MAYBE

Problem:
 app(app(h(),z),app(e(),x)) -> app(app(h(),app(c(),z)),app(app(d(),z),x))
 app(app(d(),z),app(app(g(),0()),0())) -> app(e(),0())
 app(app(d(),z),app(app(g(),x),y)) -> app(app(g(),app(e(),x)),app(app(d(),z),y))
 app(app(d(),app(c(),z)),app(app(g(),app(app(g(),x),y)),0())) ->
 app(app(g(),app(app(d(),app(c(),z)),app(app(g(),x),y))),app(app(d(),z),app(app(g(),x),y)))
 app(app(g(),app(e(),x)),app(e(),y)) -> app(e(),app(app(g(),x),y))
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
 app(app(filter(),f),nil()) -> nil()
 app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
 app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
 app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)

Proof:
 Uncurry Processor:
  h2(z,e1(x)) -> h2(c1(z),d2(z,x))
  d2(z,g2(0(),0())) -> e1(0())
  d2(z,g2(x,y)) -> g2(e1(x),d2(z,y))
  d2(c1(z),g2(g2(x,y),0())) -> g2(d2(c1(z),g2(x,y)),d2(z,g2(x,y)))
  g2(e1(x),e1(y)) -> e1(g2(x,y))
  map2(f,nil()) -> nil()
  map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
  filter2(f,nil()) -> nil()
  filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
  filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
  filter24(false(),f,x,xs) -> filter2(f,xs)
  app(h1(x7),x8) -> h2(x7,x8)
  app(h(),x8) -> h1(x8)
  app(e(),x8) -> e1(x8)
  app(c(),x8) -> c1(x8)
  app(d1(x7),x8) -> d2(x7,x8)
  app(d(),x8) -> d1(x8)
  app(g1(x7),x8) -> g2(x7,x8)
  app(g(),x8) -> g1(x8)
  app(map1(x7),x8) -> map2(x7,x8)
  app(map(),x8) -> map1(x8)
  app(cons1(x7),x8) -> cons2(x7,x8)
  app(cons(),x8) -> cons1(x8)
  app(filter1(x7),x8) -> filter2(x7,x8)
  app(filter(),x8) -> filter1(x8)
  app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
  app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
  app(filter21(x7),x8) -> filter22(x7,x8)
  app(filter2(),x8) -> filter21(x8)
  DP Processor:
   DPs:
    h{2,#}(z,e1(x)) -> d{2,#}(z,x)
    h{2,#}(z,e1(x)) -> h{2,#}(c1(z),d2(z,x))
    d{2,#}(z,g2(x,y)) -> d{2,#}(z,y)
    d{2,#}(z,g2(x,y)) -> g{2,#}(e1(x),d2(z,y))
    d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(z,g2(x,y))
    d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(c1(z),g2(x,y))
    d{2,#}(c1(z),g2(g2(x,y),0())) -> g{2,#}(d2(c1(z),g2(x,y)),d2(z,g2(x,y)))
    g{2,#}(e1(x),e1(y)) -> g{2,#}(x,y)
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
    filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
    filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs)
    filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs)
    app#(h1(x7),x8) -> h{2,#}(x7,x8)
    app#(d1(x7),x8) -> d{2,#}(x7,x8)
    app#(g1(x7),x8) -> g{2,#}(x7,x8)
    app#(map1(x7),x8) -> map{2,#}(x7,x8)
    app#(filter1(x7),x8) -> filter{2,#}(x7,x8)
    app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8)
   TRS:
    h2(z,e1(x)) -> h2(c1(z),d2(z,x))
    d2(z,g2(0(),0())) -> e1(0())
    d2(z,g2(x,y)) -> g2(e1(x),d2(z,y))
    d2(c1(z),g2(g2(x,y),0())) -> g2(d2(c1(z),g2(x,y)),d2(z,g2(x,y)))
    g2(e1(x),e1(y)) -> e1(g2(x,y))
    map2(f,nil()) -> nil()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    filter2(f,nil()) -> nil()
    filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
    filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
    filter24(false(),f,x,xs) -> filter2(f,xs)
    app(h1(x7),x8) -> h2(x7,x8)
    app(h(),x8) -> h1(x8)
    app(e(),x8) -> e1(x8)
    app(c(),x8) -> c1(x8)
    app(d1(x7),x8) -> d2(x7,x8)
    app(d(),x8) -> d1(x8)
    app(g1(x7),x8) -> g2(x7,x8)
    app(g(),x8) -> g1(x8)
    app(map1(x7),x8) -> map2(x7,x8)
    app(map(),x8) -> map1(x8)
    app(cons1(x7),x8) -> cons2(x7,x8)
    app(cons(),x8) -> cons1(x8)
    app(filter1(x7),x8) -> filter2(x7,x8)
    app(filter(),x8) -> filter1(x8)
    app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
    app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
    app(filter21(x7),x8) -> filter22(x7,x8)
    app(filter2(),x8) -> filter21(x8)
   TDG Processor:
    DPs:
     h{2,#}(z,e1(x)) -> d{2,#}(z,x)
     h{2,#}(z,e1(x)) -> h{2,#}(c1(z),d2(z,x))
     d{2,#}(z,g2(x,y)) -> d{2,#}(z,y)
     d{2,#}(z,g2(x,y)) -> g{2,#}(e1(x),d2(z,y))
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(z,g2(x,y))
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(c1(z),g2(x,y))
     d{2,#}(c1(z),g2(g2(x,y),0())) -> g{2,#}(d2(c1(z),g2(x,y)),d2(z,g2(x,y)))
     g{2,#}(e1(x),e1(y)) -> g{2,#}(x,y)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
     filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs)
     filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs)
     app#(h1(x7),x8) -> h{2,#}(x7,x8)
     app#(d1(x7),x8) -> d{2,#}(x7,x8)
     app#(g1(x7),x8) -> g{2,#}(x7,x8)
     app#(map1(x7),x8) -> map{2,#}(x7,x8)
     app#(filter1(x7),x8) -> filter{2,#}(x7,x8)
     app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8)
    TRS:
     h2(z,e1(x)) -> h2(c1(z),d2(z,x))
     d2(z,g2(0(),0())) -> e1(0())
     d2(z,g2(x,y)) -> g2(e1(x),d2(z,y))
     d2(c1(z),g2(g2(x,y),0())) -> g2(d2(c1(z),g2(x,y)),d2(z,g2(x,y)))
     g2(e1(x),e1(y)) -> e1(g2(x,y))
     map2(f,nil()) -> nil()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     filter2(f,nil()) -> nil()
     filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
     filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
     filter24(false(),f,x,xs) -> filter2(f,xs)
     app(h1(x7),x8) -> h2(x7,x8)
     app(h(),x8) -> h1(x8)
     app(e(),x8) -> e1(x8)
     app(c(),x8) -> c1(x8)
     app(d1(x7),x8) -> d2(x7,x8)
     app(d(),x8) -> d1(x8)
     app(g1(x7),x8) -> g2(x7,x8)
     app(g(),x8) -> g1(x8)
     app(map1(x7),x8) -> map2(x7,x8)
     app(map(),x8) -> map1(x8)
     app(cons1(x7),x8) -> cons2(x7,x8)
     app(cons(),x8) -> cons1(x8)
     app(filter1(x7),x8) -> filter2(x7,x8)
     app(filter(),x8) -> filter1(x8)
     app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
     app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
     app(filter21(x7),x8) -> filter22(x7,x8)
     app(filter2(),x8) -> filter21(x8)
    graph:
     filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs) ->
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
     filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs) ->
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs) ->
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
     filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs) ->
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs) ->
     filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs)
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs) ->
     filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x7),x8) -> filter{2,#}(x7,x8)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x7),x8) -> map{2,#}(x7,x8)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(g1(x7),x8) -> g{2,#}(x7,x8)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(d1(x7),x8) -> d{2,#}(x7,x8)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(h1(x7),x8) -> h{2,#}(x7,x8)
     app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8) ->
     filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs)
     app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8) ->
     filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs)
     app#(filter1(x7),x8) -> filter{2,#}(x7,x8) ->
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
     app#(filter1(x7),x8) -> filter{2,#}(x7,x8) ->
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x7),x8) -> map{2,#}(x7,x8) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x7),x8) -> map{2,#}(x7,x8) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     app#(g1(x7),x8) -> g{2,#}(x7,x8) ->
     g{2,#}(e1(x),e1(y)) -> g{2,#}(x,y)
     app#(d1(x7),x8) -> d{2,#}(x7,x8) ->
     d{2,#}(c1(z),g2(g2(x,y),0())) -> g{2,#}(d2(c1(z),g2(x,y)),d2(z,g2(x,y)))
     app#(d1(x7),x8) -> d{2,#}(x7,x8) ->
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(c1(z),g2(x,y))
     app#(d1(x7),x8) -> d{2,#}(x7,x8) ->
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(z,g2(x,y))
     app#(d1(x7),x8) -> d{2,#}(x7,x8) ->
     d{2,#}(z,g2(x,y)) -> g{2,#}(e1(x),d2(z,y))
     app#(d1(x7),x8) -> d{2,#}(x7,x8) ->
     d{2,#}(z,g2(x,y)) -> d{2,#}(z,y)
     app#(h1(x7),x8) -> h{2,#}(x7,x8) ->
     h{2,#}(z,e1(x)) -> h{2,#}(c1(z),d2(z,x))
     app#(h1(x7),x8) -> h{2,#}(x7,x8) ->
     h{2,#}(z,e1(x)) -> d{2,#}(z,x)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x7),x8) -> filter{2,#}(x7,x8)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x7),x8) -> map{2,#}(x7,x8)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(g1(x7),x8) -> g{2,#}(x7,x8)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(d1(x7),x8) -> d{2,#}(x7,x8)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(h1(x7),x8) -> h{2,#}(x7,x8)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     g{2,#}(e1(x),e1(y)) -> g{2,#}(x,y) ->
     g{2,#}(e1(x),e1(y)) -> g{2,#}(x,y)
     d{2,#}(c1(z),g2(g2(x,y),0())) -> g{2,#}(d2(c1(z),g2(x,y)),d2(z,g2(x,y))) ->
     g{2,#}(e1(x),e1(y)) -> g{2,#}(x,y)
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(c1(z),g2(x,y)) ->
     d{2,#}(c1(z),g2(g2(x,y),0())) -> g{2,#}(d2(c1(z),g2(x,y)),d2(z,g2(x,y)))
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(c1(z),g2(x,y)) ->
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(c1(z),g2(x,y))
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(c1(z),g2(x,y)) ->
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(z,g2(x,y))
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(c1(z),g2(x,y)) ->
     d{2,#}(z,g2(x,y)) -> g{2,#}(e1(x),d2(z,y))
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(c1(z),g2(x,y)) ->
     d{2,#}(z,g2(x,y)) -> d{2,#}(z,y)
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(z,g2(x,y)) ->
     d{2,#}(c1(z),g2(g2(x,y),0())) -> g{2,#}(d2(c1(z),g2(x,y)),d2(z,g2(x,y)))
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(z,g2(x,y)) ->
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(c1(z),g2(x,y))
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(z,g2(x,y)) ->
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(z,g2(x,y))
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(z,g2(x,y)) ->
     d{2,#}(z,g2(x,y)) -> g{2,#}(e1(x),d2(z,y))
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(z,g2(x,y)) ->
     d{2,#}(z,g2(x,y)) -> d{2,#}(z,y)
     d{2,#}(z,g2(x,y)) -> g{2,#}(e1(x),d2(z,y)) ->
     g{2,#}(e1(x),e1(y)) -> g{2,#}(x,y)
     d{2,#}(z,g2(x,y)) -> d{2,#}(z,y) ->
     d{2,#}(c1(z),g2(g2(x,y),0())) -> g{2,#}(d2(c1(z),g2(x,y)),d2(z,g2(x,y)))
     d{2,#}(z,g2(x,y)) -> d{2,#}(z,y) ->
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(c1(z),g2(x,y))
     d{2,#}(z,g2(x,y)) -> d{2,#}(z,y) ->
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(z,g2(x,y))
     d{2,#}(z,g2(x,y)) -> d{2,#}(z,y) ->
     d{2,#}(z,g2(x,y)) -> g{2,#}(e1(x),d2(z,y))
     d{2,#}(z,g2(x,y)) -> d{2,#}(z,y) ->
     d{2,#}(z,g2(x,y)) -> d{2,#}(z,y)
     h{2,#}(z,e1(x)) -> d{2,#}(z,x) ->
     d{2,#}(c1(z),g2(g2(x,y),0())) -> g{2,#}(d2(c1(z),g2(x,y)),d2(z,g2(x,y)))
     h{2,#}(z,e1(x)) -> d{2,#}(z,x) ->
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(c1(z),g2(x,y))
     h{2,#}(z,e1(x)) -> d{2,#}(z,x) ->
     d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(z,g2(x,y))
     h{2,#}(z,e1(x)) -> d{2,#}(z,x) ->
     d{2,#}(z,g2(x,y)) -> g{2,#}(e1(x),d2(z,y))
     h{2,#}(z,e1(x)) -> d{2,#}(z,x) ->
     d{2,#}(z,g2(x,y)) -> d{2,#}(z,y)
     h{2,#}(z,e1(x)) -> h{2,#}(c1(z),d2(z,x)) ->
     h{2,#}(z,e1(x)) -> h{2,#}(c1(z),d2(z,x))
     h{2,#}(z,e1(x)) -> h{2,#}(c1(z),d2(z,x)) -> h{2,#}(z,e1(x)) -> d{2,#}(z,x)
    SCC Processor:
     #sccs: 4
     #rules: 14
     #arcs: 59/400
     DPs:
      filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs)
      filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(map1(x7),x8) -> map{2,#}(x7,x8)
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(filter1(x7),x8) -> filter{2,#}(x7,x8)
      filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
      filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs)
      app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8)
     TRS:
      h2(z,e1(x)) -> h2(c1(z),d2(z,x))
      d2(z,g2(0(),0())) -> e1(0())
      d2(z,g2(x,y)) -> g2(e1(x),d2(z,y))
      d2(c1(z),g2(g2(x,y),0())) -> g2(d2(c1(z),g2(x,y)),d2(z,g2(x,y)))
      g2(e1(x),e1(y)) -> e1(g2(x,y))
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      filter2(f,nil()) -> nil()
      filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
      filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
      filter24(false(),f,x,xs) -> filter2(f,xs)
      app(h1(x7),x8) -> h2(x7,x8)
      app(h(),x8) -> h1(x8)
      app(e(),x8) -> e1(x8)
      app(c(),x8) -> c1(x8)
      app(d1(x7),x8) -> d2(x7,x8)
      app(d(),x8) -> d1(x8)
      app(g1(x7),x8) -> g2(x7,x8)
      app(g(),x8) -> g1(x8)
      app(map1(x7),x8) -> map2(x7,x8)
      app(map(),x8) -> map1(x8)
      app(cons1(x7),x8) -> cons2(x7,x8)
      app(cons(),x8) -> cons1(x8)
      app(filter1(x7),x8) -> filter2(x7,x8)
      app(filter(),x8) -> filter1(x8)
      app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
      app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
      app(filter21(x7),x8) -> filter22(x7,x8)
      app(filter2(),x8) -> filter21(x8)
     Subterm Criterion Processor:
      simple projection:
       pi(map{2,#}) = 1
       pi(app#) = 1
       pi(filter{2,#}) = 1
       pi(filter2{4,#}) = 3
      problem:
       DPs:
        filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs)
        app#(map1(x7),x8) -> map{2,#}(x7,x8)
        app#(filter1(x7),x8) -> filter{2,#}(x7,x8)
        filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs)
        app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8)
       TRS:
        h2(z,e1(x)) -> h2(c1(z),d2(z,x))
        d2(z,g2(0(),0())) -> e1(0())
        d2(z,g2(x,y)) -> g2(e1(x),d2(z,y))
        d2(c1(z),g2(g2(x,y),0())) -> g2(d2(c1(z),g2(x,y)),d2(z,g2(x,y)))
        g2(e1(x),e1(y)) -> e1(g2(x,y))
        map2(f,nil()) -> nil()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        filter2(f,nil()) -> nil()
        filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
        filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
        filter24(false(),f,x,xs) -> filter2(f,xs)
        app(h1(x7),x8) -> h2(x7,x8)
        app(h(),x8) -> h1(x8)
        app(e(),x8) -> e1(x8)
        app(c(),x8) -> c1(x8)
        app(d1(x7),x8) -> d2(x7,x8)
        app(d(),x8) -> d1(x8)
        app(g1(x7),x8) -> g2(x7,x8)
        app(g(),x8) -> g1(x8)
        app(map1(x7),x8) -> map2(x7,x8)
        app(map(),x8) -> map1(x8)
        app(cons1(x7),x8) -> cons2(x7,x8)
        app(cons(),x8) -> cons1(x8)
        app(filter1(x7),x8) -> filter2(x7,x8)
        app(filter(),x8) -> filter1(x8)
        app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
        app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
        app(filter21(x7),x8) -> filter22(x7,x8)
        app(filter2(),x8) -> filter21(x8)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 20/25
       
     
     DPs:
      h{2,#}(z,e1(x)) -> h{2,#}(c1(z),d2(z,x))
     TRS:
      h2(z,e1(x)) -> h2(c1(z),d2(z,x))
      d2(z,g2(0(),0())) -> e1(0())
      d2(z,g2(x,y)) -> g2(e1(x),d2(z,y))
      d2(c1(z),g2(g2(x,y),0())) -> g2(d2(c1(z),g2(x,y)),d2(z,g2(x,y)))
      g2(e1(x),e1(y)) -> e1(g2(x,y))
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      filter2(f,nil()) -> nil()
      filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
      filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
      filter24(false(),f,x,xs) -> filter2(f,xs)
      app(h1(x7),x8) -> h2(x7,x8)
      app(h(),x8) -> h1(x8)
      app(e(),x8) -> e1(x8)
      app(c(),x8) -> c1(x8)
      app(d1(x7),x8) -> d2(x7,x8)
      app(d(),x8) -> d1(x8)
      app(g1(x7),x8) -> g2(x7,x8)
      app(g(),x8) -> g1(x8)
      app(map1(x7),x8) -> map2(x7,x8)
      app(map(),x8) -> map1(x8)
      app(cons1(x7),x8) -> cons2(x7,x8)
      app(cons(),x8) -> cons1(x8)
      app(filter1(x7),x8) -> filter2(x7,x8)
      app(filter(),x8) -> filter1(x8)
      app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
      app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
      app(filter21(x7),x8) -> filter22(x7,x8)
      app(filter2(),x8) -> filter21(x8)
     Open
     
     DPs:
      d{2,#}(z,g2(x,y)) -> d{2,#}(z,y)
      d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(z,g2(x,y))
      d{2,#}(c1(z),g2(g2(x,y),0())) -> d{2,#}(c1(z),g2(x,y))
     TRS:
      h2(z,e1(x)) -> h2(c1(z),d2(z,x))
      d2(z,g2(0(),0())) -> e1(0())
      d2(z,g2(x,y)) -> g2(e1(x),d2(z,y))
      d2(c1(z),g2(g2(x,y),0())) -> g2(d2(c1(z),g2(x,y)),d2(z,g2(x,y)))
      g2(e1(x),e1(y)) -> e1(g2(x,y))
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      filter2(f,nil()) -> nil()
      filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
      filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
      filter24(false(),f,x,xs) -> filter2(f,xs)
      app(h1(x7),x8) -> h2(x7,x8)
      app(h(),x8) -> h1(x8)
      app(e(),x8) -> e1(x8)
      app(c(),x8) -> c1(x8)
      app(d1(x7),x8) -> d2(x7,x8)
      app(d(),x8) -> d1(x8)
      app(g1(x7),x8) -> g2(x7,x8)
      app(g(),x8) -> g1(x8)
      app(map1(x7),x8) -> map2(x7,x8)
      app(map(),x8) -> map1(x8)
      app(cons1(x7),x8) -> cons2(x7,x8)
      app(cons(),x8) -> cons1(x8)
      app(filter1(x7),x8) -> filter2(x7,x8)
      app(filter(),x8) -> filter1(x8)
      app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
      app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
      app(filter21(x7),x8) -> filter22(x7,x8)
      app(filter2(),x8) -> filter21(x8)
     Subterm Criterion Processor:
      simple projection:
       pi(d{2,#}) = 1
      problem:
       DPs:
        
       TRS:
        h2(z,e1(x)) -> h2(c1(z),d2(z,x))
        d2(z,g2(0(),0())) -> e1(0())
        d2(z,g2(x,y)) -> g2(e1(x),d2(z,y))
        d2(c1(z),g2(g2(x,y),0())) -> g2(d2(c1(z),g2(x,y)),d2(z,g2(x,y)))
        g2(e1(x),e1(y)) -> e1(g2(x,y))
        map2(f,nil()) -> nil()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        filter2(f,nil()) -> nil()
        filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
        filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
        filter24(false(),f,x,xs) -> filter2(f,xs)
        app(h1(x7),x8) -> h2(x7,x8)
        app(h(),x8) -> h1(x8)
        app(e(),x8) -> e1(x8)
        app(c(),x8) -> c1(x8)
        app(d1(x7),x8) -> d2(x7,x8)
        app(d(),x8) -> d1(x8)
        app(g1(x7),x8) -> g2(x7,x8)
        app(g(),x8) -> g1(x8)
        app(map1(x7),x8) -> map2(x7,x8)
        app(map(),x8) -> map1(x8)
        app(cons1(x7),x8) -> cons2(x7,x8)
        app(cons(),x8) -> cons1(x8)
        app(filter1(x7),x8) -> filter2(x7,x8)
        app(filter(),x8) -> filter1(x8)
        app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
        app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
        app(filter21(x7),x8) -> filter22(x7,x8)
        app(filter2(),x8) -> filter21(x8)
      Qed
     
     DPs:
      g{2,#}(e1(x),e1(y)) -> g{2,#}(x,y)
     TRS:
      h2(z,e1(x)) -> h2(c1(z),d2(z,x))
      d2(z,g2(0(),0())) -> e1(0())
      d2(z,g2(x,y)) -> g2(e1(x),d2(z,y))
      d2(c1(z),g2(g2(x,y),0())) -> g2(d2(c1(z),g2(x,y)),d2(z,g2(x,y)))
      g2(e1(x),e1(y)) -> e1(g2(x,y))
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      filter2(f,nil()) -> nil()
      filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
      filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
      filter24(false(),f,x,xs) -> filter2(f,xs)
      app(h1(x7),x8) -> h2(x7,x8)
      app(h(),x8) -> h1(x8)
      app(e(),x8) -> e1(x8)
      app(c(),x8) -> c1(x8)
      app(d1(x7),x8) -> d2(x7,x8)
      app(d(),x8) -> d1(x8)
      app(g1(x7),x8) -> g2(x7,x8)
      app(g(),x8) -> g1(x8)
      app(map1(x7),x8) -> map2(x7,x8)
      app(map(),x8) -> map1(x8)
      app(cons1(x7),x8) -> cons2(x7,x8)
      app(cons(),x8) -> cons1(x8)
      app(filter1(x7),x8) -> filter2(x7,x8)
      app(filter(),x8) -> filter1(x8)
      app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
      app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
      app(filter21(x7),x8) -> filter22(x7,x8)
      app(filter2(),x8) -> filter21(x8)
     Subterm Criterion Processor:
      simple projection:
       pi(g{2,#}) = 1
      problem:
       DPs:
        
       TRS:
        h2(z,e1(x)) -> h2(c1(z),d2(z,x))
        d2(z,g2(0(),0())) -> e1(0())
        d2(z,g2(x,y)) -> g2(e1(x),d2(z,y))
        d2(c1(z),g2(g2(x,y),0())) -> g2(d2(c1(z),g2(x,y)),d2(z,g2(x,y)))
        g2(e1(x),e1(y)) -> e1(g2(x,y))
        map2(f,nil()) -> nil()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        filter2(f,nil()) -> nil()
        filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
        filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
        filter24(false(),f,x,xs) -> filter2(f,xs)
        app(h1(x7),x8) -> h2(x7,x8)
        app(h(),x8) -> h1(x8)
        app(e(),x8) -> e1(x8)
        app(c(),x8) -> c1(x8)
        app(d1(x7),x8) -> d2(x7,x8)
        app(d(),x8) -> d1(x8)
        app(g1(x7),x8) -> g2(x7,x8)
        app(g(),x8) -> g1(x8)
        app(map1(x7),x8) -> map2(x7,x8)
        app(map(),x8) -> map1(x8)
        app(cons1(x7),x8) -> cons2(x7,x8)
        app(cons(),x8) -> cons1(x8)
        app(filter1(x7),x8) -> filter2(x7,x8)
        app(filter(),x8) -> filter1(x8)
        app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
        app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
        app(filter21(x7),x8) -> filter22(x7,x8)
        app(filter2(),x8) -> filter21(x8)
      Qed