MAYBE

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()))
  Usable Rule 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)
   Open