app(neq(),0()),app(s(),y)) -> true()
    app(app(neq(),app(s(),x)),0()) -> true()
    app(app(neq(),app(s(),x)),app(s(),y)) -> app(app(neq(),x),y)
    app(app(filter(),f),nil()) -> nil()
    app(app(filter(),f),app(app(cons(),y),ys)) ->
    app(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
    app(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app(app(cons(),y),app(app(filter(),f),ys))
    app(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app(app(filter(),f),ys)
    nonzero() -> app(filter(),app(neq(),0()))
   graph:
    nonzero#() -> app#(filter(),app(neq(),0())) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    nonzero#() -> app#(filter(),app(neq(),0())) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    nonzero#() -> app#(filter(),app(neq(),0())) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys))
    nonzero#() -> app#(filter(),app(neq(),0())) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    nonzero#() -> app#(filter(),app(neq(),0())) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    nonzero#() -> app#(filter(),app(neq(),0())) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
    nonzero#() -> app#(filter(),app(neq(),0())) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
    nonzero#() -> app#(filter(),app(neq(),0())) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
    nonzero#() -> app#(filter(),app(neq(),0())) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
    nonzero#() -> app#(filter(),app(neq(),0())) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
    nonzero#() -> app#(filter(),app(neq(),0())) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
    nonzero#() -> app#(neq(),0()) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    nonzero#() -> app#(neq(),0()) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    nonzero#() -> app#(neq(),0()) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys))
    nonzero#() -> app#(neq(),0()) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    nonzero#() -> app#(neq(),0()) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    nonzero#() -> app#(neq(),0()) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
    nonzero#() -> app#(neq(),0()) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
    nonzero#() -> app#(neq(),0()) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
    nonzero#() -> app#(neq(),0()) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
    nonzero#() -> app#(neq(),0()) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
    nonzero#() -> app#(neq(),0()) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y)) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y)) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y)) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys))
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y)) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y)) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y)) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y)) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y)) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y)) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y)) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y)) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys))
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys))
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys)) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys)) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys)) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys)) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys)) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys)) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys))
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys))
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys)) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys)) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys)) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys))
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys)) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys)) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys)) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys)) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys)) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys)) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys)) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys)) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys))
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys))
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys))
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys))
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x) ->
    app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
    app#(app(cons(),y),app(app(filter(),f),ys))
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x) ->
    app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) ->
    app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x) ->
    app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x) ->
    app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
   SCC Processor:
    #sccs: 1
    #rules: 11
    #arcs: 143/169
    DPs:
     app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
     app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
     app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
     app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
     app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
     app#(app(filter(),f),app(app(cons(),y),ys)) ->
     app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
     app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
     app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
     app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
     app#(app(cons(),y),app(app(filter(),f),ys))
     app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
     app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
    TRS:
     app(app(neq(),0()),0()) -> false()
     app(app(neq(),0()),app(s(),y)) -> true()
     app(app(neq(),app(s(),x)),0()) -> true()
     app(app(neq(),app(s(),x)),app(s(),y)) -> app(app(neq(),x),y)
     app(app(filter(),f),nil()) -> nil()
     app(app(filter(),f),app(app(cons(),y),ys)) ->
     app(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
     app(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
     app(app(cons(),y),app(app(filter(),f),ys))
     app(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app(app(filter(),f),ys)
     nonzero() -> app(filter(),app(neq(),0()))
    EDG Processor:
     DPs:
      app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
      app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
      app#(app(filter(),f),app(app(cons(),y),ys)) ->
      app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
      app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
      app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
      app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
      app#(app(cons(),y),app(app(filter(),f),ys))
      app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
      app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
     TRS:
      app(app(neq(),0()),0()) -> false()
      app(app(neq(),0()),app(s(),y)) -> true()
      app(app(neq(),app(s(),x)),0()) -> true()
      app(app(neq(),app(s(),x)),app(s(),y)) -> app(app(neq(),x),y)
      app(app(filter(),f),nil()) -> nil()
      app(app(filter(),f),app(app(cons(),y),ys)) ->
      app(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
      app(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
      app(app(cons(),y),app(app(filter(),f),ys))
      app(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app(app(filter(),f),ys)
      nonzero() -> app(filter(),app(neq(),0()))
     graph:
      app#(app(filter(),f),app(app(cons(),y),ys)) ->
      app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys)) ->
      app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
      app#(app(filter(),f),app(app(cons(),y),ys)) ->
      app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys)) ->
      app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
      app#(app(filter(),f),app(app(cons(),y),ys)) ->
      app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys)) ->
      app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
      app#(app(cons(),y),app(app(filter(),f),ys))
      app#(app(filter(),f),app(app(cons(),y),ys)) ->
      app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys)) ->
      app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
      app#(app(filter(),f),app(app(cons(),y),ys)) ->
      app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys)) ->
      app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
      app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
      app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
      app#(app(filter(),f),app(app(cons(),y),ys)) ->
      app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
      app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
      app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
      app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
      app#(app(cons(),y),app(app(filter(),f),ys))
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
      app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(filter(),f)
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y) ->
      app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
      app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
      app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
      app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
      app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
      app#(app(filter(),f),app(app(cons(),y),ys)) ->
      app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
      app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
      app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(filtersub(),app(f,y))
      app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
      app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(app(filtersub(),app(f,y)),f)
      app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys) ->
      app#(app(filter(),f),app(app(cons(),y),ys)) ->
      app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
      app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y) ->
      app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(neq(),x)
      app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y) ->
      app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
     SCC Processor:
      #sccs: 2
      #rules: 5
      #arcs: 26/121
      DPs:
       app#(app(filter(),f),app(app(cons(),y),ys)) ->
       app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
       app#(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
       app#(app(filter(),f),app(app(cons(),y),ys)) -> app#(f,y)
       app#(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) -> app#(app(filter(),f),ys)
      TRS:
       app(app(neq(),0()),0()) -> false()
       app(app(neq(),0()),app(s(),y)) -> true()
       app(app(neq(),app(s(),x)),0()) -> true()
       app(app(neq(),app(s(),x)),app(s(),y)) -> app(app(neq(),x),y)
       app(app(filter(),f),nil()) -> nil()
       app(app(filter(),f),app(app(cons(),y),ys)) ->
       app(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
       app(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
       app(app(cons(),y),app(app(filter(),f),ys))
       app(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app(app(filter(),f),ys)
       nonzero() -> app(filter(),app(neq(),0()))
      Subterm Criterion Processor:
       simple projection:
        pi(app#) = 1
       problem:
        DPs:
         app#(app(filter(),f),app(app(cons(),y),ys)) ->
         app#(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
        TRS:
         app(app(neq(),0()),0()) -> false()
         app(app(neq(),0()),app(s(),y)) -> true()
         app(app(neq(),app(s(),x)),0()) -> true()
         app(app(neq(),app(s(),x)),app(s(),y)) -> app(app(neq(),x),y)
         app(app(filter(),f),nil()) -> nil()
         app(app(filter(),f),app(app(cons(),y),ys)) ->
         app(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
         app(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
         app(app(cons(),y),app(app(filter(),f),ys))
         app(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app(app(filter(),f),ys)
         nonzero() -> app(filter(),app(neq(),0()))
       SCC Processor:
        #sccs: 0
        #rules: 0
        #arcs: 10/1
        
      
      DPs:
       app#(app(neq(),app(s(),x)),app(s(),y)) -> app#(app(neq(),x),y)
      TRS:
       app(app(neq(),0()),0()) -> false()
       app(app(neq(),0()),app(s(),y)) -> true()
       app(app(neq(),app(s(),x)),0()) -> true()
       app(app(neq(),app(s(),x)),app(s(),y)) -> app(app(neq(),x),y)
       app(app(filter(),f),nil()) -> nil()
       app(app(filter(),f),app(app(cons(),y),ys)) ->
       app(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
       app(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
       app(app(cons(),y),app(app(filter(),f),ys))
       app(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app(app(filter(),f),ys)
       nonzero() -> app(filter(),app(neq(),0()))
      Subterm Criterion Processor:
       simple projection:
        pi(app#) = 1
       problem:
        DPs:
         
        TRS:
         app(app(neq(),0()),0()) -> false()
         app(app(neq(),0()),app(s(),y)) -> true()
         app(app(neq(),app(s(),x)),0()) -> true()
         app(app(neq(),app(s(),x)),app(s(),y)) -> app(app(neq(),x),y)
         app(app(filter(),f),nil()) -> nil()
         app(app(filter(),f),app(app(cons(),y),ys)) ->
         app(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
         app(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
         app(app(cons(),y),app(app(filter(),f),ys))
         app(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app(app(filter(),f),ys)
         nonzero() -> app(filter(),app(neq(),0()))
       Qed