YES

Problem:
 app(app(:(),app(app(:(),app(app(:(),app(app(:(),C()),x)),y)),z)),u) ->
 app(app(:(),app(app(:(),x),z)),app(app(:(),app(app(:(),app(app(:(),x),y)),z)),u))
 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:
  :2(:2(:2(:2(C(),x),y),z),u) -> :2(:2(x,z),:2(:2(:2(x,y),z),u))
  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(:1(x8),x9) -> :2(x8,x9)
  app(:(),x9) -> :1(x9)
  app(map1(x8),x9) -> map2(x8,x9)
  app(map(),x9) -> map1(x9)
  app(cons1(x8),x9) -> cons2(x8,x9)
  app(cons(),x9) -> cons1(x9)
  app(filter1(x8),x9) -> filter2(x8,x9)
  app(filter(),x9) -> filter1(x9)
  app(filter23(x8,x7,x6),x9) -> filter24(x8,x7,x6,x9)
  app(filter22(x8,x7),x9) -> filter23(x8,x7,x9)
  app(filter21(x8),x9) -> filter22(x8,x9)
  app(filter2(),x9) -> filter21(x9)
  DP Processor:
   DPs:
    :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,y)
    :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,y),z)
    :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u)
    :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,z)
    :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u))
    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#(:1(x8),x9) -> :{2,#}(x8,x9)
    app#(map1(x8),x9) -> map{2,#}(x8,x9)
    app#(filter1(x8),x9) -> filter{2,#}(x8,x9)
    app#(filter23(x8,x7,x6),x9) -> filter2{4,#}(x8,x7,x6,x9)
   TRS:
    :2(:2(:2(:2(C(),x),y),z),u) -> :2(:2(x,z),:2(:2(:2(x,y),z),u))
    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(:1(x8),x9) -> :2(x8,x9)
    app(:(),x9) -> :1(x9)
    app(map1(x8),x9) -> map2(x8,x9)
    app(map(),x9) -> map1(x9)
    app(cons1(x8),x9) -> cons2(x8,x9)
    app(cons(),x9) -> cons1(x9)
    app(filter1(x8),x9) -> filter2(x8,x9)
    app(filter(),x9) -> filter1(x9)
    app(filter23(x8,x7,x6),x9) -> filter24(x8,x7,x6,x9)
    app(filter22(x8,x7),x9) -> filter23(x8,x7,x9)
    app(filter21(x8),x9) -> filter22(x8,x9)
    app(filter2(),x9) -> filter21(x9)
   TDG Processor:
    DPs:
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,y)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,y),z)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,z)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u))
     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#(:1(x8),x9) -> :{2,#}(x8,x9)
     app#(map1(x8),x9) -> map{2,#}(x8,x9)
     app#(filter1(x8),x9) -> filter{2,#}(x8,x9)
     app#(filter23(x8,x7,x6),x9) -> filter2{4,#}(x8,x7,x6,x9)
    TRS:
     :2(:2(:2(:2(C(),x),y),z),u) -> :2(:2(x,z),:2(:2(:2(x,y),z),u))
     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(:1(x8),x9) -> :2(x8,x9)
     app(:(),x9) -> :1(x9)
     app(map1(x8),x9) -> map2(x8,x9)
     app(map(),x9) -> map1(x9)
     app(cons1(x8),x9) -> cons2(x8,x9)
     app(cons(),x9) -> cons1(x9)
     app(filter1(x8),x9) -> filter2(x8,x9)
     app(filter(),x9) -> filter1(x9)
     app(filter23(x8,x7,x6),x9) -> filter24(x8,x7,x6,x9)
     app(filter22(x8,x7),x9) -> filter23(x8,x7,x9)
     app(filter21(x8),x9) -> filter22(x8,x9)
     app(filter2(),x9) -> filter21(x9)
    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(x8,x7,x6),x9) -> filter2{4,#}(x8,x7,x6,x9)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x8),x9) -> filter{2,#}(x8,x9)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x8),x9) -> map{2,#}(x8,x9)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(:1(x8),x9) -> :{2,#}(x8,x9)
     app#(filter23(x8,x7,x6),x9) -> filter2{4,#}(x8,x7,x6,x9) ->
     filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs)
     app#(filter23(x8,x7,x6),x9) -> filter2{4,#}(x8,x7,x6,x9) ->
     filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs)
     app#(filter1(x8),x9) -> filter{2,#}(x8,x9) ->
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
     app#(filter1(x8),x9) -> filter{2,#}(x8,x9) ->
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x8),x9) -> map{2,#}(x8,x9) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x8),x9) -> map{2,#}(x8,x9) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     app#(:1(x8),x9) -> :{2,#}(x8,x9) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u))
     app#(:1(x8),x9) -> :{2,#}(x8,x9) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,z)
     app#(:1(x8),x9) -> :{2,#}(x8,x9) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u)
     app#(:1(x8),x9) -> :{2,#}(x8,x9) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,y),z)
     app#(:1(x8),x9) -> :{2,#}(x8,x9) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,y)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter23(x8,x7,x6),x9) -> filter2{4,#}(x8,x7,x6,x9)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x8),x9) -> filter{2,#}(x8,x9)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x8),x9) -> map{2,#}(x8,x9)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(:1(x8),x9) -> :{2,#}(x8,x9)
     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)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u))
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,z)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,y),z)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,y)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u)) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u))
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u)) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,z)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u)) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u)) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,y),z)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u)) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,y)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,y),z) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u))
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,y),z) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,z)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,y),z) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,y),z) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,y),z)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,y),z) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,y)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,z) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u))
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,z) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,z)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,z) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,z) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,y),z)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,z) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,y)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,y) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u))
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,y) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,z)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,y) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,y) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,y),z)
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,y) ->
     :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,y)
    SCC Processor:
     #sccs: 2
     #rules: 14
     #arcs: 52/225
     DPs:
      filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs)
      filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(map1(x8),x9) -> map{2,#}(x8,x9)
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(filter1(x8),x9) -> filter{2,#}(x8,x9)
      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(x8,x7,x6),x9) -> filter2{4,#}(x8,x7,x6,x9)
     TRS:
      :2(:2(:2(:2(C(),x),y),z),u) -> :2(:2(x,z),:2(:2(:2(x,y),z),u))
      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(:1(x8),x9) -> :2(x8,x9)
      app(:(),x9) -> :1(x9)
      app(map1(x8),x9) -> map2(x8,x9)
      app(map(),x9) -> map1(x9)
      app(cons1(x8),x9) -> cons2(x8,x9)
      app(cons(),x9) -> cons1(x9)
      app(filter1(x8),x9) -> filter2(x8,x9)
      app(filter(),x9) -> filter1(x9)
      app(filter23(x8,x7,x6),x9) -> filter24(x8,x7,x6,x9)
      app(filter22(x8,x7),x9) -> filter23(x8,x7,x9)
      app(filter21(x8),x9) -> filter22(x8,x9)
      app(filter2(),x9) -> filter21(x9)
     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(x8),x9) -> map{2,#}(x8,x9)
        app#(filter1(x8),x9) -> filter{2,#}(x8,x9)
        filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs)
        app#(filter23(x8,x7,x6),x9) -> filter2{4,#}(x8,x7,x6,x9)
       TRS:
        :2(:2(:2(:2(C(),x),y),z),u) -> :2(:2(x,z),:2(:2(:2(x,y),z),u))
        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(:1(x8),x9) -> :2(x8,x9)
        app(:(),x9) -> :1(x9)
        app(map1(x8),x9) -> map2(x8,x9)
        app(map(),x9) -> map1(x9)
        app(cons1(x8),x9) -> cons2(x8,x9)
        app(cons(),x9) -> cons1(x9)
        app(filter1(x8),x9) -> filter2(x8,x9)
        app(filter(),x9) -> filter1(x9)
        app(filter23(x8,x7,x6),x9) -> filter24(x8,x7,x6,x9)
        app(filter22(x8,x7),x9) -> filter23(x8,x7,x9)
        app(filter21(x8),x9) -> filter22(x8,x9)
        app(filter2(),x9) -> filter21(x9)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 20/25
       
     
     DPs:
      :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,y)
      :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,y),z)
      :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u)
      :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,z)
      :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u))
     TRS:
      :2(:2(:2(:2(C(),x),y),z),u) -> :2(:2(x,z),:2(:2(:2(x,y),z),u))
      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(:1(x8),x9) -> :2(x8,x9)
      app(:(),x9) -> :1(x9)
      app(map1(x8),x9) -> map2(x8,x9)
      app(map(),x9) -> map1(x9)
      app(cons1(x8),x9) -> cons2(x8,x9)
      app(cons(),x9) -> cons1(x9)
      app(filter1(x8),x9) -> filter2(x8,x9)
      app(filter(),x9) -> filter1(x9)
      app(filter23(x8,x7,x6),x9) -> filter24(x8,x7,x6,x9)
      app(filter22(x8,x7),x9) -> filter23(x8,x7,x9)
      app(filter21(x8),x9) -> filter22(x8,x9)
      app(filter2(),x9) -> filter21(x9)
     Usable Rule Processor:
      DPs:
       :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,y)
       :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,y),z)
       :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u)
       :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(x,z)
       :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u))
      TRS:
       :2(:2(:2(:2(C(),x),y),z),u) -> :2(:2(x,z),:2(:2(:2(x,y),z),u))
      Arctic Interpretation Processor:
       dimension: 1
       usable rules:
        :2(:2(:2(:2(C(),x),y),z),u) -> :2(:2(x,z),:2(:2(:2(x,y),z),u))
       interpretation:
        [:{2,#}](x0, x1) = x0 + 5,
        
        [:2](x0, x1) = 1x0 + x1 + 4,
        
        [C] = 0
       orientation:
        :{2,#}(:2(:2(:2(C(),x),y),z),u) = 2x + 1y + z + 6 >= x + 5 = :{2,#}(x,y)
        
        :{2,#}(:2(:2(:2(C(),x),y),z),u) = 2x + 1y + z + 6 >= 1x + y + 5 = :{2,#}(:2(x,y),z)
        
        :{2,#}(:2(:2(:2(C(),x),y),z),u) = 2x + 1y + z + 6 >= 2x + 1y + z + 5 = :{2,#}(:2(:2(x,y),z),u)
        
        :{2,#}(:2(:2(:2(C(),x),y),z),u) = 2x + 1y + z + 6 >= x + 5 = :{2,#}(x,z)
        
        :{2,#}(:2(:2(:2(C(),x),y),z),u) = 2x + 1y + z + 6 >= 1x + z + 5 = :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u))
        
        :2(:2(:2(:2(C(),x),y),z),u) = u + 3x + 2y + 1z + 7 >= u + 3x + 2y + 1z + 6 = :2(:2(x,z),:2(:2(:2(x,y),z),u))
       problem:
        DPs:
         :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u)
         :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u))
        TRS:
         :2(:2(:2(:2(C(),x),y),z),u) -> :2(:2(x,z),:2(:2(:2(x,y),z),u))
       Restore Modifier:
        DPs:
         :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u)
         :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u))
        TRS:
         :2(:2(:2(:2(C(),x),y),z),u) -> :2(:2(x,z),:2(:2(:2(x,y),z),u))
         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(:1(x8),x9) -> :2(x8,x9)
         app(:(),x9) -> :1(x9)
         app(map1(x8),x9) -> map2(x8,x9)
         app(map(),x9) -> map1(x9)
         app(cons1(x8),x9) -> cons2(x8,x9)
         app(cons(),x9) -> cons1(x9)
         app(filter1(x8),x9) -> filter2(x8,x9)
         app(filter(),x9) -> filter1(x9)
         app(filter23(x8,x7,x6),x9) -> filter24(x8,x7,x6,x9)
         app(filter22(x8,x7),x9) -> filter23(x8,x7,x9)
         app(filter21(x8),x9) -> filter22(x8,x9)
         app(filter2(),x9) -> filter21(x9)
        Usable Rule Processor:
         DPs:
          :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(:2(x,y),z),u)
          :{2,#}(:2(:2(:2(C(),x),y),z),u) -> :{2,#}(:2(x,z),:2(:2(:2(x,y),z),u))
         TRS:
          :2(:2(:2(:2(C(),x),y),z),u) -> :2(:2(x,z),:2(:2(:2(x,y),z),u))
         LPO Processor:
          argument filtering:
           pi(C) = []
           pi(:2) = [0,1]
           pi(:{2,#}) = 0
          usable rules:
           :2(:2(:2(:2(C(),x),y),z),u) -> :2(:2(x,z),:2(:2(:2(x,y),z),u))
          precedence:
           :{2,#} ~ :2 ~ C
          problem:
           DPs:
            
           TRS:
            :2(:2(:2(:2(C(),x),y),z),u) -> :2(:2(x,z),:2(:2(:2(x,y),z),u))
          Qed