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:
 Uncurry Processor:
  neq2(0(),0()) -> false()
  neq2(0(),s1(y)) -> true()
  neq2(s1(x),0()) -> true()
  neq2(s1(x),s1(y)) -> neq2(x,y)
  filter2(f,nil()) -> nil()
  filter2(f,cons2(y,ys)) -> filtersub3(app(f,y),f,cons2(y,ys))
  filtersub3(true(),f,cons2(y,ys)) -> cons2(y,filter2(f,ys))
  filtersub3(false(),f,cons2(y,ys)) -> filter2(f,ys)
  nonzero() -> filter1(neq1(0()))
  app(neq1(x5),x6) -> neq2(x5,x6)
  app(neq(),x6) -> neq1(x6)
  app(s(),x6) -> s1(x6)
  app(filter1(x5),x6) -> filter2(x5,x6)
  app(filter(),x6) -> filter1(x6)
  app(cons1(x5),x6) -> cons2(x5,x6)
  app(cons(),x6) -> cons1(x6)
  app(filtersub2(x5,x4),x6) -> filtersub3(x5,x4,x6)
  app(filtersub1(x5),x6) -> filtersub2(x5,x6)
  app(filtersub(),x6) -> filtersub1(x6)
  DP Processor:
   DPs:
    neq{2,#}(s1(x),s1(y)) -> neq{2,#}(x,y)
    filter{2,#}(f,cons2(y,ys)) -> app#(f,y)
    filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys))
    filtersub{3,#}(true(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
    filtersub{3,#}(false(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
    app#(neq1(x5),x6) -> neq{2,#}(x5,x6)
    app#(filter1(x5),x6) -> filter{2,#}(x5,x6)
    app#(filtersub2(x5,x4),x6) -> filtersub{3,#}(x5,x4,x6)
   TRS:
    neq2(0(),0()) -> false()
    neq2(0(),s1(y)) -> true()
    neq2(s1(x),0()) -> true()
    neq2(s1(x),s1(y)) -> neq2(x,y)
    filter2(f,nil()) -> nil()
    filter2(f,cons2(y,ys)) -> filtersub3(app(f,y),f,cons2(y,ys))
    filtersub3(true(),f,cons2(y,ys)) -> cons2(y,filter2(f,ys))
    filtersub3(false(),f,cons2(y,ys)) -> filter2(f,ys)
    nonzero() -> filter1(neq1(0()))
    app(neq1(x5),x6) -> neq2(x5,x6)
    app(neq(),x6) -> neq1(x6)
    app(s(),x6) -> s1(x6)
    app(filter1(x5),x6) -> filter2(x5,x6)
    app(filter(),x6) -> filter1(x6)
    app(cons1(x5),x6) -> cons2(x5,x6)
    app(cons(),x6) -> cons1(x6)
    app(filtersub2(x5,x4),x6) -> filtersub3(x5,x4,x6)
    app(filtersub1(x5),x6) -> filtersub2(x5,x6)
    app(filtersub(),x6) -> filtersub1(x6)
   TDG Processor:
    DPs:
     neq{2,#}(s1(x),s1(y)) -> neq{2,#}(x,y)
     filter{2,#}(f,cons2(y,ys)) -> app#(f,y)
     filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys))
     filtersub{3,#}(true(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
     filtersub{3,#}(false(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
     app#(neq1(x5),x6) -> neq{2,#}(x5,x6)
     app#(filter1(x5),x6) -> filter{2,#}(x5,x6)
     app#(filtersub2(x5,x4),x6) -> filtersub{3,#}(x5,x4,x6)
    TRS:
     neq2(0(),0()) -> false()
     neq2(0(),s1(y)) -> true()
     neq2(s1(x),0()) -> true()
     neq2(s1(x),s1(y)) -> neq2(x,y)
     filter2(f,nil()) -> nil()
     filter2(f,cons2(y,ys)) -> filtersub3(app(f,y),f,cons2(y,ys))
     filtersub3(true(),f,cons2(y,ys)) -> cons2(y,filter2(f,ys))
     filtersub3(false(),f,cons2(y,ys)) -> filter2(f,ys)
     nonzero() -> filter1(neq1(0()))
     app(neq1(x5),x6) -> neq2(x5,x6)
     app(neq(),x6) -> neq1(x6)
     app(s(),x6) -> s1(x6)
     app(filter1(x5),x6) -> filter2(x5,x6)
     app(filter(),x6) -> filter1(x6)
     app(cons1(x5),x6) -> cons2(x5,x6)
     app(cons(),x6) -> cons1(x6)
     app(filtersub2(x5,x4),x6) -> filtersub3(x5,x4,x6)
     app(filtersub1(x5),x6) -> filtersub2(x5,x6)
     app(filtersub(),x6) -> filtersub1(x6)
    graph:
     filtersub{3,#}(true(),f,cons2(y,ys)) -> filter{2,#}(f,ys) ->
     filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys))
     filtersub{3,#}(true(),f,cons2(y,ys)) -> filter{2,#}(f,ys) ->
     filter{2,#}(f,cons2(y,ys)) -> app#(f,y)
     filtersub{3,#}(false(),f,cons2(y,ys)) -> filter{2,#}(f,ys) ->
     filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys))
     filtersub{3,#}(false(),f,cons2(y,ys)) -> filter{2,#}(f,ys) ->
     filter{2,#}(f,cons2(y,ys)) -> app#(f,y)
     app#(filtersub2(x5,x4),x6) -> filtersub{3,#}(x5,x4,x6) ->
     filtersub{3,#}(false(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
     app#(filtersub2(x5,x4),x6) -> filtersub{3,#}(x5,x4,x6) ->
     filtersub{3,#}(true(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
     app#(filter1(x5),x6) -> filter{2,#}(x5,x6) ->
     filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys))
     app#(filter1(x5),x6) -> filter{2,#}(x5,x6) ->
     filter{2,#}(f,cons2(y,ys)) -> app#(f,y)
     app#(neq1(x5),x6) -> neq{2,#}(x5,x6) ->
     neq{2,#}(s1(x),s1(y)) -> neq{2,#}(x,y)
     filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys)) ->
     filtersub{3,#}(false(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
     filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys)) ->
     filtersub{3,#}(true(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
     filter{2,#}(f,cons2(y,ys)) -> app#(f,y) ->
     app#(filtersub2(x5,x4),x6) -> filtersub{3,#}(x5,x4,x6)
     filter{2,#}(f,cons2(y,ys)) -> app#(f,y) ->
     app#(filter1(x5),x6) -> filter{2,#}(x5,x6)
     filter{2,#}(f,cons2(y,ys)) -> app#(f,y) ->
     app#(neq1(x5),x6) -> neq{2,#}(x5,x6)
     neq{2,#}(s1(x),s1(y)) -> neq{2,#}(x,y) -> neq{2,#}(s1(x),s1(y)) -> neq{2,#}(x,y)
    SCC Processor:
     #sccs: 2
     #rules: 7
     #arcs: 15/64
     DPs:
      filtersub{3,#}(true(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
      filter{2,#}(f,cons2(y,ys)) -> app#(f,y)
      app#(filter1(x5),x6) -> filter{2,#}(x5,x6)
      filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys))
      filtersub{3,#}(false(),f,cons2(y,ys)) -> filter{2,#}(f,ys)
      app#(filtersub2(x5,x4),x6) -> filtersub{3,#}(x5,x4,x6)
     TRS:
      neq2(0(),0()) -> false()
      neq2(0(),s1(y)) -> true()
      neq2(s1(x),0()) -> true()
      neq2(s1(x),s1(y)) -> neq2(x,y)
      filter2(f,nil()) -> nil()
      filter2(f,cons2(y,ys)) -> filtersub3(app(f,y),f,cons2(y,ys))
      filtersub3(true(),f,cons2(y,ys)) -> cons2(y,filter2(f,ys))
      filtersub3(false(),f,cons2(y,ys)) -> filter2(f,ys)
      nonzero() -> filter1(neq1(0()))
      app(neq1(x5),x6) -> neq2(x5,x6)
      app(neq(),x6) -> neq1(x6)
      app(s(),x6) -> s1(x6)
      app(filter1(x5),x6) -> filter2(x5,x6)
      app(filter(),x6) -> filter1(x6)
      app(cons1(x5),x6) -> cons2(x5,x6)
      app(cons(),x6) -> cons1(x6)
      app(filtersub2(x5,x4),x6) -> filtersub3(x5,x4,x6)
      app(filtersub1(x5),x6) -> filtersub2(x5,x6)
      app(filtersub(),x6) -> filtersub1(x6)
     Subterm Criterion Processor:
      simple projection:
       pi(filter{2,#}) = 1
       pi(app#) = 1
       pi(filtersub{3,#}) = 2
      problem:
       DPs:
        app#(filter1(x5),x6) -> filter{2,#}(x5,x6)
        filter{2,#}(f,cons2(y,ys)) -> filtersub{3,#}(app(f,y),f,cons2(y,ys))
        app#(filtersub2(x5,x4),x6) -> filtersub{3,#}(x5,x4,x6)
       TRS:
        neq2(0(),0()) -> false()
        neq2(0(),s1(y)) -> true()
        neq2(s1(x),0()) -> true()
        neq2(s1(x),s1(y)) -> neq2(x,y)
        filter2(f,nil()) -> nil()
        filter2(f,cons2(y,ys)) -> filtersub3(app(f,y),f,cons2(y,ys))
        filtersub3(true(),f,cons2(y,ys)) -> cons2(y,filter2(f,ys))
        filtersub3(false(),f,cons2(y,ys)) -> filter2(f,ys)
        nonzero() -> filter1(neq1(0()))
        app(neq1(x5),x6) -> neq2(x5,x6)
        app(neq(),x6) -> neq1(x6)
        app(s(),x6) -> s1(x6)
        app(filter1(x5),x6) -> filter2(x5,x6)
        app(filter(),x6) -> filter1(x6)
        app(cons1(x5),x6) -> cons2(x5,x6)
        app(cons(),x6) -> cons1(x6)
        app(filtersub2(x5,x4),x6) -> filtersub3(x5,x4,x6)
        app(filtersub1(x5),x6) -> filtersub2(x5,x6)
        app(filtersub(),x6) -> filtersub1(x6)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 12/9
       
     
     DPs:
      neq{2,#}(s1(x),s1(y)) -> neq{2,#}(x,y)
     TRS:
      neq2(0(),0()) -> false()
      neq2(0(),s1(y)) -> true()
      neq2(s1(x),0()) -> true()
      neq2(s1(x),s1(y)) -> neq2(x,y)
      filter2(f,nil()) -> nil()
      filter2(f,cons2(y,ys)) -> filtersub3(app(f,y),f,cons2(y,ys))
      filtersub3(true(),f,cons2(y,ys)) -> cons2(y,filter2(f,ys))
      filtersub3(false(),f,cons2(y,ys)) -> filter2(f,ys)
      nonzero() -> filter1(neq1(0()))
      app(neq1(x5),x6) -> neq2(x5,x6)
      app(neq(),x6) -> neq1(x6)
      app(s(),x6) -> s1(x6)
      app(filter1(x5),x6) -> filter2(x5,x6)
      app(filter(),x6) -> filter1(x6)
      app(cons1(x5),x6) -> cons2(x5,x6)
      app(cons(),x6) -> cons1(x6)
      app(filtersub2(x5,x4),x6) -> filtersub3(x5,x4,x6)
      app(filtersub1(x5),x6) -> filtersub2(x5,x6)
      app(filtersub(),x6) -> filtersub1(x6)
     Subterm Criterion Processor:
      simple projection:
       pi(neq{2,#}) = 1
      problem:
       DPs:
        
       TRS:
        neq2(0(),0()) -> false()
        neq2(0(),s1(y)) -> true()
        neq2(s1(x),0()) -> true()
        neq2(s1(x),s1(y)) -> neq2(x,y)
        filter2(f,nil()) -> nil()
        filter2(f,cons2(y,ys)) -> filtersub3(app(f,y),f,cons2(y,ys))
        filtersub3(true(),f,cons2(y,ys)) -> cons2(y,filter2(f,ys))
        filtersub3(false(),f,cons2(y,ys)) -> filter2(f,ys)
        nonzero() -> filter1(neq1(0()))
        app(neq1(x5),x6) -> neq2(x5,x6)
        app(neq(),x6) -> neq1(x6)
        app(s(),x6) -> s1(x6)
        app(filter1(x5),x6) -> filter2(x5,x6)
        app(filter(),x6) -> filter1(x6)
        app(cons1(x5),x6) -> cons2(x5,x6)
        app(cons(),x6) -> cons1(x6)
        app(filtersub2(x5,x4),x6) -> filtersub3(x5,x4,x6)
        app(filtersub1(x5),x6) -> filtersub2(x5,x6)
        app(filtersub(),x6) -> filtersub1(x6)
      Qed